NOAA Technical Memorandum NOS NGS-58 GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS (STANDARDS: 2 CM AND 5 CM) VERSION 4.3 David B. Zilkoski Joseph D. D'Onofrio Stephen J. Frakes Silver Spring, MD November 1997 U.S. DEPARTMENT OF National Oceanic and National Ocean National Geodetic COMMERCE Atmospheric Administration Service Survey
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NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS (STANDARDS: 2 CM AND 5 CM) VERSION 4.3 David B. Zilkoski Joseph D. D'Onofrio Stephen J. Frakes Silver Spring, MD November 1997
U.S. DEPARTMENT OF National Oceanic and National Ocean National Geodetic COMMERCE Atmospheric Administration Service Survey
Geopotential numbers “C” are taken as relativequantities of gravity potential (measured in
“gals”. 1 GALILEO = 1 CM/SEC2
ACCELERATION). “C” is usually given in geopotential units –
“gpu”1 gpu = 1 k gal m (a non-geometrical value)
17
18
N 45
19
NGS data sheet- N 45
21
• For Helmert orthometric heights, G is approximated from a measured surface gravity value at the point and evaluated at the midpoint of the plumb line using the formula:
HHE = C / (G surface + 0.0424 H)where C is an estimated geopotential number in gpu, G is the
modeled gravity at the point in gals, and H is the orthometric heightin Km.This is an iterative process
ORTHOMETRIC HEIGHTS
22
Heights Based on Geopotential Number(C): C = G × H or H = C/ G
– Relative differences typically less than 1 cm in 10 km
2.x (?) cm RMS about the mean nationally
0.5 cm error in 10 Km
• Leveling-Derived Heights
– Less than 1 cm in 10 km for third-order leveling
NOAA Technical Memorandum NOS NGS-58
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS (STANDARDS: 2 CM AND 5 CM) VERSION 4.3 David B. Zilkoski Joseph D. D'Onofrio Stephen J. Frakes Silver Spring, MD November 1997
U.S. DEPARTMENT OF National Oceanic and National Ocean National Geodetic COMMERCE Atmospheric Administration Service Survey
This means we could expect 0.12’ orthometric accuracy from the CORS
• USE A TROPO MODEL RATHER THAN FIELD MET DATA UNLESS PROVEN
BETTER
• USE RELATIVE TROPO SCALE PARAMETER FOR STATIONS OVER 15 KM
AND FOR LARGE INTERSTATION RELIEF
• BASELINE RMS ≤ 1.5 CM
• REDUNDANT BASELINES DIFFER BY ≤ 2.0 CM
Independent Baselines in GPS
# of Baselines =
N(N-1)
2
# of Independent
Baselines =(N-1)
N = Number of receivers observing simultaneously
Precise (Final)•14 days latency•1 cm accuracy•updated weekly
Rapid•1 day latency•2 cm accuracy•updated daily
UltraRapid•24 hrs observed / 24 hrs predicted•5 cm / 10 cm accuracy•updated 4 times/day
NGS/IGS PRECISE ORBITS
BASELINE PROCESSINGREDUNDANCY NEEDED: ≤ 1.5 CM, ≤ 2.0
DIFFERENCE IN “h”
ELLIPSOID ADJUSTMENT
FAIRFAX COUNTY, VA HTMOD PROJECT
450 SQ. MILES
4-6 RECEIVERS
124 stations
439 baselines
Summary-Vector Processing Accomplished
• Elevation Mask - 15 degrees
• Ephemeris - Precise (typ. 14 days latency)
• Tropospheric Correction Model
• Iono Corrections - All baselines longer than 5 km.
• Fix Integers
Baselines less than 5 km: L1 fixed solution
Baselines greater than 5 km: Iono free (L3) solution
• Baselines must have RMS values ≤ 1.5 cm
• Baselines must have difference in “up” ellipsoid height ≤ 2.0 cm
Table 1. -- Summary of Guidelines
Table 1. -- Summary of Guidelines
(continued)
Guidelines for Establishing
GPS-Derived Orthometric
Heights
(Standards: 2 cm and 5 cm)
http://www.ngs.noaa.gov/
SEARCH: “NGS 59”
• Three Basic Rules
• Four Basic Control Requirements
• Five Basic Procedures
3-4-5 System
A Guide for Establishing GPS-Derived Orthometric Heights
(Standards: 2 cm and 5 cm)
(Assumes we have completed NGS 58 – ellipsoid heights and met criteria:-all local monuments ≤ 10 km, avg ≤7 km-Ellipsoid heights from processing compare ≤ 2.0 cm-- baselines RMS ≤ 1.5 cm)
3 BASIC RULES:
A Guide for Establishing GPS-Derived Orthometric Heights
(Standards: 2 cm and 5 cm)
• USE NOS-NGS 58 – GPS DERIVED ELLIPSOID HEIGHTS
• USE PUBLISHED NAVD 88 CONTROL
•USE CURRENT HYBRID GEOID MODEL
78
Estimating GPS-Derived Orthometric Heights
Four Basic Control Requirements-Occupy stations with known NAVD 88 orthometric heights
(Stations should be evenly distributed throughout project)
-Project areas less than 20 km on a side, surround project
with NAVD 88 bench marks, i.e., minimum number of
stations is four; one in each corner of project
-Project areas greater than 20 km on a side, keep distances
between GPS-occupied NAVD 88 bench marks to less than
20 km
-Projects located in mountainous regions, occupy bench marks
at base and summit of mountains, even if distance is less than
20 km
FAIRFAX COUNTY VERTICALS USED
40 KM
80
Procedure 1: Perform a 3-D minimum-constraint least
squares adjustment of the GPS survey project, i.e.,
constrain one latitude, one longitude, and one orthometric
height value.
Estimating GPS-Derived Orthometric Heights
Five Basic Adjustment Procedures
Procedure 2: Using the results from the adjustment in
procedure 1 above, detect and remove all data outliers. The
user should repeat procedures 1 and 2 until all data outliers
are removed.
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Procedure 3: Compute differences between the set of
GPS-derived orthometric heights from the minimum
constraint adjustment from procedure 2 above and
published NAVD 88 bench marks.
Procedure 4: Using the results from procedure 3 above,
determine which bench marks have valid NAVD 88 height
values. All differences between valid bench marks need to
agree within 2 cm for 2-cm surveys and 5 cm for 5-cm
surveys.
Estimating GPS-Derived Orthometric Heights
Five Basic Adjustment Procedures
82
Procedure 5: Using the results from procedure 4
above, perform a constrained adjustment fixing one
latitude and one longitude value and all valid NAVD
88 height values.
Estimating GPS-Derived Orthometric Heights
Five Basic Adjustment Procedures
Topography
AB
C
D
E
F
GPS-Derived Heights from GEOID03 Separation
= Published NAVD88 Orthometric Height = New Control
Ellipsoid
hh
h
h
h
h
GEOID09
N N
N NN
N
Hh-N
Hh-N
Hh-N
Hh-N
Hh-N
Hh-N
Constrained Vertical Adjustment
Topography
AB
C
D
E
F
hadj
hadjhadj
hadj
ha
dj
hadj
AdjustedEllipsoid
Ellipsoid Height Adjusted to Fit Constrained Orthometric Heights
GPS-Derived Orthometric Heights
= Published NAVD88 Orthometric Height= New Control
H
HH
H
Geoid based on Ortho Heights
GEOID09
Ellipsoid
hh
h
h
h
hHGPS
HGPS
N N
N NN
N
GEOID09
Summary
• Mistakes and systematic errors must be removed before the adjustment
• A least squares adjustment handles random errors and provides a single solution
• The Minimally Constrained adjustment checks the internal consistency of the network
• The Constrained adjustment checks the existing control and references the network to the datum
• The vertical adjustment estimates GPS-derived Orthometric heights
CONTROL COMPARISON
OUTLIERS?
PASSIVE CONTROL QUALITY
(OVER TIME)
GEOID MODEL QUALITY
Elevation published
to centimeters
Orthometric height
determined by GPS
Identified as
Height Mod
survey station
ADJUSTMENT TO PASSIVE CONTROL
SUMMARY• Mistakes (blunders) and systematic errors must be
removed before the adjustment
• A least squares adjustment handles random errors and provides a single solution (Try to eliminate all systematic errors)
• The Minimally Constrained adjustment checks the internal consistency of the network
• The Constrained adjustment checks the existing control and references the network to the datum
• The vertical adjustment estimates GPS-derived Orthometric heights- Approaching 3rd order leveling accuracies
• OPUS with redundant observations can produce 5 cm orthometric heights in areas of high accuracy hybrid geoid coverage