Acoustic Doppler Velocimeter Flow Measurement from an

2038 VOLUME 18J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y

q 2001 American Meteorological Society

Acoustic Doppler Velocimeter Flow Measurement from an Autonomous UnderwaterVehicle with Applications to Deep Ocean Convection

YANWU ZHANG*

MIT/Woods Hole Oceanographic Institution Joint Program in Oceanographic Engineering,and MIT Sea Grant Autonomous Underwater Vehicles Laboratory, Cambridge, Massachusetts

KNUT STREITLIEN1 AND JAMES G. BELLINGHAM#

MIT Sea Grant Autonomous Underwater Vehicles Laboratory, Cambridge, Massachusetts

ARTHUR B. BAGGEROER

Department of Ocean Engineering, and Department of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts

(Manuscript received 12 October 2000, in final form 29 May 2001)

ABSTRACT

The authors present a new modality for direct measurement of ocean flow, achieved by combining the resolutionand precision of an acoustic Doppler velocimeter with the mobility of an autonomous underwater vehicle. Toobtain useful measurements, two practical integration issues must first be resolved: the optimal location formounting the velocimeter probe to the vehicle, and alignment of the velocimeter with the vehicle’s attitudesensors. Next, it is shown how to extract earth-referenced flow velocities from the raw measurements. Vehiclehull’s influence on flow velocity measurement is removed by modeling the vehicle as a spheroid in potentialflow. This approach was verified by a tow tank experiment in the David Taylor Model Basin. The authors thendescribe mission configuration and signal processing for a deployment in the Labrador Sea to study deep oceanconvection during the winter of 1998. Analysis of the vertical flow velocity data not only shows that this formof measurement can detect ocean convection, but also gives detailed information about convection’s spatialstructure.

1. Introduction

Autonomous underwater vehicles (AUVs) have in-herent qualities that make them uniquely adapted tosampling fine-scale ocean phenomena (Bellingham1997). Unencumbered by tethers and controlled by pro-grammable mission specifications, AUVs possess a highdegree of agility and can execute very precise surveys.Enhanced power sources are extending AUVs’ opera-tion range to the order of 1000 km. Acoustic, radio, andsatellite communications have made it possible to mon-itor and reconfigure AUV missions from afar.

AUVs accept a variety of off-the-shelf payloads, as

* Current affiliation: Aware, Inc., Bedford, Massachusetts.1 Current affiliation: Bluefin Robotics, Cambridge, Massachusetts.# Current affiliation: Monterey Bay Aquarium Research Institute,

Moss Landing, California.

Corresponding author address: Dr. Yanwu Zhang, c/o Aware Inc.,40 Middlesex Turnpike, Bedford, MA 01730.E-mail: [email protected]

long as they have a reasonable power consumption andare small and light enough to be fitted. One such deviceis an acoustic Doppler velocimeter (ADV). Flow ve-locity is one of the most important physical quantitiesfor ascertaining the ocean’s state and its circulation. AnADV (SonTek 1997) measures three-dimensional watervelocity using sound waves.

As illustrated in the left-hand panel of Fig. 1, an ADVis an active sonar that transmits acoustic signals andthen receives their echoes reflected by sound scatterersin the water, like plankton or other floating particles.The scatterers are usually passively advected by watermotion (Gordon 1996; Plimpton et al. 1997). From themeasured frequency shift between emissions and ech-oes, flow velocity is deduced based on the Doppler prin-ciple.

An ADV has one transmitter and three receivers, asshown in Fig. 1. An echo at each receiver has a fre-quency shift proportional to the component of relativevelocity along a line bisecting the transmission and re-flection paths. Hence, three-dimensional velocity can becalculated. Acoustic beams of the transmitter and the

DECEMBER 2001 2039Z H A N G E T A L .

TABLE 1. Specifications for SonTek ADVOcean.

Sound frequencyOutput data rateVelocity’s dynamic range (x and y)Velocity’s dynamic range (z)Measurement noise

(at 25-Hz data rate)Velocity resolutionDistance of sampling volume from transmitterSampling volume sizeDepth ratingSizeWeight

5 MHz0.1 ; 25 Hz0–0.5, 1.2, 2.0, 6.0, 7.2 m s21, programmable¼ of above

1% of velocity range1024 m s21

0.16 m2 cm3

2000 m0.36 m 3 0.18 m (diameter of stem: 0.05 m)1.5 kg

FIG. 1. (left) Side view of an ADV probe. (right) Cross-sectional view and side view of the ADV’s mounting on the vehicle. In the upperright panel, the big circle represents the vehicle’s outer fairing. In the lower right panel, the lower half of the vehicle’s inner fairing is placedupside-down for ease of installation, while the outer fairing is removed.

three receivers intersect at a small sampling volume (,2cm3, deemed a ‘‘point’’) located away from the instru-ment base (16-cm distance for SonTek model ADVO-cean, as listed in Table 1). Three-dimensional flow ve-locity obtained at this distant focal point can thus beconsidered undisturbed by the probe. As shown in Fig.1, the ADV’s local z axis is defined along the probestem; the x axis is coplanar with one designated receiverarm; the y axis is accordingly defined by the right-handrule. Table 1 gives the specifications (SonTek 1997) ofthe ADV device that we have installed in an OdysseyIIB AUV (Bellingham 1997).

It should be mentioned that an acoustic Doppler cur-rent profiler (ADCP) is another common flow velocitymeasurement device. It profiles velocity over a largedepth range, in contrast to an ADV’s point measurement.

However, an ADV’s spatial focus and low noise (lessthan a tenth of an ADCP’s measurement noise at thesmallest bin size) makes it uniquely suitable for exper-iments that require high resolution and high precision.Published applications include flow measurement nearriver beds (Lane et al. 1998; Bouckaert and Davis 1998),and the seabed (Kawanis and Yokosi 1997). In Voulgarisand Trowbridge (1998), Reynolds stress measured byan ADV was found to be within 1% of that obtainedby laser Doppler velocimetry.

In the above applications, ADVs monitor current ve-locity only at spatially fixed positions. Integration of anADV into an AUV enables point flow measurement ofhigh resolution and high precision from a moving plat-form. The paper presents theoretical and experimentalwork in building such a system. System integration is


FIG. 2. Definition of velocity vectors in the AUV coordinatesystem (plan view).

FIG. 3. AUV behavior sequence in mission B9804107.introduced in section 2. The data processing algorithmis derived in section 3.

The Labrador Sea lies between northern Canada andGreenland. It is one of the few locations in the worldwhere open ocean convection occurs (Marshall et al.1998; Lilly et al. 1999). During the winter, the sea sur-face is subjected to intense heat flux to the atmosphere.The resulting buoyancy loss causes the surface water tosink to large depths, initiating ocean convection. In con-vection regimes, the water column overturns in numer-ous convective cells (also called plumes; Marshall andSchott 1999). Therefore, vertical flow velocity and itsspatial periodicity are the key signatures of ocean con-vection.

Previous measurements by floats and moorings showthat convection’s vertical flow velocity is on the orderof several centimeters per second (mainly depending onsurface heat flux and latitude). For example, Fig. 20 ofMarshall et al. (1998) shows rms vertical velocity of2.3 cm s21 measured by floats in the Labrador Sea in1997.

During January–February 1998, researchers from theMassachusetts Institute of Technology (MIT), theWoods Hole Oceanographic Institution, and the Uni-versity of Washington, made an expedition to the Lab-rador Sea to study ocean convection. This experimentprovided a unique opportunity of testing and utilizingthe AUV-borne ADV system. The challenge was to mea-sure small vertical flows from a comparatively rapidlymoving vehicle. The AUV-measured flow velocity de-tected convection’s occurrence, as demonstrated in sec-tion 4. Computation of AUV hull’s influence and a towtank validation experiment are given in the appendixes.

2. Instrument integration

The mounting location and orientation of an ADV onan AUV must meet the following requirements: (i) avoidsaturation of velocity measurement, (ii) avoid interfer-ence with other AUV instruments, (iii) keep the ADVprobe out of harm’s way during AUV launch and re-

covery, (iv) minimize corrections of the vehicle hull’sinfluence so that the measurements are as direct as pos-sible, (v) locate the sampling volume outside wakes asmuch of the time as possible, and (vi) exploit the lower(by a factor of 1/4) measurement noise along ADV’s zaxis than the other two axes.

According to the above requirements, the followingoptions are ruled out. (i) At AUV’s nose. The vehicle’sup to 2 m s21 speed could saturate the ADV’s z velocitywith the probe in the alongship direction. The ADVwould also interfere with and be affected by the AUV’sdocking latch and the ultrashort-baseline hydrophonearray that are mounted at the nose. The velocity mea-surement would need considerable corrections becauseof the ADV’s closeness to the vehicle’s stagnation point.(ii) At AUV’s top or bottom. Either upward or down-ward flow velocity measurement would be in the wake,and the AUV’s launch gear or the storage cart wouldjeopardize the ADV probe. (iii) At the horizontal-planeflank of the vehicle. The ADV probe would interferewith the vehicle’s recovery hoop.

Our choice is to mount the ADV at the vehicle’slargest vertical cross section, with its probe pointing 458from the vehicle’s horizontal central plane, as shown inthe right-hand panel of Fig. 1. The ADV’s three receivertips reach the brink of the hull but do not protrudebeyond it. This satisfies all the requirements listedabove. Inside the vehicle, the ADV probe is mountedwith a horizontal plate and a 458 slanted bracket.

The vehicle’s heading and attitude sensor box is ori-ented in the alongship direction. For transformationfrom the ADV’s to the AUV’s reference frame (as willbe formulated in section 3), the ADV’s mounting anglesneed to be accurate. During installation, we use a laserpointer to ensure alignment accuracy.

The ADV works at 24 V, provided by the AUV’sbatteries. ADV data are read by the vehicle’s computerthrough a serial port and saved in the vehicle’s central


data file. This guarantees time synchronization with oth-er instrument data. The bandwidth of the AUV’s databus limits the ADV’s data output rate to 2.5 Hz.

3. Algorithm of extracting earth-referenced flowvelocity from AUV’s raw measurements

The AUV-borne ADV measures flow velocity relativeto the moving vehicle. Hence, to obtain the earth-ref-erenced flow velocity, that is, the true flow velocity, wemust subtract the vehicle’s own velocity from the rawmeasurement. Another issue of concern is the vehiclehull’s influence on the measurement. As shown in Fig.1, the ADV probe’s sampling volume is located about13 cm from the vehicle’s hull surface (an Odyssey IIBAUV has a length of 2.2 m, and a diameter of 0.6 mat its largest vertical cross section where the ADV ismounted). This distance is small enough to necessitateremoval of the hull’s influence on flow measurement.In this section, we present the algorithm of extractingthe earth-referenced flow velocity.

Figure 2 shows the plan view of the spheroid thatserves as our model of the AUV. We choose the spher-oid to be of the same aspect ratio as the vehicle’saxisymmetric fairing. The length of its major and mi-nor axes are a and 0.293a, respectively, where a 50.991 m. These values represent closely the shape ofthe fore half of the hull. The ADV’s sampling volumeis located at

Tr 5 [0 0.304a 0.304a] .m

At a normal straight-ahead flight attitude of the AUV,the ADV’s sampling volume is far outside the boundarylayer and also out of any wake, in accordance with themounting criteria laid out in section 2.

The AUV coordinate system is at rest in the earthcoordinate system, but its origin and orientation are co-incident with the vehicle’s at any instant under consid-eration. Velocities U, V, V, vm, and um listed below areall in the AUV coordinate system, and U 5 [U1U2U3]T

is the current velocity, which is assumed to be constantover the length of the vehicle. The vehicle translateswith speed V 5 [V1 V2 V3]T, and rotates with angularvelocity V 5 [V1 V2 V3]T. Those motions are alsoreferred to as degrees of freedom 1–6, respectively. Thesampling volume, located at rm, translates with velocity

v 5 V 1 V 3 r .m m (1)

The vehicle’s motion relative to the water surroundingit imparts a disturbance at rm. The flow velocity thatthe ADV measures, um, therefore has a difference fromU 2 vm. According to the potential flow theory (Lamb1932), the disturbance is a linear combination of thecomponents of V 2 U and V. So um equals U 2 vm

plus a correction term:

u 5 U 2 v 1 [A(V 2 U) 1 BV]m m

5 (A 2 I)(V 2 U) 1 (B 1 r 3 )V, (2)m

where Eq. (1) has been incorporated. Here A and Bare two square matrices describing the AUV hull’seffect on flow velocity measurement: A for transla-tional motion and B for rotational motion. Calculationof the two matrices is given in appendix A, and theresults are

20.0678 0 0 A 5 0 0.0563 0.4053 (3)

0 0.4053 0.0563

0 0.0687 20.0687 B 5 0 0 0 a. (4)

0 0 0

Thus, for instance, if the vehicle is moving forwardwith velocity [1 0 0]T relative to the ambient current,the ADV’s sampling volume will see a velocity of[21.068 0 0]T due to the accelerated flow at the hull’smaximum diameter.

To validate the above theoretical modeling of vehiclehull’s influence on flow velocity measurement, we con-ducted a tow tank experiment in the David Taylor ModelBasin, as detailed in appendix B. Experimental resultsagree well with theoretical predictions.

The earth-referenced flow velocity is extractedthrough the following steps.

1) Transform the velocity measurement from the ADVcoordinate system to the AUV coordinate system(both systems shown in Fig. 1):

u 5 T u ,ADV→AUVm ADV (5)

where uADV is the velocity vector originally measuredin the ADV coordinate system.

Matrix

0 21 0 T 5 2sin(a) 0 2cos(a) (6) ADV→AUV

cos(a) 0 2sin(a)

transforms from the ADV coordinate system to theAUV coordinate system, where a 5 458 is themounting angle of the ADV probe’s stem relative tothe vehicle’s horizontal central plane.

2) Compensate for the AUV hull’s influence and sub-tract the velocity induced by the vehicle’s rotation,by applying Eqs. (2) and (5). Then the relative flowvelocity in the AUV coordinate system is obtained:


21U 2 V 5 (I 2 A) [u 2 (B 1 r 3 )V]m m

215 (I 2 A) [T uADV→AUV ADV

2 (B 1 r 3 )V], (7)m

where the angular velocity (i.e., the vehicle’s yaw/pitch/roll rate) vector V is measured by the AUV’sKVH Digital Gyro Compass and Digital Gyro In-clinometer (KVH 1994).

3) Recover the relative flow velocity in the earth co-ordinate system using the vehicle’s heading, pitch,and roll measurements:

U 2 Vearth earth

u1 5 u 5 T (U 2 V) AUV→earth2

u3

215 T (I 2 A)AUV→earth

3 [T u 2 (B 1 r 3 )V] (8)ADV→AUV ADV m

where

cos(u ) 2sin(u ) 0 cos(u ) 0 sin(u ) 1 0 0h h p p T 5 T T T 5 sin(u ) cos(u ) 0 0 1 0 0 cos(u9) 2sin(u9) (9) AUV→earth h p r h h r r

0 0 1 2sin(u ) 0 cos(u ) 0 sin(u9) cos(u9)p p r r

where uh, up, and are the AUV’s heading, pitch,u9rand corrected roll angles,1 respectively.

4) Extract the earth-referenced flow velocity, that is,the true flow velocity. The vehicle’s own horizontalvelocity, that is, the first two components of Vearth,can be estimated by a long baseline acoustic navi-gation system (Bellingham 1997) in deep ocean orby acoustically tracking the ocean bottom (RDI1996) in shallow water. The vehicle’s own verticalvelocity, that is, the third element of Vearth, can beestimated by differentiating its depth sensor mea-surement. Knowing Vearth, we can obtain the earth-referenced flow velocity Uearth from Eq. (8):

u1 U 5 u 1 V earth 2 earth

u3

215 T (I 2 A)AUV→earth

3 [T u 2 (B 1 r 3 )V]ADV→AUV ADV m

1 V . (10)earth

When we are only concerned about the true verticalflow velocity, that is, the third component of Uearth,we only keep the third row of Eq. (10) (note thatthe z axis points downward, as shown in Fig. 2):

1 Note that the measured roll angle ur is referenced to the horizontalplane, rather than the rotational angle needed in matrix Tr. Trigo-nometric derivation gives the relation between the desired rotationalangle and the roll measurement ur asu9r

cos(2u ) 1 cos(2u )r p21u9 5 cos 3 sign(u ).r r2 2[ ]2 cos(u )Ïcos (u ) 2 sin (u )p p r

When the pitch angle up is small, the difference between ur and u9ris small too.

w 5 u 1 ydown earth 3 down AUV

d5 u 1 [AUV depth z(t)]. (11)3 dt

To comply with the commonly adopted upward con-vention, the earth-referenced upward flow velocityis written as

w 5 2wearth down earth

d5 2 u 1 [AUV depth z(t)] . (12)35 6dt

4. Labrador Sea convection experiment

a. Data processing results of AUV-measured verticalflow velocity

AUV mission B9804107 took place at 0446 ; 0700UTC 10 February 1998. The mission launch locationwas about 568429N, 528469W, where the (AutonomousOceanographic Sampling Network (AOSN; Curtin et al.1993) mooring was anchored. The AUV behaviors inthis mission are illustrated in Fig. 3. The vehicle firstspiraled down to 426-m depth, then it spiraled up to250-m depth. At this depth plane, the vehicle made a‘‘diamond’’ run, that is, closed a four-leg loop with 908turns, each leg lasting for 720 s. After that, it spiraledup to 20-m depth, making an identical diamond run. Atthe end, the vehicle ascended to the sea surface. Thevehicle’s speed in level legs was about 1 m s21.

On the vehicle, the ADV probe measured three-di-mensional flow velocity, while the conductivity–tem-perature–depth (CTD) sensor suite measured other waterproperties. Those measurements are shown in Fig. 4,


FIG. 4. During AUV mission B9804107, flow velocity was measured by an ADV. Conductivity, temperature, and depth were measured byonboard CTD sensors.

where potential temperature and potential density arededuced from in-situ measurements.

We apply the algorithm in section 3 to process theADV measurements. Vertical flow velocity is a key sig-nature of ocean convection (Schott et al. 1993, 1996).For detecting convection, we only extract the earth-ref-erenced vertical flow velocity wearth as formulated in Eq.(12). The data processing result for the 250-m depth isshown in Fig. 5. The vehicle’s own vertical velocity(middle panel) has been removed for producing wearth

(top panel). The AUV’s roll (bottom panel) shows whenthe vehicle made 908 turns. At an AUV speed of about1 m s21, 1 s of time on the abscissa can be approximatelytranslated to 1 m of distance for interpreting convectioncells’ spatial scale. The rigorous time–space relationshipof an AUV measurement is governed by the mingledspectrum principle (Zhang 2000).

In Fig. 6, we overlap wearth of the 250- and 20-mdepths. A shift of 3550 s is added to the time index forthe 250-m depth, during which the vehicle completedthe diamond loop at the 250-m depth and ascended tothe 20-m depth plane (illustrated in Fig. 3). We note

that for about 600 s in Fig. 6, consistency between thetwo signals is pronounced.

As will be analyzed in section 4b, a convection layeris believed to exist in the upper 350-m water during thisAUV mission. According to the MIT ocean convectionmodel (Jones and Marshall 1993; Klinger and Marshall1995), over a depth difference of 230 m and a timedifference of 3550 s, vertical velocities at the same hor-izontal position should show strong similarity. The rea-son is that convective cells are vertically aligned, andthe field varies very slowly as convection approaches astationary state. Compared with 250-m depth, the 20-m depth shallow water is complicated by additional at-mospheric forcing. Nevertheless, similarity betweendepths still offers a means for checking measurements.The consistency of wearth between the two depths asshown in Fig. 6, although only lasting for a short du-ration, adds to our confidence in the data processingalgorithm.

To remove bias in wearth, we have corrected installationerrors of the ADV probe and the heading and attitudesensor box. In AUV mission B9804107, the two errors


FIG. 5. (top) The earth-referenced vertical flow velocity wearth at the 250-m depth of AUVmission B9804107.

FIG. 6. Comparison of wearth of 250- and 20-m depths, with a time shift of 3550 scorresponding to AUV’s cruise time.


TABLE 2. Measurement/estimation noise.

Measurement/estimation Sensor

Rms noise after50-s smoothing

Flow velocity

Heading/attitude rateAUV vertical velocity

wearth

ADVOcean5 MHz

KVHParoscientific

8B-4000

0.45 cm s21*

1.4 3 1023 rad s21

0.32 cm s21

0.7 cm s21*

* For AUV mission B9804107 in the 1998 Labrador Sea Experi-ment.

FIG. 7. Profiles of potential temperature, salinity, and potentialdensity during AUV mission B9804107.

were 28 rotation of the ADV probe and 18 pitch-up ofthe heading and attitude sensor box. The pitch-up angleof the heading and attitude sensor box was determinedusing the criterion that the mean value of convectivewearth during an AUV level run should vanish. The re-maining noise of wearth comes from three sources of mea-surement noise: (i) ADV, (ii) KVH heading/pitch/rolland rate sensor, and (iii) AUV’s depth sensor. The sourceerrors propagate into the final result wearth by followingthe four-step transformations in section 3. The noisesources and the result (all after 50-s smoothing) aresummarized in Table 2. The standard deviation of noisein wearth is 0.7 cm s21.

It is noted that in the Labrador Sea Experiment theAUV-borne ADV experienced low correlation coeffi-cient and low signal-to-noise ratio, although still withinoperational ranges. This was probably due to low den-sity of floating particles in the water. As a consequence,ADV’s measurement noise was relatively high. Inter-ference from an acoustic modem’s transmission alsoadded to the ADV’s measurement noise during that ex-periment. Modem interference with the ADV was easyto remove, because it was periodic (every 28 s), andcreated clearly anomalous spikes in velocity measure-ment. Even in the presence of the 0.7 cm s21 total noisein wearth, the AUV-based classifier successfully detectsconvection against internal waves, as will be discussedtoward the end of this section.

b. Detection of convection’s occurrence by wearth

During the 1998 Labrador Sea Experiment, meteoro-logical data were recorded by an Improved Meteorolog-ical (IMET) system (Hosom et al. 1995) on board R/VKnorr. Prof. Peter Guest of the Naval PostgraduateSchool calculated the ocean surface heat flux based onthe IMET measurements. During AUV missionB9804107, the heat flux was about 300 W m22. Let usmake comparisons with previous open ocean convectionexperiments. In the Greenland Sea Experiment (Schottet al. 1993) during the winter of 1988/89, the heat fluxfluctuated between 100 and 500 W m22, with an averagevalue of about 250 W m22. Ocean convection was ob-served during that experiment, using moored ADCPs. Inan earlier Labrador Sea experiment (Lilly et al. 1999)

during the winter of 1994/95, the average heat flux wasabout 300 W m22. Using a moored ADCP and ProfilingAutonomous Lagrangian Circulation Explorer (PAL-ACE) floats, ocean convection was observed. The seasurface heat flux value in our Labrador Sea Experimentis close to that of the two previous experiments. Wetherefore have reason to expect ocean convection’s oc-curring.

Besides surface heat loss, a vertically mixed watercolumn is another key condition for ocean convection.Across the Labrador Sea Basin (about 600 km), a mixedwater layer of depth 270;500 m was observed by aseries of CTD casts from the ship deck (data providedby Prof. Eric D’Asaro, personal communication 2000).During two different AUV missions, mixed water layerswere also clearly recorded by CTD sensors on the ve-hicle. During AUV mission B9804107, the mixed layerwas down to 350 m, as shown in Fig. 7. The 250-mdepth plane in AUV mission B9804107 is within thismixed layer.

From the wearth panel in Fig. 5, convection cells’ spa-tial periodicity of about 150 m can be observed (theAUV speed was about 1 m s21). Using the MIT con-vection model (Jones and Marshall 1993; Klinger andMarshall 1995), we have designed an AUV-based clas-sifier (Zhang 2000) to distinguish ocean processes bytheir spectral features. Based on wearth’s spectrum, whichcorresponds to convective cells’ periodicity ‘‘seen’’ bya cruising AUV, the classifier declares that the 250-mdepth vertical velocity data is convective. This result isin agreement with meteorological and hydrographic ex-pectations.

During the same experiment, Prof. Eric D’Asaro ofthe University of Washington deployed seven Lagrang-ian floats to study convection [float design can be foundin D’Asaro et al. (1996)]. The floats’ records confirmnot only the existence of mixed layers, but also the


occurrence of convection. Furthermore, the rms verticalflow velocity is found to be 2;3 cm s21 based on thefloat data (calculated by Prof. Eric D’Asaro). In the 250-m depth AUV data analyzed above, the counterpart is2 cm s21. Measurements by those two independent plat-forms are consistent.

5. Conclusions

We have enabled an AUV to make flow velocity mea-surement using an acoustic Doppler velocimeter (ADV).The usefulness of an ADV lies in its ability to acquireaccurate measurement at a focal point. Incorporation ofan ADV in an AUV provides a mobile measurementmode, which enhances coverage and responsiveness inocean surveys. For classifying ocean processes, flowvelocity is a key feature. Acquiring this measurementfrom a vehicle is crucial to realizing an AUV-basedclassifier (Zhang 2000).

The AUV-borne ADV measures flow velocity relativeto the moving vehicle. We established an algorithm toextract the earth-referenced flow velocity from the rawmeasurement. AUV’s own velocity and its hull’s influ-ence on flow measurement are removed. A tow tankvalidation experiment was carried out in the David Tay-lor Model Basin. In January/February 1998, an AUVacquired flow velocity in the Labrador Sea. Using aspectral classifier, convection is detected based on thevertical flow velocity. The results are in agreement withobservations made by Lagrangian floats.

Acknowledgments. This research was funded by theOffice of Naval Research (ONR) under Grants N00014-95-1-1316 and N00014-97-1-0470, and by the MIT SeaGrant College Program under Grant NA46RG0434. Theauthors are thankful to ONR Program Manager Dr.Thomas Curtin and MIT Sea Grant Director Prof.Chryssostomos Chryssostomidis for their support. Theauthors thank Mr. Cliff Goudey, Mr. Joseph Curcio, Mr.Neil Best, Dr. Bradley Moran, and Mr. Robert Grieveof MIT Sea Grant for their help in experiments. Thanksalso go to Mr. Robert McCabe of the WHOI machineshop and Mr. Richard Norton of the David Taylor ModelBasin for their assistance during the calibration exper-iment. The authors thank Prof. Peter Guest of the NavalPostgraduate School, and Prof. Eric D’Asaro and Ms.Elizabeth Steffen of the University of Washington forsharing their Labrador Sea meteorological and floatsdata. The authors thank Prof. John Marshall and Dr.Helen Hill for providing the MIT ocean convectionmodel. The authors appreciate the comments and sug-gestions from the reviewers. Special thanks go to WHOISenior Scientist Dr. Albert Williams III for his importanthelp in the calibration experiment design and the Lab-rador Sea Experiment data processing and analysis. Thefirst author would also like to express his gratitude toDr. Albert Williams III and MIT Prof. John Leonard fortheir guidance from the Ph.D. thesis committee.

APPENDIX A

Potential Flow Velocity Disturbances Caused by aProlate Spheroid

The velocity potentials exterior to a prolate spheroidmoving in each of the 6 degrees of freedomA1 have beencompiled in Lamb (1932). Here, the steps necessary forcomputing the flow velocity components are shown andapplied to our particular case.

The natural coordinate system for the spheroid is thespheroidal coordinates, m, z, v, related to the CartesiancoordinatesA2 through

x 5 kmz (A1)2 2y 5 kÏ1 2 m Ïz 2 1 cosv (A2)2 2z 5 kÏ1 2 m Ïz 2 1 sinv (A3)

where x 5 6k are the foci of the spheroidal coordinates.The spheroidal body is defined by its major and minoraxes, a (along the x axis) and c, its surface given byeither

2 2 2x y z1 1 5 1

2 2 2a c c

or

z 5 z .0

We have2 2k 5 aÏ1 2 c /a , z 5 a /k.0

The velocity potentials found by Lamb (1932) aremost compactly written by mixing the coordinates

f 5 f(x, y, z, z)

with z(x, y, z) as an intermediate variable. In order toextract the velocities in the direction of the Cartesianaxes, we must evaluate =f where f is a function of (x,y, z) only. Hildebrand (1976) shows how to apply thechain rule for such a case:

]f ]f ]f ]z ]f ]f ]f ]z5 1 , 5 1 ,1 2 1 2]x ]x ]z ]x ]y ]y ]z ]y

y,z x,z

]f ]f ]f ]z5 1 . (A4)1 2]z ]z ]z ]z

x,y

A1 The degrees of freedom are

j 5 1, surge, translation in the x directionj 5 2, sway, translation in the y directionj 5 3, heave, translation in the z directionj 5 4, roll, rotation about the x axisj 5 5, pitch, rotation about the y axisj 5 6, yaw, rotation about the z axis.

A2 For brevity, subscript ‘‘AUV’’ has been omitted in the notationfor the vehicle coordinate system. As in Fig. 2, x, y, z of the AUVare coincident with the body at the instant under consideration, butat rest in the earth coordinate system.


TABLE A1. Potentials and velocities for flow around a spheroid.

j fj A u1j u2 j u3j

]f

]x

]f

]y

]f

]z

]f

]z

11 z 1 1 1

Ax ln 2[ ]2 z 2 1 z1

1 z 1 1 z0 0ln 222 z 2 1 z 2 10 0

]f ]f ]z1

]x ]z ]x

]f ]z

]z ]y

]f ]z

]z ]z

f

x

2Ax4 2z 2 z

21 z 1 1 z

Ay ln 22[ ]2 z 2 1 z 2 1

121 z 1 1 z 2 20 0ln 232 z 2 1 z 2 z0 0 0

]f ]z

]z ]x

]f ]f ]z1

]y ]z ]y

]f ]z

]z ]z

f

y

2Ay2 2(z 2 1)

31 z 1 1 z

Az ln 22[ ]2 z 2 1 z 2 1

121 z 1 1 z 2 20 0ln 232 z 2 1 z 2 z0 0 0

]f ]z

]z ]x

]f ]z

]z ]y

]f ]f ]z1

]z ]z ]z

f

z

2Az2 2(z 2 1)

4 0 0 0 0

523 z 1 1 3z 2 2

Axz ln 23[ ]2 z 2 1 z 2 z

21

33 z 1 1 6z 2 7z0 0 023z 2 ln 20 21 22 z 2 1 z 2 10 0

]f ]f ]z1

]x ]z ]x

]f ]z

]z ]y

]f ]f ]z1

]z ]z ]z

f

x

f

z

2Axz3 2(z 2 z )

623 z 1 1 3z 2 2

Axy ln 23[ ]2 z 2 1 z 2 z

21

33 z 1 1 6z 2 7z0 0 023z 2 ln 20 21 22 z 2 1 z 2 10 0

]f ]f ]z1

]x ]z ]x

]f ]f ]z1

]y ]z ]y

]f ]z

]z ]z

f

x

f

y

2Axy3 2(z 2 z )

The convention is that the right-hand sides are evaluatedas if z were independent.

To arrive at expressions for the derivatives of z withrespect to (x, y, z), we start by inverting the coordinatesystem relations:

ztanv 5 (A5)

y2 2 2 2 2 2 2 2 22k m 5 r 1 k 2 Ï(r 1 k ) 2 4k x (A6)2 2 2 2 2 2 2 2 22k z 5 r 1 k 1 Ï(r 1 k ) 2 4k x (A7)

where

2 2 2 2r 5 x 1 y 1 z .

Direct differentiation of z with respect to the Carte-sian coordinates is tedious. Instead we use an implicitapproach, differentiating both sides of Eq. (A7):

2 2 2(r 1 k )rdr 2 2k xdx22k zdz 5 rdr 1 (A8)

2 2 2 2 2Ï(r 1 k ) 2 4k x

where

rdr 5 xdx 1 ydy 1 zdz.

Combination of Eqs. (A6) and (A7) simplifies Eq. (A8):

2 2(z 1 m )rdr 2 2xdx22k zdz 5 rdr 1

2 2z 2 m

22z rdr 2 2xdx5

2 2z 2 m2 2z 2 1 z

5 2 xdx 1 2 ydy2 2 2 2z 2 m z 2 m

2z1 2 zdz. (A9)

2 2z 2 m

Since by definition]z ]z ]z

dz 5 dx 1 dy 1 dz,]x ]y ]z

we can conclude]z z 2 1/z x

5 (A10)2 2 2]x z 2 m k

]z z y5 (A11)

2 2 2]y z 2 m k

]z z z5 . (A12)

2 2 2]z z 2 m kTable A1 shows, for each degree of freedom, j, the

expressions for the potential f and its amplitudeA3 A

A3 Compared with Lamb’s formulation, we use the opposite sign forf, restrict motions to unit velocity, and absorb a factor k or k2 into A.Our amplitudes therefore differ from Lamb’s by a factor 21/k/(velocityamplitude) for the translational degrees of freedom, and 21/k2/(angularvelocity amplitude) for the rotational degrees of freedom.


FIG. B1. (top) Assembly diagram for the tow tank experiment, and (bottom) photo of the AUVbeing mounted on the carriage strut using a 58 wedge, with three ADV receiver tips visible.

adapted from Lamb (1932). Listed next are the the non-zero terms in the chain rule (A4) for the velocities. Theseventh to ninth columns show the derivatives of f withrespect to (x, y, z) as needed in the chain rule. Becauseeach of these coordinates only appears linearly in thepotentials, the derivatives are compactly written as f/x,etc. Finally, the derivative of f with respect to z is shown.With the coordinate derivatives from Eqs. (A10)–(A12),any flow velocity component (u1j, u2j, u3j) due to unitmotion in any degree of freedom can then be computed.A4

In our case, a/c 5 1/0.293, and (x, y, z) 5 (0, 0.304a,0.304a), leading to

A4 MATLAB routines that evaluate fj and uij, as well as examplesof their use, can be downloaded from ftp://ftp.mathworks.com/pub/contrib/v5/physics/pfs/.

u 5 20.0678 u 5 0.0000 u 5 0.000011 12 13

u 5 0.0000 u 5 0.0563 u 5 0.405321 22 23

u 5 0.0000 u 5 0.4053 u 5 0.056331 32 33

u 5 0.0000 u 5 0.0687a u 5 20.0687a14 15 16

u 5 0.0000 u 5 0.0000 u 5 0.000024 25 26

u 5 0.0000 u 5 0.0000 u 5 0.0000.34 35 36

These are the components of the disturbance matricesA [Eq. (3)] and B [Eq. (4)], respectively.


FIG. B2. Comparison of the calibration experiment results and the theoretical predictions. Velocity componentsy x, y y, and y z are in ADV’s coordinate system. Symbol color denotes velocity component of experimental data:blue—y x, green—y y, red—y z.

APPENDIX B

Calibration Experiment at the David Taylor ModelBasin

To ascertain the AUV hull’s influence on the flowvelocity measurement, we carried out a calibration ex-periment in the David Taylor Model Basin before theLabrador Sea Experiment. The tow tank has a large crosssection to minimize influence from the boundaries, andthe carriage has a precise speed control. In the tank, acomplete AUV hull equipped inside with an ADV wastowed by the carriage at different attack angles underdifferent speeds.

a. Experiment design

Let us present the experimental setup in relation toEq. (2) and Fig. 2. In consideration of the availablefacilities, we did not attempt to generate the vehicle’srotational motion, so V 5 0 in Eq. (2). The tank wateris still, so U 5 0. Then Eq. (2) is simplified to

u 5 (A 2 I)V.m (B1)

Matrix A, as given in Eq. (3), is computed by thepotential flow theory described in appendix A. This ma-

trix depicts the AUV hull’s influence on the flow ve-locity measurement, which is induced by the vehicle’stranslational motion. At a series of AUV speeds, ADV-measured flow velocities are to be compared with theo-retical predictions computed by Eq. (B1) using matrixA in Eq. (3). To test out various flow orientations relativeto the AUV, we need to enable different combinationsof the vehicle’s yaw and pitch angles.

The experimental structure is illustrated in Fig. B1.The structure is composed of three parts: a rotatingbracket, a wedge, and a hull platform. The upper rect-angular plate of the rotating bracket attaches the wholeload to the tow tank carriage. Its lower circular plateconnects to the wedge via four bolts. This circular platehas multiple bolt holes to permit yaw angles of 08, 58,108, 158, 308, and 458. The wedge is for realizing theAUV’s pitch/roll angles of 58, 108, 158, and 308. Thehull platform’s upper circular plate connects to thewedge, and its lower rectangular plate attaches to theAUV’s inner fairing. Its 458 slanted clamp (not visiblein Fig. B1 from that perspective) holds the ADV probe.Two installation errors were found by two calibrationruns (zero yaw and zero pitch with the AUV hull on,and zero yaw and zero pitch without the AUV hull): (i)2.78 rotation of the ADV probe in the clamp, and (ii)


TABLE B1. Tested combinations of yaw and pitch angles (8).

PitchYaw 215 25 0 5 15

21525

05

XXX

XXX**

XX*,**X

XXX

X*XX

X ADV Mounted in hull, latch attached.* ADV only.** ADV Mounted in hull, no latch.

TABLE B2. Relative errors between experimental results andtheoretical predictions.

PitchYaw 2158 258 08 58 158

2158258

0858

4%4%3%

3%2%3%*

3%2%2%

3%3%2%

2%2%2%

* Only at 1-knot carriage speed.

2.28 misalignment between the hull platform’s centerlineand that of the AUV.

It should be noted that in this calibration experiment,the ADV probe pointed 458 upward on the vehicle’s portside, as shown in Fig. B1. In the Labrador Sea Exper-iment, the ADV probe pointed 458 downward on thevehicle’s starboard side, as shown in Fig. 1. The purposeof the change is to facilitate field recovery of the AUVat the end of missions, which requires contacts at theupper half of the vehicle. This difference is trivial, sinceit is equivalent to rotating the vehicle for 1808 about itsalongship axis. It can be shown that this diagonal moveof the ADV position from the port side to the starboardside causes no change to matrix A, but only sign flip-pings in TADV→AUV [the coordinate transformation matrixgiven in Equation (6)]. In the 1998 Labrador Sea Ex-periment, the AUV had a V-shaped latch at its nose fordocking to an underwater station. We also added a latchto the vehicle during the calibration experiment.

As shown in Fig. 2, the AUV coordinate system isdefined such that its x axis points forward, y axis tostarboard, and z axis downward. Accordingly, yaw isthe angle between the AUV’s alongship central verticalplane and that of the tow tank; pitch is the angle betweenthe AUV’s x axis and the horizontal plane. A plus signof yaw means that the AUV steers to the starboard side,while for pitch it means the vehicle’s nose is up. Dif-ferent combinations of yaw and pitch angles as shownin Table B1 were tested. At each AUV yaw/pitch, thecarriage ran successively at 1, 2, and 3 knots, each speedlasting for about 40 s. We distributed neutrally buoyantglass powder (Potters 1997) in the tank water to providestrong echoes for the ADV’s measurement.

b. Comparison of theoretical and experimentalresults

Figure B2 shows the comparison of experimental re-sults (with the AUV’s latch on) and the theoretical pre-

dictions. The components y x, y y, and y z are in the ADV’scoordinate system. The two installation errors have beencompensated for in computations and also in plottingof Fig. B2. Each velocity point in Fig. B2 is the meanvalue of 600 data points (sampling rate 5 25 Hz) underone constant carriage speed, which is further normalizedby the carriage speed for display. With bias removed,the total measurement noise for each mean velocity isabout 0.1 cm s21.

One setting in the fourth panel of Fig. B2 was pitch5 58 (nose up) and yaw 5 22.28 (both steered to theside where the ADV was mounted). We tested this dou-bly unfavorable orientation to determine whether wakeinduced by the latch had impact on flow measurement.In AUV cruises in the 1998 Labrador Sea Experiment,attack angle due to current flow was no more severethan the above setting. Tow tank experiment results inthe fourth panel of Fig. B2 maintain agreement withtheoretical predictions at all three speeds, not affectedby the latch’s wake at the above orientation.

Relative errors between the experimental results andthe theoretical predictions (corresponding to Fig. B2)are shown in Table B2, defined as

\V 2 V \experiment theory 2relative error 5 ,\V \experiment 2

where \ · \ 2 denotes the Euclidean norm. Relative errorsat different carriage speed (1, 2, 3 knots) are averagedto give the tabulated values. Based on the good agree-ment between experimental results and theoretical pre-dictions, the algorithmic step of removing AUV hull’sinfluence on flow measurement is validated.

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