Final Year Project For obtaining the hydrographic surveyor diploma in the specialty “Data processing” Prepared by Geraud NAANKEU WATI TOTAL E&P Company supervisor: Jean‐baptiste GELDOF Academic supervisor: Pierre BOSSER August 2015 Error budget analysis for hydrographic survey systems; comparative study of methods and existing softwares; implementation on an inspection campaign of pipelines by AUV
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1. STATE OF THE ART ...................................................................................................................................... 6
1.1 Description of hydrographic survey systems ...................................................................................... 6
1.2 References frames and transformations ............................................................................................ 9
1.3 Error budget of hydrographic survey system ................................................................................... 12
1.4 Analysis of actual methods of error budget estimation for hydrographic survey systems .............. 16
1.5 Analysis of the uncertainty sources of hydrographic survey system ............................................... 25
2. PROPOSED METHOD FOR ERROR BUDGET ESTIMATION FOR HYDROGRAPHIC SURVEY SYSTEMS ......... 28
2.1 Equations of sounding position of a surface survey system ............................................................. 28
2.2 Equations of sounding position for underwater survey system ....................................................... 38
3. ERROR BUDGET ESTIMATION FOR HYDROGRAPHIC SURVEY SYSTEMS ................................................... 44
3.1 Error budget estimation for surface survey system ......................................................................... 44
3.2 Error budget estimation of underwater survey system ................................................................... 46
3.3 Implementation on pipelines inspection by AUV ............................................................................. 48
CONCLUSION AND OUTLOOK ........................................................................................................................... 50
5. LIST OF FIGURES ........................................................................................................................................ 56
6. LIST OF TABLES .......................................................................................................................................... 57
In the late 1990s, with the world’s growing demand for hydrocarbons and the discovery of numerous deep
offshore reservoirs, TOTAL set out to conquer the deep offshore. Today, many oil fields are operated in depths
exceeding 1000 m around the globe (West Africa, North America, South America and South‐East Asia). These
operations require huge investments related to surface (FPSO1, drilling ships, etc…) and subsea (pipelines, subsea
wells) infrastructures installation and operations.
A good knowledge of the marine environment, the seabed and the sub‐seabed contexts is crucial to ensure
the safety, the reliability, the performance of these installations. One of the main tasks of EP/DSO/TEC/GEO2
service in which I worked from 23 March to 07 September 2015 is to plan, acquire and use data from topographic,
bathymetric, oceanographic, surface geophysical and geotechnical campaigns. The analysis and interpretation of
the results from these operations are used in engineering studies to design sustainable installations while
ensuring the safety of operations throughout the entire field life. Bathymetry, sub‐seabed nature and geological
hazards are key entry data to define the optimal architecture for future pipelines network and production
infrastructures.
The acquisition campaigns are not directly led by TOTAL, but subcontracted to specialized contractors such
as Fugro, C&C, Gardline, DOF Subsea, etc. The analysis of tender documents and reports from hydrographic
campaigns highlighted discrepancies in error budget estimation methods and results. Two contractors recently
delivered different error budgets while using the same survey system. The error budget estimation is an
important phase of a hydrographic project, as it will enable to estimate how far the soundings are from their true
value.
In this context, the purpose of TOTAL is to verify that error budgets proposed by hydrographic companies
during the tender phase comply with their internal specifications. Thus, TOTAL wishes to have an error budget
estimation tool in order to estimate the data uncertainty provided to engineering teams. The objective of this
traineeship is to study and compare different methods of error budget estimation used by TOTAL contractors and
other existing tools on the market, in order to better qualify the hydrographic data. The deliverables are the
development of an error budget estimation tool applied to hydrographic survey systems and a report detailing
(this document) the different steps of the study. These supports will be used by TOTAL to better evaluate the
technical aspects of contractor proposals, in order to qualify the acquired data to guaranty their usability in
exploration‐production activities.
The report is organized in two parts. Part I shows the state of the art which includes four sections: the first
section presents a detailed description of the (underwater and surface) hydrographic survey systems commonly
used by TOTAL contractors in order to better understand their mode of operation. The second section introduces
the notions of reference frames and transformations between the frames to understand how to express sounding
coordinates in a terrestrial frame. The third section presents the concept of error budget. The last section
discusses the actual methods of error budget estimation for hydrographic survey systems. Part II presents an
error budget estimation method for the hydrographic survey systems which includes the establishment of the
equations of a sounding position acquired by each type of hydrographic survey system. Finally, part III goes on to
implement the error budget estimation algorithms of these systems and validate the error budget estimation
algorithm of underwater survey system using the data of the pipelines inspection campaign in 2014 in Angola.
1Floating Production Storage and Offloading 2EP, DSO and TEC are the respective acronyms of following entities: branch Exploration‐Production, direction Development and Support at Operations and TEChnologies division of TOTAL group. The GEO department includes skills related to the oceanography, meteorology, geophysics, geotechnical of engineering and geomatics.
As part of the Exploration and Production3 operations at TOTAL, internal specifications such as GS EP GEO
201 (TOTAL, 2014) and GS EP GEO 202 (TOTAL, 2013) define the procedures and rules to be applied for two types
of hydrographic survey systems: surface survey systems (generally used in near shore and in shallow water (0‐100
m)) and underwater survey systems (generally used in deep offshore (100‐3000m)). These systems are generally
used for the pre‐installation geohazards4 evaluation and subsea infrastructures inspection/monitoring surveys.
The choice of hydrographic system also depends on several parameters such as the accuracy required, the type of
application, the area of interest and the weather conditions.
1.1.1 Surface survey system
Classically, a surface survey system is composed of several sensors: a SVP probe, a GNSS positioning system
(GNSS receiver), a motion sensor (IMU5 /MRU6 and a gyro‐compass) and an acoustic sounder (Single or Multi‐
Beam Echo Sounder/MBES), all mounted on a vessel (see Figure 1 below). The MBES measures the depth of the
water. The SVP probe is used to determine the sound velocity profile (SVP) in the water column in order to
correct the depth measured by the MBES from sound speed variations. A sound velocity sensor (SVS) located
close to the MBES allows correcting the sound velocity close to transducer head. The motion sensor (IMU)
measures the attitude of the vessel (roll, pitch and yaw). The GNSS positioning system measures the vessel
position. The heave sensor is used to measure the vertical displacement of the vessel (heave). With most of
modern IMU, it is possible to measure both the attitude (roll, pitch and yaw) and the vertical displacement of
vessel (Ixblue, 2004).
Figure 1: Sensors and frames of a surface survey system (Bjørn & Einar, 2005)[modified]
Each sensor acquires its data in its own frame. The multiplicity of frames is a source of error. The various
frames of sensors (IMU frame and MBES frame) need to be aligned (Debese, 2013). As much as possible, sensors
alignment is achieved during the installation of the system. Possible misalignments between sensors are generally
corrected during the calibration phase (patch test) or after data acquisition (by automatic calibration methods
3Total Exploration & Production’s branch aims to discover and develop oil and gas fields to meet the world’s growing energy demand. 4These surveys identify any conditions at the seabed or in the foundation zone where hazardous subsurface features or unstable soil conditions exist. 5Inertial Measurement Unit 6Motion Reference Unit
based on least squares). The Figure 2 below presents an example of misalignment between the MBES frame and
the IMU frame. More details about the manual calibration methods are further explained in the work of
(Skilltrade, 2012), (Debese, 2013) and (Seube, 2014). See (Seube, Levilly, & Keyetieu, 2015), for further
information about the automatic calibration methods.
Figure 2 Misalignment between MBES frame and IMU frame
After the data acquisition phase, all the data of various sensors are loaded into data processing softwares.
The most used are CARIS, EIVA, HYSWEEP and QINSy. Data from the various sensors are not acquired exactly at
the same time (see Figure 3 below). Latency is introduced or can exist between sensors to take into account the
time of information transmission and the computation. It is commonly determined during the system calibration
phase because the data from different sensors needs to be synchronous during acquisition.
There are two main techniques to synchronize data. The first technique is to transfer the data on a single
system to date the time of receipt. To overcome transfer delays between the sensors, it is preferable to
synchronize the clocks of each sensor (second technique). The time stamp of data is then made at acquisition
time. Synchronization of various sensors is generally performed using a PPS signal (Pulse Per Second) from the
GNSS positioning system. For a detailed study on the synchronization methods, see the work of (Bjørn & Einar,
2005).
Figure 3: Illustration of asynchronous measurements in a surface survey system and Interpolation to MBES measurement time. (Bjørn & Einar, 2005)‐ [Modified]. The true measurement time is the time at which a data is measured. The time stamp is the time at which
are: Terrestrial reference frame (TRF), Local geodetic frame (LGF), local navigation frame or map projection
system, body frame and sensor frames.
1.2.1 Terrestrial reference frame
The Terrestrial reference frame (TRF) is an ECEF (Earth‐Centered Earth‐Fixed) frame. Its origin is located at
the Earth’s center. Its ‐axis points along the Earth’s axis of rotation from the center to the North Pole. The ‐axis
points from the center to the intersection of the equator with the prime meridian. The ‐axis completes the right‐
handed orthogonal set, pointing from the Earth’s center to the intersection of the equator with the 90° East
meridian (see Figure 7 below).
Figure 7: Different frames used in this report
According to (Seube, 2014), two kinds of coordinate systems can be attached to the TRF frame:
Rectangular coordinates: They are usual rectangular coordinates in the following frame: the axis intersects the prime meridian and the equator, the axis is oriented towards the true north, and
the axis complements the frame in order to get a right‐handed coordinate system.
Geodetic coordinates: In geodetic coordinates, the Earth's surface is approximated by an ellipsoid
and the sounding position is described in terms of latitude, longitude, and ellipsoid height . A
reference ellipsoid is defined by itssemi‐minor axis and flattening.
1.2.2 Local geodetic frame or tangent frame
In (Seube, 2014), the local geodetic frame (LGF) is used to define the vessel orientation with respect to TRF.
It is defined as follows:
Its origin is the IMU frame origin.
The ‐axis, denoted ‐Northing, points to true north.
The ‐axis, denoted ‐Down, points toward the interior of the Earth, normal to the reference
ellipsoid.
The ‐axis, denoted ‐Easting, completes the right‐handed coordinate system, pointing to east.
The ‐axis and ‐axis lie on the tangent plane to the ellipsoid (which depends on the geodetic
system chosen) at the interest point (see Figure 7 above).
At the end of the 20th century, the error budget estimation of a hydrographic survey system has been the
subject of several studies. Scientists like Erik Hammerstad (Hammerstad, 2001) and Rob Hare (Hare, 2001) have
proposed an estimation method for the error budget of a surface survey system. In 2005, a work group with
representatives from Statoil, Norwegian Hydrographic Service, Blom Maritime, Deep Ocean, Subsea 7 and
Geoconsult (Bjørn & Einar, 2005) has worked on the estimation of the sounding position offset due to the latency
effect between the sensors. The objective of their work was to derive well‐founded specifications on referencing
in hydrographic survey systems. In 2014, a group of researchers (Yanhui, Shuai, Shuxin, Zhiliang, & Hongwei,
2014) have analyzed the error budget of an underwater survey system.
But the most commonly used method in the industry for the error budget estimation of a surface survey
system was developed by Rob Hare in his technical report (Hare, 2001). It is implemented in various data
processing softwares such as CARIS, EIVA, HYSWEEP and QINSy and used by the TOTAL contractors (C&C, Fugro,
Gardline, etc.).The error budget estimation method of an underwater survey system can be used in a similar way
as surface survey system as mentioned in (Bjørn & Einar, 2005) and (Seube, 2014).
The objective of this section is to analyze Rob Hare’s approach and to identify the error sources classically
considered in the error budget estimation of underwater and surface survey systems. The results of this analysis
will be used in part II to propose an error budget estimation method for these systems. This analysis isn’t focused
on sensors error model estimation such as the model proposed by Xavier Lurton of IFREMER for the measurement
uncertainty estimation of MBES (Lurton, 2001). The popular methods of error sources estimation such as
(Hammerstad, 2001) and (Lurton, 2001) will be used in this study. Appendix 5.3 summarizes the methods of
estimation of measurement uncertainties of sensors in real time and post‐processing (Jason & Rob, 2011).
1.4.1 Analysis of the traditional method of the error budget estimation for
surface survey systems
In his technical report (Hare, 2001), Rob hare proposes a simplified method of error budget estimation for a
classical MBES surface survey. It consists in assessing separately the horizontal and vertical total uncertainties of
the sounding position as the square root of the sum of the variances of various uncertainty sources which
contribute to the sounding position. Nowadays, lots of hydrographic surveys are referenced relative to the
ellipsoid, commonly called ellipsoid referenced survey (ERS) (International Federation of Surveyors, 2006). The
position equations of a sounding acquired by the Ellipsoid referenced surveys will be also analyzed in this section.
1.4.1.1 Equations of sounding position for the surface survey systems
1.4.1.1.1 Classical hydrographic survey (Tide)
In the case of a classical MBES hydrographic survey, Rob Hare first expresses the horizontal position of a
sounding , in the local navigation frame and the chartered depth of the sounding relative to a chart datum14 as shown the Figure 11 below (for more information about the chart datum, see (International
Federation of Surveyors, 2006) ):
14A vertical datum is a surface of zero elevation to which heights of various points are referred.
From (Bjørn & Einar, 2005), (Hagen, 2006), (Farrell, 2008), (Groves, 2013), (Seube, 2014) and (Seube, Levilly,
& Keyetieu, 2015), the frame transformation matrix from MBES frame to local navigation frame results of
two successive rotations:
The frame transformation matrix between the MBES frame and the IMU frame and;
The frame transformation matrix between the IMU frame and the local navigation frame .
The resulting transformation is:
, ,, , , , , , ,
This approach is mostly used in the applications such as LIDAR (Gonçalves & Jalobeanu, 2011), mobile 3D
laser scanner and AUV.
According to (Farrell, 2008), (Groves, 2013 ) and (Seube, 2014), two successive rotations cannot be
expressed simply by adding the Euler angles ( , , # , , , , . Then,
the Rob Hare’s approach is not correct. The second approach is right and is more appropriate in hydrography to
determine the matrix rotation from the MBES frame to the local navigation frame. As in a hydrographic survey
system, the roll, pitch and yaw misalignments , , angles between the MBES frame and IMU frame are
determined during the system calibration phase. While, the roll, pitch and yaw angles , , between the IMU frame and local navigation frame are measured by the IMU during the acquisition phase.
The Figure 17, Figure 18 and Figure 19 show the differences between the second approach and Rob hare’s
approach versus the depth, in easting, northing and depth, respectively. These differences are not null and vary
with the misalignment angles between the MBES frame and the IMU frame. Figure 19 below clearly presents that
a yaw misalignment affects the sounding vertical position. Other figures on the misalignments influence of
roll, pitch and yaw can be found in Appendix 7.5.
Figure 17: Influence of the misalignment yaw on ∆ with, °, °, °, ° . °.
In practice, they are very difficult to determine from a classical patch test method (see Table 3 above). As
mentioned in (Seube, Levilly, & Keyetieu, 2015), a classical patch test method first determines the roll, then the
pitch and finally, the yaw misalignment. This implies that the roll misalignment is determined with uncorrected
pitch and yaw. In case of a non‐perfectly flat sea‐floor, pitch and yaw actually contribute to the MBES distortion.
This effect of misalignment angles cross‐talk has the following consequence: the determination of roll
misalignment is biased by unknown pitch and yaw misalignments which impact data used for roll calibration over
non perfectly flat local surfaces. After the roll determination, the pitch is estimated using nadir data over a slope,
therefore without critical impact of roll misalignment error. Yaw misalignment estimation may be biased by the
residual roll and pitch errors since it uses full data over a slope. In practice, the yaw misalignment remains the
most difficult error to estimate. This is due to the fact the patch test procedure uses biased data and makes
inappropriate assumptions.
As the international and intern specifications of IHO and TOTAL are more and more restrictive on the
measurement uncertainty of the sounding vertical position, it is recommended to use automatic calibration
techniques instead of patch test in order to better estimate the misalignment angles between the MBES frame
and the IMU frame. This will significantly improves the measurement uncertainty of the sounding vertical
position.
In addition, from the automatic calibration techniques, it is possible to estimate the standard deviations of
misalignment angles. These standard deviations are necessary to estimate the measurement uncertainty on the
sounding position. The uncertainty propagation law requires that the measurement uncertainty of an input
quantity is its standard deviation and not the maximum error or other value (JCGM, 2008). For instance, if ones
replace each standard deviation of each uncertainty source by2 , the measurement uncertainty of the
sounding vertical position (Z) will be equal2 and not1 . Parameters uncertainties estimations are very
important for improving the total vertical and horizontal uncertainty of a sounding.
Nowadays, the actual measurement uncertainties of roll and pitch misalignment angles , are in the order of 0.1 °, while the yaw misalignment is in the order of 0.7° (Seube, 2014). More details about the
automatic calibration methods can be found in (Seube, Levilly, & Keyetieu, 2015).
1.4.2.2 Uncertainty of sounding position due to the latency between the
sensors
As mentioned in the Section 1.1.1, the latency can be introduced in some sensors as a system accounts for
the time delay over the transmission of different information and their computation. According to (Debese, 2013,
p. 159), the latency between the MBES and the IMU causes the ripples at the outer beams. This because the roll
measured by the IMU at the instant is not the one used for computing data. Consequently, the flat seabeds
become inclined (see Figure 20 below).
This impact is particularly visible in the reliefs when the roll angular rate is high. The Figure 20 below also
shows that the absolute value of the amplitude of these ripples increases as one goes from the central beam to
Figure 20: DTM ripples due to a constant 20 ms INS and MBES timing error for the small surface survey vessel example. The depth is 100 m. The z‐axis is exaggerated by a factor of 10; the error typically varies between ± 0.5 m. For the central beam, the error on a flat seabed is 0 m. On a sloping seabed, time induced errors in pitch, will also cause vertical errors for the central beam‐ (Bjørn & Einar, 2005)
However, Rob Hare’s approach has only considered the latency between the GNSS positioning system and
MBES, while the latency between the MBES and the IMU is not considered as negligible by (Bjørn & Einar, 2005),
(Seube, Picard, & Rondeau, 2012) and (Debese, 2013).
The Figure 21 below presents the latency effect on the sounding position. It shows that the contribution of
the latency between the GNSS positioning and the MBES (in the green rectangle) is less than the latency effect
between the MBES and the IMU (in the red rectangle).
Figure 21: Effect of timing errors for Sjøtroll. The error magnitude is calculated using the vessel coordinates and the error dynamics. Water depth is 100 m. (Bjørn & Einar, 2005, p. 97)
It should be noticed that the results above could be improved because each rotation matrix of each
attitude angle (roll, pitch and yaw) is performed in each frame and not in the same frame. It is then necessary to
make these rotations to better compute the angular rate of each attitude angle. This should affect the skew
symmetric matrix of the angular vectorΩ / . For more details, see (Farrell, 2008).
Figure 24 : Expression of the sounding position in the IMU frame.
From the Figure 24 above, it is clear that the sounding position, resolved about the axis of the IMU frame,
denoted , can be written as follows:
, With,
The matrix is the rotation matrix from the MBES frame to IMU frame, usually called the boresight
matrix. It is described by the misalignment angles (roll misalignmentδφ, pitch misalignmentδθ and yaw misalignment ψ) between MBES frame and the IMU frame.
The calculation of the boresight matrix is performed into a series of three successive rotations and can be
In practice, the lever arms measurements are generally expressed in the IMU frame. In this case, the lever
arms measurements are attached to the vessel frame . This is required to express them in the IMU frame as
below:
The Figure 26 below resumes the different steps used to express the sounding position equations in the
local navigation frame.
Figure 26: Summary of the different rotations (in red), transformations (in blue arrow) and approximations (in green) necessary to determine the sounding position in the local navigation frame.
2.1.3 Reduction of measured depth acquired by a surface survey system
In hydrography, all the depths must be referenced to a common chart datum. Consequently, corrections
must be applied to previous position equations in order to get a chartered (or reduced) depth. The purpose of this
section is to present the equations of sounding reduction for the types of classical and ellipsoid referenced
As mentioned in the Section 1.4.1.1.1 and in the Figure 28 above, the chartered depth acquired by a
classical hydrographic survey is given by the formula below:
is the dynamic draft;
is the measured heave (Heave sensor);
is the measured tide;
is vertical offset between the MSL and the chart datum;
is the vertical offset between a sounding located at seabed and the IMU frame origin;
The vertical offset between a sounding located at the seabed and the IMU frame origin, is denoted . It is equal to the difference between the vertical offset between the seabed and the phase center position of GNSS
positioning system, denoted and the vertical offset between the phase center position of GNSS positioning
system and the IMU frame origin, denoted∆ .
∆
With:
∆ ; With,
The chartered depth becomes:
∆
The absolute sounding position acquired by a classical hydrographic survey can be given as below:
∆
As mentioned in the Section 1.1, the data acquired by the various sensors of a surface survey system are
not synchronous. Latency is introduced in some sensors of the system to take into account the time delay for
information transmission and computation. This creates a non‐negligible offset on the sounding position (Bjørn &
Einar, 2005). The purpose of this next section is to model the offset position of sounding due to the latency in
order to estimate the contribution of its latency measurement uncertainty on the sounding position during the
patch test. The measurement of latency by the classical patch test method is challenging. As an example, a
variation of latency GNSS/MBES of 0.53 s was observed between the start and the end of a bathymetry survey
around Cap Lopez‐Gabon in 2012.
Table 6: Calibration using the patch Test on the vessel Fugro IMPI‐Cap Lopez‐Gabon 2012
2.1.3.3 The dynamic equations of sounding position of surface survey system
The mathematical modeling of the sounding position offset due to the latency between the sensors has
been studied by (Seube, 2014) and (Bjørn & Einar, 2005) in a different way. The proposed approach in this section
is based on the approaches of (Seube, 2014) and (Bjørn & Einar, 2005) . It will allow improving the estimation of
Starting of project 15/12/2012 End of project 17/12/2012
Where: is the difference between the UTC and AUV time references.
For an underwater survey system with an ROV, as all sensors normally remain synchronized to one single
time server, the should be close to zero. In an AUV survey system, time reference drifts by a
magnitude of 50 ms from the vessel time reference when the AUV is submerged (Bjørn & Einar, 2005), see Figure
34 below.
Figure 34: Block diagram of an ROV and tow fish survey system where sensors in the survey vessel and the ROV / tow fish are continually synchronized to the survey vessel Time Server. This is in contrast to an AUV survey system where the AUV is synchronized to the Time Server in the survey vessel only prior to launch. When the AUV is submerged, the AUV clock is dependent on an accurate oscillator to remain acceptably well synchronized‐ (Bjørn & Einar, 2005).
3. The true position of transponder is computed at the TP time as below:
4. The true position of sounding is computed at the MBES time as below:
Figure 35: Total vertical uncertainty for ellipsoid referenced MBES survey. For a depth=250 m, roll=6°, roll uncertainty=0.1°, roll misalignment=0.5°, Latency GNSS/MBES=0.1s, latency GNSS/IMU=0.01, angular rates uncertainties roll, pitch and yaw =0.1°, 0.1° and 0.2 °, roll misalignment uncertainty=0.1° and measurement uncertainties of SVP, SVS are equal 0.25 m/s. The other parameters can be found in Appendix 7.13.
Figure 35 above shows the contributions of each measurement uncertainties of sensors and procedures on
the sounding vertical position acquired by ellipsoid referenced MBES survey. The contribution of an uncertainty
source is estimated by neglecting the other uncertainty sources. It is clear that the measurement uncertainties of
roll and roll misalignment have a significant influence on the sounding vertical position. They increase with the
incidence angle. The latency effect MBES/IMU has a direct impact on the angular rates (more on the roll angular
rate which is the major component of skew‐symmetric matrix (Farrell, 2008), for more details, see in the Section
2.1.3.3.1). It is important to notice that the accuracy of angular rate is approximately equal to the accuracy of its
angle.
An in‐depth analysis of the tool has allowed noticing that it is very important to use an IMU with a accuracy
less than 0.01° in roll, a circular MBES, a good calibration and a latency with millimeter order (it depends on the
vessel size) to better improve the vertical uncertainty of sounding. The TVU for surface survey system is on order
Figure 36 : Total horizontal uncertainty for ellipsoid referenced MBES survey. For a depth=250 m, roll=6°, roll uncertainty=0.1°, roll misalignment=0.5°, Latency GNSS/MBES=0.1s, latency GNSS/IMU=0.01, angular rates uncertainties roll, pitch and yaw =0.1°, 0.1° and 0.2 °, roll misalignment uncertainty=0.1° and measurement uncertainties of SVP, SVS are equal 0.25 m/s. The other parameters can be found in Appendix 7.13.
From it is clear that the yaw uncertainty is the major contributor to the total horizontal uncertainty of
sounding. Moreover, a very accurate calibration of angle misalignments and latencies (GNSS/IMU and
GNSS/MBES) is necessary to significantly improve the total horizontal uncertainty of sounding.
From Figure 35 and Figure 36, ones can conclude that the improvement of hydrographic data processing
softwares, sensors and procedures should be significantly improved the data quality in final survey products.
It is important to notice that this tool takes into account 3 specifications: IHO, IMCA and TOTAL. The IMCA
specifications are similar to LINZ specifications. The user has the opportunity to choose several confidence levels
(TVU and THU) and the MBES shape (linear and circular).
3.2 Errorbudgetestimationofunderwatersurveysystem
The sounding position acquired by an underwater survey system depends on lot more parameters than
with a surface survey system. The measurement uncertainty on the horizontal position is equal to the square root
of the sum of variances of the measurement uncertainty of the transponder horizontal position and the
measurement uncertainty of the sounding position relative to the transponder position. The measurement
uncertainties on the transponder position and the sounding position relative to the transponder are estimated by
applying the law of uncertainty propagation to their position equations described in the in the Section 1.3.3. The
vertical position of sounding is determined in a similar way.
In practice, the transponder position (or underwater vehicle) is usually determined from the acoustic
(DGNSS/USBL) and inertial (IMU) positioning methods, as they have complementary qualities. Acoustic
positioning being characterized by a relatively high and evenly distributed noise and no drift in the position, while
inertial positioning having a very low short‐term noise and relatively large position drift over time (Kongsberg,
2015). Data post‐processing via navigation software (NavLab) allows enhancing the measurement uncertainties
on transponder position by 50% to 70% (Kongsberg, 2015). The yaw uncertainties could be improved by
Figure 1: Sensors and frames of a surface survey system (Bjørn & Einar, 2005)[modified] ............................ 6
Figure 2 Misalignment between MBES frame and IMU frame ........................................................................ 7
Figure 3: Illustration of asynchronous measurements in a surface survey system and Interpolation to MBES
measurement time. (Bjørn & Einar, 2005)‐ [Modified]. The true measurement time is the time at which a data is
measured. The time stamp is the time at which .......................................................................................................... 7
Figure 4 Illustration of sensors frames in an underwater survey system ‐ (Bjørn & Einar, 2005, p. 39) ‐
Figure 6: An approach for position estimation of underwater vehicle with KF‐ (Seube, CIDCO)‐[modified] .. 9
Figure 7: Different frames used in this report................................................................................................ 10
Figure 8: The local navigation frame .............................................................................................................. 11
Figure 9: Error model for a surface survey system (Hare, 2004)‐[modified]. Note that all the errors sources
are not illustrated. ...................................................................................................................................................... 14
Figure 10: Error model for an underwater survey system (Hare, 2004)‐[modified].Note that all the errors
sources are not illustrated. ......................................................................................................................................... 14
Figure 11 : Depth measurement corrections in the case of classical hydrographic survey ‐ (International
Federation of Surveyors, 2006)‐[modified] ................................................................................................................ 17
Figure 12: Depth measurement corrections in the case of GNSS survey‐ (International Federation of
Figure 15 Contribution of different uncertainty sources on the measurement uncertainty of sounding
horizontal position relative to IMU frame origin ........................................................................................................ 20
Figure 16 Contribution of different uncertainty sources on the sounding horizontal position. .................... 20
Figure 17: Influence of the misalignment yaw on ∆ with, 60°, 6°, 1°, 350°andδ0.1°. ................................................................................................................................................................... 22 Figure 18: Influence of the misalignment yaw on ∆ with, 60°, 6°, 1°, 350°andδ
0.1°. ................................................................................................................................................................... 23 Figure 19 : Influence of the misalignment yaw on ∆ with, 60°, 6°, 1°, 350°andδ
0.1°. ................................................................................................................................................................... 23 Figure 20: DTM ripples due to a constant 20 ms INS and MBES timing error for the small surface survey
vessel example. The depth is 100 m. The z‐axis is exaggerated by a factor of 10; the error typically varies between
± 0.5 m. For the central beam, the error on a flat seabed is 0 m. On a sloping seabed, time induced errors in pitch,
will also cause vertical errors for the central beam‐ (Bjørn & Einar, 2005) ............................................................... 25
Figure 21: Effect of timing errors for Sjøtroll. The error magnitude is calculated using the vessel
coordinates and the error dynamics. Water depth is 100 m. (Bjørn & Einar, 2005, p. 97) ........................................ 25
Figure 22: Multi beam echo sounder Surface survey system, frames and lever arms (Bjørn & Einar, 2005)‐
Figure 23: Sounding coordinates in MBES frame expressed in the roll angle convention (the roll angle is
positive when the starboard sinks) ............................................................................................................................ 29
Figure 24 : Expression of the sounding position in the IMU frame. ............................................................... 30
Figure 25 : Expression of the sounding position in the Terrestrial frame (TRF) ............................................. 31
Figure 26: Summary of the different rotations (in red), transformations (in blue arrow) and approximations
(in green) necessary to determine the sounding position in the local navigation frame. ......................................... 33
Figure 32: Estimation of the sounding vertical position acquired by an underwater survey system ............ 40
Figure 33: Estimation of the sounding vertical position acquired by an underwater vehicle using a pressure
sensor close to the USBL transducer .......................................................................................................................... 41
Figure 34: Block diagram of an ROV and tow fish survey system where sensors in the survey vessel and the
ROV / tow fish are continually synchronized to the survey vessel Time Server. This is in contrast to an AUV survey
system where the AUV is synchronized to the Time Server in the survey vessel only prior to launch. When the AUV
is submerged, the AUV clock is dependent on an accurate oscillator to remain acceptably well synchronized‐
Figure 35: Total vertical uncertainty for ellipsoid referenced MBES survey. For a depth=250 m, roll=6°, roll
uncertainty=0.1°, roll misalignment=0.5°, Latency GNSS/MBES=0.1s, latency GNSS/IMU=0.01, angular rates
uncertainties roll, pitch and yaw =0.1°, 0.1° and 0.2 °, roll misalignment uncertainty=0.1° and measurement
uncertainties of SVP, SVS are equal 0.25 m/s. The other parameters can be found in Appendix 7.13. .................... 45
Figure 36 : Total horizontal uncertainty for ellipsoid referenced MBES survey. For a depth=250 m, roll=6°,
roll uncertainty=0.1°, roll misalignment=0.5°, Latency GNSS/MBES=0.1s, latency GNSS/IMU=0.01, angular rates
uncertainties roll, pitch and yaw =0.1°, 0.1° and 0.2 °, roll misalignment uncertainty=0.1° and measurement
uncertainties of SVP, SVS are equal 0.25 m/s. The other parameters can be found in Appendix 7.13. .................... 46
Figure 37: Total vertical uncertainty for AUV survey at 1500 m water depth. Other parameters can be
found in Appendix 7.13. ............................................................................................................................................. 47
Figure 38: Total horizontal uncertainty for AUV survey at 1500 m water depth. Other parameters can be
found in Appendix 7.13 .............................................................................................................................................. 48
Figure 39: Definition of accuracy and precision ............................................................................................. 61
Figure 40 : Difference between random and systematic errors‐ (Exell, 2001)‐[modified] ............................ 70
Figure 41: Vehicle position ‐ (hagen, 2008) .................................................................................................... 81
Figure 42: Depth comparison between as‐built frame elevation and as‐found depth during the AUV
campaign using pressure‐to‐depth conversion with (1) UNESCO formula and (2) observed mean water density. .. 84
6. LISTOFTABLES
Table 1: Symbols of some sensors frames used ............................................................................................. 12
Table 2: Measurement uncertainties of corrected attitude angles from (Hare, 2001) ................................. 21
Table 3: Calibration using the patch Test on the vessel Fugro IMPI ‐Cap Lopez 2012 ................................... 24
Table 4: The considered uncertainty sources by some authors and companies in the error budget
estimation for a surface survey system ...................................................................................................................... 26
Table 5 : The uncertainty sources for an underwater survey system ............................................................ 27
Table 6: Calibration using the patch Test on the vessel Fugro IMPI‐Cap Lopez‐Gabon 2012 ........................ 35
Table 7 : Accuracies and Predicted uncertainties of LBL frames via the error budget estimation tool of
Uncertainty source Method of determination Comments
Sonar range and beam angle Empirically‐derived sonar‐specific model
Provided by Kongsberg; adapted to other sensors using best fit with some field data
Roll, pitch, heading and heave Motion sensor manufacturer's specification for instrument
A priori (estimated in advance)
Boresight of roll, pitch and yaw Usually, half the manufacturer's specifications for the motion sensor, but sometimes same uncertainties as motion sensor
A priori
Dynamic draft Educated guesswork, possibly based on some squat tests and repeated measurements of the vessel under different loading conditions
A priori
Surface sound speed SVP manufacturer's specification for instrument
A priori
Sound speed profile Simple two‐layer uncertainty propagation based on estimate of spatio‐temporal change since last cast was taken
A priori
Tides or water levels (vertical datum)
Educated guess work depending on quality of constituents, proximity to nearest gauge, method of spatial prediction
Provided by tidal analyst on a case‐by‐case basis
GNSS positioning system Manufacturer's specification for instrument and positioning method or software used
A priori
Sensors lever arms Estimated standard deviation of coordinates for sensors
Based on method used to survey in each sensor in the boat coordinate system (e.g. cloth tape, Electronic Distance Measurement (EDM), photogrammetry)
Latency correction Estimates only Fixed value, perhaps based on some testing
Table 9: Status of uncertainty source estimation today‐ (Jason & Rob, 2011)
Uncertainty source
Method of determination
Comments Status
Sonar range and beam angle
Sound theoretical model based on real S/N of each instrument (Lurton QF)
Implemented for RESON and Kongsberg beam‐forming sonar systems, with other manufacturers slowly getting on board
Work in progress. Still need an estimate of sonar angular uncertainty. Still work to do on phase‐measuring bathymetric side‐scans
Roll, pitch, heading and heave
Real‐time and post‐mission estimates
E.g. POS/MV, True‐Heave, POSPAC MMS
Need more motion sensor manufacturers to get on board
Boresight of roll, pitch and yaw
Realistic outputs from e.g. SeaCal
Based on least‐squares estimation approach
Essentially solved, although estimates may be a bit optimistic
Dynamic draft Use an ERS approach Some uncertainties introduced‐ see below in table
Can be eliminated, but the uncertainty of datum separation models requires more research
Surface sound speed
SVP manufacturer's specification for instrument
Real‐time measurement at the transducer face, apply to beam steering/forming in real‐time
Essentially solved
Sound speed profile
Rapid sampling of spatio‐temporal sound speed structure, using e.g. MVP
Use uncertainty wedge analysis to estimate realistic values for amount to uncertainty introduced
A controllable uncertainty source overall but extremely dynamic oceanographic environments
Tides or water levels ( vertical datum)
Use an ERS approach But, we introduce new uncertainties, see below in table.
Can be eliminated, but uncertainty of datum separation models requires more research
GNSS positioning system
Real‐time and post‐mission estimates
e.g. POS/MV, delayed heave, POSPAC MMS
Need more positioning / motion sensor manufacturers to get on board
Sensors lever arms
Estimated standard deviation of coordinates for sensors
Proper over‐determined sensor survey with output variance‐covariance matrix of coordinates
Can be computed effectively
Latency correction
Can be eliminated, or at least reduced to negligible quantitiy if precise time protocols are used, or similar approaches to precisely synchronize all sensors
IEEE 1588‐2002 PTP based on a network time protocol that effectively eliminates dynamic motion residuals due to small timing errors in the instrumentation.
A solvable problem with some hardware and software
Dynamic lever arm
If using ERS approach, need to model uncertainties in roll, pitch, lever arm, in order to reduce
On the earth surface, the gravitational acceleration is not constant. It varies due to number of effects the
major effects which are:
1. The rotation and oblateness of the Earth: the rotation of the Earth reduces the force that the
underwater vehicle feels. (It would therefore feel lighter at the equator than at the poles of the earth).
Also, the rotation causes the Earth to be shaped like an oblate spheroid (flattened sphere – flatter at
the poles), which means that the radial distance you are from the center of the Earth (and hence
gravity) varies depending on where you are on the surface. Both of these effects vary with latitude). The variation due to the Earth’s rotation is on the order of 0.03 / .
2. Elevation above sea level: At higher elevations, the vehicle is further from the center of the Earth, so
the Earth’s pull is less. How big is this effect? At an elevation of about 1000 m, gravity reduces by
about0.0001 / . See Figure 41 below.
Figure 41: Vehicle position ‐ (hagen, 2008)
The gravitational acceleration formula is given by:
, 1
Yet,
, 1
Where:
is the international equation of gravity at the surface;
is the vertical gradient of gravity in ;
is the vertical gradient of gravity and is equal 2.18410 / / (UNESCO/SCOR/ICES/IAPSO,
1983).
It varies with the reference ellipsoid.
7.11.1.4 The hydrostatic equation
The underwater vehicle vertical position is inferred by integrating the hydrostatic equation below:
, , ,
The pressure equals to the weight per unit area of the water and the atmosphere column above the
ocean 35, 0, . The specific volume anomaly is about 2 m or less. A simple quadrature rule like the trapezoidal
rule is sufficient for the numerical integration task (QPS, 2013).
∆ , , 35, 0,
, ,
∆12
7.11.2.2 Empirical formula
It supposes that the sea water density in the water column is equal to the water column mean density.
7.11.2.2.1 Algorithm of Empirical formula
Based on the previous analysis, the hydrostatic equation can be written as following:
1 , , 0
1 , , 0
, , , , 0
This term , , , , has been neglected by most of companies. It can also
compute by a numerical integration as the next correction term of UNESCO formula for that this empirical formula is
very accurate.
7.12 ComparisonbetweenUNESCOandTritechformulas
Figure 42: Depth comparison between as‐built frame elevation and as‐found depth during the AUV campaign using pressure‐to‐depth conversion with (1) UNESCO formula and (2) observed mean water density.
Ecole Nationale Supérieure de Techniques Avancées Bretagne
Final Year Project in HydrographyAuthor: Geraud NAANKEU WATI Promotion 2015
Title: Error budget analysis for hydrographic survey systems; comparative study of methods and existing softwares; implementation on an inspection campaign of pipelines by AUV.
To install subsea infrastructures (pipelines, subsea wells, etc) necessary for the development of hydrocarbon resources, TOTAL regularly contracts hydrographic companies to perform hydrographic surveys. These companies mainly use two types of hydrographic survey systems: surface survey systems (generally used in near shore and in shallow water (0‐100 m)) and underwater survey systems (generally used in offshore and in deep offshore (100‐3000 m)). Each company has its own method to estimate the error budget of a hydrographic survey system. Their method is usually based on the law of uncertainty propagation (Hare, 2001). This work’s objective is to study and compare various methods of error budget estimation used by TOTAL contractors and other existing tools on the market, in order to better qualify the hydrographic data. The state of the art of classical error budget estimation methods of these systems and the analysis of their limits have allowed to propose an estimation method of error budget for the surface and underwater survey systems. This work also contributes to improving the sounding position acquired by underwater and surface survey systems, demonstrating the yaw misalignment influence between the inertial sensors (IMU, etc) and proximity sensor (MBES, etc) on sounding vertical position, stressing the importance of automatic calibration methods relative to the classical method of patch test and clarifying the issue on the methods of conversion from pressure to depth.
Key words: Error budget, Positioning, Law of uncertainty propagation, Surface survey system,
Underwater survey system, Total Propagated Uncertainty, Multi Beam Echo Sounder, Underwater Vehicle.