Department of Geodetic Science BASIC RESEARCH AND DATA ...

Department of Geodetic Science

BASIC RESEARCH AND DATA ANALYSIS FOR THE NATIONAL

GEODETIC SATELLITE PROGRAM AND FOR THE

EARTH SURVEYS PROGRAM

Tenth Semiannual Status Report

Period Covered: January 1972 - June 1972Research Grant No. NGL 36-008-093

.OSURF Project No. 2514

Prepared forNational Aeronautics and Space Administration

Washington, D'.C. 20546

The Ohio State UniversityResearch Foundation

Columbus, Ohio 43212July 1972

PREFACE

This project is under the supervision of Professor Ivan L Mueller,

Department of Geodetic Science, OSU, and it is under the technical

direction of Messrs. Jerome Di Rosenberg, Deputy Director, Communications

Programs, OSSA and Benjamin Milwitzky, Deputy Director, Special Programs,

Office of Applications, NASA Headquarters, Washington, D.C. The contract is

administered by the Office of University Affairs, NASA, Washington, D.C. 20546.

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TABLE OF CONTENTS

Page

1. Statement of Work . ... ... . . . . . . . . . . . . . . . ... . . . 1

2. Accomplishments During the Report Period . . . . . . . . . . . . . . 3

2.1 Adjustment of the BC-4 Worldwide GeometricSatellite Triangulation Net .; . . . . . . . . . ; • • . . . . ... . . . 3

2.11 Theoretical Developments . . . . ... ... . . . . . . . . . 3

2.12 Data Acquisition . . . . . . . . ... . ... . . ... . .. 7

2.2 Investigations Related to the Problem of improvingExisting Triangulation Systems by Means of SatelliteSuper-Control Points . . . V . . . . . . . . . . V • . . . . . . . 9

2.21 Introduction . . . . '. .. ... ... . . . . . . . . . .' . . 9

2.22 Data and Accuracy Estimates . . . . . . . . . . . . . . . 10

2^23 Computations and Results . . ; . ,\ > . . . . ; . . . . . 16

2.24 Summary and Conclusions . . . . . . . . . . ; . . . . . . 29

2. 3 Geodetic Satellite Observations in North America(Solution NA9) . . . . . . . . . . / . . . . . . . ; . . . . . . . . 35

2.4 Free Adjustment of a Geometric Global SatelliteNetwork (Solution MPS7) . . . \ . . . , . . . . . . . . . . . . . 53

2.41 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . 53

2.42 Description. . . . . . . ) . . . . . . . . . . . • • • * • . , . . . .53

2.43 Constraints. . . . . . ; .. . ... . . ... . ... . . . . 55

2.44 The Adjustment . . . . . . . . . . . . . . . . . . . . . . 59

2.45 Comparisons with other Solutions . ... . . . . . . . . . 59

.Appendix 1 , . ..', ... . . . . , ... . .'.•', . / , / , . ... . 63

Appendix 2 » . . . . ; . . . . . . . . > . ', •. • •.. . . . . . . . . . . 81

2.5 Determination of Transformation Parameters withConstraints . . . . . . . . . . . . . . . . . . . . . . . .. ' . . . . 91

2.6 .The Impact of Computers on Surveying and Mapping. -. . . . . .101

-111-

3. Personnel . . . . . . . . . . . ... . . ' . . . . . . . . . . . . . . . . . . 121

4. Travel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5. Reports Published to Date . ' - . ' . . . - . . . . . . . . . . . . . . . . . . 123

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1. STATEMENT OF WORK

The statement of work for this project includes data analysis and

supporting research in connection with the following broad objectives:

(1) Provide a precise and accurate geometric description of

the earth's surface.

(2) Provide a precise and accurate mathematical description

of the earth's gravitational field. '.'

(3) Determine time variations 6f the geometry of the ocean

surface, the solid earth, the gravity field, and other geo-

physical parameters.

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"Page missing from available version"

2. ACCOMPLISHMENTS DURING THE REPORT PERIOD

2.1 Adjustment of the BC-4 Worldwide Geometric

Satellite Triangulation Net

2.11 Theoretical Developments

? As was mentioned in the last semi-annual report, work was begun on

processing the NOAA TYPE irdata. The only existing computer program at

that time was designed to uae non-correlated data. The TYPE II data, being the

result of a polynbimalfitto plate images, has an associated 14 x 14 variance-

covariance matrix, and in order to use this data it was necessary to write anew

program. • . / . ' . • • .

The new linear form of the mathematical model is

: FiV= Xj '-•' X^;- R;cos a cos 6 :

F2 = Ys - YG - R sin at cos 5

; F3 = Z3 - ZG - R cos 6^ •".

(1)

where the subscripts S and G refer.to satellite and ground, respectively, and R is

the range from the ground station to>the satellite.; The observations are a and $.

The linearized form of the mathematical model is basically the same as

described in The Ohio State University, Department of Geodetic Science ReportNo. 86,

(pp. 21-27), which is AX + BV + W • = 0, (2)

where the matrices A and B are the partial derivatives with respect to the parameters

and the observations, respectively. Whenever a satellite event is defined as the

observations to one satellite position, the A matrix for one ground station and

one satellite position is of the form

A =

+1 0 0 i -1 0 0• l . .

o +1: o i o - i o; . " • . ' • T .6 o +1 i o o -i

(3)

-3-

However, in case of correlated observations an event is defined as all obser-

vations to the seven (7) satellite positions, and the A matrix for one ground

station and seven satellite positions takes the form

A .= I (4)

(21 x24)

This is perhaps easier to understand if the linearized form of the mathematical

model is split up as follows:

+ BV + W' = 0. (5)

This is essentially what was done in the original adjustment program. But

when the model in the original program is split up, the A matrices are either

-t-I or -I and they cancel out in the mathematical development, the only change

being that of signs. For the correlated data, A^ is the left side of equation (3)*

and it will not cancel out.

Another change that had to be made was in the formation of the matrix

M'1 = (BP'1B)\ (6)

The problem arises because BP^B' is a singular matrix and cannot be inverted;

For the case of one ground station and one satellite position one can use the

following

M'1 = (BP^B')"1 '= (B')'1P(B)'1 = (B'V PB'1, (?)

where

-4-

B =

dF,da ,

Msda

dF,

d]f

dF,

SF,

3R (8)

P =

0

0

0

(9)

As can be seen in equation (7), the matrix B must be inverted, which means that

it must be square. Thus even though the range R in equation (1) is not

an observed quantity, it must be considered as such in order to

make B a square matrix. This is of course compensated by inserting zeroes

in equation (9). -

The above development for M"1 is described in the above mentioned Report.

In .case of correlated images the situation is somewhat more complicated.

The matrix B is now of dimensions 21 x 21 and of the form

B =0

0(10)

where each of the blocks is a 3 x 3 as defined in equation (8).

The matrix P cannot be defined quite as simply as in equation (9). The

original variance-covariance matrix is 14 x 14, and the P matrix is 21 x 21.:

This is handled as follows:

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w =

o*ai cr<j6i-. 3

x

tfai&7 : — - OT&7

P =

C031 Ute 0

0 0 0

oo31 0)32 0

a)41 0)43 0

0 0 0

0

0

0 0

^14,1

(14 * 14)

0 0

0

0

l,H

-444,14

Wl4,13

0 0

(11)

ate, 14 0

0 0

(12)

0

0

0

(21 * 21)

By using the matrices B from (8) and P from (12), equation (7) can be

solved for M"1 (the notation M"1 is a misnomer, but this expression was used in

Report No. 86 and we have continued with the same notation). The complete

description fo the mathematical will be given at a later date.

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By using the techniques described abouve, the reduced normal equations

are formed as described in Report No. 86.

In addition to the generalized approach described above, a completely dif-

ferent mathematical model has also been developed using the method of observation

equations. The principal advantage of the method of observation equations is that

here the original given correlation matrix is used without any modifications which

is necessary in the generalized least squares approach.

2.12 Data Acquisition

As of the end of this reporting period the following BC-4 data has been

received from the data center:. I . • ' • .

(i) Type I Data - 31 Tapes,(ii) Type II Data - 15 Tapes.

The tape-wise details for type II data are as listed below:

Tape SerialNo.

A-10806

A-10268

A-11082

A-03725

A-03719

A-03727

A-03728

A-10897

A-03738

A-95575

A-11519

A-12327

A-12037

A-12010

A-14094

No. of eventson the tape

87

90

90

90

90

90

90

89

30

29

60

30i- '• .- ' i • .• •

60 •<•

30

60

1015

Break up of events withsimultaneously observing stations2 stations

73

76

70

70

74

62

68

' 71 • '

19

22

40

28

*•'• ^:- „,26

47

801

3 stations

12

13

17

20

14

25

20

17

11

7

20

2

5

-4 -::-.,,

13

200

4 stations

2

1

3:

2

3

2

1

-

-

-

-

- .

,' ' -•'

-

14

2.2 Investigations Related to the Problem of Improving Existing

Triangulation Systems by Means of Satellite Super-Control Points

2.21 IntroductionGeodetic triangulation has been accepted as an accurate method of

determining "precise" coordinates for the triangulation stations of relatively

short chains. This well-accepted idea was also given in an article "How

accurate is First-Order Triangulation?" FSimmons, 1950, pp. 53-561 with

the following introductory words:

The question is often asked, "How accurate is the positionof a triangulation station," or "To what accuracy are thedistances between triangulation stations known?" Thesequestions are difficult to answer, principally becausefirst-order triangulation gives the optimum accuracyin the measurement of great distances and there is at'present no super yardstick to which it can be compared.

Two modern technological advancements, namely, satellites and

electronic distance measuring (EDM) instruments» have questioned the

first-order triangulation accuracy, especially if triangulation is extended

to distances longer than 1000 km or more. In such extended triangu-

lation systems systematic errors like lateral refraction, propagation of

observational errors, residual polar motion effects on. latitude, longitude

and azimuth, etc. [Mueller, 1969, pp. 61, 86-87; Pellinen, 1970, pp. 34-35;

Wolf; 1950, pp. 117], which cannot be eliminated, accumulate. Lately

the question has been raised whether any significant increment to accuracy

is "cascaded" from a 1:1 million 1000 km net through a 100 km net to

local control over 10km distances.

The satellite triangulation and super-transcontinental traverse, being

of the highest achievable accuracy of today,, i.e., super-control net of

"zeroth" order, constitute a modern geodetic super structure, within

which the classical geodetic triangulation is supposed to provide a geodetic

control densification.

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' According to the classical geodetic concept, a lower order system

should be tied to a higher order system. Statistically, this means that

the variance-covarlance of the higher order system, as a lower limit

for accuracy, be at least compatible with the internal precision of the

lower order system. For all practical reasons, the accuracy of the

higher order systems should be substantially better (by & factor of two

to three) than the subordinated system, thus supplying a rigorous con-

straint in the reduction of the lower order system [Schmid, 1969, p. 4].

The objective of this investigation is to answer the question:

Whether any significant increment to accuracy could bo transferred

from a super-control not to the basic geodetic net (first-order triangu-

lation). This objective was accomplished by evaluating the positional

accuracy improvemont for station Wyola (95), which is near the middle

of ttic investigate^ geodetic triangulation not, by using various station

constraints over its geodetic position.

2.22 Data and Accuracy Estimates

For the purpose of the present investigation, the triangulation of

the western-half of the United States has been considered, as this is

more accurate than that of the eastern-half .of the United States

[Simmons, 1950, p. • 54]. The investigation is done oh the chain from

Moses Lake, Washington to Chandler, Minnesota (Figure 1), as these

two stations are also common on both the continental satellite net (CSN)

and the super-transcontinental traverse (STT). The data used were. . . " ' - . • • i • • ' • ' • " ' . -

supplied by the Triangulation Branch of Geodesy Division, and the

CJebdetip Research and pey«|ppinen| Laboratory, both p| tl>e National

Oceanic and Atmospheric Administration, Washington.

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a

3odo

.201.3

8s

Q wi-l u

a'§ PO 44

-.11-

The details of Moses Lake - Chandler triangulation chain are as

follows:

Number of stations 101

Nunibt>r of bases [Taped 27LGeodimeter 2

Laplace stations 13

Observed directions 919.

Distance between two stations ("Minimum 273mt [.Maximum 190km

Total length of the chain 1858km.

tt is assumed that the necessary,reductions have been applied to

the observed data, and the weight function P is "a priori" known to be

a sufficient good accuracy.

Super-transcontinental traverse (STT) runs across the western-

half and the eastern-half of the U.S.A. (Figure 2). Its specifications,

configuration, reduction of data and instrumentation are dealt with by

Meade [1967; 1969a; 1969b].

Continental satellite net (CSN) is, in general, planned in such a

way so that the stations are around 1200 km apart and that these stations

are evenly distributed over the entire area. CSN-statibns are either

the stations of first-order triangulation net or these are connected to

them. Its specification and configuration are dealt with in [Deker, 1967;

Mueller, 1964; Pellinen, 1970; Schmid, 1970]. The continental satellite

net of the North American Continent comprises of twenty stations which

can be anchored in the three world net stations; Thule, Greenland,

Moses Lake, Washington, and Beltsville, Maryland. Furthermore,

planned is a tie to a fourth world net station - Shemya (Figure 3)

[Schmid, 1970].

The following representative standard errors for observed data

of Moses Lake-Chandler triangulation chain has been suggested [Meade,

1970]:-12- ' ' ' . ' ' . . - ' - . ' =

t-CTJ

01ao

o

wCO

SKH

W

I •&8 3 f£ "8 H *is « s g

o oJ

g 5

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Cold Dor

John*

Collfetnle

W O U L D M E T STATIONS

Figure 3. Continental Satellite Net of North America

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Directions 0!'4

A'zinuith 0."8

Base [" Taped 1 pat I in r>00, 000

L Ceodimeler f I pprn for distance > 15 km

i cm for distances up to 15 km

[" I PPni

I 1. Set

The mean of all section closures, which is the accuracy measure

for the investigated geodetic triangulation net, is given as 1 part in

317,000 [Adams, 1930]. The standard position errors of the end

stations of superH;ranscontinental traverse, which represent its accuracy

measure, using actual data sets as given by different investigators

differ too much from each other. The proportional error, which is the

standard position error divided by the distance of the station from

traverse-origin, is used for this investigation. The proportional

errors of super-transcontinental traverse are given as follows:

1:740,000 over 318 kilometer long traverse, and 1:1,100,000 over 1270

kilometer long traverse [Foreman, 1970]; 1:670,000 over 270 kilometer

long traverse [Gergen, 1970] and 1:3,000,000 over 1858 kilometer long

traverse [ESSA, 1969]. The preliminary accuracy (i.e. proportional

error) of continental satellite net, as obtained from the supplied data,

corresponds to 1:385,000 for Chandler station. Because of this wide

range in preliminary accuracy measures of these two super-control nets,

investigations using the following accuracies (station constraints), are

made: 1:300,000; 1:400,000; 1:500,000; 1:600,000; 1:700,000; 1:1 M;

1:1.5 M; 1:3 M. The use of these accuracy measures, which are

within the limits of preliminary accuracies of the two super-control

nets, will determine a limit on the accuracy requirement of the super-

control net, which would be necessary to improve the geodetic triangu-

lation net.

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2.23 Computations and Results

During the earlier period of this investigation considerable thought

was given to the selection and use of such formulas and methods which

would not only provide high accuracies, but also minimize or eliminate

loss of accuracy in computations. This resulted in using Helmert-

Rainsford-Sodano's Iterative Solution for Inverse Problem, which is

equally applicable for short and long lines, and Conjugate Gradient

Method (Cg- Method) for the adjustment of the triangulation nets,

where the original observation equation coefficient Matrix (A-Matrix)

is used, thus avoiding direct formation of normal equations where

certain properties of the original A-Matrix are lost. To minimize

the round-off errors, computations are done in double-precision with

double precision storage [MuUer-Merbach, 1970].

From the two basic adjustment methods, i.e., Method of Obser-

vation Equations and Method of Condition Equations, the former has

been preferred for the present, investigation due to reasons of simplicity

and clarity. The reasoning of this preference has been dealth with in

[Grossmann, 1961, p. 174; Helmert, I. Teil, 1880, p. 556; Wolf, 1968,

p. 323]. Due to the large size of the triangulation net under investi-

gation and the availability of digital computers, iterative methods were

considered because (1) they are easier to program, (2) they require

less storage space as the coefficient matrix of a triangulation net is

very sparse* (3) they use directly the original set of equations through-

out the process and hence rounding-off errors do not accumulate from

one iterative cycle to another.

While searching for a suitable adjustment method, this investigator

came across the Conjugate Gradient Method (Cg-Method) [Schwarz, 1968

and 1970; Wolf, 1968], which has the following distinct advantages over

other iterative methods, such as Gauss-Seidl-, Jacobi-, Relaxtion-

and other Gradient methods:

-16- .

1. Original A-Matrix is used, thus avoiding the formation of normal

equations, where certain useful characteristics of A-Matrix, such as

very small coefficients may be lost.

2. Original A-Matrix, which has very few non-zero elements, is

easily stored in comparatively much less computer space using an

Index-Matrix.

.V No -'mesh-point numbering technique" TAshkenazi, 19671 to keep

the band-width of the system a minimum is necessary. Thus stations

can be added or taken out from the existing triangulation system with-

out caring for their numbering.

4. ft is a finite iterative process. Theoretically, the solution vector

is obtained in a maximum of n-steps, n being the number of

unknowns. Therefore, eigenvalues need not be calculated for

determining the convergence. However, experimentation shows

that the solution vector is not obtained in n-steps, as the

orthogonality'between the residue-vectors is not maintained

exactly. Consequently, the residue-vector rtnj after n-iterations

is not zero. This deviation from zero depends upon the condi-

tion of the system; the poorer the condition, the larger will be

the deviation.6. Each approximation^) to the solution vector is closer to the true

solution x than the proceeding one.

7. The ability to start anew at any point in the computation using the last

x^) as initial value so as^to minimize the effects of round-off errors.

Following mathematical model; using method of observation equations,

is used:

Let Lt be the m independent observed quantities, vt the residuals to the

observed quantities (obtained from the adjustment) and x,y, z, . . . the n unknown

parameters to be determined. Each observation gives an observation equation,

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whose general from is

LI H Vj = fi(x, y, z, . ..), (1)

where i = 1>2, 3. . . , m and f represents a linear or non-linear function. The

method of least squares however demands that (1) f should be linear, i. e.,

a linear relationship between the observations and the unknowns and (2) the

number of observations (m) should be greater than those of the unknowns (n)

i. c.,iri>n. In case of a non-linear function f this is linearized by using

Taylor scries about such good approximate values of the unknowns x0, y0, z0,

such that the second and higher order terms caa be neglected. In this

case, equation (1) can be written as

vt = aidx + btdy + c tdz + .. . + tt (2)

where

x = x0 + dxf y ' .~y0 . t dy , z = z0 + dz, ...

t t ..=. fj (x0, y0, zot . . . ) - L t .

Observation equation (2) can be written in the matrix form as

v - Ax + 1 . (4)

It will be seen later that we have preferred to use weighted con-

straints to the station Chandler. These "a priori" weighted constraints

on the station position generate observation equations of the form

vx = Fx (5)

where F is a rectangular matrix, whose elements are either zeros or

one. Thus the complete observation equation system can be written as

V ..= Bx + L (6)

where

- r v i - B-rA> — r 1 1Lvx-i ' LF-T Lo J ' ^

Due to angular and linear (distance) observations, the observed data

in a triangulation net are of a heterogeneous or dissimilar nature.1

This heterogeneous data have not only more than one dimension but also

different "a priori" standard errors. To make this data homogeneous,

i.e., dimensionless and of unit weight, it is divided by the corresponding

"a priori" standard error a. For reasons of simplicity, the mathematical

model used is assumed to be uncorrelated. The resulting homogenized

observation equation system can be written as

V = Bx + L (8)

..where • • • • ' • • * . . ' ' : . • ' ' . . • ' • ' ' ' • ' • ' • " : : " ' " ' • • • ' • " • ' • • • ' • . ' • ' ' " '

V - • ' -• A -' 1 • '•— ' • ' **-•'' r- **• i - —^ r- * -1 ' ' "

' L=f^ 0)Lo J .

and

v = v/at ; A = A/at ; L '.=? l/at .

~ , ~ ;vx = vx/ax ; F = F/orx

at = standard error of Lj ; crx - standard error of

term "heterogeneous or dissimilar" observations is used when themethods of their measurement are diverse; thus not only angles and dis-tances, but also distances and heights are heterogeneous observations[Wolf, 1968,p. 56]; [Schmid and Schmid, 1965a, p. 10] uses the term "hybridsystems" for "heterogeneous systems".

-19-

Equation (8) is used directly for adjustment by conjugate gradients method.

A complete algorithm for obtaining solution•• vector and N* by Cg-Method

is given later, which gives yTPv and Qte or Qyr for a particular column.

Using these quantities the "a posteriori1' variance of unit \yeight (mf),

standard errors (mx, my) of unknowns, standard positional error (mp) and

the elements ft. A, B of the error eUipse are computed [Wolf, 1968,

pp. .286^292]..

\ The geodetic triangulation net is adjusted as an independent or free

net, as it is not connected with other nets. For its unambiguous deter-

mination, besides the observed data which include directions, bases (to

provide the scale) and astronomical observations, i.e., longitude and

azimuth (to provide orientation of the tirangulation net upon a mathe-

matical surface, i.e., ellipsoid), one fixed station is required to serve

as origin [Gotthardt, 1968, p. 167; Grossmann, 1961, p. 175]. Moses

Lake station is kept as origin with its coordinates obtained from satellite

triangulation results; these coordinates have been assumed to be the best

known coordinates. As Moses Lake station is fixed, its corresponding

x-vector is zero, i>e., corrections dtp and dX are zero. For compu-

tational ease their corresponding elements of the A-matrix are sub-

stituted with zero.

Combining the free ttiangulation net with super-control net of zero

order, i.e./continental satellite net and/or super transcontinental

traverse means constraining the scale and/or orientation of the triangu-

lation net. The effect of this combination is comparable with "tennis

racket and string effect," where the rigid outer racket frame (super-

control) constrains the loose strings (triangulation net). If the strings

are already constrained, there would be no "visible" effect of the

additional constrain from the rigid outer frame. This is also the purpose

of this investigation, i.e., to evaluate whether the existing geodetic

triangulation is sufficiently "constrained" or needs to be constrained by

' . . ' • . - ' • ' . - • ' . - . - - -20- . ' : . • . ' . • . ' •

additional super-control net. For the present investigation triangulation

station Chandler, which is common on the three networks, provides

constraint.

(Tcocfctic trinngulation not can be combined with the super-control

net in either of the two ways:

(1) By using the actual data, i.e., .by using the actual

coordinates with their standard errors of Chandler as obtained

from CSN and STT with the geodetic triangulation; or,

(2) By adding a weight constraint to Chandler with its

cooi'dinates from the geodetic triangulation.

For this investigation, the first way could not be used, as tlie super-

control net coorxtinates of Chandler station are not compatible with those

obtained from geodetic triangulation. As such, the second way has been

preferred by using the actual preliminaiy accuracy estimates for Chandler,

which are 1 part in 385,000 and 1 part in 3 million, as obtained from

CSN ans STT, respectively. Further investigations are made by us ing-

hypothetical standard positional error accuracy estimates of Chandler

station, which are 1:400,000; 1:500,000; 1:600,000; ,1:700,000; 1:1 M;

1:1,5 M. These accuracy estimates are within the actual preliminary

accuracy estimates of super-control nets. Thus, using those various

accuracies of super-control net, a feeling for the accuracy limit of super-

control net, which would be necessary to improve the investigated geodetic

triangulation, can be obtained.

The Method of Conjugate Gradients (Cg-Method) is a nonstationary

relaxation method,

NX + u = O (11)

in n-iterative steps, where N is symmetric and positive definite.

Then the system (11) - known in geodesy as the Normal Equations -

has a unique solution. However, it is not necessary to have normal

-21-

equations, as Cg- Method can be easily modified for directly using the

observation equations without explicit formation of normal equations.

A complete mathematical derivation of Cg-Method with its program is

given by Saxena [1972a; 1972b].

A complete algorithm of Cg-Method for obtaining the solution

vector (x) and for obtaining N* using directly the homogenized obser-

vation equations can be summarized in the following systematic way:

A. For obtaining the solution vector (x)

Given; Homogenized Observation Equation: Ax + 1 = v

Select; Initial Trial Vector x;0) = O

Cumtmtej

(1) .•;::;y(9) '=.. AX(°)+ I : ' : • ' . . ; • - " •

Relaxation steps •j-'r 1, 2, ...... n

(2) r<*-0.= ATv<»j - l > T 3 " l > )

( f o r j . 2 )

(for j(for 3

(0) : x(J) . = xO

(7) :y(J) = Ax

Tests: - • . . ' • ' - . . ' . ' : ; - : . . . ' '

(8) Orthogonality Test:

r( J)ThW • = 0

r(J- l)T r(J) ; .=

~

(9)•

Termination of Iterations.

Based upon the. theory of Cg-Method and the geodetic requirements,

iterations should be terminated as soon as anj' of the following conditions are

fulfilled:

(a) if the improvement In the solution vector between two consecutive

iterations is negligibily small, i.e., jx'^-x^"1)! -1.0-10"4 seconds

(i.e. I.O'IO"''- second in <p. or X = 3.0mm),

(b) if rO)M«) - 0,

(c) if • (Ah'0))T(Ah'W) •= 0;

(d) if tlie given number of iterations is reached;

(o) if the round-off error (RFE) during iterations exceeds a certain

accuracy limit, which is given by the vector difference

lr;r=- ATAXj t AT * - ATvO) arid v^ AV,

The iterations should be terminated if r^ fr t JVs 3. RFE.

B. For Obtaining N'1 - Inverse of Normal Equations

Given: Homogenized observation equation coefficient matrix A.

Select: Initial trial vector qk(o) = O; where qk is the k-th

column vector of Q( = N"1)

-23-

Compute:

(1) r(o) =- ek ; where ek is the k-th column vector of

the unit matrix E.

(2) Cj-i, hu), Xj are to be computed according to

equations given In (A) above*

(3) <« = VJ-l) + X

Test and Termination of Iterations; Same as in (A) above.

The algorithm of (A) is programmed as a SUBROUTINE SOLN and

and (B) as a SUBROUTINE QSOLN. Both subroutines can be used for .

any feasible size of data, which can be accommodated on the available

computer, after changing KM, which is the PAT SUM Basic Block Size

for RTR.

The main program used together with these subroutines has

dimension statements and a data card for Number of Unknowns (NU),

Number of Equations (NE) and Number of Columns of Index Matrix (NI),

which can be changed if there is need for it. ,

The program is universal in the sense that it can be used for

varying data without much change and that "mesh-point numbering technique"

is not required. Therefore, stations can be added or taken out from the

triangulation system without worrying about the band-width and size of

blocks. These programs have been tested on systems from as small

as 2 unknowns, 3 equations up to as large as 804 unknowns, 1397

equations.

Although the Cg-Method theoretically gives the solution vector at

n- iterative steps (n = number of unknowns) , investigations show that the

solution vector is not achieved in n-iterations dufe to round-off errors,

ill-conditioning of the system, disturbances of the orthogonality and of

the conjugancy relations [Beckman, 1960, pp. 69; Hestenes and Stiefel,

1952, pp. 411]. The present investigation, using the actual data set,

-24- • - . - . . . - . . . . ;

shows that the number of iterations required to obtain the solution

vector by Cg-Method .using directly the A-matrix without explicitly

forming the N-matrix depends upon two factors: (1) condition of the

system, and (2) accuracy of the solution vector required.

Using the geodetic triangulation data (573 unknowns, 963 equations),

the program went up to 5778 iterations without giving any 7 decimal

accurate solution vector, while 4 decimal accurate solution vector was

obtained after 1161 iterations, i.e., 2.1 times number of unknowns

(Table 1).

Each column vector qk of N'A is generally computed in less than

1.2 n-iterations (Table 1).

Table 1.

Experiment

Number*

1

2

3

4

5

6

7

8

9

i

Number of

Unknowns

573

573

573

573

573

573

573

573

573

Equations

963

965

965

965

965

965

965

965

965

Solution Vector

Iterations

1161

1177

1175

1176

1164

1162

1166

1159

1169

• Time**m sec

9 37.13

9 23.27

5 45. 97+

9 22.32

5 53.44+

5 41. 164

9 09.46

9 24.29

9 29.41

Covariance Vectorfor Column 8

Iterations

640

657

659

682

674

G75

631

648

008

Time**m sec

3 45. 9G

3 31.91

2 12.59+

3 45.64

2 1.77+

2 0.00+

3 20.03

3 13.29

3 11. ni

*Kefer to Table 2,

**'J'ime is' (he Execution time on H-Compiler, Option ~- 2 (IBM 360/75) exceptthose marked with a plus (+) sign, which is the Execution time on H-Compiler,Option » O/(IBM 370/165).

• • • ' " ' --25- .

The results of the investigation are given in table 2 and 3, where

in the improvement of the particular geodetic triangulation by super-

control net is visible only when its accuracy is at least 1 part in 500,000.

Table 2.

Experiment

Number

1

2

3

4

5

6

7

8

9

Accuracy

1 in

300,000

400,000

' 500,000

600,000

700,000

1,000,000

1,500,000

3,000,000

' A

= .m0

2.42

2.41

2.4.1

2.41

2.41

2.41

2.41

2.41

2.41

WYOIA (95)

Qx*

G.O

6.7

5.9

4.1

. 4 . 1

4.1

3.7

„ ._ .

2.1

Qyy

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

6.5

m/

35.2

38.9

34.3

23.8

23.8

23.8

21.5

18.6

12.2

my2

2.9

2.9

2. 9

2.9

2.9

2.9

2.9

2.9

2.9

Remarlcs

Free Net

xxt Qyy and in;', my3 are given in 10~- seconds"'.

-26-

Table 3.E

xper

imen

tN

umbe

r

1

2

3

4

5

6

7

8

9

Accuracy

1 in

Free Net

300,000

400,000

500,000

600,000

700,000

1,000,000

1,500,000

3,000,000

WYOLA (f

•ni.

1.83

1.93

1.81

1.51

1.51

1.51

1.43

1.33

1.08

my

0.37

0.37

0.37

0.37

0.37

0. 37

0,37

0.37

0.37

mp

1.9

2.0

1.8

1.5

1.5

1.5

1.5

1.4

1.1

)5)

Positional ImprovementRelative to Experiment 1

Meters

-0..1

0.1

0.4

0.4

0.4

0.4

0.5

0.8

%

- 5

5

21

21

21

21

26

42

Standard Errors of Unknowns (mx, ray) and Standard IPositional

Error (mp) are given in meters.

-27-

1X3 CO

Worth mentioning is that the longitude terms, which are Qyy and

my3 in Table 2 remain practically uneffecteel. This could be explained

by the fact that station Wyola is very close to Laplace stations, which

control the azimuth error accumulation and thus control the longitude

terms.

ft is interesting to note from Table 3 and Figure 4 of the inves-

tigated geodetic triangulation chain lies between 1:300,000 and 1:400,000,

which is quite in agreement with its presumed accuracy of 1:317,000.

2.24 Summary and Conclusions

The super-control net, i.e., continental satellite net or super-

transcontinental traverse j can provide a useful constraint to the inves-

tigated geodetic triangulation netj and thus can improve it only when the

accuracy of super-control net is at least 1 part in 500,000; in this case,

this corresponds to ±3.7 m standard position error for the station

Chandler.

The preliminary accuracy of super-transcontinental traverse is

already better than this limiting accuracy of 1 part in 500,000. The

preliminary accuracy of continental satellite net is, however, lower than

the limiting accuracy of 1:500,000; the preliminary standard position

error for Chandler as obtained from continental satellite net corresponds

to ±4.8 m, i.e., 1:385,000. The future will show whether the limiting

accuracy could be achieved by continental satellite net, especially because

numerous spatial triangulations of CSN have produced accuracies within

the range of 1 part of 400,000 and 1 part in 700,000 [Schmid, 1965, p.22].

Schmid [1970, pp. 23-24] indicates that continental satellite net will

fall short on an optimum solution with respect to both its coverage and

its accuracy. The three-dimensional positions of CSN-stations will

-29-

probably be determined to no better than ±4 meters in all components,

which does not seem to be good enough at least for this particular

investigation.

ft might be useful to have a "block constrain" instead of "chain

constrain", that is, to use four well separated satellite stations, namely

003, 102, 112 and 134 (Figure 1).

Super-transcontinental traverse can provide a better constraint, if

more than two of its stations are common to the stations of geodetic

triangulation net. Also, a "block constrain", as explained above, might

be more useful instead of a "chain constrain".

The development tendencies of instrumentation indicates that the

future super-control nets will use VLB! (Very Long Baseline Inter-

ferometry) and Laser ranging systems.

-30-

REFERENCES

Adams, Oscar S. (1930). "The Bowie Method of TriangulationAdjustment as Applied to the First-Order Net in the WesternPart of the United States." U. S. Department of Commerce,Coast and Geodetic Survey, Special Publication Number 159.U.S. Government Printing Office, Washington.

Ashkenazi, V. (1967). "Solution and Error Analysis of Large GeodeticNetworks," Survey Review, Number I4_7_f S. 194-206.

Beckman, F.S. (1960). " The Solution of Linear Equations by theConjugate Gradient Method, " Mathematical Methods for DigitalComputers. Volume I, edited by Anthony Ralston and H. S. Wilf.John Wiley and Sons, New York.

Decker, Hermann (1967). "Die Anwendung der Photogrammetric inder SatellitengeodUsie," Deutsche Geod'atische Kommission,Reihe C. Heft Nr. 111.

ESSA (1969). "Precise Traverse Chandler, Minnesota to Moses Lake,Washington," Environmental Science Services AdministrationCoast and Geodetic Survey, Rockville, Maryland, May 12.

Foreman, Jack (1970). "Spatial Traverse: Scale for SatelliteTriangulation," Paper presented at American Geophysical UnionNational Fall Meeting, San Francisco, December 7-10.

Gergen, John (1970). "The Analysis of a Short Segment of the U.S.Coast and Geodetic Survey High-Precision TranscontinentalTraverse, " Master of Science Thesis, The Ohio StateUniversity, Columbus.;

Gotthardt, Ernst (1968). Einflihruhg in die Ausgleichungsrechnung.Herbert Wichmann Verlag, Karlsruhe.

GroBman, Walter (1961). Grundzuge der Ausgleichungsrechnung.Springer-yergal, Berlin.

Helmert, F.R. (1880). Die mathematischen and physikalischen Theoriender hoheren Geod'asie, I. Teil. E.G. Teubner Verlag, Leipzig.

-31-

llcstiMU's, M. K. &St ie lo l , K. (1952). " Methods of Conjugate (I radientHTor Solving Linear Systems, " ; Journal of Kcseareh of the NationalBureau of Standards, Volume 49, Number (i, December, S. 409-4:?<;.

Mc3.de, B.K. (1967). "High-Precision Geodimeter Traverse Surveys in theUnited States, "Paper presented at the XIV general Assembly ofIVGG, Lucerne.

Meade, B.K. (1969a). "High-Precision Trans-Continental Traverse Surveysin the United States, " Paper presented to XI. Pan AmericanConsultation on Cartography, Pan American Institute of Geographyand History, Washington, D.C.

Meade, B.K. (1969b). "Corrections for Refractive Index as Applied to: Electro-Optical Distance Measurement, " Paper presented to the

Symposium on Electromagnetic Distance Measurement and AtmosphericRefraction, International Association of Geodesy, Boulder, June.

Meade, B.K. (1970). Private Mitteilung, Jult.

Mueller, Ivan I. (1964). Introduction to Satellite Geodesy. Frederick UngerPublishing Company, New York.

Mueller, Ivan I. (1969). Spherical and Practical Astronomy as Applied toGeodesy. Frederick Unger Publishing Company, New York.

Muller-Merbach, H. (1970). On Round-Off Errors in Linear Programming:Springer-Verlag, New York^

Pellinen, L.P. (1970). " Expedient Means of Joint Processing of Ground andCosmic Triangulation, " Bulletin of Optical Artificial EarthSatellite Tracking Stations-USSR. Joint Publications ResearchService, Washington, D.C.

Saxena, N.K. (I972a): "Untersuchung liber die Moglichkeit einer Verbesserungbestehender Triangulationssysteme mit Hilfe von Superkontrollpunkten, "Dissertation der Technischen Hochschule in Graz.

Saxena, N.K. (I972b): "Investigations Related to the Evaluation of AccuracyImprovement of Geodetic Triangulation by Super-Control Points, "Report of the Department of Geodetic Science, No. 177, Columbus.

Schmid, Hellmut H. (1965). "Precision and Accuracy Considerations for theExecution of Geometric Satellite Trianguliion. " U.S. Departmentof Commerce, Coast and Geodetic Survey, Rockville, Maryland.

' ' ' • ' • ..-32- ' . - . . • ' • • '

Schmid, H. H. and Schmid, E. (1965a). " A Generalised Least SquaresSolution for Hybrid Measuring Systems, " U. S. JDepartment ofCommerce, Coast and Geodetic Survey, Rockville, Maryland.

Schmid, Hellmut H. (1969). " A New Generation of Data Reduction andAnalysis Methods for the Worldwide Geometric SatelliteTriangulation Program," Paper presented at the Departmentof Defense Geodetic, Cartographic and Target MaterialsConference, October 30.

Schmid, Hellmut H. (1970). "A World Survey Control System and itsImplications for National Control Networks, " Paper presented atthe Canadian Institute of Surveying, Halifax, April.

Schwarz, H.R. (1968). Numerik Symmetrischer Matrizen. B.C. Teubner,Stuttgart.

Schwarz, H.R. (1970). "Die Methode der konjugierten Gradienten in derAusgleichungsrechnung, " Zeitschrift fur Vermessungswesen, Number 4.

Simmons, Lansing G. (1950). "How Accurate is First-Order Triangulation?"The Journal, Coast nad Geodetic Survey, Number 3, April, pp. 53-56.

Wolf, Helmut (1950). "Die strenge Ausgleichung grosser astronomisch-geodUtischer Netze Mittels schrittweiser Ann'dherung, "Veroffentlichungen des Instituts fdr Erdmessung, No. 7, Bamberg.

Wolf, Helmut (1968). Ausgleichungsrechnung nach der Methode der Kleins tenQuadrate. Ferd. Dummlers Verlag, Bonn.

-33-

2.3 Geodetic Satellite Observations in North America (Solution NA9)

The coordinates of several tracking stations tied to the NAD datum were

computed through available observations to the GEOS-I satellite. Up to date

the NAG adjustment [Mueller, Reilly and Schwarz, 19691 and NA8 adjustment

fMueller, and Reilly, 1971] had been published. The latter solution was performed

using height constraints deduced from the SAO69 geoid [Gaposchkin and Lambeck,

1970].

Recently a new detailed geoidal map with claimed accuracies of ±2 m,

(on land), based on gravimetric and satellite data, was presented ("Vincent, Strange

and Marsh, 1971]. With the new geoid, and the orthometric heights given in

FNASA, 1971] more reliable height constraints were calculated as follows:

From the initial values of the shifts SAO-NA8 (computed using the published

shifts SAO-NAD and NAD-NA8 in [Mueller and Reilly, 1971]) and by an iterative

process self-explained in Figure 1, the initial NA8 rectangular coordinates were

shifted to the SAO origin and the geodetic coordinates computed. The ellipsoidal

heights then were constrained using the undulations from [Vincent, Strange and

Marsh, 1971]. With the original <p and X and this new height a new set of rec-

tangular coordinates was obtained. Following this procedure iteratively,

several shifts of this kind to the "geocenter" were performed until the sum of

the undulation differences was very small. Through this process "best" shift

to the geocenter was obtained. This shift was also used to compute the pre-

liminary coordinates to obtain the reduced normal equations for the MOTS and

PC-1000 optical data in the solution MPS7 ([Mueller and Whiting, 1972] and

Section 2.4).

At all stations, a weighted height constraint was imposed, after shifting

(with the above obtained values) to the final "geocentric (GC)" coordinates. Also,

as in the NA8 adjustment, a distance constraint was imposed between stations

3861 and 7043. Due to a recent correction in their coordinates a difference of

3m from the previously used value was taken into consideration FMeade, 19721.

-35-

Finally, unlike in the NA8 solution, "inner adjustment constraints" were

also imposed in order to define the origin of the system in its most favorable

position from the error propagation point of view fBlaha, 1971].

The coordinates of the NA9 solution are presented in Table 1 with cor-

responding standard deviations. The coordinates transformed to the NAD datum

are in Table 2.

Table 3 shows the constrained heights at each station and the final undula-

tions compared with those published by Vincent et.'al. In column AN and in

parenthesis, the differences published previously in [Vincent, Strange and Marsh,

1971] are shown. It can be seen from Table 3 that only two stations show sub-

stantial disagreements (3903 Herdon, Virginia and 3407 Trinidad). It seems

clear that the orthometric height as given in [NASA, 1971] for the station 3903

has a gross error. Appropriately, the NASA Directory of Tracking Stations

points out in the description of the referred station: "coordinates unverified,

survey details are lacking. " The discrepancy with respect to station .'5407 may

be due to the fact that it is situated in the Caribbean, where large geoidal

gradients are present.

Table 4 shows the transformation parameters between the different systems.

Listed on the first page are the 3 parameter-transformation solutions (only shifts

considered), and the general 7 parameter solution. In this latter transformation

the rotations were first computed through direction cosines independent of

translations and scale factor (see Section 2.5). These rotation parameters con-

strained with their variances were used in the final solution shown pp. 2-5 of

Table 4 with the resulting variance-covariance matrix and the correlation co-

efficient matrix for each transformation. In the variance-covariance matrix the

angular units are in radians.

-36-

AX = -41.1m

AY = 189.3m

AZ - 158.0m

Initial

Shifts

SAO-,

NA8-

(Xo, •*

- NA8

»SAO

o, Z0)

SAO - NA8 = (SAO-NAD) + (NAD-NA8)

NA8 -» SAO = NA8 + (SAO - NA8)

IProgram

"INVTRF" Y0

LZ0J

(a, b)SAo

Xo

LhoJ

h* - H +NG = undulations interlopatedfromgeoidalmapin f4]

H = orthometric height from [5]

Program

"DIRTRF"

(X*. Y*, Z*)

'00

Xo

Lh*J

/SAO rx*i

y*L Z*l

Program

"DATMTR"

NA8t - NA8

NA8

(X,Y,Z)NA8 |

(X,Y,Z)NA8l j

'. X*,Y*Z*S . .(X,Y,Z)N A8 l '

NA8-*NA8,' - NA8 + (NA8t - NA8)

Program

"INVTRF"

rx

Lz.J

(a,b)'SAO.

Program

"DIRTRF"

(a,b)'SAO

Lh*J

Figure 1

-37-.

Program

"INVTRF"

7SAO

. = ht+l. - H

AN . = .NM - N6

=• o

"Geocentric"("GC")System

Program

"DATMTR"

NAD - "GC"

• 'Program

"DATMTR"

NAD - NA8

(X, Y, Z)NAO

49.8m

AY = -145.2m

AZ - -211.1m

AX = 5 .0m(X,Y,Z)NA6i

(X,Y,Z)N A D

NAlO -» NAD

(X, Y, Z)

Program

"INVTRF"

<P, X, h

NAlO -» NAD =• NA10 + (NAD - NA10

X'

Y

LZJ

(a,b)NAD 05

L h .

Figure 1 continued

-38-

Re: Table 3

Re: Table 1

Re: Table 2

New Height

Constraints

h

Program

"OSUGAP"

Solution ofNbrmalEquat

(X, Y, Z)NAO

Program

"DATMTR"

NAD - NA9

NA9 -» NAD

(X,Y,Z)

Program

"INVTRF"

<p, X, h

Program

"DATMTR"

"GC" - NA9

NA9-» "GC"

, Ya, ZG)

(X, Y, Z)NA9

(X, Y, Z)NAO

AX - -6.7m

AY = 0 .2m

AZ = 0 .4m

NA9 -*NAD •••=. NA9 + (NAD - NA9)

•x-

Y

-Z-

(a. b)NAD 'V

X

.h.

(X, Y, Z)NAg

(X,Y,Z)GC

AX =•. -51.7m

AY = 144.1m

AZ = 210.5m

NA9 -» "GC" =. NA9 + ("GC" - NA9)

Figure 1 continued

-39-

Table 3

Program

"INVTRF"

<Ps,

N =

\ 3 >hG

h,. - H

r*8!YG

LzJ

(a,b)sAO

LhGJ

Figure 1

-40-

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-44-

Table 3

Height Constraints and Undulations(all units in meters)

Number

102110221030

103210331034

104231063334

340034013402

340434053406

340736483657

386139023903

500153335649

586170367037

703970407043

704570727075

7076

Station

Blossom Pt. , Md.Fort Myers, FloridaGoldstone, Calif.

St. John's, Nswf.Fairbanks, AlaskaE. Grand Forks, Minn.

Rosman, N. C.Antigua, W.I.Stoneville, Mississippi

Colorado Springs, Col.Bedford, Mass.Semmes, Alabama

Swan IslandGrand Turk, B. I.Curacao, N. Antilles

Trinidad, TobagoHunter AFB, GeorgiaAberdeen, Maryland

Homestead, FloridaCheyenne, WyomingHerndon, Virginia

Herndon, VirginiaStoneville, MississippiHunter AFB, Georgia

Homestead, FloridaEdinburg, TexasColumbia, Missouri

BermudaSan Juan, P. R.Greenbelt, Maryland

Denver, ColoradoJupiter, FloridaSudburg, Canada

Kingston, Jamaica

Constraintsh

923

898

102165256

9168

45

21848984

790

44

28519

7

161882132

1324523

2272

270

265756

178726

276

473

a

333

5103

333

553

755

533

353

335

333

353

333

3

• • • N"GC"*

- 27- 16- 23

1216

- 13

- 23- 45- 20

- 4- 27- 21

- 32- 51- 30

- 50- 19- 27

- 22— 8-100

- 27- 17- 23

- 27- 8- 17

- 38- 40- 30

- 7- 23- 28

- 20

[Vincent et al. ]

-26-18-27

13

-18

-22-40-19

-10-21-18

-47-26

-34-24-26

-22-10-26

-26-19-23

-22-11-24

-36-41-26

-13-24

-31

-23

AN

- 1 (- 7)2 ( 1)4: ( 8)

- 1

5 ( 11)

- 1 (- 3)- 5 (- 2)- 1

6- 6- 3 (-12)

- 4 (-27)- 4.

-165 ( -5 )

- 1 (- 4)

02

-74 •

- 120

-.5 (- 5)37 ( 10)

- 2 ( - 2 )1 ( 5)

- 4 (-15)

6 (16)

1 ( 1)3 ( 2.0)

3 ( 20)

*The geocentric coordinates were obtained from the NA-9 by adding the followingshifts: AX = -51.7m, AY = 144.1m, AZ = 210.5m-.

-45-

Table 4

Transformation Parameters

No. Stations

s •2 1

*U-lwCJH

para

met

er

t-

AX(m)

AY(m)

AZ(m)

AX(m)

AY(m)

&Z(m)

:;;";e(xl(I6)

NA9-NAD32

6.7 ±1.3

- 0 . 2 ±1.1

- 0.4 ±1.2

- 1.9 ±3.0

-20.9 ±5.0

23.5 ±4.3

- 0.80 ±0.09

0. 56 ± 0. 07

- 0.25 ±0.11

- 4.82 ±0.89

NA9-"GC"34 .

51.7 ±0 .7

-144.1 ±0.8

-210.5 ±0.9

39.1 ±1.7

-144.4 ±4 .0

-202.5 ±2.8

- 0.37 ±0.04

- 0.22 ±0.03

- 0.22 ±0.05

- 0.48 ±0.72

NA9-SAO11

35.3 ± 2.6

-148.3 ± 2 . 6

-175.0 ± 2 . 6

24.9 ± 9 . 4

-200.0 ±11.7

-173.5 ±11.1

- 0. 66 ± 0.29

0.14 ± 0.24

0. 94 ± 0.35

- 6.78 ± 1.88

"GC"-NAD32

-44.8 ±1.3

144.8 ±1.1

209.8 ±1.2

-37. 8 ±2 .6

124.3 ±5.0

227.7 ±4.0

- 0.35 ±0 .07

0.84 ±0.06

- 0,10 ±0.09

- 4.28 ±0.89

^Rotation parameters constrained (see Section 2.5)

-46-

ROTATIO.N^ PÂMETERS CONSTRAINED

lTIflW; FOR 3 TRANSLATION, 1 SCALE AND 3 R O T A T I O N P A R A M E T E R S

-' •• AY : :

V'.AZ;:.. . c :._.._-_£*_:._ ..,._.__JY__ ^ 9.x.- ..METERS METERS MffERS '(xlO"*) SECONDS SECONDS SECONDS

•-37.78 124.34 227.66 -4.28 -0.35 __CU8£,____.. Q_-.l 0.

• ;, V A RI AN C E . - . C 0 V A R I A N C E MA T R I X

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Q.339n»01 •-0«lI.5p + Q2 0. i^LD+Q^ -G.289D-05 0.3820-06 0 ...LU.D- 0.6 . - 0 . 9 6 0 D- 06

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0 . 3 5 60-06 0. 9?8p-07 Q . \ \ IDÔb 0.312 Q I5._.jg_.10AD±I3 ...... ;.0...7;24D- 13.. - C . 2 60 C- 1 3

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F.F-1€ l

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Q.JBO|DVQ2' p;i;OOD^Ql -0.58qD>00^ 0.923CtOO Q. 1420+00 ;. ..Q . 7 3_2 D- 0 1 . - 0 .2 8.1 D t. C 0

-0.806 C + OQ Q.278Q + 00 0 . 1 G 3 D » Q O -0. s §9J> 00

-0.8060^00^ O . I O O D + 01 - 0^2.7 IfcOl _ 0,._1. 30D-JP 2 0 . 2 5 7 1:- 0 1

0.278D>OG^:.-0.272 Crsfil. ....... fi '-LQ. PAtPA ..P ?. ?.?iP ± 00 - Q . <+ 7 9 D + 0 0

0-<..5i..7D»QQ 61-7-3-2.Q-01 0. t Q 3 P Q ^ 0.13,00-02 0.221D+00 ____ Q.ilj002±P_l_-0A2 2^t D+ 00

^-CLjTJLt - 0.100C«-J1

Table 4 continuedROTA TI ON P-AR'AtoE TERS CONSTRAINED

SOLUTION: FOR 3 TR ANSLAT10NV. 1 SCALE AND 3 ROTATION PARAMETERS

: .. , • __ _ ev'.. , __ _ _ _METERS '-' M£ÊRSt, METERS. < ( x l (T6) < 'SECONDS . S E C O N D S S E C O N D S

24.69 ^200.00 -173. 46 -6.70 -0.66 0_. 14_ 0 .94

. V A R I A N C E - C O V A R I A N C E M A T R I X

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£U165D±Q2_ O.I38p»03 -0.1I1D + Q2' 0.178D-04 g_...39^D-05 0.1340-05 -0.1100-04

Jk_2iojD>jC£_TJ).'.^^ 0A_3.81 fir05 Q...8500-06 -0 .1 ^l D- 0A

5_ Q.JL78D-Q4 -0.129D-Q4 ^0.354C-1I 0.116D-13 C. 7660-14 .rJj. 2 3 0 D- 13

-04 0.394D-05 0.381D-05 Oi.ll6D-12 0.192C-11 0^.4050-12 -0.3110-12

.. 0^ 701 D-Q5_ 0.134D-05 0.85QD-06 0.766C-14 Q._._405C-JL2 O..J.J50- 11 .-6.3040- 1 2

-Q.515D-05 -0.1100^(34 -Q.i42D-Q4 -0.230C-13 -0. 8110-12 -0. 3040-12 0 . ? H90- 11

CQEFFIGI-ENTS .OF £QRREJL.AJ10N

O.lQOD^-01 ___ O.L49D+OQ 0.266D+"00 r'O .8580-01 _____ 0_._8.48. .0+00, 0 . 6 4 C D + 00 -0.3220^-00

..._._ -0. . 10DO»01 -Q. 847D-pl •; 0 .8060+ 00 ____ _Q_. 2A2.Q.+ 0 0 0 .9. 800-01 -0.5530^00

-Q.647D-01 O.lQQDÔl ^-0 .615C + 00 Q .246G + 00 0.6550-01 -0 . 7 <»8 U+ 00

..O_«,8,§:,8_Qr<3.1.. ..... P. .Jj9j&Pjt00. .0..41JlH4.Q___.0. 1 P_QD.t-Ci _____ 0 . .444_D- 02; 0 ,_3 5.00- 02 -0 . 7 2 1 D-0 2

J3..«3A9PtM.,.,.0». 4 .P..tM ___ 9^j46JDi;P_Q_..jO_._444^ .0. 251D+-00 -0 . 34^0 + 00

0.6400+00 0.98QD-01 Q..655D-01 Q.350D-C2 0.251D->-00 _.0_._l,C_CO.t_Cl.. -0 . 1 5^0-eOO

JCU.3Z2.9tfl P.... r-Q •.55-3.P-t.0r6_-Q . .74.8.D±QO._r.O.. 7.2 1 C-Q.2.....-.0..34_6: P±P.Q . - 0.. 1 54 D ^-.0 0 0.1000+0 i

-48-

Table 4 continuedROTATION .fÂMETERS CONSTRAINED

- NAD:

SOLUT:|QN>;FOR 3 TRANSLATION, 1 SCALE AND 3 ROTAT ION P A R A M E T E R S

,,METERS MffERS METERS .(tiff*) SECONDS SECONDS SECONDS

-20.95 23.51 -4.82 -0.80 0*56 -0.25

' ^ V A R I A N C E - COVARIANCE M A T R I X

0.524D-Q6 -Q.fa65D-Q6

Q. 843D*OO 0.2:5^10^02 >a«10lO*037 0,4Q7D-Q5 Qj.3.5JLC-;p6_ ,,0.1430.-P,6.-0.8740-O.ft

^-0.1;01p^d2 0.18404-02 -0.2910-05 £..55J?fc,G6;..,,;,.Q.. 1.6.3D^Q6 . -0.1 ^1D-05

>|D^Q5 -0.291D-05' 0.7970-12 -Q.122D-I3 O-j lDrlS^ 0...144U-13

M^_4. 5J.fc£6_lrO.12_2_D-13 ^«J_7_2Or 12 ,0..2J990^ 13 -0.1030-12

Q.jig^p-^Qfe 0..JLr4l3J}-0,6; Q.« 16jg-p6r 0.447U-15 QJ299D-13 0. 1060-12 -0.3800-13

06-0.1410^-05" 0.1440-13 -0.1030-12 -0.380D-13 0.'2660-12

:A^-^^:';V-..-..-COEFFICIENTS OF

0.352D-t-QO -0.132C»QQ OêblDtOO Q.542D^Q 0 - 0 . 4 3 2 0 ^ 0 0

0>1;OQD+01;-0. 4650^00 0.903CVQO Qe.169p-frOO 0.872D-01 -0'. 3 3^0+ 00

0.35^0^Q.-0.w4^5DÔa 0.10o6»0l' -0*759D-»-CQ 0.314D-»-QO 6.117D-«-00 -0 .6 *30+00

-0. 759D+00, 0.1QOD + 01 -Q.329D-01 0-1,5 4D- 02 0.3HD-01

0.8020*00 O . i ^ f Q X ) : 0.314 Q * 0 0_ _r 0.3. 29J>01 •. . _Q.iOODjHOJ ____ £. J.2 1 D vp 0 . - C .. 4 7 9 0 + C 0

0. lOOD+01 -0 . 226 D + 00

- Q »4l^^5:~-3j^ Q.,3 1 1C rM.._z5ÎiQ±.Q5_r.P^22.6 D + 00 C . 1 G 0 D + C

ROTATION PARAMETERS CONSTRAINED

NA9 - "GC"

SOLUTION PQR 3 TRANSLATION* 1 SCALE AND 3 R O T A T I O N P A R A M E T E R S

C- £ ^*7': V V "'X

"ME~TERS?: METERS METERS, .« .(xior*) S'ECONDS SECONDS SECCNOS

39.14-144.40 -?02;.51 -Q.4fi._ rJQ-..lJ rAtZL. _-.Q.fc22

--" -VARIANCE - COVARIANCE MATRIX

n-? 7^04-01 -Q. 13QP:»01 0.177D+Q1 -Q.349p-0fe __ 0 .0.0 fir. 0.6. . ,0 ...1.2 6 D.rjQ o - 0.. 1 3,1 p- 06

•n.l3-on»JQ.i Q. l feQO-»Q2 -Q.838D»01 0.2 15LQ- 0.5, ....._0.»_SJ. Dr.OJ;. ...0.^060-07 - 0 . 1 7 0 D- 0 6

-n rftâO»'Qy: Q.76qD>Ql -Q.173D- Q 5_... Q.....5..93 D- 07 . 0 . 2 7 L 0- 0 7 - 0 . 2 5 7 D- 0 6

0.7790-05 -0.173D-Q5 Q.522D-12 -Q.8A9D-15 .0.119D-14. 0 .232D-15

0.8140^07 Q.993D-Q7 -Q.849D- 15, . _J5... 33.5 0-1.3 ._ 0 . 7_$. ID- .1 <t -.y . i 9 3 D- 1 3

Q.4Q6D-Q7 Q.271D-07 0.119C- 1.4. ..... _..Q,...74J,J>:.1.4 . .0 . 2.6 3D- 13 - 0 . 9 1 2 D- 1 A

a. v^rjô*. -0.1700-06 -Q.257D-Q6 _ Q^23,.ZQ- ll_âJL23Jta_ - fii.9. 1 .2 0-1 A. : Q... 500 p- 1 3

E_LA.lIPJi.

-0.1970*00 _Q.365D>QQ -0.2920-*-00

r l-q-7-P^QQ- Q.lQQO'fQl^ -^0.7550*00 0.9640^00 .jCLUJLLR-tOfi Q..62.50-pl • -0.1 ÛD +

' 0.40QD->-01 : --0.6.65000 0.195D-«-OG ^•

0.96»D + QQ . -0. 865D»Q..O , 0«100D-»-Cl -Q. 642O-02 0. .1 02.Q-Q1 0 . 1 -4 C-GZ

0.111D:»bQ 0.195DVOQ ^0.6^2C-02 OL.AO_Q.Ct01_ .0- 2^90 + 00 -0 .',71 0+ 00

0.6250-^0.1 ^Q.6Q2D-JQ1 0-.102D-G1 0.2490+00 . 0,0^00+ 01 - 0 , 2 t .1 D + 00

-Q.415D»qQ 0.144C-02 -O.a 4 7_1.CÔO. - 0 ...2510*00 0.1 00 C+ 0 1

REFERENCES

Blaha, Georges. (1971). "Inner Adjustment Constraints with Emphasison Range Observations. " Reports of the Department of Geodetic ScienceNo. 148. The Ohio State University, Columbus,

Gaposchkin, E.M. and K, Lambeck. (1970). "1969 Smithsonian StandardEarth (II). " SAO Special Report No. 315, Smithsonian AstrophysicalObservatory, Cambridge, Massachusetts.

Meade, B.K. (1972). Private Communication;

Mueller, Ivan I. and James P. Reilly. (1971). "Geodetic Satellite Observat-tions in Nor America Solution NA-8. " Presented at the Annual FallMeeting of the American Geophysical Union, San Francisco, California.

Mueller, Ivan I., James P. Reilly and Charles R. Schwarz. (1969, revisedJanuary 1970). "The North American Datum in View of GEOS-I Observations. "Reports of the Department of Geodetic Science No. 125. The Ohio StateUniversity, Columbus.

Mueller, Ivan I. and Marvin C. Whiting. (1972). "Free Adjustment of aGeometric Global Satellite Network (Solution MPS7). " Presented at theInternational Symposium Satellite and Terrestrial Triangulation, Graz,Austria.

NASA. Directory of Observation Station Locations. (1971). Goddard SpaceFlight Center, Greenbelt, Maryland. Second Edition, November.

Vincent, S., WÊ. Strange and J.G. Marsh, (1971). "A Detailed Gravi-metric Geoid from North America to Europe. " Presented at the NationalFall Meeting of the American Geophysical Union, San Francisco, California.

-51-

2. 4 Free Adjustment of a Geometric Global Satellite Network

(Solution MPS7)

2.41 Introduction

The basic purpose of this experiment was to compute reducednormal equations from the observational data of several differentsystems described below to combine them eventually with the normalequations of the Wild BC-4 observations taken in the DOD/DOCcooperative worldwide geodetic satellite program and provide stationcoordinates from a single least squares adjustment. The solutiondescribed in this paper is a partial one obtained without the use ofthe BO4 data. The observational systems combined were theBaker-Nunn simultaneous camera observations from the SAO world-wide network; the C-Band range observations from the NASA net-work; the MOTS and PC-1000 optical observations in North America;miscellaneous camera observations in Europe which were includedin the SAO69 solutionând, lastly, a group of optical observationswhere Baker-Nunn cameras observed simultaneously with MOTSand/or PC-1000 cameras in the previously mentioned group.

2.42 Description

Smithsonian Data

A set of optical observations were obtained from the SmithsonianAstrophysics! Observatory. These included 14,356 simultaneous obser-vations from 28 stations in the SAO 69 Network. For each observationthe track angle was provided along with the uncertainties along andacross the track. The variances and covariances, in terms of rightascension and declination, were computed as described in [Girnius andJoughin, 1968].

MOTS and PC-1000 Data

The set of optical observations used here were the same as thoseused in the NA6 adjustment described in [Mueller, et al., 1969). Theobservations had been previously screened and a set of reduced normalequations, referenced to the North American Datum, obtained.

In. the meantime [Vincent, et al., 1971] published a geoidal mapbased on gravimetric and satellite data. By an iterative procedure anew solution was computed which constrained the hew undula-tions, and thus a set of geocentric coordinates were obtained. Withthese coordinates as.= initial values, but with the original set of

-53-

observations, new reduced normal equations were computed to be usedin the solution described in this paper.

' C-Band Observations

The C-Band solution is a least squares adjustment of the range.observations from twenty-eight C-Band radar stations operated by NASAin a worldwide network, which resulted in distances between the stationsand a set of coordinates of the stations on the SAO C-G ellipsoid alongwith their standard deviations [Brooks and Leitao, 1970]. Upon request,NASA/Wallops Island kindly sent us the correlation matrix for thesesolutions, which enabled us to reconstruct the full variance-covarianccmatrix.

Some of the stations in this adjustment could be related throughground triangulatioii to nearby Baker-Nunn, MOTS or PC-1000 cameras,thus the interstation distances provided indirectly the scale of thesolution. The C-Band data was treated as though they were lengthobservations between the stations and developed a program that com-puted- the normal equations that would correspond to these length-observations utilizing also the reconstructed variance-covariancematrix.

The computed lengths are listed in Table 1.

Table 1

Stations Length (m)

Merritt Island (4082) to Pretoria (4050)

Merritt Island (4082) to Kauai (4742)

Merritt Island (4082) to Bermuda (4740)

Merritt Island (4082) to Grand Turk (4081)

Merritt Island (4082) to Antigua (4061)

Kauai H.I. (4742) to Vandenberg AFB (4280)

10,909,592

7,362,142

1,593,106

1,230,691

2,288,026

3,977,684

-54-

Mixed Optical Observations

We also received from the NASA, National Space Science DataCenter a magnetic tape containing records of' optical-observations onGEOS-I from November of 1965 to August of 1966. These included2322 simultaneous observations between Baker-Nunn cameras, MOTScameras and PC-1000 cameras located on and around the NorthAmerican continent.

E being intended to combine the normal equations developed fromthe above observations with a act of normal equations developed froma much larger set of SAO, MOTS and PC-1000 described above, observationsthe possibility of duplicating observations had to be considered.

In the case of the majority of the MOTS and PC-1000 and all ofthe Baker-Nunn observations, the few duplicated observations wereoverwhelmed by the large number of other observations at thesestations. However, a number of MOTS and PC-1000 stations in theCaribbean area contributed only a few observations to the NorthAmerican normal equations. Any duplicated observations here wouldhave had an inordinate effect. Therefore, all such observations wereeliminated.

2.43 Constraints

Inner Adjustment Constraints .(Free Adjustment)

The large number of optical observations effectively determinedthe orientation of the total network while the C-Band observationsprovided a scale. Only the origin remained undetermined. Todefine the origin of the system in its most favorable position (fromthe error propagation point of view) we imposed "Inner AdjustmentConstraints" compelling the trace of the variance-covariance matrixto be a minimum [Blaha, 1971].

Length Constraints

The C-Band observations described earlier introduced scale intoour adjustments. They also provided much needed extra connectionsfrom Africa across th,e Atlantic and to the Caribbean Islands, andthe length Kauai to Vandenberg Air Force Base greatly strengthenedthe geometry in the western United States.. "

In addition to the C-Baud scale we also introduced a weighted

-55-

chord length constraint between Homestead, Florida and Greenbelt,Maryland derived from updated Gape Canaveral datum coordinates of thesetwo stations determined from the high precision geodimeter traversein the eastern United States.

'.£.; Height Constraints ;

At all stations, a weighted height constraint was imposed. Theheights above mean sea level were obtained from [NASA, 1971] andto these, the undulations 'referred to the SAO 69 ellipsoid were added.The undulations were determined from a--number of sources. BetweenNorth America and Europe the geoid of [Vincent, et al., 1971] wasused. In this report, the undulations of some stations were alsotabulated (computed). These tabulated values were constrained withweights corresponding to a standard deviation of 3m. Other stationundulations were interpolated from the geoid map itself and, allowingfor interpolation errors, received assigned standard deviations of 5mexcept in those areas near the Caribbean where, because of largegeoidal gradients, a standai'd deviation of 8m was estimated. Forstations in other parts of the world (not covered by the above geoidmap) the undulations were obtained from the SAO 69 geoid map, andstandard deviations from 8m to 15m. were assigned depending uponthe number of gravity measurements available in the surroundingarea. All heights constrained (H) are shown in Table 2.

These height constraints, which are in effect independent obser-vations, provided a valuable strengthening of an otherwise weakgeometric network. A test adjustment was run (MPS9) in which allpreviously described constraints were held except the height constraintsand in this adjustment the final standard deviations of the coordinateswere more than doubled and at poorly determined stations more thantripled.

. , / Relative Position Constraints

These weighted constraints were used to tie together the C-Bandradar stations with nearby camei'a stations through the connectingtriangulation, and also helped to connect the Baker-Nunn stations withnearby MOTS and/or PC-1000 stations.

In every case, Cartesian coordinate differences were computedon the local datum and the weights determined from' standarddeviations computed from a formula given in [Simmons, 1950],This estimate was used in all cases except between Mcrritt Islandand Jupiter, Florida, where the uncertainty was estimated to be

-56-

Table 2

Height Constraints and Undulations

(all units in meters)

Number

1021

1022

1030

1032

1033

1034

1042

3106

3334

3400

3401

3402

3404

3405

3406

3407

3648

3657

3861

3902

3903

4082

4280

4050

4742

7036

7037

7039

7040

7043

Station

Blossom Pt. , Md.

Fort Myers, Fla.

Goldstone, Cal.

St. John's, Nswf.

Fairbanks, Alaska

E. Grand Forks, Minn.

Rosman, N. C.

Antigua, W.I,

Stoneville, Miss.

Colorado Springs, Col.

Bedford, Mass.

Semmes, Alabama

Swan Island

Grand Turk, B.I.

Curacao, N. Antilles

Trinidad, f. & T.

Hunter AFB, Georgia

Aberdeen, Md.

Homestead, Fla.

Cheyenne, Wyo.

Herndon, Va.

Merritt Island, Fla.

Vandenberg AFB, Cal.

Pretoria, S.A. .

Kauai, H.I.

Edinburg, Texas

Columbia, Mo.

Bermuda

San Juan, P.R.

Grccnbolt, Md.

ConstraintsH

- .20

- 13.

902

82

188

238

887

- 37

20

2173

63

55

31

- 29

- 19

221

- .12

- 20

- 22

1872

142

- 12

91

1604

1157

48

249

- 5

9

27

a

3

3

3

5

15

3

3

3

5

5

5

3

15

3

8

8

3

3

3

5

5

3

3

6

9

3

3

3

3

3

, . N.MPS7

- 30

- 18

- 27

12

4

- 15

- 24

- 41- 20

- 8

- 28

- 24

- 38

- 39

- 29

- 59

- 25

- 26

- 24

- 11

- 33

- 27

- 30

- 1

- 4

-11

- 20

- 37

-41

.- 29

f Vincent et nl. , 19711

- 26

- 18

- 27

14

- 18

- 22

-39

- 19

- 11

- 20

- 18

- 31

- 26

- 34

-24

- 26

- 22

- 10

- 26

- 23

-.32

- 12

- 24

- 36

- 41

-26

-57-

Table 2 (continued)

Number

7045

7072

7075

7076

8009

8010

8011

8015

8019

8030

9001

9002

9004

9005

9006

9007

9008

9009

9010

9011

9012

\9021

9028

9029

9031

9051

9091

9424

9425

9426

9427

9431

9432

Station

Denver, Col.

Jupiter, Fla.

Sudbury, Canada

Kinsgton, Jamaica

Delft, Holland

Zimmerwald, Swiss.

Malvern, England

Haute Provence, Fr.

Nice, France

Meudon, France

Organ Pass, N. M.

Pretoria, S. A.

San Fernando, Spain

Tokyo, Japan

Naini Tal, India

Arequipa, Peru

Shiran, Iran

Curacao, N. Antilles

Jupiter, Fla.

Villa Dolores, Arg.

Maui, Hawaii

Mt. Hopkins, Ariz.

Addis Ababa, Ethiopia

Natal, Brazil

Comodoro tf ivadavia,Ar{

Athens, Greece

Dionysbs, Greece

Cold Lake, Canada

Edwards AFB, Cal.

llarestua, Norway

Johnston Island

Riga, Latvia

r/.hgorpd, USSR

ConstraintsH

1767

- 10

251

423

72

957

165

702

432

214

1633

1564

81

99

1874

2477

1588

- 19

- 9

618

3036

2362

1911

37

;. 215

242

454

684

756

622

17

32

236

CT

3

3

3

3

3

3

5

3

3

5

3

6

3

6

8

9

10

5

3

8

9

3

10

10

15

5

3

6

3

3

10

3

3

• • " . , . ' N . .MPS7

- 13

- 26

- 30

- 22

48

51

57

59

45

47

- 16

0

45

41

- 45

19

-20.

- 29

- 27

6

19

-37

52

- 12

- 9

46

78

- 30

- 24

45

28

22

45

[Vincent et al. , 1971]

- 13

- 24

- 31

- 23

47

54

52

55

- 18

55

,

- 26

- 24

-22

54

54

- 28

46

24

4?

-58-

one part in 750,000. The relative constraints used and their weights(1/Cr3) are all given in Table 3.

2.44 The Adjustment

The four sets of normal equations (See Section 2.42),and the previously explained constraint equations were added togetherand a single solution was obtained for the combined systems.

We decided to run three different adjustments to investigate theeffects of the constraints we were using: MPS7 was ultimatelychosen as the best adjustment. It contained all the constraintspreviously explained, inner adjustment plus height constraints.MPS8 included the height constraints but without inner adjustment.MPS9 was run with inner adjustment constraints but without holdingthe heights.

After MPS 7 was run, we immediately computed the undulations(N) at selected stations and compared them with the values given in[Vincent, et al., 1971]. This comparison is given in Table 2. Thereare some discrepancies, but generally the fit is good, indicating thatdespite the free adjustment, the height constraints had held (thus ourorigin is reasonably close to the center of mass).

The results of the MPS7 adjustment are tabulated in Appendix 1.The number of degrees of freedom was 10586; the quadratic sum ofall the residuals 12201; and the standard deviation of unit weight 1.07.

2.45 Comparisons with other Solutions

Table 4 summarizes the transformation parameters (systematicdifferences) between the MPS7 coordinates and those published in[Gaposchkin and Lambeck, 1970], and in [Marsh, etal., 1971], forthe global network and for both the European and American nets.Two sets of parameters are listed. The first was obtained throughthe assumption that only translations exist between the sets ofcoordinates. In the second solution, the rotations were first computedthrough direction cosines independent of translations and scale factor.Subsequently the general seven-parameter transformation was carriedout with the three rotation parameters constrained with their varinnec-covariances obtained in the direction cosine solution. Appendix 2 givesthe general solution and variance-covariance and correlation coefficientmatrices obtained in each case.

-59-

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APPENDIX 1.

(all coordinates in meters)

-63-

.STATION NUMSEfv - ? l [iLLIP.S'JlQ

• . . . : .:-... -.: ...,-. .. x .:....:...Y.:... :PREL. COORD, - ,1116032.4168 -4876323.0294 3943045.8335

CORRECTIONS - i 4 V 3 1 0 3 - 6 . 9 1 4 A -50.3740

ADJ. COORD,,- 1118016.7271 -4«76329.9438 3942995.4Sc : .7

VAHIANCE-COVAMANCE . M A T R I X OF. THE STATION POSIT ION

12.3135161.406271

-0.50648'.

.1.496271 -C .5064S49..574164 ._.._... . .4 .55476!4 .554761 11.640591

ST AT I ON-.NUMBcR, _- ...

p R E C . r " " '

POUT M Y E R S FLA. E.LUP.S.OI.Q.

x ___ y '_„_307621.3234 -5o51992.6336 2633574.2911

CORRECTIONS ,;•--

ADJ.

1A.6979 -3.8427 -43.35'VZ

807fc46. 0263 -565lV9fe. 4763" ~~2633"530.9369

E MATts IX OF THE STA'fToN POsTrloN ........ ~"

8.464229.'..... 0.425u09

-0,775519

0.425609 -0.775519...6.91.76.4_..__ :. ^ 2.50S412... __2.508412 8.352733

.STATION. NlK-iBER . -_ . . . : . 1&33,

PREL.

: :ELL] RS.Q1.D

i. x' . -._..„...¥.._..- _....... L..:.-2357271.1364 -4646320.959% 3668373.024S

"cGRREcTtio'lMS - 13.2372 -10.974S -46.2868

ADJ. COORD. - -2357257.3992 -4fa463 21.9338i 3666326.7330

VARIANCE-COVARiANC*: M A T R I X OF THE STATION POSITf lON •

-11.73.93-4312.9,5^35A.

1.754S96

4.245il- '».... 1.. 7546.9.6 „__12.444189

ST. . io>'\ '5;

. , .PRFL. COORD. -

:.- ,:,......X\...... „.._._-...... ...... ..Y,:.. ......26Q2652. 1506 -3419240.9226&

ELL IPSOID

4697706.7911

CORKECTI'qNS - 31.1331 ; 15.00177

ADJ. COCRO.— 26026R3.2f>37 . -34192^5.840'*

Vf lR!ANC6-COVAKlA,\ 'Ci ; ; 1 A T ^ I X ' O F THE S T A T 1 D N PUSlTl ' ICN

-36.9271

4^-5..io<; 2.?;-

30^.030226

STATION NUMBER -

PR EL. "COUKD". -""

.ALASKA. tLLIPSOJD

-144 56e9;. 3178 57518^6.7179

C O R R E C T I O N S -

AUJ. CCOftU. -\ 4

V A R I A N C E - C n v A ' 63917_ _1.4.74 .7.03556.

-22.60M573

184.008270~

STATION

PREL. COGnD. -

i - _ . .. . _..-.t.LL.JR.Si"lb.

X -...: ...;. .Y...._ '..; ..Z _. .

-521731.2lt? -42.420.49i70lt . 471S7B5.4161

C O R R E C T I O N S - !9.D'?i>l -13>3933 -41.1352*"• "— _• - — ' _ ^^J

ADJ. COOPO. - ' r-521712.1»J96 -42420'o3.0949 471874-*. 2809

V A R f A N C E - C u V A R I A N C r M A T R I X O F T H E S T A T I O N . P O S I T I O N

-3.443950..-3.443-^50. _ _.

-2.3*F826(S..Q5.A.O.'l3...

10.666619

STATION N U r t C t H -

p"?cL."ecorRo. -

AC-S MAN - . . C . ;..£LLI,P.SOID..

...' Z... _,_.:..!.__.

C O R R E C T I O N S - 14 .&U35 -'3;,9251 : -44.9581

ADJ.^ C0010. - 647^90.9933 -517794Q.S080 3656730.3703.

V A R I A N C t - C O V A R I A N C E M A T R I X OF THE S T A T I O N PCsl'TTON ~"~'~~ ~; ~"~~

V 3.4-40431.

-1.203739.: ...3.1^40431.

S T A T I O N , N W H E H - ...... ELLIPSOID

' X-18.6861-4.2^94

t CPRR'ECnONS - -<>2.. 48' ft 5

1 £6 8571.60 0 'v

IANC5 l .xTPIX Jf- TH£ SI

t.*- tc'» -72. c'».J2.i"i

.'2.. 2 9«T2.>5'

-65- *•'

3 . 24 '•* '.i O'J' l !> .227372

Y ... . . . . . . . .... /,-5337367.4.54-3 ji '3351-r; 32'

20.1273 •

ADJ.

AlA.-'.Ci: > i » T ; .! X .;)> THi. S T A T I O N P O S . I T I C M

.25.-i!f . if»:: . ^^f.OT^.v'r.C^. ______ 1..'.. _./» 3 • 0 5 8 31'

S T A T I O N . . N U M B E R ..-. 3AOQ CCLCrJVPG S P R I N G S ELLIPSOID..

. . : ' ' . ' . : . _ . : . _ . . . „ . ! . . . .:' ' . . x . . . . .--. ...... •...' ..... ....:Y ............ :...,_„...: ______ , . z . ..... -PRE'L. . C0q'«p;' ;-- -1273219. IS-.? -'»79'50i'*.2 603 399*2#i .6200

. . . . ' : -11.9150. -^ft .61s3

ADJ, COCBD. -"•'• -1275222^31^7 -479"Sp2.A .17b3 ~ ~399*233. Ool 7

V A R I A N C E - C O V A 3 I A N C E . ^ f i T K I X ,0>: ; ThE~ iTATlbN,~PL^sT'fl Oi\T "~~

1.453025. 5..43<U,rt> ; ...... . _______ 39.. V3.1 72,0 ________ :..__1.8.,..01. -53025 13.0676P6 2tJ . 12

S T A T I ON . . N U N f l u R . . -„ ......... 34-01 .. BEDFCXRJ") M A S S . . u.. ___________ ..E.LL.l RS'J iD

...... _______ „..;•. ______ : ...... „.__...,.. ' . . X < .. . ______ ..... _____ ......Y...,. .. ______ .. ___________ _..ZP R E L . COORD. - 15i?-lZl'.i-4':J2 -A '-i. 357'*. 701 7 42S31T- &. 2634

-5.0.9707

AOJ. ' C C U P.O. - " 15'l-3ii'9V3-b'i S " ->46353o" .062~0 ^2S30t 5 .~29?.7

V A R I A N C E - C . O V A R I A i \ C - E V i A T f i ' l X . d f : TML: S T A T I O N P O S I T I O N

. 9 7 i 2 .956042 o 6 4i..9560^2 ....... !.. J..19...S73991 ____________ ... 3.aO0.6426^2 3.80H765 14 .25H3B3

t *' - 3407 • 1 SffW-S A L A ^ A V A - ..._ .-.._. .t.LLlESoI.O.

....... . ... X ... ....._..Y...._ :.„.. _.2L . .\.. .COOK.D..-T 167135,. 57-J3 -S-t". 1076.7.6<i5 2 ?-%511 -. 91 6 =

ADJ. CrOKO. .- l';7>52. Jk3C -5^3 1977. K95U • 3;>5;06 7 . 7200

A.NCtrCGV/i^lA/v'C.- 'iTMix ••- Th-. STATION POSITION... -_ ....._.__ ........ -. .- _.. ... ___-___.- . ^ _ _ _

. . ; . ; . . - . . . . ; . . -o .o?2i?v , ^ . i v ? j i t . . . . . . . . . . 4..":' • • ' • v ; ' . • '• 0.' 7 !.-:•>.-'•••' ^ . 27 -> lOi . l4 .S

-66-

ISLAM) . E.LLIPSl.'ID

: ' . . . .X . _______ Y _________________ ______ Z .. ........R t l . .CdCMO. -• 442471.8473 -6053959.6531 l«957r>° . 11 49

C C P K E C T I C M S - r : . - - f - ? 5 22.53.46 - S 5 . 5 & o

ADJ. C C C R D . - t>42C-10.?.3'i9 - 6J33'i3V.-.31 8s ' ] ?9?713 .3539

VAP.I-ANCt-COVARI. ; . ' - . 'CS S A l R i X ' JF Tr-Z STAT. I f . 'N

-1.933513 5.3004C92:..003;J6.c _______________ 0... .7.3 .K .6?..? ..... _. ..... ....0.73b63« 27.691902

STAT.Il-N NUMBER -. ... ^y'3 .......... GP/.J-D. T U V K .-*.'!. ______ ........ ELLIPSOID.

..... . ......... ........ ;.. ________ :.-x ..... ... ..... ... ..... . .......... y._ ....... '..:...'.....:. _________ '..z_ _____ - ------P R E L . COfJRU. - iv l° 'V74.8i07 -562 10=38 . 25f i3 2315c':. 3 . 469 1

CORRECT! CMS - t.526'« -9.5&0fc -?9.2i70

AuJ. CCQRD. - ..... •"' ' l-j"i«479."i772~" -562H 07 .9 1 39 " 23 l&Si^-. 2021

VARIANCE-c6 'VAr< lANCE M A T R I X OF THE STATION. ' P O S I T I O N

10.9275 . 547803 3.290664.B47a-.)3.: .......... _____ 10..2.1..1.5/..4 ....... . ....... __..3 ..5.3 1 1.71

3.581171 14.&53133

, T AT IDW NU .-••.(:•>:•:* - B'VOfc _ C UR AC JQ_ M. A N T II. L f: S ..... _r.U.I.PS O

• . ' . , ...... ;-. X •• ..... :;.;.Y- ...... '..'.._ ./ ______ Z ___ ' __.'FL.. CCCKD. - 2J5I788.8707 -.!5:il6921 .9460 1327276. 8 = 2*

i J M S - - 0 . : > ; > 7 7 -0.7047 -53.7261. . . . . . . . . • . . . . _ _ L

ADJ . • CC-JRD. - 22 i i l 79o .42b ' - r -5316922.6527 1 3 2 7 2 2 3 . 1 2 6 f c

VARIANCE-CUVA'-1 lAKCt V A T S i X OT TH= bT AT IC'N "pOS I f! L-N

l-l. 25573 Is ' 7~.e...224.37.9.0 .212203

STATION..NUMBER - .. 3-07 -. .. TPJNI .OAD T O B A G O ^LLIP5C!0

•.•.; ...x. y _ z.PRSL. COCRO. - 2">7°S£23.-5'«6':! -5512535.9595 1131 22 '•). 61 = 5

C G K k t p T I C N S - -2 .33^9 . 18.3H34 -55.103.v

A O J . - . C C C K O . - J")79HsU.31.V9 "-.5513537 .V/c.-1 1 LSI 17-. 51 6?

V A R I . A N C f c - C O V A S I A . V C t : i A T M X O l ; T H = S T A T I O N P C S I T I L N

- '1 •'• . 4 i H !J I 0 • -1 •'•-67-

S T A T U S NUMlic?. -

P p - l - . L .

3643 ;-!'Jf..'T AF ............. !:LLIP.SQID

........83Z544-.6662 -b3495 46. 1754 3360660. >}:.:-?

-1.631o -41.2352

ADJ. C C O S O . - 43£557.^ -0 -ti-^S^. 8569 3260619.5277

V6r IA: - ;Ct -COVA:< ! A'NCE V.TKIX OF Thh S T A T I O N P O S I T I O N

1.753^13 .. .31. .>£3 ;273 ..6. 7? ;»1«

nii' ».»M^Wi i»'">'i'.i i •»'• ITirf«««ii»« iVbiiiiiinijii i »^

S T A T I O N 'NUMBER. .- . ,3 f. 5 7 A !U'R 0 j] f: iV .". AR YL AND,. FLU PSD 10

'. . • . . . . ; . . ... . -X . '. Y_ _..._.z_ ..:....!P»EL. COORD. - 113676fi.51I3 -•'»78I>190.10 73 4032C<60 . 525?

"c^RRTcTi"ONS~^ 12.7733 -10.1142 -*•>>. W?.

ADJ. CCORU. - 11867<Jl.?fc46 -47b5200.2215 4032914.253 3

V A R I A N C E - C O V A S ! Ai^ jCF M A T R I X OF THE S T A T I O N P O S I T I O N

. . . _______ _____„__ -0.03075 9 '

'""". -0.0?0739 5.306246 12'. C365 35

S T A T I O N KUMcrik - 3fr6_t HC;MFS.Ji.:_AU- FLiJP I HA _.._..L:'.LLi£S.ilI.i)

.'. X Y 2_._.__PP.fL. CCJGi-'D. - 96L7-V9.7864- -56>79161 .0394 2 7 2 9 9 6 0 . 9 7 6 ?

C U R P r C T I G M S - i?..57«7 -3.1751 - 4 5 . 3 3 ? o ~

ACJ. CCJORLJ. - 96176^.4651 -3o79164.2645 2729915 .6437

VARI i - \C-£ -CUVAf< I ANCu ' - 'VTi- IX .JF THc S T A T I O N POSITION

1?.: I Vb38 0.630201 -1 .550960 ~. . ..- .. O.f.'iOJUl . . . . . .....6.1 3.197-5. .<..l-34.4tf

- l .Sô'J 'JO 2.1"ti'.'*5 11.199167

S T A T I O N .MJMdtR..-. . ?90Z C'^ Yt;N:<^.. ...!xYJDt"I ^y. _..... H L1.1.•? S 0! 0

: ..X. . j .:_.....Y ...'.; . . - • ... I .... ._PftEL. COCrtD. - -1224711.0923 -4oU 12 2 J .4264 41 7-rS33 . 699 .-}

" C O R R E C T I O N S - : ^ .3^60 -».fv;83 -49.i2'-i

ADJ. 'CCCRP. - -12?^700.7C- j7 -^6512 33 . 3^""6 4 1 7 4 7 ^ 4 . 5 7 ^ ^

V A R I A \ C £ - C C ' V A - 4 1 A : > i C E M A l S J j X .)F T! :-: S T A T I O N PL'S IT-I I 'M

"\ " ..v... -68T..'..!.".."'..'.' :. *.'...".

[> 0 10'Ou ......I LL.I.FSU.IU.

x .PPCL. HO -3 . 25 HC

7 . 3S.3767 n

ADJ. CCOr.O. - ' - l'6;!?07:>.i>97:i -«t 9v 301 1 .^S23 3991 81 1 . 1 7 1

; V A k I A N C c - C i ' V A : s I A . \ ' C t M / . T K 1 X - ) F T H L S T A T I O N P O S I T I C N

- .'.'. 15i.65?£-v~ 5.9 0'3 0^4 - 30 . iTVTTi«0t- '.7>V61 A-3

' - - • • • ' ' ' " - • • • •

S T A T I O N NUMc- : -< - '.:.. 4050 PRETf! f i f / \ ____________ EL.L'JiSiJI.D.'

. • . .. : ....... - . ' . . • - . . - - . x. ...'.. _ ... y ...'..: .__' _______ .; _____ i_..._ ....... _____ :,P R E . L . ' COOftU. - 505lfcOS.7772 •27265<?5 . l A l f c ' -27 7^1<i3. 7107

Co"RRi-C T I C K S - . - .4S.5116 "~lt . .5d02. 97.80^0

ADJ. CCOHO. - 505,i6;>i:.2B6.9 2726s 1 1 .72 f? ~ -27?Vo95". 9007 : ~

' V A R l A V C S - C f . V A r t . - I A N C C :>UTP!.X '.!|- Thu S T A T I O N P O S I T I O N

174.6.60583 3A3. 201160. .... 6.5.7 ./U.J.&5.2 _________ 10'7^..ît.!.3..A.'3 _____ '.._:_.

.. . '3^3. - ."Oi ' l iO lC49.2il'3<r3"~ 1732

S T A T I O N MJ.v-Hc:X - fOfe t ' ETfiANT ______ __ ...... £i.L!.PS(Ui>.

• . ' . • ' . • . ,: ......... ' . •;„ . ' ' • . . : X -. ......... ..:.....Y_ ______ : ____________ _j? _______ ___PPEL'. ' ' COCKU. - ZgSl^^^-.^MO -537? ?5i 'V.5A»3 1660020.2753

CC'PK'CC'TipNS- - ' - -3.2296 -ii .^2:-^ 3fc .99As

ALJJ. CCO«D. - 235 159 1.1 2—'. - i)372536.77l6 1866057.3717

• V A R . l A ' N ' C E i - C U V A r t l - A r t C e ^/.T^ I X - ; r T h e S T A T I O N P O S I T I O N

<s . t lS2 ! ih 2.2-^0063........ ^ . k ^ U J - i j . .a.5 31 6.7.8 „

: ' . t . i b lWt -. 2^112

•':' !-. • . "i« -

"STAT IO iN NUKHci\ - ' 4Q'>.\ _ . g T R G ^ T . _____ ...... .JLLLI P.S.OI.O

• - . ' ' .•• . . . ' 'x . . . ._ .. . . . . -_.'.v. . . . _ . . . _ : _______ .. ___ z ___________ . ________PR-6L. C O O R D . - - l-J20/Ol.-!6:i^ -5cl 93 ^rt . 3302 221911 5 . 50--

C O R K E C T I G N S - b . ' JSî -3°. 0^2 l i i . H l p ^

ADJ . CCOKO. - ' l9>v) . 'V07.<- i< 'V<»J -;61 -> 37 .f Oc4 Z 31^ 166. Vi ' i 'S

V A R I A N C c - C U V A K J A M C c M A T F I X Q H f M t - S 7 V , T l U i \ P S I T I C k '

'ST AT Ipii. iVJi-iBcK -

PAtL. CUC'r-'D. -

I TT I S L A M O ti.LL ! PSOI L>

... x . . ________ Y...1. 7663 -i .o2rlCv. '*7.: . 262?

-U.iSIi-i -10.36-'.-; 23..',777

AOJ. CGOfcO-. - 910060.*107 -553911?. 6631 3017905.7'«05

VA*IAi-iCE-C(:VAP I A:\Ci. ••••«.•! TRIX OT T--r SIATJU,^ POSiTJCN'

r, v-i

.STATION NUMbER - A? SO ^NDrN^l-^.;? - A!;i?, . .. _______________ ELL1.P.SC.I.D.

X.:PR!fL. CHORD. - -267J8.59.9360 . 57'»S. S6 07 SO 5. 67-^3

COKRECTIUNS -

ADJ. COORD. -

-15.2215

2671675.159?

-6.9001

—V52121 1 .<r 2607J>01 . 1301

VAPIA.v iC£-COVA.-<IAi \CE M A T K I X OF THE S T A T I O N .POSi

l ' . .7 ' t r )53 - 0.959315..... _______ 1.6 ..QA.y.49.8

15.^04103

5. 7^8" 991.5.. 50-1(132*5.961:08'*

S T A T I O N -47A&- _tLJL.l .P.S.U.1J2

. . • . - . • • X :. COCPU. - -467 4293.01'rOi . 91 '^

ADJ. COOrlD. .- 23088SL.5853 "*o7-',;iOi. 2y 17 3295 1 15. 177s

V A f < l A N C n - C C V A R ! ANC5; M A T S I X OH Tnc S T A T I O N P O S I 1 1 C M . ' v

S T AT I ON i\U ,"• B r. S -

PKhL. ;COCRD. -

. I ....... t L L ! I? iC' I 0

X Y

CCRK.KCTI'CNS -

•XUJ. COOriD. -

.. 5..55c»5

5>'-39"i.-7.:5 -X0."/-'i530.52 53

•MAIM X JT Tilt S T A T I O N PCfSITi l

i iTT? ')!::•. 3 ? • . h.)'•) 2 ..^3.'i" -i.

-70-

23^7506 . 9t> '.6

S T A T I O N .N'Jr!&ER .-.., 7036 CD-INSl^r . T E X A S .... ......... cLL.l PS'j i 0.

. _-._.....: .: ... .x. : ;.Y. zP R E L . COOKD. - -6.16519.5?.2 7 -5657465.9567 2 B 1 6 3 8 5 . 7 7 0 5

C O K R E C T I O N S - 23 .2956 '-7,12ô'- -43.7482

ADJ. ' .CCURO. - —J2&496 .2 i90 -5&57*-73.6i?<«7 2816342.022*.

V A R I . A - ' J C E - C U V A S I A N C E M A T R I X O K . T H E S T A T I O N P O S I T I O N '

I ' t .3 '4»i40 -0 .792797 1.531550...' _„ ."..„.-0:..7.91-7-?. 7 fi..2.e.72A«_l 2.. .1.7.3 5.0.0

. . . . 1.322553 2.173500 11.162002•••MMiMMMMKMMw^MMMaiHMMMinvaiaQtaavOTHMBCVEBttiuuiwanMWvnou&M 'i lilrtMtjBiiilrtfnfiiiiiii <TTHTMTB"

STATION NUMBER.,- ., -7.037 COLUMBIA MO. ._D.LL I.PSP.I.O.

_ x _Y_ LPPEL. COORD. - -I?.l317.0or,4 -4S672 82.1392 39.y:-i32b. 7103

" C O R R E C T I O N S - 1 5 . 1 4 2 0 - I 4 . 2 c i 5 -4^.1249

ADJ. COORD. - .-1.91298.9264 -4967296.4507 39«32C1.535-

VAP-IANCE-COVARIANCE MATRIX OF THE: STATION POSITION

~ 11.105130 -1 .^37472 -1.4371*3

-1.A37143 3.652438 9

. .S T.4.T I .CM., .NU M BE 8.._r. ..10.3,9 . _ t j H M U Q A E.L L J .P. S 010.

.. .._ — ,.—...- ' X :. _.Y . L. :.PSEL. COORD. '*• . 2?.6b200.5i40 -437.?60i. 7o26 2394620 . P205.

C O R R E C T I O N S - . t - ,3249 -^.H^SO -39.53~6~2~

ADJ. COORD. - 2306207.33n9- -4873607.7576 3394591.2S43

V A F I A N C E - C C V A R I / ' N C i : ^ A T h l X JF THc" S T A T 10 i\i p"6 sTfJO*N ~

9.304137 - 1 . 3 4 7 l T 2 - 4 . M 9 6 2 f t. ......... : ..: _-1.34717? _.. ?.9.2:VS02 3..«f-.7.7.C.7

-4.419,S:'fr 3 .547707 15 .934007 .

STATION .NUMKER..-.._•: 70~0 • • - . _ • _ SAK Jl.l.\,\ P.!!. ELL! iJSO! C1

. . ' . . i'.:.. . . • • . . - : „ x ..._:...Y_ _.zP R f c ' L . COORD. - 2''6503t:.6:>57 -553--931.4949 19655^5.^070

C.ORRF:CTIC!-:S - ' '. 8.^647 - 9 . 4 ( ) f p ^Ti7î7^

ADJ. C 'HJRJ . - ! 24.65045.1304 -553-940.696^ J9o55'.6. lf> 5»

V A R l A K C E - C C V A k i A M C r . M A T R I X OF Tuti ' S T A T llif.N POSiTlON "

. S T A T ! O N . _ N U M B c R _ r

P*EL. COD*D. -

70^3 i; I f >AE Y L A M P _ . . . . . . . . . . .ELLJ .PSO.IO

X1 l .->U£91;3~035 4831530.1355 3994?! i . 7*59

CGP.KcCTlCMS -

ADJ. ' COUR.D. -

11.3710

1130702*6795

-5.3198 -46.2172

3S94165. 5&87"

V A R 1 A N C E - C O V A . U A N C E -iAmx 0-F THE S T A T I O N P O S I T I O N

. 0.72--1334 ...3...2.3.12 2.6-0.37*702 2 .P1V593

-O.S7S7C2... .*.. 8.1 .<?.!>. 2'3

5 .7S4oS3

S T A T I U N . N U M t t f c R .-. _ ... ..7045 D t f N V E K COLCP MXi _______ ELU P.S.G1.D.

_._ ______ L _______________ .....P R E L . CntJRD. - -1240491. 20:53 -47fr0227 . 8963 ^04905^ . 2->->

CORF. r C T I G N S " 12.=).£29 -7.12SS -^B.

A D J . C O O R D . ' - ' -12tOA ;78.2;8^4 --760235.0^52 A C A 9 0 0 5 . 3 . ? 7 6

V A k J A N C E - C D V A - .?. 3.79 a _______ : ________ 4,.6.:rs;.93 ____________4.633193 11.860496-

.S.TAT10N..NUMDHR..- ..... ..... 7072- JUPITER FLC'ÎDA ............ ... ..ELL.! PSQI 0

PREL. 'COCR.D. - 970243.9724 -5601403.7081 2880316.4199

C O R R E C T I O N S -

ADJ . COOKU. -

,12.4:010 -2.4220 -44.3242

976256.4532 . -5601406.1311 2 t f f c 0 2 7 ? . 0957

r 5 A T R I X 3 F T H E S T A T I O N P O S I T I O N

11 -0 .847620,.0..9fi('lM.; .......... _. ___ 3.. ..8.41 3.3.2 ._.' ___________ .._'.2;..3277?9._.'...

-0.347620 2 .8277t i9 7 .7 r>660?

. ST AT I ON . . N U K U E R . rJ ...... .... 7075

...... ,:..,.-.,:•:..•_•.PREL. CnOKD; -

S U C i t M P Y . C A . N A D A _______________ E LL I P.SOI U.

: ..x ..... .. ...... ........ ....... .... Y .. ..... _. _____________ 2'.V2-5.92-.3703 -4347069.9512 46005/- 6. 15

CORRECTIONS -

ADJ. CUOKO. - fS»

V A H I A N C S - C O V A X l A M C t ••iA

P0.1092 -41. 40*4

7 .

Ot- fhi STAT lU. PQSI T I ON

-0.4-4426*-72-

ST AT I ON • NUMbER ..-.. _.l ...„ 7076 K I N G S T O N Jf lK/ i iCA ....... ... .. . E LL3 RSC I 0

; ' - : - • . - • ' : : : ' . : .. _....; '..._..'. ....•;.:. x ..................... ...y ................ ..... __ . . . * ...... _______ .......P P E L . COORD. - 13.?413:>.0074 -5905665.5321 1966cl 6. 7L 14

C C J R S f c C T I C M S - 14.7259 -3.0746 -42.6771

. .ADJ.., GOOKD. - 1384151.3333 -5905663.6069' 1^6657 <». 024;.'

- V A R I A N C E - C u V A ^ l A N i C E • • ' •AT*! / O F T H Z S T A F I C J . V P O S I T I O N

." .• • • • : ; ! ~ ^. s I ^ T T 1 . 7 1 2 3 5 9 -7 .262447:.-.,.. .••;.-:•_.;....'....-•...,..,...:. 1.7123 <9 . ...S.S.7.7.17.0 .......4 ...3.<? 12^0 _,.';_.. '..- '• . . : . ; ~7.26?.447 .4.381240 28.680015

.STATION-: NUMBER.'..- ^09 DHL?" V H-L/'-'iD KLL I.PS.O.I.O.

. ' ; . . L:'....i ..• .,;i.. . . . . . . . x_ y : _z '..P R E L . COOK D. - 3023410.9853 29VEJ2 .0032 500294'-.-'391

C.ORKIC'TIGNS - . -6.0431 • rF.TTTi 6o7~9Îo

ADJ. C O O K D . . - - . 39234()/, . .?A22 299993.1323 5C03005.95i77

VARi A N C E - C O V A R I A N C E M A T K I X CJf-V THc ~STAlToN "CfSi'l f l UN

^ S 6 4 • -22.152040 51.662614 . "

IJ~* '' rJ~J*J '-"^T"'VlTrr^<TrrT»M»TT«*rirl I^QMTTlTni WHI»'Ti''»'T~' T'T^ »»'H&W_mntt*fi4r*f*<\ •* >-'

-; zuii ' iE'«wALi)_ $v; iss. .._E:LI.IPS.UL.U>..

x., '....y..'. '. L. ,_..... ..'iE-jL> COOKD. - 4331309. V9fc!i 567511.Ofc55 4633092 .9783

C O R H r C T I G N S - n .3275 0.^567 50.6166

Vj..:. COORD. ~ ' 4331,31-4.'J243 567511.5422 '463314 3.5948

M A T R I X O f - T H E S T A T I O N P O S I T I O N

.40. 321 597 0 .3 c >i67> -30. 69 45 :H

. ,0..352->75 ...L... 53...57030.'i r 5 .9^7v i . v-5.907214 35. 34 !•>'•::;

. . fMLv : . -K-. \ ' •(•;-.GU\O . . ' L i L i P . s n i ' ;

: . " " • / ' . .' . ' • J. . :• , . . X . ' . . . . Y . . . _....-. ,. ,iP R c L . COOKD. - 3?20177 .9Vo4 -13473l».0054 & C 1 2 7 0 7 . 9 7 « 2 '

C O R S ( F C T I Q : N S . - -15.4531 -US. 3-174

VARI-ANC :E-CCVARrANC£ .'V.lTt-:X ;)F Tilt STf,T!( ; - vJ

STAT ION .NUMU2R.-. --. .~50;5 . HAUTE PPOVE.VCE i F!-. ELLIPSOID

-. ________ ... . ...... _:. .. X ............. _ ......... .. ________ Y_ ....... _.._ ......... :_.... ZP R E L . GOCR'U. :- 4578327. -J964 45796L .?9;?6 440317-?. O O J 9

C G K K b C T I C i . N S - -0.3565 -5.0354 ' * 7 . 6 ? 7 2 .

ACJ. COORD'. - 457«327. 63-73 457960. Or>32 4403226. 6900

V A P . I A N C E - C C V A R I ^ N C E N I A T R I X O F T H E S T A T I O N P O S I T I O N - . . . . . ".""

5t. 1.970S06 - 1 6 . 3 V 3 5 ,. ..... l .«70?0* . ..... ______ 5 5... .7.5.7.5 16 ...... ..... _- . -6 .&i2p°ts

-Ifi . 396335 -6.612036 2'* . ''5 i-»00

STATION, .NOMB.L? . . . - ..... 8019 . ...... . . . H I C = , . . . F R A M C b ..... . ..... ___________ {- ll.I

. . . . . ....x...!; _ _ _ _ _ _ _ _ _ _ . . . . . . . . . . _ _ _ _ _ Y...._ . . . . . _ . _ . . . . . . . . . . . . _ _ _ _ _ _ _ _ J . _ _ _ _ _ _ _ _. CCOkD. -

2.3-669 -9.136't ' ^'-.4101

ADJ . "c.'bORO. '""-'• 45794&6.36- ' t7 5f6590.So4I ^3'36^5? . ^rl 77

R I A N C t - V A T r i l X O f THif S T A T I O N P O S I T I O N

1?<

_ Q..1& 196.5 __________ ...^JS.StT^ ___________ -5. ..2.1.1. .3-17.395617 ^5.21<?^43 21.592170

S r « I i l ; l < MJKa.tr^ - . S050> M r U O Q f - i . FpANCE-T. . . . . . ________ ___ 1J.L1PS.DJD.

..... __.z_.... _____________^776501 .6402

- . - ; ;;,t'-5'J,.2:;62 - ?e . i s l6 -9.0951

AOJ. CCORO. 4. 420563'5.':.f2-3 16?70S. 7':(63 4776572.7451

NCEHCOVARIANCt :-iAT;K!X OF THc S T A T I O N P O S I T I O N

14 3 . 4 9 a a o ^ O -103. 56 2 H.'.3 3. tbOO^p .. . 1.79.540.26.5 ____________ -7.2.25^619

STATIOU .NUMBER - 9001 _ OSGAN PA^SI N.;- ............ ELLIPSOIO

... :'; ;~ ... . . . . .. . i.I..x....:' ...... .... ....... _.. ____ y. ...... :. _________ _ ............ z._P F E L . G O G K C . - -1535756.9090 -Side 995. 9 9 5^ 34010-V2 . 00 '1 3

CCf K tC T liiN.S - l . l S T b 14 . 8 5 U ? i . .0t>77

ADJ. CQGKD. - -1535755. -3114 * - 5] &7010 ,.?46>.< 340106;. 0710

KAT?UX'.)F TH£- STATION POSITION

^.-fi.^î'.*"'? . 9 .4Sf .90 '« . . . _ . . ~*.\)b-'''-):)t.

10.7u- .7r7

STAU-JN .\U."«L-* - . 9002 P R E T O R I A , s. A H P . I C ... .HLLIPS-.U.O

. _ . . • . ; . - . . . ,.... x .Y iP P E L . CnCKO. - 505fcl25.00lj5 2716511.0017 -27757»4.0D66

27.2 .V-05 6.2dc.c £-6

ADJ. ' 'CCOSC. - 5056132.;: .110 ?7 l&517 .2<U3 -2771- &«7. 9630

V A » ! A N . C L — C ' O V A l k . ! A ! < C E * A T « I X ; ; F T r f - S T A T I C S P G S I T i C M

I l*..6'i?.a-?-» !74.o26J37 343.170663.I ?-V. 6230.1 7 6>?../-.:'1226 .104.9. I 7.0.2 72.

•v. l 702-72 171/2. 7'-i: 3'5

9004 S A N . Fc^f jArrô, S P A T ..'•.LL.IP.S.OJJ)

• '.. . • ;....'.' •:-.......• ....X _ Y. ..._ '_'_ ...7.P K E L . CO.GHD. - 5?055ft7.^'^0 -555222.0010 ?7c '5fc^7.

C O R K E C T 1 0 N S - ;.' -<- .99sy -21.3000 ^2.4355

ADJ. CGOKD. - 5105532.-^9^2 -555249.2010 3769709.-»926

V A R l A i S C E - C C V A K l A N C T I - U T H I X O F T H E S T A T I O N P O S I T I O N

13.135i.?fr -5.5 'r l513 -10 .721-563

•10^721963 ~ ~ 11.033475 17.7?6254

S T A T I U N , NUMlS = R - .. 90O5

X. ' ....._Y. _„ - Z...

- . l6.04.f jC 3 2 . 2 7 6 2

AOJV. -COORi ) . - -3 ?46 67 6.-><•'•: 2 3365331 .27?2 2

'VASrANCI--C.l /V*AÎ ANCi: • • U T r ' ' I X ' IF THL- S T A T I O N P O S I T I O N .

' 1339.7572- tS 13 1 8 .?.Hs?.910 1.90. 14.-;97o..60 190.143<;7c- 242. 7 O S « 4 0

STATION ..NUMttER. - . ... .202*1 NA.?liL,TALi INDIA, tLL IPSCUU

.Y.. _ I3 2 . 9 3 6 2 31 0962'i. 002 2

HS - -42.-9173 10.3435 3«.- ' ." •'?'•• -• ' '. •

AUJ. CpCfif) . -.. ; 101«l60.08iS 5"7ill3.33 ;3 .? 31096M .

i f - C r V A ^ I A N C r M A T l - l X O r T|.c. S T A T I O N P O S i T I C N

': -75-

• 5 T A T ION VNUK'CCH' -

X . . . . . ...Y

nPi-KU-..- .£• U I.P.S.'JI!..'.

Z . ..„_

ADJ. C G U & . -

Tl ' r STMK'H P O S I T I O N

. 7 3 < / 0-j . 24l<- >7

-0.24140717. H'V?.9.o->

S T A T I f J N i

; ." . -. VPKcL. COQKD. -

9006 ' ' -5H.I.X .'>,!.,.

. X !

_ ....... ELLl.PSO.i.D.'

...... _..__ ........ I ..... ________ ...... ..-..

ADJ.

-13.3703

3376&79.b.29'f S. 4751

VAK!ANCE-COVA«I ANCE- M STATION POSITION_3S^?61<:>3 2 3. 409 y oo

._.:^__;;L.!--.j-'--...T:3B;.Aa6i-r3;. : ....... .:._.:? 6.. A,ftS2.?.U;... .._ ...... 19. 3.0 177.7. .... .......... ..7;: ' * : . ' • • • Z.5i:!%b'9.VC!'.p; .;' -19:. 501,7?7 64.6t;2400

' " ' " "

S T / * - T i : j N 90C9 C U R A C A O . I l . t ^ S . . . . . . . . . . L L L I.P.Sf::.U.

• P P . t L . .

C O R K EC riCN.S ;-

'.'../'. :.:...' .. . • :i X . -.^ . - , - .

- ' . 2251625. ^99i Ql* .?91'2 1327160. 00?5

"; ' -20.^-707 - . - 6 5 4 4

' A D J . C C U R D . ; - , . • : . 2^ 5 ; ^ f O a . *2VtA -561 6925. 6527 1 ?27 195. 12 6-3

'AK;.i*^cc HATP:IX or TH?; STATION "" ......... " ..... "

13..2.5373A 2

U. 212202

STAT I ON NUivLieR. ..- ________ . JUP . ILLHi F L ^ . : . . ...... :... .F: l.L 1 PSQI .D

J762-90. '?v:> -5N01398.0027

CpKKtCTlONS -

ADJ. COORD . -

2^0. C056

2-» .250?-IS. 731^ - IG. IOS 'A

i . S f c d i -560 K0 ' . ' 3

-0.'A761v _ 2 . V 2 7 7 8 J 7 .756: :C1

STAT:M;N- 9011 vui./ D U L U ^ L S , A H _ _ _ _ _ _ _ _ E L L I P S O I D

X.. Y Z-4014572.9991": -335542a.0070

C C ' j R f t f c C T l C ' N S - -10.nil -2.551fc .. 41.6426

A C J . CC030. - 2280.5sT3..0«7i -491-t 57b .5514 -2255384.3644

V A R I A N C E - C C V A R i / . N C E M A T ? ! * O F T H E S T A T I O N P O S I T I O N

._._.....- .It...5315 *0 5.16777cJ -12.638693. . . . ; . - ; ; . • ; . . . . ' . . . - . ? . !&777C .; 53.070.05.5. _..._r7.C. .6 n 0.6.8 2

"' '" . ' • " . : ' -v l2 . f t .H&6V3 -70 .6&06S2 133.616794

-- ' ' , ml i 'n . ir i iiiiMiiii i ii IT • ••••..!• iiiini¥irl ir- ri 'l 'l •---'~-^' B1 'ic.i.fcrj u*« i . a^M»%hAj«*«'***-* »»- "l»""«""«1 * *'A•»'****•

. i

STATION NUMBER ..T.......... 012 -->"''• IJ1 J1 'M1 ^ ELL I'P.SC.'I 0..

•••'••.' ' . " . . ....... x. Y .:.._:. _ . . . - . . ?...'.....P J i t L . COORD. - -5.-»66b:>2-. ?S^« -24C4282.000 •: 2242171.0037

" C O R R E C T i D N S - -32 .H2- i4 i? .o4oo 5.9332

ADJ. .COORD. - -54.66085.5292 -24042&4.9602 22^2179.9569

VARIANCE-COVARIA^CE MATK'IX OF .THE STATION POSITION

10.6570') 7 . 5.381140 -2.BQt'946

.""•":'" .''•'"'• -2. 808-J46 -4.896343 30.730210. • :' ' • • .

STATION; NOShPK - .'. .. 2021 i l.-J:'PLAINS t.;_ft.'?J..Z . .._t.L.LJ.P.S .•..!'•.>.

• ' : . - . : . : : I ' - . ' . . V . X . ' Y. :...,..,. Z-.._ :

pKtL".; COuÔ. - -•\-"i"<:7.fJ! .--7;-0 -5077702.9979 3331916.0047' ' ' '

CO.RK5 'CTIu i \S - -64.2t : i l ? .7 . fc6bO 46 .4301

A D J ^ CGG'RO. - -1936S46. J n b O -5077676.329:: 3331962.

V A R I A N C E - C Q V A R I / . N C f c . X - T K I X OF ThL ST AT ! OM POS I T I ON

962 -213.696170

in !•»! ¥>•!««in n II IMI [ ••nuran 11- n AMVMtt *qui

i^ /^ M i*' f"" Tr t ^ f 1 (" L L

. . . . . . . : . . . . x ._ y : L.

CCSS.KT I!.'-S ~ ~ -Ir..-!"-^. . , ! • /* -

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Ni-7Al. , BRA ML CtL . IF -S . j IL?

C L - K K E C T i O . N S - 9.. 37OS

4DJ. COCaO. - - .318647.0.-57*1

-36? 335ft .0041 - t - .S-432U.0004

-16.6133 3.357-4

- « 6 5 3 f e 7 2 . 6 I 7 A -654316.6430

A R I A ^ C u - C n v A . - U A i v J C ? * A T * I X 01- TH: S T A T I O N P O S I T I O N .

9 <r . 0 7 <'< tJ M •'« 2 5 5. .3 o •'• 9 & •'•:?-. 7.. 6^5.70;^ 2.C.2.. 1.0.5it4 ...

STAT I u.N !\U ••'b::f< -

•PFE-L .

CO;£KafrQ K ! . V ; U : . J - V I A . ...... £L-. l . I .P$i '

. .. . Y_.-4112327.9956

I-.9 . 0032

ACJ. COORD',., r-.-'c. . . . l 69 ' ?707 .^2 i ,C . -411233d. 1S16 -4556657.5259

V A P I A N C c - C O V . A ^ f A N C r . - I . ^ T K i X O K Thi. S T A T - Q N 3.0SIT1CN

67.9^56.31 •.loi ..291201..... . : ..r 1 3.2 ..63.0l.fi.3

29«.8^0930

. ' S T A T I O N

PRht. COOKU. -

CC!'<K LCT ION'S -

Al> J.

3.0.5.1 EL.L1 P S O I . i i . "

.Y55.1016

. 15.8611 ' 23.0139 71.0936

4606573. i 02« 202-97 .13 .1205- 3903605.3*70

• v l ' A N C s "AT-r . ' IX 'JF. T H : S T A T I O N P O S I T I O N

47.7o-Stl -7'j. 7 /6i77 0.1Z2217..:.:..,;._ T 76. 776107:, ' ' ' J. 12221 7

>T;^ T I L \ .\U;V':VJ r" •» -

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CCfiKLCTlCMs" -

90 91

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4^7407~- !<?.<>!«:• I

45 f ' i l v y . : ? ^ " ' ; 203-3429 .7402 3 9 1 i 6 V O . 7601'

I'1-'. ' , f ^ I X - Y r T-.;: S T A T I U N P U S I T I C N -

-78-

-1 ?. 1 •• -:* ?" .^

S T A T I O N "X'UWBfc'K -

• • • • . . ' • • : • •PF-FL. coosir. -

"04 24 COlD LAKK t f./'N^pa. . _______ ...... £t..L.l RSUI.D

, . X •-126^337. 9937

-11.6673

-126-633. ;J.763 -i4co3-o.6655

I Af iCc-COVA*! A S C H M A T P I X D r T h t S T A T I O N P O S I T I O N

3. 7.V3.6

27 . fc01371 0.750136 1.095511.-0.7,50136 _...><?.. 163^04 I/-.35.1.202.

1.095511 I^ .B512Q^: 35.66.-. 17;:

S T A T I O N - ^ U M l ? E R - . . . 9 4 2 5 M'Jf-iC;, CAL... ... _____ ..... _ ELL.IP.SQJ.D..

• - - . ' • • : . . . . • . . . „ . . - . • • ; ; X - . . . . - Y . _ - I -....'.^tl.. C U C R r j . - -2450010.9973 -A 624^ 2 0 . 9 V 55 3635035.001*2

CORRECT TONS - ' >4 .84 /7 -10.3622 12.1509

ApJ. Ct;CRD. - . -2A 39(3 i-5.'844? -<V62-i 'V 31 .3577 2635047 .1541

V A . R i A ' N . C ' t - C U V A f t ' I A N C s M A T R I X O r T h e S T A T I O N P O S I T I O N

• "-16.tO<?406 0.007S!i.i 6.u?6793....; . ..'.-. '.0.30.7832 13.3.3^0.03 15..V.1.173.-2 -

: 6.066793 IS .218732 2g .7oc iO<;5

S T A T ! ON N U M B E R - 9-416 H ARjS JU A . NOR K1 /I Y ; • . . ' . r L L ! PSO.I •).

:• .. ,' '• .'••;.' .... ' X Y. '. i L.'.P P . E L . . CGOHO. - 3121-27^.9959 ^ ? -642- .9953 5512701.0014

CUKP. r : C T I CirtS -. M 2 . i 04 i -.16.7612 5 4 . 2 f t S 4

." • . .31212 .66 . 8'il 6 59J6?6.23bl 551P.755 .2d98 '

A i ; C h > " X T F J A J r TM:- S T A T I O N P O S I T I O N

:; '.•;.::';• . '.. '..,2 1.5 i 77 JO 9?.?i307v ......20. 24-T.6.6 ?...._

STATION .N0>:!3ti>- - ; 94^7 .J..^-:STO^ T.CL. , P4C .. .cLLlPSOlu

- ' • ; ' ! . . . ; . . - . . ' . '• A :.Y ! L. • . . . .P " c L . C C C K U . - -6007402. OOOS -1 11 IK 5-i .9=Vi:^ ! b 2 ? 7 3 u . 0040

A O J . CUOhi ) . - --r>007it)S.0506 '-111 1.7«3 .'=359 1621171 7. 35<.;0 '

A N C e ' • • • ! A T ; K i / l r li-i- Sl / .T-JO-i P O S I T I O N

i T ' ) l . j 4 3 : > 6 7 - Ic3 .&4 ' ; / / . 7 b'J.-iêoO-1-O.S.-- /..:7 4 ^ 7 . 7 2 - 4 . » - - r . . . ...-1 7) .-JOc.0-0

...-•'»•:•*•' - '•' _79_"- •.*- J-'V'l) wij.4.-, ,;\

S T A T I O N NUMcit^ - . .3*3 IV "RIGA UUV^ A- E.Ll J.PSQ! C>.

";;M:.'.:•'. . . . . . . . '".:•• A ...Y..._ ;i ,_ z.__ „..,PfcL. eOCKD.. - 3i8390i;.O3i.5 14i Itt? . <;2 1-6 S32277 1 . 9790

-3.0i>55.

ADJ. CCGivP i . ' ' - > • • • " • • ; • • ; 3!R3o^.30>:> 1'V.i l-fÂ . C65u

V A K l ANCE-CCVAK UNCL - l A T P i X j! : THE: STAT !U i \ PU51T1GN

1^3.746692 . -65.070=3:8 -9V.f-7Y7l:',

S T A T I O M NUK&ER. - 943?._/l_ . .UZCHOBCiCi . U S S P

; • .f. - ... . , ••'..'•;. ..x.. • ............ Y..-.. _____________ ............. .-.l _____ 'PRtL. CCO-rD;. - 39 07420:. 9 94 7 160S397.00?0 4763>390. 01 0-'-.

CURB ECU O.MS ,- . . ! .264t» i. i6A3 &5

AOJ. Cli;DRD.'.> ?90;7^22.:.2i>93 i6023c>ti. 366i: 'T76?9:>:'. 4610

H ••iATf-.l.X Of Tht ST AT !ON IJDS I T 1 uW

80.693:362 -50 .D1500S ' -î l,*'f -l)3;3:-30:.5I-HpO« . 94- .46327V _.1Z.0..7?AHO-<tl.444639 1*. 0773^0 3« .571770

-80-

APPENDIX 2.

-81-

; ÂRW' f iTERS C C N S T K A I K t C MPS7 - GSFC (GLOBAL)

SG.LUTIG.N FOK 3 TR^ foLAT IC\,. 1 SCfL? AMR 3 R O T A T I O N PAK WE TE RS

_'..D'X. Civ I l-'••$•£>-' >"!L _ CPtGfl PS!:'"MET"SKS """METES' yEjSf'.s" (xicr7) ' " SCCONOS S^CCNOS SECUN

.:rMl-..^6...._.:6._47 ,_;_.,J.S_._eZ ^.-.55 „..._.0..ft;?.. ,0.2?. .-0.40

-P;-J.^JP>Ci..P...ll4p-C:5 Tq._ie2D-Ot! -C.-friO-07 -0.1 760--C6,

iLÛ;P'£C2 Ji0.6_5?j3-06 _'0.5Jvlf--p7 7p.l26D-06 '-p ."J ":" !>06

j-JJ.J?iEp-p6 > p. 1140-05 -Oi 69 '?.Dr'C.6 0.317C-I2 —0.1120-3? -0. 597;)-l 4 0. «J It!'.'-14

.'.._0. 29i 0-06;.-0,.:lS 30-C8 0^5?i(feCJ..-p .1.120-1; C ..851 C-1 3 0. C, 190-14 -0.. 1 I >C-1 ?-

jOvI'-'TlBP I-iO:-^^ .P.'AO/*':'-.i2 .. 0. 1 7 3..G-1 3

-0.173D-07' -0.1760-06 -0.39'5D-C6. 0.2 16C-14 -0.3 3 3D- 1? C.1730-12 0.1 .VvP-12

COcff IC:;ENTS CF CCRR'£

:,;H>^ q.345n<-oo p. i640+oo -0.1770-01

J3 •! QQjl. J: PI _-v> «-J j.

0.1COC + C1 _ -Gi6f?0-Cl . -0.3^c=n-c i 0.11 '0-01

-p..-o?c-ci -o.;i'. "n*-po . - o . a c - o i p. 65*0-01

:-oi ;-JD ;;:;'•/?£:« oo -j.2j-.:«-oc o.iiic-yi -c.n:i:voo

; ?;v v ; ;,;:;/ ROTAJ,IG<N| F ;4RA;^Tf :KS C O N S T R A I N E D MPS7 -SAO (GLOBAL)

.; :SÎ^T,10K..'FOH, l>;TKr\NS:LATICNI, 1 SCALE AND 3 P O T A T I O N P.AMMF Ti= &S-

.' .' OL C>L:G4 PSI" ......._.Mt'fisS M S S S WETS*S io"* S t C U N P S S E C O N D S S E C O N D S

. • . . - . , - • . . , • • -.'Il-i.13 ".' 0..30 0.53 -0.1A

E - C G V A R I A N C E M A T R I X

.1210-05 o . i ?o n- o?

-O.lI p>01 i '0 .:?'?5t?jKClVôa|o.QB-» C.l- O r_8 ? 5_C- 0 c 0 .1 5 ? !'- C 7 - C . 2 5 Pi^ 0 7 - 0 . 9 8 7 C- 07

0. 787{^fJOO:;'-:<J;ÔpiJtQ;l ___ 0> J^y^C I _ - p_._6£2.C^J%: 6 ____ .0..1? C !> C 7_- p I .A 9 C p-p 7 r 0 . 1 2 5 p - 06

O^L >>^15P- C6 > 0..,<5L? 2 C- C6__ 0_. 2J 5 D-J. 2 - 0 . 3 fr p C- 1 4 - 0 . 2 ! f; D- 1 4 C . ;< 5 1 D- 1 5

Z:feA520^7.;._pî^CID^ C.42-!;-14 - :C.2o7n-14

Of) ^-0.2590-C7: -C. ^CD-07 - C . P l ^ D - l A 0.^2^,0-14 0. 5070-13 0 . ^ 7 ? r - i A

C. 12vOn^07.-0.9R70-07.'. rd; l.?-5C-Ct C.851C-15 -0.2£71>

CF

_ . . . . . . . . . _ _ 0 ._223-p + O p _ 0 . ? 030+00 0 .;?! i D-01

-0.1310-»-00\0.!OOLÔ!-0.2140 + 00 0.524CK10 0.247C-01 -0.36"D-01 -0.1'-iOf 00

VlilCD + CI - C . t 6 ? D + C p 0.2240-01 -0.1 O^L +OO -0 .1 : i 7C<

O . l O O C t O t -0.3S4C-01 -0.1v3D-01 0 . 7 b l C - C ?

___ -Cl_ -p.P-l '-C-CJ _ 0 .1COC + C1 _ C. '»60P-Ol - 0 . 6 7 v r - C l '

-01 -0. r.J4P+CO -C.193C-01 C.9ÛC-pl O . l C O D + O l 0 . 2 0 1 H + 0 0

C . 7 r i l C - C r -C.67=r-C1 . C . 2 C

_r83-.

R O T A T I O N PAR/V!rJcT£:RS C C N S T R A 1 N E - D MPS7 - GSFC (EUROPEAN)

SOLUTIJGN FQR 3 T«Ur*S;lAT,ION, 1 SC' ILE AND 3 R O T A T I O N ' P A R A M E T E R S

PY ' • ' ' ' ? • D7 - D1 CI" rGA PS I F P S I L C NT-CSS''"'-METERS. (x'l<r7)" S E C O N D S ' "SECbub's" S E C O N D S

-JS , 77 -4 9 . 50 I ; 4.53 ____ -73..30_

x

. ^ ."-Pi.rA.r. JfPrPfe. . 0«S570-p5_ ,-p. 13.70-05

__Tjp_. _5«OC- :!-._ p..:M?P.r PJL.. 0. 2: eOp-05 -0 .642.D- 05

JL-15J/J±P_i_JL« li20±£i. o.g».ic»Pj;.;-ov4goc-i)4^-_p.ii£-pr-p5_j-c.icpp-p4 p.j^so-os

C.9?6!;-il 0..134C-12 0. 1 710-12 -0.1 59C-13

-p. Afl9D-06 Q.^X)2|?-05 -p. 1 SOD-:p!i» J^.p. 13'rD-i2 p.l.lJ'D-U C.17QD-12: -0.2350-]^

;0. 8570-05 : Cv28 : OD-05 - 0.108 C-IJtj 'j 0 .1 71 C-12 0.17CH-12 0.2KD-11 -C.460D-1?

-OvlR70-05: -0.6:20-05 0. 295D^C5>-0.159C-13 -0.23f:r-12 -C. 4800-12' 0.119D-11

OF CORRELATION

. . , . . _ . . . _ 0 . 3750^00, -0.1 I I ' D-t-00

0.2:79P»00 ;C.lqg>01 0.73:20-1: -030000^ 0. fc6?.*0p __ OrZ

jO. 61 10 + Op tp!.;7;3_20-p;l;. 0^ WCp*,C^_-p.884f + 0u -0 .&87C-OJ. -0.-V6R:)

:0,. &.?- C + pp. -Q.;2;?dD+pp -0 . - .'t[J+ CO.. 0. ! COC+ Cl 0.4Cf C-pl .__ 0. 37tM)-01 -0 . 4 77 P-0?

- 0 ._f_9 7 D- cX_ _P_! [ lf :P_L __ 2.,'j P U .^ *PJ_...P..r.r P6 P_*.9° ~ ° • ! ? ° P * ° °'\'. '-. '•'(> • \ '

C. ICCDtCl -0.297C+CO

. o.rc7:'«-oo o.iooc-io:.-84-

" ROT AT 1 ON P A S A M t T Ef- S "c CNST R M N JTiT " ~MP37 - SAO (GLOBAL)

•$:pUU;T 1CN FOS:'3 jRANSLATIONt 1 SC/iLc AND ?. R C T A T ! G N P A R A M E T E R S

.CL C ^ r G A PS!KS' ' MfTf.RS••'•••OYETFRS («10"7) SECONDS S t C G N O S SECC' ;Ob '

'/Mf^.5^ 23 26.6/4 ••'.•'^«.3S. 76.66 1.2.0 -0.30 -1.04

- - C C V A R - I A f - J C E " A T K I X

_T.c..?13.r_Qr.o_?:__Pi.i.J!JP_r9.1 _P• -1

??c-o* -o.i

_ v 5 ; t f 8 C r ^ .!°-I??D-^

l.31pTj?A_^

ll2i^CA_igO<- 2 ^C4 0_.3_?OC-_13 O..ll_0l>n ..Pr?4.«D-l 1 -0 .1^ ID-.! 1

!57C;-OH ;:iO.. 62-CL-C5 0

.•GOEFF'iCIfjNTS OF CGRRELATION

_^. 1 pOD'+;01;_5:Q;« 35 f.0_+'Cp_'_£;2,. 6^ 70+pp -0 .911C + 00 0 .1 *• 1 D+00 0.2710 + 00 - 0. 2 H '; D + 0 C

_0...35i.EjyOQ r-O.iOOe+.Ql, ..±-Q.IP-IL + CO -O.I6i :Cj-pO _C. 7 8 Z C * 0 0 C . 5 R C : ) » 0 0 __-0_ . a _3.- ?t 00

Ât.l.P.'-' ^SP.' C.J ; pCn+.Cl_ -0 . 9 9 r C + Op -0 .230C + 00 -O.-'.l OCM 00 0.2 ?.->0«- 'OC

00 ..C.lCCt?*Cl_ : ,_q..?_79C-Cl C

J?A??."rj:01ijJ?-vc_0J:*?! _c.

0.579C-02 0.4«;CC+pJ 0.1000*01 -i

"NOTATION ' P A R ' A « C ' T E K S " ' C C N S T P A I N E C MPS? - ED 'so

SOLUTION! FOR 2 T K A N S L A T ION, 1 S C 4 L E AND ?. R O T A T I O N

PX ____ OY _ p'Z _ DL C V c G A PS I 5PSILGNJff'fcS METfAS' "VcT- j ^S (xl(T7) SECONDS SECONDS SECONDS

-5

R ^ g , T

. 0. 76 6 D+ 0 2....I.P...1; 1,6.0.+ 0 > _. p. 1 fl 3 D * 02- - 0 ._? 80 C - 0 5 .- 0. 244 C- 0 5.. 0. 5 5 4 D - 0 5 - 0 .1" 5 0- 0 5

J»..ilfcDt.P2.1lp.3J-dp.+ p2 . p..l5:in*C;2 -0 .379C-05_... _0 .2390-05 -0 . 3A50-06 -p. 1 7 5 0 - C f >

1 C. 9 8 G P- 0>... -0 . .V.'9:0.-.P5 - p . 9.6 l.pr C5 / . 0.23 i C-11 -.0 .3040-13 -0.2'? 51)- 13 0. 2 19D- 13

:P.«.244.Pr.P.5 ... 0 .2.2.9.0-C.5 .....0... 111.0-C5. -0.3.040--1 3 . .0...6<rAD-12 -0.41 ^D-.J. 2 0.9•'• 1 0-11-

35 -0.2C5H-13 -O.^l.cC-12 0.1190-11 -0. 3000-12

:p;.K2prp!>..-0...1,7=p-05 Q.;i74Cr;C5.,..0..219C-13 0.94I'D-13 ;-C. ? COO-12 0 .50ID-12

COEFFICIENTS OF COKR ELATION.

._C.1.00pfpL ....p. 2? en + Op 0.2450+00j:p.7^^37C+Op -0.32?G+00 p_.5SiD

_0 .2 2_3 D-tQO 0. ..1.0PJT+^01 _. .p_. 3J.i D^C 0 7_0_._4 § P_ C + C C _ 0_._49 3 0_+_00 __- C. f> 4_5 D-01 - 0.4 ? S C 4- 0 0

_p .2 f .5D*OC 0.3120+00 C. iOCU*-Ci -0 .75oC + 00 0.26 = C+00 -O.S371UOO 0 . 2 F * D + 0 u

-0.737P + OC -C^Z'-'iP + OO -0.75tC*00 C.!GO[>G1 -C.24CC-C1 -0.1780-0! 0 . 2 C ^ O - C !• • ' ' . ' . " . ' . • • ; \ I . '

:P_.3.3.ôq.c • o.'.932+qp p.^jer.ôc^-p.zôp-q' q.i'ccctoi -o.^S'ic^co o.i6.on«-oo

0.5R10 + 00 -C.5450-U1 -O.V37D+CP -0.17'JC-Ol -0 .45 c -CtOO 0..1COL!fpl -0.3'l = C*00

0. ?'': 9 L : * O C ,0..?C'.r-Oi 0.1eCl>00 -C. 3(? t ;n<-CC C . l C O f : » 0 1

MPS7 - NAD '27

.:.-SCl'UTIO?J FOR 2 TR 'YNSLAT!C f \ t 1 S C 4 L E AKC 3 C C T A T I O N P A R i M E T E r

DX ' . - . • ' D V ' • ' ^ • ' • - • • ' . 0 7 . ni CN'FG/- PS: FPSILO\DETERS''~>£T"EkS:r>ETEKS (xlO"7) SFCCN'CS SE-COKOS ' SECL^DS

..-0.

C.j_96_0t)^;0;llj;.lp-i 1 MH'tC l_,_ _C. 500D101 -0 .3 570-C6_ 0. 11 OH-05 0. 601D-06 -0.7 71 0-Oi

-9r..'^.fiP.tP.'.....0.f.?'?3C-C5_ 0.*3i C-0.6 _ 0. !610-06-0.1020-0^

_c._is 1 .c-06 -o . i5f : -D-p-; .

.0:.322D-0?:;;-q.2;3;2n-05_ 0.6370-12. -C.11 1 C-l ? -0. 7530-3 5 0.1010-1 5

.-.p..n,cprP.r5- P..>?..i'D-c,6;.;.p."|.3eprP'-: -o.iiic-i? p_.i92!>i :2 o . -53C; - i? -o.i?u.c-};:

,P^y.ô±06__oî61p-c6:._.a.ifiir-ot...-o ..753•:-15.._ 0 .25?n-1? o. \ ?in-12 -c.A42n-1:?• . " . ' ' , , - ' - ' ' ' ' ' i , . . • " • . " • " - '

-0.7'7iD-d6.:-0.102D-C!;!-p. 1550-C5 0.1010-13 -C.12CC-12 -0.^30-13 0-.30?:0-ir

C O E - F F I C I H N T S C F C C r < R E L A T I C N

.. 0.557LJ + 00 -0 . -»5?

, _ . _ . . . r P . f _ 4 . 1 ^ ^ ^ ^ Q.v'r.^-itQP- _.°-<?Q':>u~0.1 -o.3?c;

p.'-39:'pE.,*'p:0 -0.3?6D*-ob^ OiiOCU + 01 -O.?0-l>00 0.35:c*-00 0. i3.?rHOO -0. '>33

-0. V^4t>pp.; C.'37'»OfCP;.-p..7p'trHOO O . l O O n + ' O i -0.?IGO01 -0.271i>02 0.2?

9 • .nj.^r^'O.b'.- 0. 212l>o6.;._ 0_.-35_?p * P.O. -0.3 1« C- 0 • _ _ 0 .!' C C i: * C1 _C. ?. 3 10 f 0 0 - C. 5 0 0 0+0 0

0.53?pVpp C.$°5p-Ci; ' ; 0. l '32DtCC -0.271 T-C? p . ? 3 U f O O 0.! QOr + Ol -0 ,:? 3! C t JO

t .2~ir-o: -o.5ccr«-oo -c."?.'.iuoc c . i c o c < c :_87_ . ' •

' R O GSFC (N.A.)

TICN::F'3P. 3 TRANSLAT^N,: i scîs AND ? POTATION

ex- •:..•:••'•• OY . •..• ozS _ OL CÊGA PSI EPSILCN' ~ M E f t^S' INTERS (xl(T7) " S L C C N O S S E C O N D S SECONDS

5v29 -?5.20 39.3? -31.77 0.51 0.27 -0.12

V A F J ANC E-: - C 0V AK I A N C E M A T R I X

0. R90C-06 -0.829 R-G6

q. 1720-06 -0.2170-05

t _ O.^CcP-C6 -0.325C-0?)

^^^^C>j)^l ? 3 C--1 1_ -C . 3 7 9 C- 1 '* - 0 . 56 50- 14 0 . 2 -V A D- ! 5

j_t45l> "•;_. 0. 2,3 1 f> 12 0 . 4 1 2D- 1 3 -C. 1 2-V D- 1?

o ! ^ ^ P -- 2 17:0-05' -0.22:50-03 0.24^.0-15 -0.12AC-12 -O.S78D-13 0.636T-12

S ' ; ' V ' COEFr iCIE .NTS C F C C P R E L A T I C N

l:M^^ °*776D*°P 0.5600+00 -0 .293D+JO

C.125OOO C.5S3D-C1 -O.

0.??5C+00 C.117C + 00 -0 .6B7C<-00

, 1 -0 . 1 9CC-0? -0.1130-01 0 . 2 70C- C ?i'tf' :,Af;pr '•'!'"' ';';:.y:'" ".7"'"j''-'''-,-* .!::.;& "'" " ''r ' "" '

«? J c..r.9..?_... /' • PP.1:!.?.1. ._.. C . _! ? 2 q 1 0 C - 0 . 3 ? 1 P «• CO

' ~: • - " . . .'.' ">~--- - ' • •. -~-i. . x~ • -;.•-„•1 "" "••"."•OO"*

C C N ' S T K AI K R C ' " MPS7 - SAO (N.A.)

':'. SCL ' JTIO-N FCH,: J . V J F A K J S L ' i T I O N , 1 S C 2 L E AND 3 K O T A T I C f s

V$;v:.:pX.,.__: '.-.pY. V.Ll., f).Z. . . !.'L OfcG.i . . PS I V P S 1 L C M-V I ' ME-TSKS M = T t r r S - . ' . ("ETc^'S idO"7 S F . C u N O S S f C C N D S S t C C N O S

Q.0.9 O..n.

06_. 0..: 360-05 0 . 9 Q < D - O f e -0..

*p.-i.O. 3AfiOtQa._r f3 ; ,OJ .U + QV.....0.5C2u.--P§....Q..f.06C-Q6. C..?.(.OD-06 .-0 .1 ^9D-Of i

.^ 0..?.^.:5?-0f: ..-O..?.f.7n-0rr

:3.0.|p^04:l.\Q'-..5.0.':.!3.-Q.!5!.rP...J;i7.C-.0.5. „. C,9 74C-12 ...r P., 5?-:• 0-15 ...,-C .1350-1^...-0..7 nO.D- I V

-0.0,.39.C-11... 0.51.6Q-U. ... C..206D-1. < ..-.0..7.&30- 15

8C-06.,-0., i.45?D-.65;_^C)..i!2fi7.D-0.l:i. -0....7 :JOn- 1 A_-0 . IZ'iC-l 2 ...-C. 7i30-i^ 0.53^0-1?

.-.C . 1.0LO.!).±.C;l=.0..:26.>.i:- * OC)..._0 . 9.f!..7.C.t.O.C_ .0 . ! 7 A f>QO ... 0 ..a 74 Dr-0 1 . -0 .H> 20+ -TO

Cl .-P. t^ - -C+JO . 0.?'?2C*00 . 0 .1^6 'MOO -0 . - b ^ S i

ci -c.?.?î)-C2 -c .? ion-02 -o. ic°r-oi' ^ ' •

. . . o o . . - P . . o.;.oor+o.i . . . o.?^-.n*po -p.?ap*-oo

P. c7;fO-oi£..0..|i^C<*JJ -0 .? luC-C2 0.^3^0*00. C . 1 C C O + 0! - C . 2 ? A

_89.

REFERENCES

Blaha, Georges. (1971). " Inner Adjustment Constraints with Emphasis onRange Observations," Reports of the Department of Geodetic ScienceNumber-148, The Ohio-State'University, Columbus.

Brooks, R.L. and C.D. Leitao. (1969). "C-Barid Radar Network Inter-site Distances, A Status Report, "presented at the National Fall Meetingof the American Geophysical Union, San Francisco, California.

Gaposchkin, E.M. and K., Lambeck. (1970). "The 1969 Smithsonian StandardEarth (II)." SAO Special Report 315, Smithsonian Astrophysical Observa-tory, Cambridge, Massachusetts.

Girnius, A. andW.L. Joughin. (1968). "Optical Simultaneous Observations,"SAO Special Report 266. Smithsonian Astrophysical Observatory,Cambridge, Massachusetts. . :

Marsh, J.G., B.C. Douglas and S.M. Klosko, (1971). "A Unified Sot ofTracking; Station Coordinates Derived from Geodetic Satellite TrackingData, " Report Number X-553-71-320, Goddard Space Flight Center,Greenbelt, Maryland, July. ' . • " . .

Mueller, Ivan I., James P. ReiHy,and Charles R.Schvvarz. (19G9). "TheNorth American Datum in View of GEOS I Observations," Reports ofthe. Department of Geodetic Science Number 125, The Ohio State Uni-versity, Columbus. ;

NASA: Directory of Observation Station Locations, (1971). Goddard Space FlightCenter, Greenbelt, Maryland. Second Edition, November.

Simmons, L.G. (1950). " How Accurate is First-Order Triangulation ?"The Journal, Coast and Geodetic Survey, Number 3, pp. 53-56, April.

Vincent, S:, W.E. Strange and J.G. Marsh. (1971). "A Detailed GravimetricGeoid From Noi'th America to Europe, " presented at the National FallMeeting of the American Geophysical Union, San Francisco, California.

-90-

2.5 Determination of Transformation Parameters with Constraints

The relationship between any two geodetic reference systems would generally

consist of seven parameters - three translations (dX, dY, dZ) between the two

origins, three rotations (co, 0, c) of the Euler's angle type between the two sets

of axes and the scale factor (AS), if any.

A general transformation for the seven parameters is given below FBadekas,

1969]: .

fjV

^Tl_

A

~"x"Y

Z

-

j

Ax"

Ay

_Az_

-1 CO -0*

-CO 1 e

_I|) -C 1_

u"V

w-AS

u"V

w- 0 (1)

where w, 0 and € correspond to rotations about Z, Y and X axes respectively - the

positive direction of rotations taken in counterclockwise mode from UVW-system to

XYZ-system. The above equation can then be further modified as below:

1 0 0 - 1 0 0

0 1 0 0 - 1 0

0 0 1 0 0 - 1

vv

VM

- 1 0 0 -U -V W 0

0-1 0 -V U 0 -W

0 0 -1 -W 0 -U V

AX"AY

AZ

AS

CO

f

+

X-U

Y-V

-Z-w.

= 0 (2)

However, in the above transformation, if the geodetic reference systems are

properly defined for Laplace condition ( parallelism of minor axis of the

reference ellipsoid and earth's rotation axis) the three rotations arising out due to

the improper orientation of the system are generally never more than a few

seconds of arc while translations may amount up to 200 to 300 meters. Thus due

to the presence of high correlation between the rotations and translations, satis-

-91-

factory estimates for rotations are difficult in a combined general trans-

formation. .

An alternative method separates the determination of the rotations inde-

pendent of the translations and the scale factor [B.ursa, 1966]. The mathema-

tical model is as follows:

$- Tjl2)+ cu- ecos T^tan 6^+ 0 sin T^tan 6$ = 0

(3)

where Tik and 6ik are defined as the geodetic hour angle and declination of the

(i-k)th direction of the observed point at kth station and the observer at ith station.

The indexes (1) and (2) denote the two systems with transformation proceeding from

system #1 to system #2. .-... ;

If we take A^, Blk, Ctt as the direction cosines of the (i-k)th direction,

Rlk as the length, then for the first system we get

v k - V i ' • • • • V/AV

wv - w, .•'-.'. '&""

and

= - arc tan

arc tan

^•ik

In the abovei relations (3,4^ and 5) the elements of translation do not enter

the picture and a similar set of relations as per (4) and (5) above can be established

for the second system.

-92-

The equation (3) then can be written as below:

tt£0)

- 1 0 1 0

0-1 0 1Ik

(1) (1) (I)1 sin T^ tan 6lk -cos Tlk tan 5

0 cos sin

to

-Mk ~

6(0_

rp(2)"Iik

*>(2) = •0 (6)

Using the variance-covariances matrices SX andSU in respect of ith and

kth points for the XYZ and UVW systems, the variance-covariance matrices

Lf6 were computed for the two systems through propagation of errors as per the

following relation [Uotila, 1967]:

= G G (9)

where

and

G =

-dTftan

.-a Tikavk

-aTtt.dWk

AU,AU

*

-93-

_^ _ _ tic

dWt ~ BWk ~ '. .Ruf

• f a ) . ' - ' ' " ' ; ' • ' ' ' • - • ' ,Obtaining similarly S^ the combined variance-covariance matrix to be

used with the equation (6) would be given by

The above transformation model was used to study the relationship between

various datums with the recent free adjustment of a Geometric Global Satellite

Network, Solution MPS7 ^Mueller, Whiting, 1972] and Section 2. 4). Firstly, the

three rotations were obtained independently of the translations with their variance-

covariance matrices. Secondly, using the same set of cpmnipn points a general

transformation for seven parameters (including the three translations and the

scale factor) was obtained utilizing the rotations in a constrained solution. This

transformation was carried out in three broad groups based on the area-wise

study i.e., global, European and North America, with the following datums:

(i) Goddard Space Flight Center Reference System (GSFC) rMarsh, Douglas

andKlosko, 1971].

(ii) Smithsonian Astrophysical Observatory's Global Reference System

(SAO) TGaposchkin and Lambeck, 1970],

(iii) European Datum 1950 (ED50).

(iv) North American Datum 1927 (NAD).

Table 1 gives the results for three rotations as obtained independently of trans-

lations, while Table 2 gives the constrained solution for seven parameters. Table 3

shows the results of a non-constrained general transformation for a comparative study

-94-

The comparison shows that the constrained solutions show an overall

improvement in all the transformations. The standard deviations in all the cases

are smaller and the variances of unit weight show a better fit in the constrained

solution as against the non-constrained transformation.

-95-

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-98-

IREFERENCES

Badekas, John. (1969). "Investigations Related to the Establishment of aWorld Geodetic System. " Reports of the Department of Geodetic Science,No. 124, The Ohio State University, Columbus.

Bursa, M. (1966). "Fundamentals of the Theory of Geometric SatelliteGeodesy, Travaux De L'Institut Geophysique De L'Academic TeheeoslovaqueDes Sciences," No. 241.

Gaposchkin, E.M. and K. Lambeck. (1970). "The 1969 Smithsonian StandardEarth (H). " SAO Special Report 315, Smithsonian Astrophysical Obser-vatory, Cambridge, Massachusetts.

Marsh, J.G., B.C. Douglas and S.M. Klosko. (1971). "A Unified Set ofTracking Stations Coordinates Derived from Geodetic Satellite TrackingData. " Report No. X-553-71-320. Goddard Space Flight Center, Green-belt, Maryland.

Mueller, Ivan I., James P. Reilly and Charles R. Schwarz. (1969). "TheNorth American Datum in view of GEOS I Observations. " Reports of theDepartment of Geodetic Science, No. 125, The Ohio State University,Columbus.

Mueller, Ivan I. and Marvin C. Whiting. (1972). "Free Adjustment of aGeometric Global Satellite Network (Solution MPS7). " Paper presentedat the International Symposium Satellite and Terrestrial Triangulation,Graz, Austria.

Uotila, Urho A. (1967). "Introduction to Adjustment Computations with Matrices. "Department of Geodetic Science, The Ohio State University, Columbus.

-99-

2. 6 The Impact of Computers on Surveying and Mapping

Keynote Address Presented by Ivan I. Mueller at the Annual Meeting of the PermanentCommittee.International Federation of Surveyors, Tel Aviv, May 29-June 3, 1972

Most keynote speakers usually start with the statement that they are honored

and privileged for the opportunity to present their views. I will not be an

exception to this custom because I truly feel honored and privileged being

selected by the organizing committee to deliver one of the keynote addresses

at this ireeting. Over the years, the International Federation of Surveyors has

coflsl&tfcntly sponsored a full range of valuable meetings dedicated to the exam-

ination of Important problems facing this very diversified profession. Among

the most Innovative of the convocations called have been those associated with

the meetings of the permanent committee.

What then is the purpose of a keynote address ? It is generally understood to

have a double aim. The first is to arouse unity and enthusiasm in the audience.

But I need not concern myself with that, because I am sure that everyone here

is equally excited at the potential of computer usage in surveying and mapping

and at the new vistas visible on the horizon of this ancient profession. The

other purpose of a keynote address is to present the issues inherent in the theme

of the meeting. I shall try to present these issues, first as they are related

to the computers, then how these machines affected traditional areas within our

profession, what new exciting areas came into existence because the machines

happened to be around, and finally what are those new vistas just around the

horizon which are visible to this observer.

The Computer

When the computer was invented in the fifties, there was a great diversity of

opinion on its usefulness, from skeptics who proclaimed it a toy to the more

adventuresome prophets who predicted phenomenal growth and widespread appli-

cation. Reflecting now on some of those early prophecies, it is obvious that

they were vague about specific applications, real benefits, actual costs and the

technological advances required to make the computer practical. And yet, the

-101-

usefulness has outstripped the dreams of the most adventuresome prophets.

Undoubtedly, most people's ideas (not ours of course) about computers are

associated with erroneous electricity or bank accounts, TV science fiction,

moon shots or tax collection. Contrary to these beliefs, computers have a

great deal more to offer. They work as calculators too, as repositories of

information, as controllers, as aids to decision making in such contexts as

banking systems, reservation systems, air and road traffic control. The use of

computers as simulators is an application which is growing in importance:

Examples include training astronauts, observing the effects of car crashes,

playing war games instead of real ones, and business strategies. Computers

have also penetrated the field of art to the dismay of some of us: Attempts have

been made, with varying success, to use the computers as language translators,

as writers of poetry and prose, as producers of visual art, to create ballet

routines, and both write and synthesize music. There is plenty of scope here

for those of us who enjoy a debate guaranteed to have no conclusive outcome.

On the serious side, because of its varied applications, the computer demands

from society, including the surveyors, decisions as important as any it has made,

certainly as important as those forced on our predecessors by the industrial

revolution. It is sad that the level of discussion, even in some "professional"

circles, has so far been so puerile, to understanding of the issues so limited

and so inadequate.

With this in mind, allow me, in a few minutes, to review the progress over the

past two decades to see how the use of computers has developed and then to

examine current trends.

The first decade of computer development, in the 1950's, saw the use of

machinery largely as an aid to scientific research; many research projects in

physics, chemistry and engineering demand elaborate calculations - the design

of an aircraft wing or engine, for instance, or the design of a nuclear reactor.

As a matter of fact, there is one project - atomic bomb development - which has

always demanded more and more calculations in order to progress with as little

-102-

testing as possible. It is easier and also rather more socially acceptable to

simulate an explosion on a computer, however large and expensive, than to

explode a live bomb. This one use played an important part in the development

of very large and very fast computers during that first decade. It was not until

after 1960 that such machines found their way into other than atomic research

laboratories. The second decade of computer development, in the 1960's,

saw the development of the computer as an electronic office, a data handler and

processor. The computers initially used in this era were designed not as

calculating engines for scientific use but to make the processing of card files

cheaper and easier. The jobs being done were those which are carried out

within the administrative and accounting departments of a business. Such jobs

placed more emphasis on the storage capacity available in the machine than on

its calculating speed - in contrast to the research applications in the first decade.

As the users became more confident in and more used to computers, new

applications appeared using both the calculating capacity of the machinery and

its data handling capabilities.

In looking back, it becomes relatively easy to separate the demarcation points

between post generations of computers. Historically, these have occurred following

advances in hardware technology: vacuum tubes for the first generation around

1950/51, transistors for the second (between 1958 - 60), and integrated transistor

circuits for the third between 1963 and 1965. Lately, however, the introduction

of many other new features - in peripherals, communications, remote terminals,

operating systems, and the like - have made the distinction between the generations

increasingly fuzzy. We have now passed the eve of the fourth generation computers

which is best characterized by the ability to provide information which is constantly

on the tap. In other words, while the roles of the first three generations were

computations, data and information processing, the current generation also pro-

vides on-line information. The rapid evolution through the fourth generation -

spurred on primarily by the immense proliferation of minicomputers - is under-

way and one can now begin to imagine the hardware and software components

-103-

which will characterize the fifth generation projected to be born between 1975

and 1978.

I will not elaborate on the technical aspects of these future babies of the

computer industry. Let me just say that these new machines are being viewed

as man's "intelligent" assistants.. Many of them will be portable, hand carried

or in the car and in the home, that can be plugged into telephone and electric

outlets or even carry their own power supply. This will tie the computer

completely to the telecommunications systems, allowing the computer to

'remote' its power to where it is needed. Indeed, the telephone will become

probably the most widely used terminal of the 1970's - incorporating voice

output and touch tone input. Such an availability of computer power can have

nothing less than an immense impact on society, greater perhaps even than

the impact television has had.

New major innovations are likely to occur also in the software area. For

instance.the cost of programming, which has been held almost constant (per

line of code) throughput the past three generations, should be reduced by more

than a factor of ten in fourth generation systems. This should come as a direct

result of interactive programming using time shared facilities. A further factor

of ten reduction in costs can be expected with the fifth generation. With the

remote terminal and the packaged programs (to which I will return a little later)

will come a truly conversational use of the computers. Many such systems are

now being designed and use languages suitable even for the non-professional. By

the end of the fifth generation - by the early 1980's - literally anyone will be able

to use a computer and many programs should be available for helping us perform

our daily tasks. Computers and terminals could then become as common as

telephone and television today.

In passing through the second and third generations of computers there was

approximately a four fold increase in the number of computers in use per generation.

Throughout the 1960's there was a ten fold increase. Assuming that these trends

-104-

continue, then by 1975 - at the onset of the fifth generation - there will be more

than 200, 000 computers in use around the world. By 1980 there could be over

500,000. But if we count the remote terminals, then these numbers grow by a

further factor of ten. Moreover, if we include all the telephones used for

remote access to computers, then practically everyone with a telephone will

have access to a computer by 1980.

What are the uses of all these computers? In addition to applications in our

own profession there are of course countless applications. Let me select for

illustration probably the most sophisticated one, the applications in management

science:

The major object of modern computer applications in this field is the setting

up of a computerized data base to enable better analysis to be made of alternative

uses of resources. At present, many important decisions are taken on inadequate

data or on information which is out of date. In a stable and well-established

business this may be of little consequence, but for firms in rapidly changing

markets or involved in rapid growth or technological change, timeliness of data

can be vital. Rapid and convenient access to the data base is therefore required,

and it is necessary that the whole system be designed so it can react to the users

urgent demands. Modern computer techniques enable the user to converse with

the computer over a terminal. The user can ask questipns of the computer,

which can then, by questioning the user, ellicit further information to retrieve

the answers required from its memory. In this way, the data base can be

searched, and the result of a requested analysis can be made instantaneously

available.

The nature and complexity of the analysis required may differ considerably,

so that it would be inefficient to have the most powerful processor tied up wholly

with one user. The equipment needed to implement such an enquiry system is thus,

not one computer, but a collection of units, some of which are devoted mainly to

manipulating data, some to the calculations needed for analysis of the data, some

-105-

to up-dating the files as new data arrives, and some to conversing with the

users. As the users and the data sources may be physically distributed over

a wide geographic area, the whole complex must be connected by communications

channels, and thus, becomes a computer-network. At present such networks

are being built for several applications. Several already exist - for instance,

to carry out airline and hotel reservations on a world-wide basis. Others are

being installed to link hospitals into the data base containing information on

patients, availability of beds, etc. There is no intrinsic reason why, in due

course, single overall systems should not serve the needs of all the users in

any technical or geographical group desired. Several computer bureau operators

with machines in different countries are planning to link their machinery so

they can work on whichever machine is most readily available or most economic

at the time. Such arrangements could well form the basis for an international

computer-network..

The establishment of such a network naturally will contain some inherent

dangers for the individual, primarily related to his status within the community,

who can be affected without his knowledge. In order to bring about beneficial

applications, the computer must have data - not only about money and materials

and the rest of the physical environment in which we live, but also about people

and their attitudes and circumstances. Until recently the clerical effort needed

to cross-reference all these files has fortunately been prohibitive. But once ;

these data find their way into a computer system, cross-connections could be ,

made in a matter of second. Thus, on applying for an insurance benefit you

might find the amount of your last unpaid parking fine deducted automatically,

or perhaps find yourself arrested to answer a charge of speeding. Would we

be happy under an efficient tyranny - one in which every movement and action

of the citizen was recorded, analyzed, cross-checked instantaneously and no

incident, no matter how trivial, ever forgotten ? Yet, such is the mechanism we

now have the capacity to create. It is not a far stretch of the imagination from

here to see that Orwell's 1984 predictions on surveillance could also be fulfilled

-1-06-

and on schedule.

It is not, of course, the computer itself which creates social problems,

but the human beings into whose hands it is placed. The computer is a tool

and it can be used or abused by man at his discretion. Compared with such

tools as nuclear energy, the computer does seem to possess more potential for

good than harm.

Whether this picture appeals to you or frightens you, I have no way of knowing.

A recently published book entitled Future Shock, concerned itself with the plight

of modern man attempting to cope with "an environment so ephemeral, unfamiliar

and complex as to threaten millions with adaptive breakdown. " The book is an

indication of the apprehension with which some people view the future and it is .

worthwhile for those of us who are contributing agents of technological evolution

to do some hard thinking about where we are going - to alleviate the fears of

some and help all prepare for the coming advance in technologies.

Let us now take a look at how the availability of the generations of computers

affected surveying and mapping. Obviously, this review will have to be a selective

and a subjective one. I will be able to mention only the most spectacular examples

and only those which are likely to be in the interest of this convocation, and of

course, only those which are in my area of competence.

The Shape of the Earth and its Gravity Field

I should make it clear at the outset, that I am not concerned with local ir-

regularities in the earth's surface, the mountains and the valleys. I shall be

discussing the mean sea level surface of the earth, carried through under the

land, the surface usually called the geoid. This geoid, being a surface on which

the potential of the earth's gravity field is constant, will, at the same time serve

as a pictorial representation of the variations in the gravity field of the earth as

well.

In the United States, a historical review on the subject in "which shape the

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earth is in, " probably would start from the time when the Declaration of

Independence from England was signed in 1776. In this country, however, one

is obliged to start with the prehistoric man, who, if he thought about the subject

at all, presumably concluded that, apart from local oddities like rocks or

mountains, the earth was flat. This is also the view held today by the Flat-Earth

Society, also in England.

The idea of a nearly-spherical earth was surprisingly late in becoming

established, or so it seems to us, with the advantage of hindsight. Neither the

Babylonians nor the Egyptians favored this idea, and the credit goes to Pythagoras

and his school in the sixth century B»C. I should add that the idea was derived not

from observations but from their conviction that the sphere was "the perfect"

shape. Three-hundred years later Eratosthenes did more than adopt the idea,

he actually measured the earth's circumference, using the propagation velocity

of a camel caravan as his scale.

It was not until the seventeenth century that the shape of the earth was improved

upon. The first indication that the earth may be flattened at the poles was obtained

in 1672 by Jean Richer's French expedition to South America, where he found

that his pendulum clock, accurate hi Paris, was loosing time at Cayenne. First

numerical estimates on the flattening came from Newton in his "Principia"

published in 1687, but practical measurements to establish the value of the

flattening were made by the Cassinis, who measured arc length in France,

and who came to the conclusions that the earth was flattened indeed, but not at

the poles, but rather at the equator, thus, it looked like an egg or a lemon. This

was in 1720, and. fierce controversy followed: Was the earth flattened or elon-

gated at the poles? Who was right, Newton or the Cassinis? The French

Academy sent the two famous expeditions of Maupertuis to Lapland, and La

Condamine's to Peru. After ten years of labor and an equal number of years

spent in quarrels, the conclusions tended to confirm Newton's idea, and

Voltaire congratulated the expeditions saying, "You have successfully flattened

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the poles and the Cassinis. " Not much happened after the regarding the shape of

the earth, until the middle of the present century, when first analysing gravity

measurements on a global basis, and after 1957, analysing the orbits of

artificial satellites, a complete new picture of the earth's shape emerged.

These analyses, of course, were made possible only because by that time, the

computers came into existence.

I shall not describe how from the perturbations to satellite orbits, caused

by the various possible oddities in the earth's shape, these oddities can be deter-

mined. It should suffice to say that a new value for the flattening has emerged,

indicating that the earth's equatorial diameter exceeds the polar diameter by

42. 77km, which is a full 170 meters different from the previously adopted

value. This difference may not seem much for most of us, but it is important

for the geophysicist, who may conclude that the earth's interior has great

strength, and the assumption that it can be treated as if it were a fluid, an

assumption which in the past, was, widely made, is illegitimate.

The more accurate value for the flattening is, however, only a very small

part of tiie information obtained from satellites. Without going into technicalities,

let me simply illustrate the improvement by the fact, that in the pre-satellite era,

the shape of the earth and its gravity field was described by four basic parameters,

while today, the number of known parameters exceeds two-hundred and fifty. This

new information pictorially represented as the aforementioned geoid above the

ellipsoid shows that the most prevailing features are the healthy depression

around the South Pole, a bulge south of the equator, and also around the North Pole,

indicating, in the language of the press, that the earth is "pear-shaped. " This

discovery came as a relatively great surprise to most of us, but it should have

been no surprise to Christopher Columbus, who gave it as his opinion "that

it has the shape of a pear that is very round, except where the stem is, which is

higher... " Other important features are the depression south of India, (113m),

the elevation near New Guinea, (81m), and the elevation centered in England

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and the south Atlantic.

To sum up, satellites and the computers have brought us from the earth of

1957, which was merely a sphere flattened at the poles, and flattened by the

wrong amount, to a complicated figure which when seen in the round looks

perhaps like a potato with dips and humps all over it.

By-products of this satellite-orbit analysis are the coordinates of the tracking

stations with respect to the center of the earth. In the pre-satellite era, such

information, which is vital in relating the numerous geodetic systems of the

world, practically did not exist. Today, geocentric coordinates are known

for about 150 stations fairly evenly distributed around the globe.

Satellites also help in mapping, as geometric triangulation points in the sky

in connection with the method called:

Satellite Triangulation or Trilateration

This method found wide range applications in connecting another 150-200

tracking stations in the relative sense both on a continental and on a global

basis. Better known projects in this category are the programs under the coor-

dination of the Eastern and Western European Subcommissions for Satellite

Triangulation of the International Association of Geodesy; the U.S. National

Geodetic Satellite Program now in its final stages, including observations by

the Smithsonian Astrophysical Observatory, The National Geodetic Survey,

(formerly Coast and Geodetic Survey), NASA and various other agencies; the

French coordinated ISAGEX Program; other French works in southern Europe

and northern Africa; and some other local national network developments in

North and South America.

I will not attempt to offer you a glimpse at the software used in the calculations

related to satellite geodesy, mainly because some of them are rather lengthy.

The fact that some of these programs took 100 man years to develop is an indi-

cation not only of the complexity of the problem, but also of the need for better

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programming methods. Clearly, when one needs to work with several

ten-thousand observations in order to determine several hundred unknown

quantities, like station coordinates, gravitational parameters, and at the same

time, attempts to recover at least some of the systematic errors burdening

the observations, the computer software and hardware will have to be impressive

indeed.

This leads us to an application where the impact of computers is and will

probably be the greatest both in its economical aspects and also in the number

of people affected. This application is generally known in surveying circles as:

Adjustment Computations

Adjustment in the surveying and mapping terminology is the method used to

derive unique and "best" values for parameters from redundant measurements

of those parameters, or parameters related to them by a known mathematical

relationship. It is a device which should be used by everyone in the profession

involved in the evaluation of survey data from leveling to satellite laser ranging

or, from cadaster surveys to lunar mapping. The fundamentals of this science

were laid down by Karl Friedrich Gauss in the eighteenth century at the age of 18.

Every geodesist and photogrammetrist of note since then, has contributed to

the literature by refining (or confusing) some aspects of the topic.

Without going again into the technical details to the extent possible, let me

remind you that in the pre-computer era, up to the early fifties, one did not

enter lightly into an adjustment computation; one looked very closely at the

model; one checked and double-checked the input data, and in very special cir-

cumstances, one might undertake the extra computations necessary to check the

possible correlations between the unknown parameters, or to compute the error

ellipses for certain selected points of special interest. In other words, it was

not practically feasible to put adjustment computations on a sound statistical basis.

The number of unknown parameters was also limited, since the computations

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for one medium-sized network (50 -100 unknowns) were likely to require

several man-months of time, thus, it was a very expensive undertaking indeed.

The use of statistical methods for planning a network to make sure that it is

the most economical and most favorable from the point of view of the propagation

of errors was almost out of the question because of the costs involved. For

tills reason, in a given country, very few organizations were doing adjustment

computations.

Today, thanks to the computers, this situation is part of history. Very large

numbers of organizations are doing adjustment computations using computer

programs, either developed by themselves or procured from other organiza-

tions. These programs are (or should be) based on correct statistical theory

and techniques, and running them, even with a very large number of unknowns,

costs very little.

Advances in this regard were most spectacular in that part of the mapping

industry which deals in photogrammetry, where the wide applications of aerial

triangulation or analytical photogrammetry using block adjustment techniques

with a great number of unknowns is part of the daily routine. Another spectacular

area where adjustment computations are routinely used to full capacity is

satellite geodesy, where the number of unknown parameters, mostly highly

correlated, and to be adjusted for in one huge simultaneous adjustment, may

reach several thousand. .

It is interesting to note that a significant number of rather sophisticated

"package programs" written for different purposes, like aerial triangulation,

horizontal control, satellite triangulation or orbit determination, have been widely,

distributed and used by a great number of organizations other than those who

designed the programs. It is a small step from here to arrive to the point, where

the average surveyor can pick up his phone and dial the computer or go to his

remote terminal, specify his object, read the input data in the specified manner,

and receive his results with all the statistical trimmings faster and cheaper

than he ever dreamed of. He has a powerful design tool at his command; he

can now make full use of law of error propagation and optimize any system he

is designing; he can build in constraints; he can test options and find the

option that meets his specifications with the least effort and cost. At the con-

clusion of the project, he can do an evaluation and test the assumptions that it

was necessary to make about his instruments. If data from a variety of sensors

have been combined in an adjustment, he can test the distribution of residuals

for normality; he can test his mathematical model, his weighing procedure.

In theory, this always has been possible, but until modern computer facilities

became available, it was out of the question as a regular tool.

Equipment Oriented Areas

There are also equipment oriented areas where the availability of the gen-

erations of computers (directly part of, or tied to, the sensor-system) affected

surveying and mapping. To mention a few, let me start with the AN/USQ-28

Mapping and Surveying System, which comprises the most advanced group of

equipment integrated to collect accurate raw data for mapping purposes. It

was specifically designed to acquire photography suitable for 1:50, 000 scale

topographic mapping in areas where ground control is insufficient. The system

is built into a Boeing 707 aircraft and consists of precision mapping cameras,

an Lnertial navigation system,electronic distance measuring equipment, a terrain

profile recorder, and other auxiliary equipment. All data, with the exception of

the photography, are recorded on magnetic tapes for direct input into digital equip-

ment to speed the data reduction process. It is a pity that as of this moment,

the system is not operating because there seems to be lack of money to pay for

the operation of the aircraft (for gasoline!).

Another example is the progress that has been made in automated computation

equipment. These computer-driven machines use image sensing and correlation

techniques to produce horizontally correct images while simultaneously detecting

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and recording height Information. This equipment is supposed to reduce map

compilation time by 75%.

Another development of significant interest is the automatic or semi-

automatic coordinate readers. This equipment is designed to measure,for

example,the coordinates of star images on photographic plates obtained for

astronomic or satellite geodetic applications. The instruments have a pre-

programming feature which moves a detecting head tQ the approximate location

of each required star image. The detection head then centers itself precisely

over a star image, at which point the coordinates are measured and recorded

on punch cards for input in the computer program.

Another and rather esoteric computer application in this equipment oriented

category is the Apollo mapping system for accurate lunar mapping. The main

purpose of the system is similar to that of the USQ-28 mapping system mentioned

earlier, i. e., to provide maps in areas where ground control is insufficient.

The lunar orbiter and Apollo programs through Apollo 14 have produced phenom-

enal photography to support landing site selection and surface operations. How-

ever, the new metric camera system which was flown first on Apollo 15, then

on Apollo 16 and which will be also on board the last manned flight to the moon,

offers an order of magnitude Improvement towards lunar mapping, the deter-

mination of the lunar .gravity field, and of the motion of the moon in space. It

is again a pity that the system is included only in the last three missions, and

was left out from the previous seven missions. Of course, the astronauts on

Apollo 7-10 were rather busy preparing the landing of Neal Armstrong on Apollo

11, but only NASA knows why the system was not flown on Apollo 12 - 14. The

area coverage would have been certainly better.

This system consists of three cameras, a laser altimeter and timing equipment.

The first camera is a 3-inch metric mapping camera which photographs the lunar

surface while the second stellar camera built into the same housing takes simul-

taneous pictures of the star field just above the lunar horizon to aid the deter-

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mination of the orientation of the mapping camera. The laser altimeter is

synchronized to fire simultaneously and provides the distance from the camera

to the lunar ground for each photograph. All this information together with

the earth-based tracking data should give sufficient information on the position

and orientation of the mapping camera (to about 2.5 m relative). The third

24 inch panoramic camera provides very high resolution photographs (2m at

the nominal 110km altitude).

As I mentioned, the main application of the system is to establish geodetic

control on the moon and provide maps for the areas covered. In addition to.

these, information is expected on the rotation of the moon about its axis, com-

monly known as the phenomena of libration. The data will also be analyzed in

conjunction with the laser distances measured between earth-based observatories

and the reflectors placed on the moon surface by Apollos 11, 14, and 15, and

Luna 17. This combination of data should be most helpful to improve on the lunar

ephemeris, i. e., on the knowledge of the relative motion of the moon around the

earth, which lately seems to be part of geodesy also.

The Future

From here, there is only a short step into the future. What will the next

decade bring? I already described what is expected from the computers and how

they will change the job of the surveyor in the adjustment area. Let us see

briefly that in addition to the routine mapping and surveying activities, what

miracles the surveyor is to perform during the next decade or so. First of all,

he is going to get some new customers: the geophysicists and the oceanographers.

He will need new tools, because their demand for a full magnitude and better

positions (from 10m to 1m to 10cm) than what is available today exceeds present

capabilities. Most of these instruments are already in the development stage

and undoubtedly will be ready for applications in the not too distant future. Let

us take a quick look at these machines:

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First of all, existing laser distance measuring devices will be improved to

the point where the only factor limiting the accuracy of the observations will

be the uncertainties in tropospheric propagation, which is expected to be reduced

to about 6cm (from the present 15-30cm).

On the radio frequency systems with prospects of 1m or better accuracy,

Very Long Base-Line Interferometry (VLB!) seems to offer the greatest

versatility. This technique depends upon local frequency standards of high

quality - preferably hydrogen masers - at two or more radio antennae separated

by distances on the earth as great as allowed by the common visibility of a radio

source, like a quasar or a water vapor source. The frequency standards provide

time references for magnetic tape recordings of signals from these galactic

energy sources. The tapes are later correlated at a central computing facility,

and the time difference for arrival of the same wave is determined. From this,

it will be possible to calculate the distance between the two antennae to an

accuracy of about 15cm and the direction between them to about 0.001 arc second,

provided that the position of the energy source is known.

Satellite to satellite (range rate) tracking also will offer substantial advantages

over current techniques limited by our dirty window towards space, the atmos-

phere. Very high satellites will track a low satellite continuously through the

vacuum of the universe with very high precision.

Such continuous tracking technique, coupled with the so-called "drag-free"

satellite, will further improve our knowledge of the gravity field of the earth and

the geoid. The essential element of such a system is an unsupported mass

contained in a spherical shell. A control system in the satellite senses motions

of the shell relative to the proof mass and actuates small thrusters that force

the shell to follow the proof mass without touching it. Hence, the proof mass

follows an orbit influenced only by gravitational force.

Improvement in the knowledge of the gravity field, the shape of the geoid is

also expected through the satellite to ocean radar altimeters, measuring contin-

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uously the distance between sea level and the satellite. The first of these devices

will be flown probably in 1974 on an experimental basis.

From these new instruments, a wealth of information will be made available

to the earth scientists, who, in turn, will be able to produce unpredictable

but certainly substantial advances about the rotational motions of the earth,

tide interactions, temporal variations in the gravity field, continental drift and

other large scale deformations of the earth crust and mantle. The interactions

of these motions and deformations appear to be responsible for a wide variety of

effects, including large earthquakes, mountain building, generation of tsunamis

(tidal waves), and confinement of nearly all active volcanoes to only a few narrow

belts. The satellite born radar altimeter eventually will provide valuable ocean-

ographic information on tides, storm surges, general ocean circulation, and

other dynamical processes affecting sea level.

Most of these problems are global in nature, thus, require observations

globally distributed. The interaction between the several dynamic subsystems of

the earth demands coordination of the observations. Hence, for maximum effec-

tiveness, technological integration and international cooperation are essential to

a progressive investigation of these topics.

Is the International Federation of Surveyors willing and ready to participate in

this cooperation? It it ready and willing to take this challenge and serve the new

customers ?

What else is coming? - Automated data banks with national and international links.

- Automated data reduction systems

- Kemote sensing satellites for environmental monitoring,

ocean sensing and for land use and resources management, producing 15, 000,000

bits of information per second - equivalent to an Encyclopedia Britannica every

couple of minutes. We certainly will be able to verify the conjuncture that as civi-

lized man evolved from his primitive ancestry, he developed an appetite for large

masses of data, recording observations about his individual or collective activities

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with ever greater precision and detail.

Concluding Remarks

On the surface, it would seem that surveying presents no serious issues as

a technology. It is a useful tool in the service of mankind and extends the capa-

bilities of science. Unlike some technologies, surveying does not pollute. On

the contrary, it may help to preserve the quality of the environment. It is not

likely to be wiasteful economically. Instead, it could stimulate and guide resource

development as well as scientific research in the earth sciences. What is more,

it has some popular attributes. It requires a private and public sector team

effort, and is multi-disciplinary as well as multi-institutional and multi-national.

But, if we were to conclude from such reasoning that no major issues are

involved, we would be badly mistaken. The issues are not technological, but

sociological. In my view, they effect the unity of the profession of surveying

and mapping.

Let me quote a recent editorial from the transactions of the AGU on the

"Surveyor Geodesist":

"For over two thousand years, the land surveyor and the astronomeroften joined by the mathematician, collaborated in the developmentof geodetic science. This symbiotic relationship, which reached itszenith in the last three hundred years, resulted in inferences of geodeticsignificance from observational data and also led to the establishmentof the science on a rigorous mathematical foundation. The surveyor,to some degree and to a limited accuracy, participated in this develop-ment in the small; but, today he is severely hampered by the restrictivelimits to his data base, by the limited scope of his observing instrumentsand computing methods, and, in no small way, by the deemphasis insurveying education at the university level. In addition, photogram-metric methods and, in more recent times, developments in spacetechnology have made enormous inroads into his areas of competence.In fact, the phenomenal geodetic fallout from the space program has soobscured the place of the surveyor in the geodetic scheme of things thatthere is a tendency to downgrade his continued vital contribution to thescience. Hence, more and more the average surveyor finds himselfoutside the geodetic mainstream, relegated to a supporting role as aprovider of cadastral and lower order engineering data.

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The new team combines the expertise of the mathematician, thephysicist, and the space scientist. From space-oriented observations,this group of scientists has obtained data in regions inaccessible tothe surveyor and has obtained results that the geodesist using classicaltechniques could never hope to achieve. As the space scientist refineshis measurements and increases his sampling rate, thereby providingmore precise data at ever decreasing wave lengths, the geodesist findsthat among many applications he can support the oceanographer inresolving ocean surface problems; the tectono-physicist and theseismologist in measuring continental drift and crustal movement;and the astronomer in determining polar motion and variations in earthrotation.

Will this expanded geodetic role further divorce the surveyor fromthe geodetic community ? Not necessarily; a great deal depends uponthe willingness of the profession to broaden its horizons. The newusers of geodetic information require baseline information at accuraciescomparable to and sometimes exceeding those the surveyor is accustomedto providing on a day-to-day basis. The surveyor needs to seek out hisnew customers and needs to become aware of his problems; he needs toupgrade his field operations, using the most precise instrumentationand adjustment techniques; and he most certainly must insist uponimproving and expanding the university curriculum in surveying."

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3. PERSONNEL

Ivan I. Mueller, Project Supervisor, part time

Muneendra Kumar, Graduate Research Associate, part time

James P. Reilly, Graduate Research Associate, part time

Narendra K. Saxena, Research Associate, full time

Tomas Soler, Graduate Research Associate, part time

Emmanuel Tsimis, Graduate Research Associate, part time

Marvin C. Whiting, Gradute Research Associate, part time

Susan Breslow, Research Aide, part time

Barbara Beer, Research Aide, .part time

Evelyn E. Rist, Technical Assistant, full time

4. TRAVEL

Ivan I. MuellerBronx, New York, February 22, 1972Attend GEOP Research Conference Steering Committee Meeting

Ivan I. MuellerGraz, Austria, May 29-June 2, 1972Present a paper at IAG International Symposium on Satellite andTerrestrial Triangulation

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5. REPORTS PUBLISHED TO DATE

OSU Department of Geodetic Science Reports published under Grant

No. NSR 36-008-003:

70 The Determination and Distribution of Precise Timeby Hans D. PreussApril, 1966

71 Proposed Optical Network for the-National Geodetic Satellite Programby Ivan I. MuellerMay, 1966

82 Preprocessing Optical Satellite Observationsby Frank D. HotterApril, 1967

86 Least Squares Adjustment of Satellite Observations for SimultaneousDirections or Ranges, Part 1 of 3: Formulation of Equationsby Edward J. Krakiwsky and Allen J. PopeSeptember, 1967

87 Least Squares Adjustment of Satellite Observations for SimultaneousDirections or Ranges, Part 2 of 3: Computer Programsby Edward J. Krakiwsky, George Blaha, Jack M. FerrierAugust, 1968

88 Least Squares Adjustment of Satellite Observations for SimultaneousDirections or Ranges, Part 3 of 3: Subroutinesby Edward J. Krakiwsky, Jack Ferrier, James P. ReillyDecember, 1967

93 Data Analysis in Connection with the National Geodetic Satellite Programby Ivan I. MuellerNovember, 1967

OSU Department of Geodetic Science Reports published under Grant

No. NGR 36-008-093:

100 Preprocessing Electronic Satellite Observationsby Joseph GrossMarch, 1968

106 Comparison of Astrometric and Photogrammetric PI ate Reduction Techniquesfor a Wild BC-4 Cameraby Daniel H. HornbargerMarch, 1968

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110 Investigations into the Utilization of Passive Satellite Observational Databy James P. VeachJune, 1968

114 Sequential Least Squares Adjustment of Satellite Triangulation andTrilateration in Combination with Terrestrial Databy Edward J. KrakiwskyOctober, 1968

118 The Use of Short Arc Orbital Constraints in the Adjustment of GeodeticSatellite Databy Charles R. SchwarzDecember, 1968

125 The North American Datum in View of GEOS I Observationsby Ivan I. Mueller, James P. Reilly, Charles R. SchwarzJune, 1969

139 Analysis of Latitude Observations for Crustal Movementsby M.G. ArurJune, 1970

140 SECOR Observations in the Pacificby Ivan I. Mueller, James P. Reilly, Charles R. Schwarz, Georges BlahaAugust, 1970

147 Gravity Field Refinement by Satellite to Satellite Doppler Trackingby Charles R. SchwarzDecember, 1970

148 Inner Adjustment Constraints with Emphasis on Range Observationsby Georges BlahaJanuary, 1971

150 Investigations of Critical Configurations for Fundamental Range Networksby Georges BlahaMarch, 1971

177 Improvement of a Geodetic Triangulation through Control-PointsEstablished by Means of Satellite or Precision Traversingby Narendra K. SaxenaIn press

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The following papers were presented at various professional meetings:

"Report on OSU participation in the NGSP"47th Annual meeting of the AGU, Washington, D. C., April 1966

"Preprocessing Optical Satellite Observational Data"3rd Meeting of the Western European Satellite Subcommission, IAG, Venice,Italy, May 1967.

"Global Satellite Triangulation and Trilateration"XlVth General Assembly of the IUGG, Lucerne, Switzerland, September 19G7,(Bulletin Geodesique, March 1968).

"Investigations in Connection with the Geometric Analysis of Geodetic SatelliteData"GEOS Program Review Meeting, Washington, D. C., Dec. 1967.

"Comparison of Photogrammetric and Astrometric Data Reduction Results forthe Wild BC-4 Camera"Conference on Photographic Astrometric Technique,Tampa, Fla., March 1968.

"Geodetic Utilization of Satellite Photography"7th National Fall Meeting, AGU, San Francisco, Cal., Dec. 1968;

"Analyzing Passive-Satellite Photography for Geodetic Applications"4th Meeting of the Western European Satellite Subcommission, IAG, Paris,Feb. 1969.

"Sequential Least Squares Adjustment of Satellite Trilateration"50th Annual Meeting of the AGU, Washington, D. C., April 1969.

"The North American Datum in View of GEOS-I Observations"8th National Fall Meeting of the AGU, San Francisco, Cal,, Dec. 1969 andGEOS-2 Review Meeting, Greenbelt, Md., June 1970 (Bulletin Geodesique,June 1970).

"Experiments with SECOR Observations on GEOS-I"GEOS-2 Review Meeting, Greenbelt, Md., June 1970.

"Experiments with Wild BC-4 Photographic Plates"GEOS-2 Review Meeting, Greenbelt, Md., June 1970.

"Experiments with the Use of Orbital Constraints in the Case of Satellite Trailson Wild BC-4 Photographic Plates"GEOS-2 Review Meeting, Greenbelt, Md., June 1970.

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"GEOS-I SECOR Observations in the Pacific (Solution SP-7)"National Fall Meeting of the American Geophysical Union, San Francisco,California, December 7-10, 1970.

"Investigations of Critical Configurations for Fundamental Range Networks"Symposium on the Use of Artificial Satellites for Geodesy, Washington, D. C.,April 15-17, 1971.

"Gravity Field Refinement by Satellite to Satellite Doppler Tracking"Symposium on the Use of Artificial Satellites for Geodesy, Washington, D. C.,April 15-17, 1971.

"GEOS-I SECOR Observations in the Pacific (Solution SP-7)"Symposium on the Use of Artificial Satellites for Geodesy, Washington, D. C.,April 15-17, 1971.

"Separating the Secular Motion of the Pole from Continental Drift - Where andWhat to Observe?"IAU Symposium No. 48, "Rotation of the Earth, " Mori oka, Japan, May 9-15, 1971.

"Geodetic Satellite Observations in North America (Solution NA-8)"Annual Fall Meeting of the American Geophysical Union, San Francisco,California, December 6-9, 1971.

"Scaling the SAO-69 Geometric Solution with C-Band Radar Data (Solution SC 11)"Annual Fall Meeting of the American Geophysical Union, San Francisco,California, December 6-9, 1971.

"The Impact of Computers on Surveying and Mapping"Annual Meeting of the Permanent Committee, International Federation of Surveyors,Tel Aviv, Israel, May 1972. .

"Investigations on a Possible Improvement of Terrestrial Triangulation by Meansof Super-Control Points"LAG International Symposium - Satellite and Terrestrial Triangulation,Graz, Austria, June, 1972.

"Free Adjustment of a Geometric Global Satellite Network (Solution MPS7)"LAG International Symposium - Satellite and Terrestrial Triangulation,Graz, Austria, June, 1972.

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