Dynamic calibration of multibeam systems

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Dynamic calibration of

multibeam

systems

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Jeroen Dunnewold

DEOS Report

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Dynamic calibration of multibeam systems

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Dynamic calibration of multibeam systems

J

eroen Dunnewold

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Published and distributed by: Delft University Press P.O. Box 98 2600 MG Delft The Netherlands Telephone: +31 15 2783254 Telefax: + 31 152781661 E-mail: DUP@DUP.TUDelft.NL ISBN 90-407-1824-5 Copyright 1998 by DEOS

All rights reserved. No part of the materiaI protected by this copyright notice may be reproduced or utilized in any form or by any means, e1ectronic or mechanical, inclu-ding photocopying, recording or by any information storage and retrieval system, without written permission from the publisher: Delft University Press.

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-Summary

Multibeam echosounding is a relatively new acoustic technique to obtain the relative or absolute position of points underwater. The system uses the measured two-way-travel-time of the acoustic signal to calculate the coordinates of the point on the sea bottom from which the signal returns. In contrast to already longer existing singlebeam echosounders multiple beams are submitted at once using a fan-shaped beam-pattern. During the last few years the accuracy and error-propagation of this system has been investigated thoroughly, but little has been done with the validation of the system.

One way of validating the system is to do extensive calibrations in advance of a measurement campaign. Existing calibration methods can be subdivided into a dynamie and statie part. In this thesis the dynamie calibration procedures have been studied. The present calibration methods do have a few important disadvantages, which may be the reason to develop a new approach of calibration. The result of a better calibrated multibeam device would be better or more valid end results.

Therefore the main question of this research is:

Is it des ira bie and possible to develop a better approach of dynamic calibration of multibeam systems and if so what is the practical value of this method compared to the presently used procedures?

This question can be divided into three sub-questions:

1. What is the presently used method for dynamie calibration of multibeam systems and what are its advantages and disadvantages?

2. Is it possible to develop a better approach for calibrating?

3. What is the practical value ofthe newly developed method when compared to the presently used procedures?

As a result of this division, the research was done in three parts. At first a literature study is performed in order to study the currently used methods for dynamic calibration of multibeam systems, and describe its advantages and disadvantages.

During the second part a new approach for dynamie calibration of multibeam systems is introduced from a theoretical point of view, while the last part consists of experiments using simulations with MATLAB in order to test the new procedure.

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The present method of dynamic calibration of a multibeam system determines each parameter in consecutive steps. The method starts with determining one parameter by using a specitic measurement configuration with two survey lines, which isolates this first effect. The displacement between the two measured objects gives the calibration parameter. When the measurements are corrected for this error, the second parameter is calibrated by using another measurement configuration of two lines. This configuration now allows the previous error to be present, because it is assumed that this error is removed completely. The second error is then determined and removed and the complete procedure repeats itselfuntil all parameters have been determined.

The disadvantages of this method are evident. If all parameters could be solved using only one model of observations, it would be very easy, using the Delft method of adjustment to derive values, which indicate the precision or intemal and extemal reliability of the determined parameters. Another disadvantage of using separate steps is the possibility that undetected parts of a specific parameter are assigned to another parameter. Both disadvantages could be prevented if a method would be used which calculates all unknowns in one single step. Another reason for developing a method, which solves all parameters in a single step, is that it is to be expected that the number of survey lines needed for the calibration is reduced.

For this reason a new and different approach is used to calibrate the multibeam system. This approach uses the absolute displacement between the measured object and real one, which has a known position and shape. In this approach the influence on the measured surface of each ofthe calibration parameters is calculated with a derived formula. This formula is derived under the assumption that the multibeam device is measuring locallevel (no initial movement ofthe vessei).

The deveioped method was tested using a simulated environment. Three tests have been done. One test was done to indicate which measurement configuration was most optimal from four chosen configurations. One of them being the minimal configuration of two measurement lines and the other three with two extra survey lines. This shows that a configuration which uses survey lines run back and forwards is the most optimalof the four tested ones. The second test was to indicate the influence of a different slope-angle in the underwater-threshold used for the calibration. The test results show a big improvement in the accuracy of the determined calibration parameters with increasing slope-angles. The third test was done to indicate the influence of increasing the measurement frequency of the multibeam device. The results of this test indicate that when the frequency is doubled the standard deviation increases with about the square root of two. On average it can be conc1uded that the tests show that under the given conditions and circumstances the proposed procedure is able to determine the calibration parameters with good standard deviations in the most optimal situation.

Final conclusions

It is possible to calibrate the multibeam device dynamically by applying the newly developed method. This method is however developed under the assumption that the multibeam device is measuring roughly at local level, except for the unknown

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calibration parameters. Whether it is desirabie to use another approach depends on a

few aspects. The accuracy values of the currently used calibration methods show that

the errors made by this method Can be considerably large. This does not mean however that the errors on the final results, which are the coordinates of the sea bottom, are large as weil. When measuring in very shallow water and with a relatively flat sea bottom, or when the desired accuracy values are not set too high, the present method suffices. The developed method on the other hand has the big advantage of

providing possibilities to assess the 'accuracy and reliability' ofthe calibration, which

may be a reason to use the method anyway. Besides this, the new procedure needs

less survey lines to solve for the six parameters and this may lead to a better accuracy using the same amount of data.

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Chapter 1 Intro ducti on

A relatively new system in the field of underwater acoustics is the so-called multibeam

system. This system can be used to obtain the geometry of the sea bottom be10w the vessel on which it is mounted. Information about the geometry of the sea-bottom is important and can be used for many applications e.g. dredging or making bathymetric maps.

In contrast to the traditional echosounder, which uses only one vertically aimed beam, multibeam is able to measure much more data during a shorter time-interval, because it transmits many beams simultaneously. The multibeam system however has to cope with a lot of extra errors, as a consequence of the fan-shaped beam-pattem. The propagation of these errors into the resulting 3D coordinates and the precision of the multibeam measurements are aspects, which have been investigated thoroughly the last few years. The subject of this thesis however is the calibration ofthe multibeam system.

Calibration of a multibeam system is essential, because even if the system is measuring a correct range it can still measure an erroneous geometry, because the system's motion sensors may not be correctly aligned with the multibeam system. Calibration of underwater systems is however not very easy, because the measured geometry should somehow be related to the real known geometry. In order to solve this problem a known calibration object can be used.

Present calibration methods have a few important disadvantages, which may be the reason for the development of a new and better approach for calibrating multibeam systems. The result would be more accurate multibeam data with a higher quality.

Therefore the main question ofthis research is:

Is it desirabie and possible to develop a better approach of dynamic calibration of multibeam systems and if so what is the practical value of this method compared to the presently used procedures?

This question can be separated into the following sub-questions:

1. What is the presently used procedure for dynamic calibration of multibeam systems and what are its advantages and disadvantages?

2. Is it possible to develop a better approach for calibrating?

3. What is the practical value of the new developed method when compared to presently used procedures?

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As a consequence the research can be divided into three separate parts. At first a literature study, which is performed to study the existing methods of calibration of multibeam systems. In the second part a new approach is introduced from a theoretical point of view, while the last part consists of experiments using simulations with MATLAB in order to test the new calibration procedure.

This report is divided into seven chapters. The second chapter gives an overview of the field of echosounders in general and provides an introduction to the multibeam system specifically.

After this more general introduction it is possible to discuss the multibeam system more profoundly. In chapter three various coordinate systems involved win be discussed as wen as the error budget of multibeam. The systematic errors can be calibrated using procedures, which are described in chapter four, using the procedures of Rijkswaterstaat. These procedures however have a few disadvantages, which can be solved when using a different approach. In chapter 5 a new method for dynamic calibration of multibeam systems win be presented, while chapter 6 contains various test results to judge this new method and find an optimal procedure. The last chapter finally gives the conc1usions and recommendations.

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Chapter 2 Principles of multibeam

Acquiring topographic data underwater can be done using a variety of instruments. Section 2.1 gives a short overview of the different types of available echo sounders. All instruments have in comrnon that they send out an acoustic signa! and deterrnine coordinates of its target underwater by using the signal's travel time and exit angle. In this study, the multibeam echo sounder has been used. The characteristics ofthis device will be described in section 2.2. In section 2.3, different methods of deterrnining signals exit angle and travel-time are presented. The last section of this chapter contains a comparison of three often-used multibeam systems in a tabie.

2.1 AN OVERVIEW OF EXISTING ECHOSOUNDER TYPES

Many different types of echosounders exist nowadays. This section gives a short overview of this area. One possible division of existing bathymetric systems is:

I. The classical singlebeam echo sounder, which measures only one point, with a small footprint, by emitting a singlebeam vertically downwards;

2. More sophisticated systems, which measure (almost) simultaneously multiple points, or actually cells, at once.

The latter type of systems, which are able to measure a complete swath at once, can be subdivided in three different groups:

a. Multiple echosounders, which are mounted in a row on a boom and emit their beams at the same time straight down over a complete swath. An example of such a system is the Bomasweep (see e.g. Harre 1992);

b. Mu/tibeam systems, which are usually mounted be10w the ship's huil and produce a fan-shaped beam pattern. Many beams are emitted at once using beamwidths of approximately 2° angle in cross-track direction (see e.g. Blacquière, 1995). Examples of this type are Fansweep, which uses a V -shape array or the devices of Seabat and Sirnrad, which use cylindrical arrays (see for different types of arrays figure 2.2);

c. Interferometric systems, which use phase shifting to discriminate between the signals returning from different angles (see e.g. Moustier, 1988). These systems

are mostly mounted on a side scan tow-fish. One example is Bathyscan.

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In literature, the use of the words swath sounding and multibeam echosounding is sometimes very confusing. Swath sounding uses only one broad beam, while multibeam emits many narrow beams at once.

2.2 THE MULTIBEAM SYSTEM

History of the multibeam system

Obtaining information of depths of rivers and near-shore waters is one of the activities of

Rijkswaterstaat, which is the Dutch Directorate-General of Public Works and Water Management. These depths can he used to produce bathymetric maps useful for e.g. dredging or hydrographic maps. One very old system and predecessor of the multibeam system, for determining depths is the traditional echosounder. Already in 1912, a system existed based on this principle. A big disadvantage of this type of echosounder is the rather low density of data that will be attainable. This will prevent you from getting a good picture of the sea bottom. SONAR on the other hand wiB be able to give you a good image of the underwater scenery, but fails to give depth coordinates. A re1atively new development in this area is the multibeam system. The tirst operational fan-shape multibeam system appeared around 1975. The main advantage of a multibeam system is the larger amount of data covering a larger area, which can be collected during a shorter time interval. This does not only provide a dense sampling and therefore a more reliable image ofthe underwater-topography, but also a tooI to check the measured depths, with help of neighbouring measurements.

Principle of mu/tibeam

Many different designs of multibeam systems exist, but they are all based on the same principle. A large array of transducers emits many beams of acoustic pulses simultaneously. Depending on the waterdepth, the speed of the vessel and the beam angle, it may be possible to cover swaths up to 7 to 8 times the waterdepth below the transducer.

Due to diffraction, only a small part of the emitted energy wiIl return to the transducer. Diffraction causes acoustic energy to be spreaded in all possible directions as a result of irregularities on the sea bottom. For a profound description of diffraction, consult a textbook about underwater-acoustics, e.g. Urick (1975). The signal's travel path can be determined by measuring the two-way travel time and using knowledge about the speed of sound along the travel path. This di stance is called the slant-range. Together with the measured exit angle of the beam, it is now possible to determine a depth coordinate relative to the transducer's position in swath direction. These in principle two-dimensional local coordinates can be linked with agiobal coordinate system by using e.g. GPS measurements. The formulas for determining the coordinates of the sounding will be given in chapter 3.

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Figure 2.1: The principle of multibeam measurements

Possible errors

During the whole measurement process numero us things can go wrong and introduce errors in the resulting coordinates. These errors can be of random and systematic nature. One example of an error source is imperfect knowledge of underwater speed of sound. Besides this, transitions between salt and fresh water, which causes the beam to change direction according to Snell's law will introduce errors. Another problem concerning measuring with a ship is, of course, the movement of the vessel. Although these motions, like pitch, roll, yaw and heave can be measured by the motion sensors, there will still be some errors left. This is just a small selection from the large group of possible errors. Most of these errors will be discussed in chapter 3 as well.

Performance of multibeam

According to Moustier (1988), existing multibeam systems can be divided into shallow water, medium-depth water and deep-sea systems. The decisive factor for the attainable depth range of an echo sounder is the frequency. This results in the following division:

1. Shal/ow water multibeam sounders using frequencies ranging from 100-300 kHz, which have a depth range from almost 0-100 metres below the transducer;

2. Medium depth sounders with frequencies between 30 and 90 kHz, which can measure at depths between 100-1500 m;

3. Deep-sea systems, which are used to explore the bottom of the deep oceans, generally use frequencies below 10-15 kHz.

Frequency is the decisive factor, as mentioned earlier, when determining the performance of a multibeam echo sounder. This is due to the fact that sound attenuation is frequency dependent. The higher the transmitted frequency the greater the effect of attenuation. This is why a statement about the coverage range to which it applies, should always accompany a quality

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value about performance.

Another important factor, which determines the amount ofbackscattered energy, is the material of the sea bottom. Mud for example will have Ie ss backscattering power as sand bottom. This can also be seen from the signal's point of view. The higher the frequency, the more backscatter, because now the sea-bottom becomes relatively more rough, due to smaller wavelengths. Sirnrad's EM950 for example uses a relatively low frequency of 95 kHz, which causes the system to have troubles with muddy sea bottoms. Harre (1992) gives some values of depth performance with 100% coverage (swath width equals water depth) in relation to the specific frequencies:

Table 2.1: Depth performance with 100% coverage

2.3 THE

OB SERV ABLES OF MUL TIBEAM

This section will discuss the two observables of multibeam, which were already mentioned in the previous section, more profoundly. The first one is the direction ofthe emitted signa! and the second one is the signal' s travel time. They will be discussed in sections 2.3.1 and 2.3.2 respectively.

2.3.1 BEAM STEERING

The process of determining the direction of the energy of a beam is called beam steering. Beam steering can be done during transmission, or after reception. The first is called directional transmission, while the latter is directional reception. It is also possible to combine the two methods.

According to Harre (1992) three kinds of configurations can be distinguished when considering hull-mounted multibeam systems:

1. Line array type transducers;

2. V-shape transducers, e.g. the Fansweep system; 3. Cylindrical arrays, e.g. the EM950 and Seabat 900112.

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v u

V-shape _Cylindrical Lineair

Figure 2.2: Three existing types oftransducer arrays

Depending on which type of array is used, two possibilities to steer a bearn in a specific direction exist. This can be done using travel-time delays, or using the shape of the array combined with the travel-time delays. The choice between the two methods is only a matter of practical considerations, because it does not change the attainable accuracy.

Trave/-time delays

One possibility to steer a bearn in a specific direction is to use uniquely determined time delays for every transducer in the array. In figure 2.3, the principle is explained. Every transducer in the array is used to steer a bearn. By changing the delay for each transducer a bit, a bearn is formed in a certain direction. This can be repeated to form all bearns for the complete swath. All these bearns together are called one sweep.

The time delay needed for the signalof a specific element to achieve a bearn angle {} can be calculated, Blacquière (1994):

with,

xsin{}

t =

-c

x : Distance between two transducers c : Signal's travel speed

(} : Bearn exit angle

(2.1)

This implies that an erroneous value for the speed of sound gives consequently a wrong value for the time-delay. That will result in an error in the direction of the bearn, which follows from formula 2.1 (because x is a constant).

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Figure 2.3: Beam steering using travel-time delays

Combining the shape of the array with travel-time delay

Cylindrical arrays, as those of Simrad and Reson, make it possible to use the shape of the array combined with the above-mentioned possibility, of delaying the travel-time for each transducer separately. In this case, the array-element that is already orientated in the right direction is used combined with its neighbour-elements on both sides. In contrast with the previous method, the angle of the beam is independent of the speed of sound directly near the transducers. The width of the beam on the other hand is influenced by the speed of sound when the assumed speed of sound is different from the real speed of sound. The errors are not very large (hundreds of degrees).

2.3.2 TRA VEL-TIME DETECTION

After determining the direction of a retuming beam, the system still has to determine the signal's travel-time. This can be done using two different methods. One is called amplitude

detection, the other one phase detection. Both have their advantages as well as their disadvantages, which will be discussed hereafter.

Amplitude-detection

The first method is amplitude detection, which uses amplitudes to determine the travel-time of the echo. Determining travel-time in this way can be done using three different methods. Every method will first define a time-window in which the retuming echo is expected. This avoids false echoes as a result of e.g. fish. This time-window is usually determined with help of the previously received signal. Figure 2.4 shows the principles of the three possible methods.

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A. The first method uses a threshold to determine the exact travel-time. When the signal exceeds a certain value, the travel-time is determined. This method is in relation to the second method quite sensitive to noise. The method can also,result in erroneous measurements for large angles. It can however be corrected in a

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calibration procedure, because it is a systematic offset. The threshold method provides the best performances directly under the vessel (for the middle beams). This is because the difference between the middle point and the edge of a footprint is not too big. The threshold method is used by the Reson company for their multibeam systems 9001/2;

B. The second method uses the eentre of gravity of the backscattered energy of the signal to determine the travel-time of a particular beam. This is the most advanced method. This method also needs uniform distributions of the scatterers, but provides better results because it 'averages out' the data. This method is used for the EM950 as weil as for the Fansweep;

c.

The third method uses the travel time, which corresponds to the maximum amplitude of the signa!. No systems exist in practice, which uses this method because it is very sensitive to noise. Scatterers are supposed to be divided uniformly over the beam's footprint. When this is not the case, the travel-time that is detected will be different from the travel-time to the mid-point ofthe footprint.

Energy axis

Threshold

A

=

Threshold detection B = Centre of gravity detection C = Maximum amplitude detection

A B C

Time-window

Figure 2.4: The three possible methods for travel time detection

Time axis

It turns out that errors made using amplitude detection with the most advanced method, which

is the centre of gravity method, remain small for small exit angles. For larger exit angles however the errors increase to unacceptable heights. Blacquière (1995) gives some values for this: angles larger than 65° result in depth errors of 10 cm, while the lateral error (horizontal

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Phase-detection

The other method used for travel-time detection is called phase detection. This method is

more suited for detecting the travel-time of the outer beams. It is therefore a good option to

combine the two methods and use an amplitude method for the inner beams and the phase detection method for the outer beams. The Sirnrad EM 950 for example uses such a hybrid method. This results in a better detection of the trave1-time, which will of course influence the quality ofthe final results.

The principle of this method is based on the interferometric idea of determining phase differences, which can be converted into differences in travel-time. The array will (usually) split itself up into two separate parts, which each send a beam to the same spot on the bottom. The two beams will return with slightly different phase angles. To determine the correct travel-time, a time-window is defined where the signal is expected. In this time frame the phase difference is determined and plotted as a function of time. The zero-phase crossing

determines the correct travel-time (the mid-point signal). When this method is used for the

middle beam almost vertically under the vesse1, the zero-phase crossings are hard to determine, because in then the phase differences are smal!. For this reason amplitude detection

is a better choice for these beams. The advantage on the other hand of phase detection is the

small signal-to-noise ratio, caused by averaging out the signal's energy.

2.4 COMP ARISON OF SOME DIFFERENT MUL TIBEAM SYSTEMS

In this last paragraph of this chapter, some characteristics of three in practice often-used

multibeam systems are compared. Some of the information in the table below has already

been mentioned in the previous sections. Most of the information is taken from Blacquière

(1994) who did a comparison of different multibeam systems.

This concludes the chapter about the principles of the multibeam systems yielding depth information relative to the point of transmission. A logic next step is to combine this range system information with attitude and position information of the measurement system, which is the subject ofthe next chapter.

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Chapter 3 Coordinate determination and error budget

Before starting to analyse the error budget of multibeam, it may be convenient to define every coordinate system involved. These coordinate systems can be divided into three categories: Systems tied to the vessel, systems tied to the different sensors and finally a coordinate system tied to the entire earth. With help of these coordinate systems, the forrnulas for calculation of the coordinates, resulting from the multibeam measurements are presented in section 3.2. The last section of this chapter will discuss the error budget of multibeam. For each error its influence on the resulting coordinates is given. This will be used later in following chapters, which deal with calibration of multibeam systems.

3.1

COORDINA TE SYSTEMS

This section will describe the various systems involved, starting with the vessel-tied systems, then continuing with the sensor-tied systems and ending with the mapping systems. After this section the forrnulas to relate the various systems are given.

3.1.1 VESSEL SYSTEMS

Bodyframe

This coordinate system describes the relative positions of all the sensors and antennas on the vessel. The origin of this body-frame can be chosen arbitrary. It is a good idea however to choose this origin at an identifiabie point that can be found again. This means that the centre of gravity is not a good point. The u-v plane is perpendicular to the waterlevel of the ship. The u-axis is defined with the line pointing from the stem towards the bow of the vessel, with positive u towards the bow. The positive v-axis points towards the port side of the vessel. The w-axis completes a right-handed coordinate system. The positions of the different sensors in this body frame can be measured with standard surveying techniques like tachometry.

Locallevel

Each sounding results in a three dimensional vector with respect to the body system. The vessel however is not a very static object, with respect to the sea bottom and will be subject to three rotations (see figure 3.1). These rotations, which are called pitch, roU and yaw, will be described more profoundly further on in this chapter. The local level system is the resulting coordinate system after rotating about the three orthogonal coordinate axes of the body frame with -Cl, -~ and -y according to forrnula 3.2. This results in a system, which has its origin at the same place as the body-frame, but with the V -axis pointing to RD-North, the z-axis upwards

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' b t d F l l b l l l l l W I I Y 11

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parallel to the local vertical and the U-axis axis East. The resulting vector in the local level system is a first step towards calculation of coordinates in the global reference frame. This will be discussed below.

W-axlS" _Yaw_(y)

U-axlS

Pitch (C()

Figure 3.1: The three possible rotations of the vessel

3.1.2 SENSOR SYSTEMS

Surveying with a multibeam system does not only involve data from a multibeam device, but also brings along measurements from a variety of other sensors and antennas recording all at different time-intervals. All these data is post-processed in an integrated fashion, using for example NESA's PDS 1000 or QPS' QINSy. Possible sensors and antennas are motion sensors, which measure the ship's attitude, and the GPS receiver, which measures the vessel's position at a certain time-interval.

The measurements of the motion sensors, the

aps

antenna and the multibeam device can be described using separate coordinate systems for each device. The ideal situation would be that these sensor systems are correctly aligned with the body frame and would have a correctly known position in the body frame. This is however, as often when ideal situations are involved, not the case. The sensor systems are influenced by bOth random errors, because every measurement device has a limited accuracy, and systematic errors. Systematic errors have a certain, constant or periodic correlation in time, which makes it possible to identify the error and remove it during post-processing.

If a systematic error exists due to misalignment of the sensor-system with respect to the body frame, it will be represented by the rotation angle added to (the constantly varying) three rotations 11, ~ and y. Rotations due to misalignment are not the only possible cause of

differences between the sensor systems and the body frame. The sensor system can also have a systematic offset, for example due to time delays, geometry errors or an erroneous speed of sound.

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The rotations and translations, which represent systematic errors, can be calibrated prior to the measurements, using the so-called standard procedures for multibeam calibration. These standard procedures wil! be described in chapter 4.

3.1.3. MAPPING SYSTEMS

Making bathymetric maps of the Dutch rivers and coastal waters requires regional coordinates, which allow comparison ofthe sounding's position on the sea bottom with points ashore. Many different regional coordinate systems are in use, both horizontal and vertical coordinate systems.

The most often used system for horizontal coordinates in The Netherlands, is the

'Rijksdriehoeksstelsel' (RD). This is a coordinate system based upon the ellipsoid of Bessel.

It has a known transforrnation with the WGS'84 coordinate system, which is the global

reference system for GPS measurements.

Many other systems are in use outside the Netherlands. These systems use different mapping forrnulas and ellipsoids, which may fit better to the local geographical situation. In any case, it is important to know the exact transforrnation ofthis particular system to the WGS'84 system.

For vertical coordinates different approaches may be used which depend on the

method used for height deterrnining. The most popular method used lately is height deterrnination with Differential GPS. GPS measures heights with regard to WGS'84, while

the desired heights are NAP-heights. The latter are heights with respect to the geoid, which is

an equipotential surface ofthe earth's gravity field. The measured GPS height consists oftwo

parts, the height of the ellipsoid and the height of the geoid, with regard to the ellipsoid. This means that the geoid is the link between the NAP-heights and WGS'84 heights. The second method to deterrnine height coordinates uses the actual water level at the time of measurement. This actual water level can be related to a defined mean sea-Ievel. This mean water level is monitored at several measurement points and deterrnined with regard to NAP. The differences between the actual sea-level and NAP are time-dependent.

3.2

EQUATIONS FOR DETERMINATION OF DEPTH AND POSITION COORDINATES

As it was shown in the previous section the whole process of measuring with multibeam involves many different coordinate frames. These systems can be related using transforrnation

fonnulas. This section will present these forrnulas. The first one is the transforrnation from the

actual multibeam measurement frame to the body frame of the vessel. This body frame can be rotated to align it with the locallevel system. Finally a transforrnation to some kind of global reference system can be perforrned.

Relating the multibeam measurement with the body frame

The depth and position of a particular sounding in the body frame can be ca\culated with very

basic geometric formulas, which is shown in figure 3.2:

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[: ] = [ r

s~n

8]

w -rcos8

(3.1)

r

(u,V,w)

Figure 3.2: The actual multibeam measurement

The first observabie is the measured two way-travel time. The range r, which connects the origin and the measured point (u,v,w) can be calculated by multiplying the measured sound speed with half the two-way travel time. The second observabie is the exit angle of the specific beam. Together these two parameters give the coordinates u,v,w in the body frame, with formula 3.1. It can be noticed that the u-coordinate is per definition zero and the measurement system is in fact a two-dimensional system.

Relating the body frame with the locallevel system

To transform these equations from the non-level body frame to the local level system they have to be rotated back around the three axes with the negative rotation angles to form the local level system. This transformation is different at every epoch and can be done using different sequences, e.g.:

[~L

=

{R,(-Pl R,(-rl R,(-ant]

(3.2)

The origin ofthe locallevel system is equal to the origin ofthe body-frame. It is assumed that the zero direction of the INS system is the North-direction of the RD-system. The V -axis is now pointing to the RD-North, the second axis to the East and the third is pointing parallel upwards to the local vertical.

Relating the locallevel frame with RD/NAP

These local level coordinates can be transformed into RD-NAP coordinates. Therefore the height of the transducer with regard to NAP and the translation from the local point to the origin of RD at every epoch t, should be known. This information can be acquired with help ofthe GPS measurements (see e.g. HTW (1996) or Strang van Hees (1993) for information

about height systems and transformations from the WGS '84 coordinates to RD). The

transformation can symbolically be written as follows:

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With dx, dy the translations from the transducer point to the origin of RD and dz the height of the transducer with regard to NAP. lt is also possible to ca1culate first the coordinates in WGS'84 and with a transformation afterwards to RD/NAP.

3.3

MUL TIBEAM ERROR BUDGET

Multibeam has many potential errors, which can influence the results. These errors can be either systematic or random (see for a profound description ofthe error propagation e.g. Hare (1995)). When a systematic error occurs in the final coordinates it may be possible to find it using a smart calibration procedure. These procedures will be described further on in this report. This section willlist the possible systematic errors and gives an idea oftheir influence on the resulting coordinates.

3.3.1 YAWBIAS

The so-called yaw movement is the rotation around the vertical z-axis. Figure 3.3 shows the consequences of a yaw-bias, which is sometimes also cal!ed swath misalignment. Due to a misalignment of the coordinate system tied up to the gyrocompass and the body frame systematic errors are introduced, which cause the complete swath to make an oblique angle with the ship's track. lt can easily be ca1culated that the propagated errors as a result of a yaw bias can be large, depending on the geometry of the sea-bottom. A measurement at a water depth of lOm with a swath width of 4 times the depth and a yaw-bias of 0.1 degree wil! re sult in a horizontal error at the end of the swath of about 3.5 cm. Because a horizontal displacement is existing, which is unknown to the system, an incorrect vertical coordinate will be placed on the sounding's computed position in case of a non-flat measuring area. This is an important concept when considering calibration of multibeam systems. The resulting effect on the z-coordinate can be large, depending on the present slope in the sea-bottom. For example: A slope of 45" propagates this horizontal error, resulting in a wrong z-value of 3.5 cm as weil. In chapter 4, a table will be presented providing some more examples.

measured line computed line

y

vessels

---~ track heading

Figure 3.3: A yaw-bias causes an oblique measured line

17

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3.3.2 PITCH BIAS

Pitch is defined as the rotation around the across-track y-axis. Because the beam width in

sailing direction is small, it may be possible to neglect this effect if the measured surfaces are not too steep. One example of a multibeam system, which neglects pitch biases is Fansweep (see also paragraph 2.4). Another possibility is to use a sensor, which measures the pitch effect. Due to a misalignment of the coordinate system, tied up to the pitch sensor it is possible that beams are actually pointed forward or backwards instead of vertically down. In figure 3.4 it is made clear that this pitch-bias does not only influence the vertical coordinates but has a horizontal component as weB.

real sea boltom

com uted sea boltom

horizontal error

vertical

error

Figure 3.4: A pitch-bias causes a flat bottom to be measured too deep

Basic geometrical formulas give some indications of errors involving a pitch bias. A pitch angle of 0.10 _{results in a horizontal error of 1.7 cm with lOm waterdepth, while the vertical}

error can be neglected, when measuring a flat sea-bottom, because it is within mm level. When the measured sea-bottom is not a flat surface, the horizontal error wil! result in an erroneous vertical coordinate due to this slope-angle. Table 4.2 provides some calculation examples.

3.3.3 ROLL BIAS

The roB motion is the rotation around the along track x-axis. This motion is being monitored by the attitude measurement system (AMS). The roB effect is a very important parameter, when considering the error budget of multibeam, because the roB effect has a direct influence on the non-vertical beam direction. Corrections for roB can be applied by a real-time mechanical correction, a real-time electronic correction, or a post-processing correction. Figure 3.5 shows how this roB bias ~ introduces a depth error as weB as a positioning error.

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real sea bottom

computed sea bottom

Figure 3.5: A roll-bias causes the measured bottom to be rotated and shifted downwards

Errors in the roU of 0.1 0 will re sult in depth errors near 0 cm for the inner beams to 3.5 cm in

the outer beams. This is again calculated using waterdepth of lOm, a swath width of 4 times

the depth and with a flat measurement surface. Whenever the sea-bottom is not flat, this error

will be bigger. In chapter 4, resulting errors are presented in table 4.2 for different sea-bottom

geometry and waterdepth.

3.3.4 GEOMETRYERRORS

As mentioned before a multibeam system consists of several components: The multibeam

transducer array, the motion sensors and the GPS positioning antenna. The offsets between these three components are known within the body frame and are measured when a system is instalied on the vessel. Due to measurement errors, it is possible that systematic errors are present, which will reveal themselves as constant offsets in all three directions. The influence

of these errors is 1: 1, this means that 1 cm offset will cause the same error in the resulting

coordinates.

3.3.5 LATENCY (ERRORS RESULTING FROM TIME DELAYS) .

Because all sensors measure their data at different time epochs and at different time-intervals it may be possible that an error will occur as a result of interpolation errors. This effect is called latency. These errors resulting from time delays are variabie with the ship's speed and will result in a bigger error, when moving faster. The three possible time-delays are delays between transducer and positioning system, between transducer and AMS, and between AMS and positioning system. A simple example shows that a delay error of 0.01 seconds will result

in 5 cm offset along-track, when moving at a speed of 5 mis. The error is, like geometry

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errors, independent of depth.

3.3.6 ERRORS IN SPEED OF SOUND

In order to calculate the travel range of an acoustic signal, it is necessary to know its speed of sound. The most preferabie situation would be to know it at every point inside the fan-shaped area through which the acoustic signal travels. In practice however it is common to measure the speed of sound only once. It is assumed that the speed of sound at a specific point doesn't change much in space and in time. For more information on this subject, e.g. Blacquière (1995) did some investigations on this subject.

The error made with the speed of sound can be divided into two parts. It may be that the speed of sound is not correct, but that it doesn't change along its travel path. In this case, the whole bottom will come up or down. To give an indication: An error of 0.1

mis

in the measured speed of sound (e.g. 1500

mis)

,

results in avertical bottom shift of 6.7e-4 m, with a measurement depth of lOm.

The other case is that the speed of sound does change along the travel path. In this case the bottom will curl up or down towards the end of the swath. Blacquière (1995) gives some indications for the impact ofthis error.

computed sea bottom

real

sea bottom

Figure 3.6: An error in speed of sound will shift the measured bottom up or down

FIOm the different types of coordinate systems involved in the total measurement systems and the types of systematic errors that may be present, it can be concluded that some only cause horizontal or position errors, and some cause both position and depth errors. This is an important aspect to keep in mind once an integrated calibration is set up in order to determine the systematic errors.

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Chapter 4 Existing dynamic calibration procedures

This chapter will describe the present version of the dynamic part of Rijkswaterstaat's

calibration procedure. Dynamic in this context means, that measurements are used which are acquired with a moving vesseJ. The procedure aims at removing the systematic errors by following a very specitic sequence. The basic idea behind this is that in the first measurement configuration only one error will influence the actual measurement. After removing this systematic error, the procedure continues using a different measurement configuration, in which another error will manifest itself in the measurements. It is assumed now that the first error has been removed completely up to this point so that it is now allowed to use a configuration where the first error influences the measurements as weIl. The second error is removed and the complete procedure repeats itself until all errors have been eliminated. The whole procedure will be described step by step in more details below, with a short evaluation at the end. For more information see Rijkswaterstaat Voorschrift nr: 923.00.LOlO (1998). In practice the measurement system is thoroughly calibrated, using a known calibration object, when the system is installed on the vessel, and is calibrated before every measurement campaign with a natural slope in the sea-bottom. Further reading about dynamic calibration of multibeam systems is e.g. Godin (1996).

4.1

RIJKSWATERSTAAT'S DYNAMIC CALIBRATIONPROCEDURE

Yaw

The yaw-bias is defined as a systematic error in the vessel's heading angle. It causes oblique measurement lines, instead ofperpendicular ones. For more information about the yaw-bias or one of the other errors, see chapter 3. The prescribed method of Rijkswaterstaat uses two parallel survey lines, which have been taken in the same direction over a certain underwater object. This object may have an unknown position and shape, but one can also use a known object. For this object an underwater threshold as described in appendix A can be used. One line is run on the left side and one on the right side of the object as shown in figure 4.1. Both lines must be run with the same velocity. As a consequence ofthe unknown yaw-bias (r), the object will be misplaced with as shown by figure 4.2. When a threshold is used, the yaw-bias is calculated by:

_1(dx/2)

y=tan -dy (4.1) 21

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With,

- - - -- - - -

-'Y : Yaw-bias.

dx : Along-track displacement between two measured objects.

dy : Across-track displacement between ship and object.

left

Figure 4.1: Helicopter view oblique measurement lines over the threshold

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Delay between multibeam and positioning system

The total de1ay can be split up in two components: De1ays between positioning system and

attitude measurement system (AMS) and between positioning system and multibeam system.

Rijkswaterstaat presents a dynamic calibration method for the de1ay between the positioning

and multibeam measurement. It is assumed that the delay between AMS and positioning

system has already been calibrated using a static calibration procedure.

The method uses identical lines run over a threshold, with a slope at least 1:5 and at

most 1:2, surveyed at different speeds. One line run with low velocity (2 mis) and one with

normal measurement velocity (3 - 4 mis) should be enough to identify and eliminate the

delay. Rijkswaterstaat in practice uses an extra line run at high speed (6 mis), because delays

can be hard to detect otherwise. Figure 4.3 shows the resulting effect on the measured

thresholds compared to each other and the real threshold. The delay can be determined by introducing a time-de1ay in the processing software and repeat the procedure until the

measured threshold at high speed is identical to the threshold measured at very low speed.

'"%7/

_______ "C_

...

/~

/

/no'

mis

Figure 4.3: The consequences of a delay

Pitch

The pitch angle is a rotation around the across-track axis y. To detect a systematic error in the

measured pitch value of the motion sensor, Rijkswaterstaat uses two lines run over the same

location at identical speeds, but from opposite directions. These lines can again be run over a

known object, like the previously used threshold, or an unknown object. Figure 4.4 shows the

resulting situation. To ca1culate the pitch error one first has to eliminate the geometry effect, which can be identified by extrapolating both the measured thresholds. The geometry effect can now be determined by the difference between the two lines at instrument level. Finally the

offset caused by the pitch error (a), which is dx, can be determined by taking the difference

between the two thresholds at an arbitrary depth and subtracting the determined geometry-offset. The pitch error is then ca1culated by:

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-I(

dx/2 ) a = tan Depth (4.2)

1

0 \

.7-geometry

geom~

\~~

pitch +

Figure 4.4: Combined pitch and geometry error

Offset along-track

Errors in the determined transducer, sensor or GPS-antenna positions in the vessel system may cause offsets. The offset in along-track direction can be determined using the same measurement configuration as was used to detect the pitch-bias. This means two lines, back and forward, run at identical speeds over an object like the threshold. Plotting the two measured thresholds yields two displaced objects because of a geometry effect together with possible remainders of a delay or pitch error. When these errors have been removed completely, the offset along-track is calculated by half the displacement between the two thresholds, see also figure 4.5.

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Offset across-track

Offsets across-track can be identified by again using lines, which are run back and forward.

This time however, the lines are not run over the same position, but one on the left of an object and one on the right side. Figure 4.6 gives a view from above to illustrate this configuration. An offset across-track will result in shifted measured objects. The offset is calculated by halfthe measured difference across-track between the two objects.

Rol!

real W

object

l'

computed

2

--

~

- '

tG-1E---=-F

-=-.,

--+-

)

Figure 4.6: The cross-track geometry error

A roIl-bias is caused by a misalignment ofthe motion-sensor, which measures the vessel's roIl movement. This error expresses itself as a rotation around the along-track axis. A flat sea-bottom wiIl be measured as if it has a slope perpendicular to the vessel' s heading. In order to remove the systematic effect Rijkswaterstaat proposes again a back-and-forward-line configuration, with both lines run at identical speeds over a completely flat sea-bottom. Figure 4.7 shows how the roIl effect will influence the measured sea bottoms for both lines. The roIl effect, which has to be corrected for during the norrnal measurements, can now be deterrnined from the angle between the two measured surf aces. More specifically said: The roIl-bias (~) is calculated by the half vertical difference (dz) between the two measured surf aces at the end divided across-track di stance dy:

(4.3)

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If the sea-bottom is not flat an error will be introduced. In this case the intersection of the two measured sea-bottoms will not be directly below the transducer, because this geometry influences the shift.

computed sea bottom

real sea bottom

Figure 4.7: A roll-bias causes the bottom to shift downwards and rotate

4.2 EVALUATION OF THE PROCEDURE

In the previous section an outline of the dynamic part of the present method of

Rijkswaterstaat was given. The dynamic part of this method calibrates six different parameters, which are mentioned in table 4.1. The calibration of speed of sound is left out, because this effect is calibrated in the method introduced in chapter 5. After each parameter in table 4.1 it is indicated, which measurement configuration Rijkswaterstaat uses to isolate the effect. When the number of used lines are added up, it can be seen that the total number of lines used by Rijkswaterstaat to solve the six parameters is at least six.

~ Line 1 Object

;

Line 2 Line 3 Line 5 ... 1 - - - + - - - 1 1 - - - . Line 6 ... 1--_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ---. ~ Line 4

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Table 4.1: Summary ofthe used survey lines by Rijkswaterstaat-method

Advantages and disadvantages Rijkswaterstaat 's method

This section wil! summarize the main advantages and disadvantages of the present method for dynamie calibration. The main advantage is that this method can be used without a calibration

threshold. A slope in the sea-bottom suffices. This on the other hand can be a disadvantage.

When e.g. the geometry is incorrectly supposed to be a flat surf ace as is being done when

calibrating for a roll, the b.y in the roll formula does not cancel out when running back and forward, which it should do.

lt is on the other hand a big disadvantage that the method is not solved in one single

step. If all parameters could be solved using only one model of observations, it would be very

easy, using the least-squares method of adjustment to derive values, which indicate the

precision or internal and extemal reliability of the determined parameters.

Another disadvantage of using separate steps to calculate all the different parameters is the possibility of residuals of previously removed systematic errors, which are now assigned

to another parameter. In other words: when an error is not removed correctly at a certain stage,

it is possible that the residual is assigned to the presently evaluated effect. Both disadvantages can be prevented if a method would be used which would calculate all unknowns in one single

step. Besides these two aspects, it is more than likely that using a single step to solve for all

parameters will decrease the number of survey lines needed. A last disadvantage of the present method is that the usual procedure in practice is to make a cross section of the measured surfaces back and forward and use the displacements between the two to find the

calibration parameters. This can not be done on exactly the same position, because the

measurements back and forwards are usually not taken at the same position. This also

introduces an error.

Attainable accuracy of determination of parameters

The procedures described above provide the calibration parameters with a certain precision.

Because in practice they do not use a model to derive the parameters it is not possible to

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calculate a variance-matrix immediately. It is however possible to use the spread of several repeated calibrations, to derive some kind of a standard deviation. These values are available for the three rotation angles.

The roll can be regarded as the best determinabie parameter. It can be determined within 0.1 o. The pitch can be determined within OS _1.0

0

in the most optima! situation, and the yaw can be determined within 10

_20

(Personal communication with Dutch Survey Department of Rijkswaterstaat, 1998). The va1ue for the pitch-bias seems rather optimistic, when compared to the test results in chapter 6.

These values can now be used to ca1culate the resulting error on the vertical coordinates under water. Table 4.2 gives the results for this in several situations. They have been calculated with a depth of 5 meters and with a depth of 20 meters. Besides that the influence of various slope angles, ranging from 140

up to 630

, in the sea-bottom has been

computed.

It can be seen in this table that the influence of the erroneous1y determined ca1ibration parameters on the vertical coordinate can be quite large for steep s10pes and at greater depth. This mayalso be a reason to develop a different method of dynamie calibration, which is able to determine the parameters with a higher accuracy and in one adjustment inc1uding the appropriate precision and reliability measures.

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Chapter 5 A new dynamic calibration method

This chapter contains a new and completely different approach for dynamic calibration of

multibeam systems. This method uses an object, which is known in shape and absolute

position. The used calibration object is the before mentioned threshold, which is described

more profoundly in appendix A. This approach uses the residuals between the surface of the

known object and the measured surface, instead of residuals between two measurements. The

measured surface of the threshold will be deformed whenever errors are present and this

measured deformation can be used to ca1culate several parameters, like pitch, roll and yaw. In

section 5.1 the formulas are presented, which relate six of these unknown calibration

parameters with the measurements individually. These six parameters are pitch, roll, yaw, tx,

ty and tz. The next section discusses in which way these formulas can be combined into one

model, applying the arising cross-terms. In section 5.3 it is described how the combined

equation can be used to form the model of observation equations. This model can then be used to do a series of tests in order to indicate the potentialof the developed method and give some indications about the precision of the derived calibration parameters. The actual tests

will be described together with their results in chapter 6.

5.1

RELATING THE MEASURED SURF ACE TO THE CALIBRA TION PARAMETERS

In this section the formulas are presented, which give the relation between the measured

surf ace of the threshold, which is deformed as a result of the unknown calibration parameters

and the real surface. The method is derived and tested with a few important constraints. One

constraint is that the method is derived for a level measuring system. This means the system is measuring straight down with no time-varying pitch or roll angles present. This is not very strange, because in practice the calibration threshold is situated in a quiet side-arm of the Waal-river near St. Andries. Under these quiet circumstances and when the vessel is moving very slowly the conditions are correct. When the calibration takes place under less quiet circumstances the model has to be extended to account for the changed measurement direction. Due to time-limitations during this research, the method has only been derived

using a one-dimensional model. In other words: the model treats the measurements of the

multibeam system like an endless row of z-coordinates, which are situated on a certain

across-track distance from the point directly below the transducer. This local y-coordinate is assumed

non-stochastic. This is of course not completely correct. Formulas for y can be derived similar

to the formulas for z, which are derived hereafter, especially for the roll and pitch, since these

effects also cause a change in y-coordinates. In practice the effect of these changes in y will

be that small however that it may not even be necessary to add formulas for y (see appendix

D). All effects will be treated separately considering the other effects not to be present, and

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the results are summarised in section 5.1.6. The last section will discuss possible forrnulas for an error in speed of sound and an error in the delay between the positioning system and multibeam device. These forrnulas are similar to the forrnulas for errors in the vertical and along track offset and are not taken into account in the derived model.

5.1.1 U SED DEFINITION FOR THE ORIENTA TION OF THE VESSEL

This section will briefly introduce the approach, which is taken to develop the forrnulas. In this thesis, the slope of the threshold has been called

ao.

This slope

ao

can be divided into a slope along-track, which is called al and a slope across-track to this one, called a2. This idea is explained graphically in figure 5.1. This figure shows the vessel running over the threshold along the so-called x-axis. The z-axis is defined parallel ofthe local vertical and the y-axis is the across-track axis perpendicular to these two. This coordinate system (x,y,z) is related to the RD-NAP system (X,Y,Z), defined in chapter 3, as:

(5.1)

with Xo and Y_othe RD coordinates of the transducer and X and Y the RD-coordinates of the measured point, "(0 the heading angle with respect to the object, and "(object the orientation of

the calibration object with respect to the Y (see figure 5.2). This approach provides opportunities to separate the effect of a certain parameter in an along-track part and an across-track part. The basic forrnula, which represents the z-value of a measurement on an arbitrary perpendicular distance y from the transducer, can be written as:

(5.2)

with Zo being the correct z-value perpendicular below the transducer (point P), and y the cross-track di stance (A'P). This formula is only correct if no error is present and all observations are perfect. lt is the start for developing the forrnulas in the following sections.

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z-a:J-iS . x-axis y-axis

o

i

!

Figure 5.1: Clarification ofthe different used slope-angles

y

x

~yobject I

....

...

Xobject

Figure 5.2: The orientation ofthe vessel and calibration object with respect to the RD system (X,Y)

5.1.2 PITCH FORMULA

The formula describing the influence of a pitch-bias for the beam directly be10w the transducer, with exit angle zero can be derived with help of figure 5.3. In this figure Zo is the line connecting 0 and P, z is the measured z-value, which is OA (and OB), resulting in formula 5.3:

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;, 11' _ti,. tij . . . . , • • n r WJ . . . ' __

Zo

cos(-a)

=

-Z

real sea boltorn cern uted sea bot!om

p

B

z-axis

ol •

horizontal error

Figure 5.3: The consequences of a pitch-bias (5.3)

vertical error

When also measurements from other exit angles are regarded the measured z-value will change because of a possible across-track slope a2. This can be accounted for with help of the basic formula 5.2, derived in section 5.1.1, resulting in:

( ) zO+ytana2

cos -a

=

- - " - . - - - ' . - - - = - (5.4)

Z

Formula 5.3 however is only valid when the measured sea-bottom has no slope along-track. This is not always the case and the non-tlatness in along-track direction has to be introduced in the formula in order to be able to use a threshold for the calibration. Figure 5.4 explains this graphically. Distance Zo is again OP, while the actual measured z-value is OA. The co-sinus ofthe (negative) pitch angle is now given by OA' divided by OA. OA' can be calculated by Zo minus A'P. This distance A'P can be calculated by some geometry formulas in triangle AA'P and is given by zsin(-a)tan(al) as can be verified in figure 5.4. This finally results in:

( ) Zo + ytana2 -zsin(-a)tana,

cos -a

=

-=----=---=---'--'----'-z

Dynamic calibration of multibeam systems

Dynamic calibration of

multibeam

systems

.

.

Jeroen Dunnewold

DEOS Report

Dynamic calibration of multibeam systems

8ibliotheek TU Delft

11111111111

2410

431

"

"n

'"''''!''''.'''l

Dynamic calibration of multibeam systems

J

eroen Dunnewold

".

'

Contents

-Summary

--=

"

Chapter 1

Intro ducti on

Chapter 2

Principles of multibeam

2.3 THE

__

__

____

__

___

______

____

v u

c.

=

Chapter 3

Coordinate determination and error budget

3.1

aps

3.2

s~n

[~L

=

{R,(-Pl R,(-rl R,(-ant]

3.3

mis

mis)

,

Chapter 4

Existing dynamic calibration procedures

4.1

_1(dx/2)

'"%7/

_______ "C_

...

/~

/

/no'

-I(

1

0

\

geom~

\~~

l'

--

~

tG-1E---=-F

-=-.,

--+-

)

4.2 EVALUATION OF THE PROCEDURE

;

Chapter 5

A new dynamic calibration method