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IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 2, APRIL 2007 327

Simulation of an Inertial Acoustic Navigation SystemWith Range Aiding for an Autonomous

Underwater VehiclePan-Mook Lee, Member, IEEE, Bong-Huan Jun, Kihun Kim, Jihong Lee, Member, IEEE, Taro Aoki, and

Tadahiro Hyakudome

AbstractThis paper presents an integrated navigation systemfor underwater vehicles to improve the performance of a conven-tional inertial acoustic navigation system by introducing rangemeasurement. The integrated navigation system is based on astrapdown inertial navigation system (SDINS) accompanyingrange sensor, Doppler velocity log (DVL), magnetic compass, anddepth sensor. Two measurement models of the range sensor arederived and augmented to the inertial acoustic navigation system,

respectively. A multirate extended Kalman filter (EKF) is adoptedto propagate the error covariance with the inertial sensors, wherethe filter updates the measurement errors and the error covarianceand corrects the system states when the external measurementsare available. This paper demonstrates the improvement on therobustness and convergence of the integrated navigation systemwith range aiding (RA). This paper used experimental data ob-tained from a rotating arm test with a fish model to simulate thenavigational performance. Strong points of the navigation systemare the elimination of initial position errors and the robustness onthe dropout of acoustic signals. The convergence speed and condi-tions of the initial error removal are examined with Monte Carlosimulation. In addition, numerical simulations are conducted withthe six-degrees-of-freedom (6-DOF) equations of motion of anautonomous underwater vehicle (AUV) in a boustrophedon survey

mode to illustrate the effectiveness of the integrated navigationsystem.

Index TermsAcoustic range sensor, Doppler velocity log(DVL), inertial measurement unit (IMU), underwater navigation.

I. INTRODUCTION

STRAPDOWN inertial navigation systems (SDINSs) com-

posed of three accelerometers and three gyros are fasci-

nating sensors for the localization and navigation of underwater

Manuscript received February 18, 2006; accepted June 20, 2006. Thiswork was supported in part by the Ministry of Marine Affairs and Fisheries(MOMAF) of Korea for the development of a deep-sea unmanned underwatervehicle.

Associate Editor: L. L. Whitcomb.P.-M. Lee, B.-H. Jun, and K. Kim are with the Maritime and Ocean Engi-

neering Research Institute (MOERI), Korea Ocean Research and DevelopmentInstitute (KORDI), Daejeon 305-343, Korea (e-mail: [email protected]; bh-

[email protected]; [email protected]).J. Lee is withthe Mechatronics Engineering Department, Chungnam National

University, Daejeon 305-764, Korea (e-mail: [email protected]).T. Aoki and T. Hyakudome are with the Japan Agency for Marine-Earth

Science and Technology (JAMSTEC), Kanagawa 237-0061, Japan (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JOE.2006.880585

vehicles. The errors of inertial measurement units (IMUs), how-

ever, increase with time elapse due to the inherent bias errors

of gyros and accelerometers. Inertial navigation systems (INSs)

give accurate position information for short-time periods though

bias error accumulates with time. This accumulation leads to

a very large position error requiring that additional sensors be

needed to compensate for the position errors of the INS [1].

Successful surface navigation systems have been developedby integrating the global positioning system (GPS) with inertial

sensors. GPS is a good positioning sensor for air, land, and mar-

itime vehicles, but it is available only at surface and air. There-

fore, using GPS for underwater navigation is limited to the case

of shallow-water operations as a vehicle must surface regularly

to update their position information with GPS [2][6].

An INS, especially a directional gyro, cooperating with a

Doppler velocity log (DVL) is a successful navigation system

for underwater vehicles [7][15]. Dead-reckoning (DR) naviga-

tion is useful when it can get the absolute velocity and attitude

of underwater vehicles. Even if the gyro is highly precise, the

navigation system still needs additional reference sensors, suchas GPS, long baseline (LBL), ultrashort baseline (USBL), etc.,

when it is operated in long-term duration, because of the scale

effects of velocity sensors. Furthermore, the initial localization

of an underwater vehicle equipped with an INS, even accom-

panied by DVL, is difficult to set exactly without additional in-

formation. Acoustic positioning systems have no accumulative

error, while they do have high-frequency error and their update

rate is usually low. LBL use is also limited when it comes to

arctic undersea surveys because of difficulties in launching and

recovering the transponders under ice.

USBL is hard to use alone for the accurate navigation and

control of an underwater vehicle [16]. However, USBL is one

of localization sensors, and it can be applicable for underwaternavigation combined with complementary sensors [17]. Jouf-

froy and Opderbecke [18] developed a trajectory estimation

technique using gyro-Doppler and USBL measurements, which

consists of diffusion-based observers processing a whole tra-

jectory segment.

Larsen [7], Beiter et al. [19], and Uliana [20] successfully

proposed a hybrid navigation system based on an inertial sensor

combined with acoustic velocity sensors. Whitcomb et al.

[8][12] proposed navigation systems integrating a DVL signal

to an LBL system for the enhancement of position accuracy.

Leeet al. [14], [15] proposed an inertial navigation algorithm

assisted by DVL, depth, and heading sensors. The IMU-DVL

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328 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 2, APRIL 2007

Fig. 1. Navigationalcoordinates of theunderwater vehicle with range measure-ment.

Fig. 2. Coordinates of an AUV and two range transducers.

navigation system gave slow drift in the estimated position

because of the integration of inherent errors from the sensors.

The error sources of the DVL-based INS are misalignment,

environmental noises, scale effects, and acceleration drifts,

which are directly reflected to the navigation performance.Range measurement can give useful information to under-

water navigation systems having simpler structures than LBLs.

Lasen [7] proposed a synthetic LBL navigation system using a

precise DR navigation system with range measurements from

a single transducer. Gadre and Stilwell [21] proposed under-

water navigation systems by utilizing range measurements from

a single location, and showed observability of the method. Lee

et al. [22], [23] proposed hybrid underwater navigation sys-

tems based on a strapdown IMU accompanied by one or two

range sonar sensors as well as DVL, depth sensor, and magnetic

compass. The main ideas were to improve the performance of

the IMU-DVL navigation system with range aiding (RA) andrange-phase aiding (RPA).

This paper revises the integrated IMU-DVL navigation

system of an underwater vehicle with one range sensor [22],

and evaluates the navigation performance in the drift charac-

teristics of estimation and the effect of initial position error on

the navigation system. We suppose that one or two transducers

are installed on an underwater vehicle [e.g., autonomous un-

derwater vehicle (AUV) or remotely operated vehicles (ROV)]

and measure the distance from the vehicle to an underwater

reference station, where the transducers have been installed,

as shown in Figs. 1 and 2. We can get phase measurement

as well as range by processing the time delay of the arrival

signal with the two transducers on the underwater vehicle.Hereafter, the proposed navigation system with RA is called

the IMU-DVL-RA navigation system, and the other system

with RPA is called the IMU-DVL-RPA. Two measurement

models for the integrated navigation system including the range

measurements are designed to implement an extended Kalman

filter (EKF) in multirate, where the order of the navigation

system states is 21 and 22, respectively. The multirate EKF

propagates the error covariance with the inertial sensors, and itupdates the measurement errors and the error covariance and

corrects the system states when the external measurements are

available.

Navigational simulations were conducted with experimental

data obtained by a rotating arm test of a small fish model in the

Ocean Engineering Basin (OEB) at the Maritime and Ocean En-

gineering Research Institute (MOERI), Korea Ocean Research

and Development Institute (KORDI), Daejeon, Korea. Thefish

model was equipped with an IMU, a DVL including heading

sensor, and depth sensor, where we can receive the known mo-

tion and position data in the basin. Experimental simulations

were conducted with the IMU-DVL-RA navigation system. In

the navigation simulation, the range data is artificially gener-ated. We confirm the effectiveness of the integrated navigation

system with the experimental data and show that the navigation

system reduces the estimation error by eliminating its growth

with time. This paper checks the convergence characteristics of

the integrated navigation system when the initial position error

exists. This paper also surveys the robustness of the naviga-

tion system over signal dropout from acoustic sensors. Finally,

numerical simulations were conducted with the 6-DOF equa-

tions of motion of an AUV in a boustrophedon survey mode

to demonstrate the effectiveness of the integrated navigation

system with RA.

II. IMU-DVL NAVIGATIONWITH RA

A. Navigation Equation of SDINS

For an SDINS, the navigation equation of a vehicle can be ob-

tained with the differential equations from the body frame of the

inertial sensors on board the vehicle calculating the frame rota-

tion. A navigation frame mechanism, earthcenterearth-fixed

reference coordinate, is generally used when underwater vehi-

cles maneuver around the earth. The ground speed is ex-

pressed in the navigation coordinates of this mechanism. The

rate of change of with respect to the navigation axes can be

found in terms of its rate of change in the inertial axes as follows

[1], [15]:

(1)

where

(2)

(3)

(4)

The variables and represent the latitude and the longi-

tude, and and are velocity components of the ve-

hicle with respect to the navigation coordinates in the north,

east, and downward directions of the Earth, respectively.is the Earths rate with respect to the inertial frame, and is

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LEEet al.: SIMULATION OF AN INERTIAL ACOUSTIC NAVIGATION SYSTEM WITH RA FOR AN AUV 329

the Earths rotation rate. is the turn rate of the navigation

frame with respect to the Earth, and and are the

components of in the north, east, and downward direction,

respectively. is the direction cosine matrix between the nav-

igation coordinate and the body coordinate. is the external

acceleration acted to the vehicle in the body frame, while is

the gravitational acceleration in the navigation coordinate. Thesuperscript and denote the components described in the nav-

igation coordinate and the body coordinate, respectively.

When we navigate the vehicle with respect to the body frame,

the turning rate vector of the vehicle takes the following form

with the direction cosine matrix :

(5)

where is a skew-symmetric matrix described by the gyro

measurement and is a skew-symmetric matrix com-

posed of and [1].

For the SDINS, the rates of change in latitude and longitude

can be expressed in terms of a meridian radius of curvatureand a transverse radius of curvature of the Earth as follows:

(6)

where

[1]. and represent the mean radius of the Earth, the

major eccentricity of the Earth, and the depth under the sea sur-

face, respectively. The change rate of depth can be expressed as

(7)

In this paper, a perturbation method is used to derive the error

equation of the SDINS algorithm. The perturbation method an-

alyzes the navigation system by defining the error as the dif-

ference between the estimated and true values. For a nonlinear

system, this method can be applied when the error is small. As-

suming the errors exist in the position, velocity, and attitude

in (1)(7), the perturbation induces the differential equations

(8)(10), as shown at the bottom of the page.

Here, is the attitude error vector:

and are the attitude errors of the vehicle with

respect to the navigation coordinate in the north, east, and

downward direction, respectively. denotes the variation of the

components. Note and . Bytaking the variation for the turn rates (3) and (4), we can derive

the additional variation equations (11)(14), as shown at the

bottom of the page.

Using (8)(14), we can formulate an error model of the

SDINS for the navigation of an underwater vehicle with RA.

The quaternion attitude representation is adopted to calculate

the direction cosine matrix in the navigation algorithm.

B. Error Model of Sensors

The errors of inertial sensors are mostly measurement errors,

acceleration-dependent biases, scale factor errors, nonlinearity,

axis misalignment, and gyro sensitivity to the force applied.Various compensation techniques are used to reduce the errors

through alignment, calibration, and initialization in the factory

and in field online calibration [1], [24]. For example, Vik and

Fossen [5] have modeled an IMU with scale factor errors, bi-

ases, and Gaussian white noise signals.

The errors of inertial sensors and gyros of an SDINS can gen-

erally be modeled as a combination of random bias and random

noise [1]. Some portions of instrumentation error are best repre-

sented as a constant but unknown random variable [24]. In this

paper, we assume that the major error of the SDINS is a random

walk bias error and Gaussian random noise. The output errors

of accelerometers and gyros and can be expressed with

the summation of random walk bias and white noise vectors as

(15)

(16)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

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where the measurement errors and are assumed

Gaussian white noises that have zero mean and the error vari-

ances and , respectively. The unknown constants and

are modeled as [24]

(17)

(18)

Here, the model states that the variables and show random

walk process and have zero initial values and the variances

and , respectively.

The auxiliary navigation sensors, that is, the depth sensor,

DVL, and the magnetic compass, are good complementary sen-

sors for the inertial sensors. This paper modeled the errors of

the sensors as the summation of random constants and white

noises. We assumed that the random constants of the biases are

unknown but the variances of the initial values are known.

Then, we can express the differences of the estimates from

the SDINS and the measured values from the depth, DVL, and

heading sensors as follows:

(19)

(20)

(21)

where is the bias error of the depth sensor, is the bias

error of the DVL, represents the heading bias, denotes theGaussian white noise, and its subscripts, and , and de-

note each component of the measurements. ^ denotes the es-

timated value. The variance of the depth, the DVL, and the

heading sensors are , and , respectively.

In (20), means the estimated direction cosine related with

the true that is found as

(22)

where is a skew symmetric matrix composed of the attitude

errors [1].

This paper introduces additional measurement of the range to

improve the navigation performance of the IMU-DVL naviga-

tion system. We suppose that a transducer installed on the un-

derwater vehicle sends an interrogation signal and a transponder

installed at a known reference station responds after receiving

the interrogation signal. The vehicle can measure the range

from the vehicle to the reference station by calculating the traveltime. Fig. 1 shows the coordinates of the vehicle.

We can estimate the range with the navigation system, how-

ever, this estimate will include estimation error . The estima-

tion error is induced by the accumulation of inertial sensor error

and the inaccuracy of the DVL, depth, and heading measure-

ment. On the other hand, the measured range also has

measurement errors. We assume that the measurement error is

also composed of deterministic bias error plus random noise.

The bias error is mainly induced by incorrect sound speed, and

by the AUVs motion between transmitting and receiving the

acoustic signal of the range transducers. Then, we can derive

the difference between the estimated distance and the measured

(23)

where and and are the relative

positions of the vehicle from the reference station in the global

coordinates. In the range measurement, we can consider that one

of the sources of the bias error is the position error caused

by the vehicles motion while the acoustic signal travels. The

variance of the random noise is defined as .

C. IMU-DVL-RA Navigation Model

The IMU-DVL navigation system with RA, calledIMU-DVL-RA navigation, can be modeled as

(24)

where (25)(27), shown at the bottom of the page, hold.

The components of the system matrix given in the

Appendix are the time-varying system matrix that are derived

from the differential equations of the SDINS (8)(10) and

the variation (11)(14). The state variable has 21 error

states including the position errors, velocity errors, error of

attitude and heading angles, the bias errors of accelerometers,

gyros, range, depth, DVL, and heading. The system error

(25)

(26)

(27)

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represents the vector of the Gaussian white random noise and

the random walk error of accelerometers and gyros

(28)

which have mean zero and the error variance matrix .

For digital implementation, we convert the system equation

to a discrete model with the sampling rate

(29)

where and .

The measurements of range, heading, depth, and velocities

provided by the external sensors constitute the Kalman filter

measurement. The measurement difference at time may be

expressed in terms of the error state variables as

(30)

where (31)(34), shown at the bottom of the page, hold, and

denotes the skew symmetric matrix of the velocity.

Note that the sampling rate of the external measurement is

different from the high-frequency rate of the SDINS. There-

fore, the error covariance of the discrete time measurement is

for the external measurement rate . Here, the

measurement error variance is .

In addition, we note that the navigation (29) and the measure-

ment (30) are observable having full column rank 21 over the ob-

servability matrix of the pair . When the system state

is observable, it is possible to estimate the state in a minimum

of discrete-time steps, however, stability and robustness are

not usually guaranteed. Error convergence and robustness will

be discussed in the following sections.

The system matrix (26) is nonlinear and time varying. For

the underwater navigation algorithm, therefore, we implement

an EKF which has optimal performance for linear systems and

ad hocnonlinear systems. We implemented the EKF [25] with

the system error model (29) and the measurement model (30).

Thefilter is multirate because of the different sample rates, and

this is achieved in two steps.

The dynamic system errors propagate forward with a high-

frequency sample rate when the external measurements are un-

available. The inertial system errors remain unchanged and the

filter propagates the error covariance matrix as [1]:

(35)

(36)

denotes the expected value of the covariance matrix attime predicted at time . The system integrates the signals

from the inertial sensors and calculates the attitude, velocity, and

position of the vehicle with the previous state errors.

When the external measurements are acquired, we can calcu-

late the Kalmanfilter gain, update the error covariance matrix,

and estimate the system state errors. The estimates of the errors

of the navigation system states are derived using the measure-

ment difference and the Kalman filter gain as follows:

(37)

The Kalman filter gain is calculated and the error covariance

matrix is updated according to

(38)

(39)

Fig. 3 depicts the schematic of the multirate EKF for the in-

ertial acoustic navigation system with RA, namely, the IMU-

DVL-RA navigation system.

III. IMU-DVL NAVIGATIONWITHRPA

This section presents an inertial acoustic navigation system

with range and phasing aiding. We assume that two range trans-

ducers are installed on the upper side of an AUV, and ,

respectively, and that a transponder is installed at a reference

station moored on the seafloor as shown in Fig. 2. The range

transducer transmits an interrogation and the transponder at

the reference station responds after receiving the interroga-

tion signal. By receiving the response signal and calculating the

arrival time differences of the two range transducers, we can

measure the distance and the incident angle of the AUV

from the station.

We suppose that the AUV is located at in global

coordinate, and that the range transducer is installed at

(31)

(32)

(33)

(34)

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from the center of the AUV in the body

frame. Then, we can calculate s position in the global frame

from , where , and are

(40)

and is the th row and th column component of .

The distance between the reference station and the range

transducer is . If the range trans-

ducer is installed at the rear of the AUV separated by distance

from along the -axis as depicted in Fig. 2, we can denote

. Then, the incident angle can be de-

fined with , where

and is confined to . For simple notation, let

and ; then, the

incident angle is reduced to

(41)

This section derives a measurement error model for the range

and phase of the vehicle. Let represent the bias error and

represent the random error of the range transducer . As

in the previous section, the difference of and can be

reduced to thefirst order as

(42)

using the partial derivatives with and . This is the same

form as (23).

The estimated incident angle also includes estimation error

due to the error of the estimated position and attitude of theAUV in a navigation system. The estimated incident angle can

be modeled as where is the true incident angle.

The incident angle measurement also includes bias error and

random error similar to the range measurement model. Let

represent the bias error and represent the random error of

the incident angle. Then, the measured incident angle can be

modeled as .

The estimation error of the incident angle can be obtained

using (40) and (41) and partial derivatives with and .

The difference of and is obtained tofirst order as

(43)

where

The difference of the incident angle (43) can be augmented to

the measurement equation of the navigation system.

If the AUV is far off from the reference station, then

and we can measure the incident angle with the arrival time

difference of the two range transducers as follows:

(44)

It is noted that the noise is dependent on the incident angle

because is the inverse cosine function of the ratio of the range

difference.

We can derive the error model for the navigational system ofthe SDINS with range and phase aiding, IMU-DVL-RPA navi-

gation. Augmenting the bias error terms for the range and inci-

dent angle additionally, the error model of the navigation equa-

tion is derived as follows:

(45)

where (46), shown at the bottom of the page, holds.

The state variable has 22 error states: is the bias

error of the range transducer and is the bias error of the

incident angle. The others are the same as (25). The system

error is the noise of the accelerometers and gyros, which

has mean zero and error covariance . The system matrices

and have the same structure with and ,

respectively, but the system order is different.

The measurements (19)(21), (42), and (43) of range, inci-

dent angle, depth, velocities, and heading are provided by the

external sensors and constitute the Kalmanfilter measurement.

The measurement difference at time may be expressed in

terms of the error state variables as follows:

(47)

where (48)(50), shown at the bottom of the next page, hold,

and denotes the measurement noise and the subscriptsdenote each measurement.

We note that the navigation system IMU-DVL-RPA is ob-

servable having full rank 22 over the observability matrix. On

the other hand, the error variance of the incident angle is not

constant. As shown in (45), the phase error variance depends

on the incident angle even if the error variance of the range dif-

ference is constant. In addition, the measurement is noisy when

the incident angle is near to zero or . It is necessary to increase

(46)

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Fig. 3. Schematic diagram of the multirate EKF of the inertial acoustic navi-gation with RA.

the measurement error variance of the incident angle when the

estimate of incident angle is near to zero or .

After converting (47) into a discrete system, we can imple-

ment the EKF with the discrete system error model and the

measurement model (47), the same as in the previous navigation

system DVL-IMU-RA. The system errors propagate forwardwith the high-frequency sampling rate when the external mea-

surements are unavailable. When the external measurements

are acquired, the navigation system calculates the Kalman filter

gain, updates the error covariance matrix, and estimates the

system state errors.

IV. SIMULATIONWITHROTATINGARMEXPERIMENT

A. Navigation Sensors and Rotating Arm Experiment

A rotating arm experiment was performed to get the known

motion, position, and inertial data of an underwater vehicle, and

Fig. 4. Rotating arm testsetup withan artificial fish model equipped with IMU,DVL, and depth sensor.

to simulate the IMU-DVL-RA navigation system with the mea-

sured data. Experiments were performed in the OEB of MOERI,KORDI, of which the size is 50 30 3.5 m in .

An artificial smallfish was attached to a rotating arm via a ver-

tical strut so that it could make exact circular motions at various

speeds. The rotating arm wasfixed at the center of the carriage

moving over the OEB. Its total length is 10 m and the fish model

was installed under the arm 8.0 m from the rotating center. Fig. 4

shows the rotating arm and the fish.

An IMU, a DVL, and a depth sensor were installed inside

thefish model. The inertial sensor used for the experiment is a

Honeywell IMU, HG1700AG11 [26]. It consists of three ring

laser gyros and three accelerometers of the resonant beam type.

The IMU has good performance for inertial measurements: the

bias, random noise, velocity random walk of the accelerometers

are 1 mg, 0.8 ft/s , 0.065 ft/s h, respectively, and the bias,

random noises, angular random walk of the gyros are 1 /h, 8

mrad/s, 0.125 h, respectively. The output frequency is 100

Hz. The DVL is a workhorse navigator (WHN) 300 from RD

Instruments, Inc., Poway, CA [27] and its operating frequency

is 300 kHz. It has four transducers in the Janus configuration

that make it possible to measure three directional velocities. It

has excellent performance of which the accuracy is 3 mm/s at

1-m/s vehicle speed and the maximum sample rate is 7 Hz. The

DVL includes a magnetic compass and a tilt sensor to measure

heading, roll, and pitch.

(48)

(49)

(50)

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TABLE ISENSOR M ODEL IN THE IMU-DVL NAVIGATION SYSTEM

WITHRANGEMEASUREMENT

The rotating experiment was performed for 23 min with con-

stant speed of the fish at 0.5 m/s, and the sampling rate of the

IMU and the DVL at 100 and 2 Hz, respectively. The higher

sample frequency is desired to get better precision. Since the

experiment was conducted in the rectangular basin OEB, the

walls and bottom of the basin reflected the acoustic signals well.

Therefore, we have fixed the DVL sample rate at 2 Hz to get

stable data. During the first 20 s, the fish was stationary at theinitial position for the navigation system to process the initial

alignment of the inertial sensors. After 20 s, its rotating speed

was gradually increased until thefish speed reached 0.5 m/s.

As the speed of the vehicle increased, the noise level of the

gyros and the accelerometers from the IMU sensor increased

due to the vortex-induced vibration around thefish and the sub-

merged parts of the strut. The rotating arm and the strut were

made of steel, but their lengths were long, therefore, it was hard

to make pure motions without vibratory random noise from the

fish connected to the flexible structure. We selected the measure-

ment error variances of the gyros and the accelerometers from

the experiment as shown in Table I.The measured heading signal showed distorted change during

the continuous rotation because of the magnetic fields variation

around the steel-structured carriage of the basin. The maximum

difference was 15 in heading angle. The magnetic compass

provides a heading reference with 0.1 accuracy but it is apt to

be contaminated by nearby magnetic bodies. Bias of the heading

sensor was set to 10 and bias of a depth sensor to 0.5 m. Tilt an-

gles obtained from the DVL were inclined due to the centrifugal

force. The DVL signal also showed noisy data due to the vibra-

tory motion of the fish and the attitude errors. We selected the

DVL error variances from the experiment as shown in Table I.

We simulated the inertial acoustic navigation with the errorvariances of the sensors. Table I also depicts the bias errors and

random noises of the other sensors to simulate the navigation

system. The variances of each sensor are bigger than the speci-

fication of the sensor in factory.

The range sonar can measure the distance without bias error

in the stationary condition. In the real world, however, the bias

error of the range measurement will increase due to the motion

of the vehicle and environmental noise. We suppose the sample

rate of the range sensor is two samples per second. Since the

speed of the vehicle is 0.5 m/s and the time interval of the range

signal is 0.5 s, we conservatively set the bias error of the range

measurement to 0.25 m root mean square (rms) and the randomerrors to 0.5 m rms.

Fig. 5. Estimatedposition and navigation errors with the IMU-DVL navigation

system excluding range measurement. (a) Estimated position in - plane.(b) Estimation errors in

-

plane and 3-D space.

In this paper, the range data was generated with an artificial

range measurement sensor, where the reference in the global

coordinate was located at ( 30.0, 30.0, 10.0) m from the initial

position (0.0, 0.0, 0.0) of the fish model. After generating the

constant bias errors and random noises for the range, the mea-

surement range was obtained by adding them to the true range

of the vehicle.

B. IMU-DVL Navigation

Before simulating the proposed navigation algorithm, the

conventional IMU-DVL navigation system [15] was tested tocompare the navigation performance. Fig. 5 shows the esti-

mated position in the global coordinate, - plane and the

navigation error for the conventional navigation system. The

navigation system updated the error covariance and revised

the state variables using 2-Hz measurement signals from the

DVL, magnetic compass, and depth sensor. The IMU-DVL

navigation system corrected the error covariance and updated

the system state variables whenever the external measurements

were obtained.

It is shown that the estimated error of the inertial-Doppler

hybrid navigation system is confined to within 1.3 m position

errors during the 23 min of a circular motion. However, the esti-

mation errors of the navigation system oscillate as time elapses,where the oscillatory drift is mainly caused by the errors of the

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Fig. 6. Estimation errors in

-

plane with the conventional DR method.

Fig. 7. Estimation errors in

-

plane with the IMU-DVL-RA navigationsystem.

accelerometers in the IMU [1]. While the vertical position es-

timation is directly corrected by the measured depth, the hor-

izontal positions are indirectly updated with the DVL infor-

mation. The DVL corrects the velocity so that the navigation

system includes integral effect of the bias error and the scale

effects of the velocity in the navigation algorithm. More pre-cise DVL and IMU measurement are required to reduce the drift

of the navigation system, but the increment of the estimation

error with time elapse is unavoidable without eternal position

correction.

C. DR Navigation

DR navigation was performed to compare the performance

of the IMU-DVL and the IMU-DVL-RA navigation systems.

The DR navigation estimates position by integrating the mea-

sured velocity after transforming the measured velocity to the

navigation coordinates. Integration was performed with Eulers

method at every DVL sampling time, which is 0.5 s in this exper-iment. Fig. 6 shows the estimation error of the vehicle with the

DR navigation. The result indicates very similar performance to

the conventional IMU-DVL navigation system. Therefore, the

DR navigation is also a good navigation method when we get

exact initial position and can measure absolute velocity with the

DVL. On the other hand, the performance of the DR navigation

system can only be improved with a higher sample rate of the

DVL, such as 5 Hz.

D. IMU-DVL-RA Navigation

Simulation of the IMU-DVL-RA navigation system was per-

formed. The error variance matrices of the system model and themeasurement model were defined with the standard deviations

Fig. 8. Estimated position errors of thefish with the IMU-DVL-RA navigationsystem.

of the sensors shown in Table I. The relative distance of the ve-

hicle to the reference station was estimated using the estimated

position whenever the vehicle received the range information,

and it is updated into the measurement matrix (30). Every 0.5 s,

the navigational states and parameters in (29) were updated and

corrected with the range data. We updated the navigational states

and parameters using range information and DVL data at the

same time to meet the convenience of simulation, however, it is

not necessary to synchronize the two data acquisition systems.

Fig. 7 depicts the tracking errors of the IMU-DVL-RA navi-

gation system. The navigation system with RAfinely estimatesthe position of the underwater vehicle in general. The position

error is increased due to the bias error of the range measure-

ment. The estimation error of the proposed navigation system

with range measurement does not increase as time passes and

the error is less than 1.1 m along the whole simulation time. The

horizontal position error of the IMU-DVL navigation system as-

sisted by the range information is less than the error of the con-

ventional IMU-DVL and the DR navigation systems.

The accuracy of the IMU-DVL-RA navigation is independent

of time elapse. The strong point of the navigation with RA is that

it is able to eliminate the error accumulation of the conventional

IMU-DVL navigation system, which is unavoidable for conven-tional inertial acoustic navigation systems.

Note that the error slightly increased at around 1000 s. This

was caused by the estimation drift along the tangential line of a

circle centered at the reference station. Here, we define the circle

asrange circle,of which the radius is the horizontal distance

between the reference station and the vehicle projected into the

- plane. In this case, the range circle is centered at ( 30, 30,

0) and its radius is 30 2 m. After the estimated position of the

vehicle reaches a point on the range circle, the range informa-

tion does not affect the error correction in the navigation algo-

rithm any more. This phenomenon is obvious especially when

the vehicle is in a stationary condition or moves along the range

circle. Sometimesit may generate wrong correction data in theseconditions.

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Fig. 9. Estimated position with the IMU-DVL-RA navigation system under 1-min dropout of DVL and range.

Fig. 8 showsthe - planar motion of the estimation error in

large. The estimation error drifts along the tangential line. Since

the vehicle moves in rotation and changes position in this simu-

lation, the tangential drift cannot grow due to the range change

and the navigation system correct estimate of the position to-wards reducing the estimation error. In a stationary condition,

the correction mechanism works similarly as well, however, the

IMU-DVL-RA navigation system shows errors in the estimated

position. The estimation error of IMU-DVL-RA increases along

the range circle with the amount of the projected components to

the tangential line of the range circle among the estimation error

of the IMU-DVL navigation system.

E. IMU-DVL-RA Navigation With Acoustic Signal Dropout

Acoustic equipment is apt to lose reception signals due to en-

vironmental noises and to receiving wrong data caused by un-structured disturbances and multipath responses of acoustic sig-

nals. This section considers practical problems such as outliers,

outages, and dropouts of signals. These phenomena can lead to

catastrophic effects in the navigation system with complemen-

tary acoustic sensors.

We can make a watch circle and remove the outliers of the

range data when it shows abrupt change in range measurement

compared to the stochastic characteristics of the sensor and ve-

hicle dynamics. We can make anotherfilter for the DVL to get

rid of velocity outliers as well. However, we cannot eliminate

the influence of the outages and dropouts from the filter.

In this section, we simulate the influence of intermittent

outliers and short-duration dropouts of the range sensor andthe DVL in the integrated navigation system IMU-DVL-RA.

When dropouts and/or outliers occur, we design the navigation

system to discard the unreliable data and to keep the old data

in its memory. The IMU-DVL-RA navigation system changes

the error variances of the failed sensors to reduce the influence

of the wrong signals when sequential failures occur in therange sensor or the DVL. In cases when two or more sequential

failures happen, in this paper, we select the noise level of the

DVL and the range sensor as 10 m/s and 50 m, respectively,

which are 10 000 times larger variances and than

the normal ones. If we use the same variances under dropout

conditions, the navigation filter can make the system unstable.

The error variances are returned to their original values after

recovering the acoustic signals.

Fig. 9 shows the - plane trajectory of the integrated navi-

gation system IMU-DVL-RA for a 1-min dropout. The dropouts

of the DVL and the range sonar simultaneously happen at 600 s

(omark) for 60 s, and the sensors recover the measurementsafter 660 s (xmark). When the dropout occurs, the range and

velocity data are fixed to their previous normal values and the

navigation system increases the failed DVL and range compo-

nents among the covariance matrix in (36). During the dropout,

IMU-DVL-RA estimates the position with only the IMU ac-

companying nonacoustic measurements of depth and heading.

The navigation system estimates the wrong position that drifts

along the range circle as shown in Fig. 9, because the stored

range is not updated. The direction and magnitude of the drift

depends on the system states before the dropout. After resuming

the measurements, IMU-DVL-RA compensates the range and

velocity errors with the recovered error variances. The naviga-

tion system can give true trajectory within 110 s after returnfrom the dropout.

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Fig. 10. Estimated position with the IMU-DVL-RA navigation system under 2-min dropout of DVL and range.

Fig. 11. Estimated position errors with the IMU-DVL-RA navigation system when dropout occurs.

Fig. 10 shows the - plane trajectory for the 2-min

dropout. The drift along the range circle is larger than the

previous one and the direction is variable depending on

the heading angle of the AUV. After resuming the mea-

surements, the navigation system compensates the rangeand velocity errors and exponentially converges to the true

trajectory. In this simulation with the 2-min dropout, how-

ever, the position error is still 5 m after 6 min of resuming

the acoustic signals. For the application with the naviga-

tion system over the guidance and control of AUVs, it is

needed to keep the stabilizing time zone for a long timewhen a long-duration dropout, longer than 1 min, happens.

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Fig. 12. Estimated results of the IMU-DVL-RA navigation system with initialposition error (

0

7.0, 7.0, 0.0). (a) Estimated position. (b) Trajectory of the po-sition error. (c) Estimated position error.

Otherwise, it is desirable to reset the position with external

position tracking devices.

Fig. 11 shows the convergence trend of the errors for the var-

ious durations of dropout. For the 5-s dropout, the error is 2.0 m

and it takes 5 s to converge 1.0-m error bound. IMU-DVL-RAcan give in-flight self-alignment for the short-time dropout, less

Fig. 13. Estimatedpositionof theIMU-DVL-RA navigation systemwith initialposition error (

0

3.7884, 9.1459, 0.0).

than 5-s dropouts, or outliers of the acoustic signal without de-

grading the navigational performance. On the other hand, for

the 10-s dropout, the error is 5.65 m and it takes 110 s to con-

verge within the 1.0-m errors. It also takes 110 s to recover the

trajectory for the 1-min dropout. The 30-s dropout shows sim-

ilar result with the 1-min dropout. IMU-DVL-RA suffered from

1 min or less dropout and needs two more minutes to recover

the true trajectory.

V. EFFECTS ONINITIALLOCALIZATION ERROR

Initial localization is required to get exact global position

when underwater vehicles begin navigation. Special techniques,

equipment, and times are required for the initialization of the

vehicle. The IMU-DVL-RA navigation system can regulate

the initial positioning error with range information. This paper

checks the sensitivity of IMU-DVL-RA to initial position errors

and convergence characteristics by Monte Carlo simulation.

To verify the convergence and stability of IMU-DVL-RA with

initial position error in local and global areas, we specify two

groups: the initial errors are small around the true position, and

the other errors are large (even located at the other side of the

reference station).

A. Convergence of Initial Errors Around True Position

Eleven points, having the same range 9.90 m apart from the

origin in - plane are selected to make clear comparisons

with their convergence characteristics. Fig. 12 shows the nav-

igation results when the initial position error of the vehicle is

( 7.0, 7.0, 0.0) relative to the true position, which is located on

the parallel direction to reference points being 0.0 . Fig. 12(a)

shows the estimated trajectory of the vehicle, Fig. 12(b) the po-

sition error, and Fig. 12(c) the magnitude of the error. The initial

error exponentially converges to zero and tracks the true trajec-

tory of the rotational motion of the vehicle. The range informa-

tion corrects the 3-D position of IMU-DVL-RA augmented witha depth sensor. The navigation system is strongly robust to the

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Fig. 14. Trajectories of the estimation errors with initial position errors.

Fig. 15. Convergence rates of the position error of the vehicle with initialerrors.

initial position error of the vehicle, where the offset error con-verges into 1.0-m spherical error radius within 2 min.

Fig. 13 shows the estimated trajectory when the initial posi-

tion error of the vehicle is ( 3.7884, 9.1459, 0.0) in relative,

which is located on the direction with 22.5 counterclockwise.

The initial error exponentially converges to the range circle, and

then slowly converges to the true position. While the vehicle

moves in rotation, the range information corrects the position

error to zero along the tangential direction of the range circle.

The navigation system is also robust to the initial position error

of the vehicle, and the offset error converges into 1.0 m after

7 min.

Fig. 14 shows the position error trajectories from the 11 initial

error points around the true position, and Fig. 15 depicts theconvergence rates of the initial position errors in the first phase.

TABLE II

INITIALLYESTIMATEDPOSITIONS OF THEVEHICLE

The convergence characteristics are similar to the four quadratic

phases. All the initial position errors exponentially converge to

the range circle in the radial direction and slowly decrease the

errors along the tangential line of the range circle. The radial

position errors converge to zero within 2 min. Along the range

circle, the convergence speed of the estimation error depends

on the magnitude of the distance to the true position. As the

error along the tangential direction is larger, the converging time

becomes longer. It takes a maximum of 20 min to converge with

a 2.0-m position error when the initial error is about 10 m in

all directions. There is a slow drift of the estimate near the true

position along the tangential direction of the range circle, whichis caused by the uncertainties of the inertial sensors.

From the simulation with IMU-DVL-RA, therefore, the per-

formance of the conventional IMU-DVL navigation system can

be improved by introducing range measurements and the navi-

gation system can estimate the true position having initial posi-

tion error. Thus, we can operate underwater vehicles by using

the inertial acoustic navigation system IMU-DVL-RA without

a special initialization process.

B. Convergence of Large Initial Errors

This section surveys the effect of IMU-DVL-RA on large

initial position errors. We suppose that the vehicle is locatedat and the reference station is

at (0, 0, 0). Twelve estimated positions are arbitrarily

selected around the reference station as shown in Table II.

Those positions are representative of all the directions against

the reference station, where are the opposite side of the

true position against the reference station. Radial errors are

selected randomly to demonstrate the effectiveness of the range

measurement.

Note that we derive the navigation error equation under the

small variation assumption in Section II. Thus, we essentially

need initialization process for the inertial sensors (i.e., gyros

and accelerations). When the inertial errors are large, the system

cannot estimate the true position and attitude. Before startingthe IMU-DVL-RA, we have to conduct the IMU initialization:

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Fig. 16. Estimated position of the IMU-DVL-RA navigation system with theinitial position

(0

12.0, 24.0, 10.0) over the reference station (0.0, 0.0, 0.0):

the true position of thefish is (30.0, 0 30.0, 10.0).

Fig. 17. Trajectories of the position errors with the IMU-DVL-RA navigationsystem when the initial location of the fish is (30, 0 30, 10).

finding heading angle, attitude, latitude, and velocity. On the

other hand, position can be compensated by the range measure-ment externally without losing the assumption of the small vari-

ation. Even for the large initial errors in position, IMU-DVL-RA

can compensate the error by using the range information after

knowing the inertial information.

Fig. 16 shows the trajectory of the estimated position of the

vehicle with the IMU-DVL-RA navigation system for the

initial erroneous position. In the early stage of the navigation,

the estimated position error grows up to the range circle along

its radial direction with the initial orientation. After reaching the

range circle, the estimation gradually slides to the true position

along the tangential line of the range circle, where the circular

motion is heavily distorted due to the oscillation of the estimated

position. As the estimated position approaches to the true posi-tion, the amount of the oscillation decreases. After 23 min of

navigation, the error is still about 22 m, but the position error

decreases in general.

Fig. 17 depicts the integrated trajectories of estimation of the

IMU-DVL-RA for the initial position errors . All the

position errors directly reach the range circle with their radial

direction toward the reference station, and converge to the true

position along the tangential line of the range circle.When the initial estimation is on the opposite side of the refer-

ence station at or , theoretically, the navigation system just

finds the imaginary position for a stationary vehicle and stays at

that position. In this simulation, since the vehicle continuously

moves along a circle and changes position, IMU-DVL-RA up-

dates the estimate with the range information and can break out

from the imaginary position. The estimation also converges to

the true position along the range circle after coming out from

the wrong position. The convergence speed gradually decreases

as the estimation approaches the true position.

When the initial estimation is on the reference station,

the initial radial direction to the range circle depends on the

moving direction of the vehicle. In this simulation, the initialmoving direction is parallel with the range circle, so that the po-

sition change is insensitive to the range variation of the INU-

DVL-RA. When the navigation system senses the range mis-

matching caused by the initial position error, the vehicle is on

the other position. The estimation moves toward the range circle

where it is noticeable on the range mismatching.

The convergence rate is relatively high at the long distance

from the true position. On the other hand, larger oscillation of

the estimation occurs in the long-distance error along the range

circle. Considering the amount of error on the range circle and

the convergence speed, we expect the estimation of the IMU-

DVL-RA to converge to the true position after a 1-h navigationover any erroneous initial position.

C. Sensitivity of Range Distance

This paper examines how the distance between the vehicle

and the reference station affects the convergence characteristics

for initial position errors with the IMU-DVL-RA. Two addi-

tional simulations are conducted with half and double the range

of the previous one.

For the first case study, we suppose that the vehicle is at

(15, 15, 5) and the reference station is at the same origin.

points depicted in Table II are half the distance from

the reference station and have the same orientations and radialerror ratios of . For thefirst case study, we suppose that

the vehicle is at (60, 60, 20) and the reference station is at the

same position. Similar to the half-range case, points in

Table II are double distance from the reference station and have

the same orientations and radial error ratios of . The

same motion data of the rotating arm experiment and the same

characteristics of the range sensor are used in these simulations

of the IMU-DVL-RA. Figs. 18 and 19 show the navigational

results for half and double the range of the previous one,

respectively.

In Fig. 18, all the initial errors including and converge

to the true position with a 2-m error bound for a 23-min navi-

gation. The convergence speed is also better than the previousone. A relatively large circular motion can reduce the drift along

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Fig. 18. Trajectories of the position errors with the IMU-DVL-RA navigationsystem when the initial location of the fish is (15, 0 15, 5).

Fig. 19. Trajectories of the position errors with the IMU-DVL-RA navigation

system when the initial location of the fish is (60, 0 60, 20).

the range circle around the true position and improve the con-

vergence rate. As the vehicle operates near the reference station,the range sensor becomes more effective for the initial position

errors.

In Fig. 19, effectiveness of the range sensor can be found in

general; however, almost all the initial position errors are still

converging to the true position and it takes a longer time than

the cases due to the larger range. The opposite side posi-

tions and are stagnated around the imaginary point of the

true position. Furthermore, shows a large drift of 5 m after

converging to the true position. As the range becomes larger,

the range circle proportionally increases and the estimated po-

sition near true position becomes insensitive for the tangential

variation along the range circle. A larger circular motion of the

vehicle is required to reduce the drift of the estimated positionand to avoid stagnation around the opposite side area.

Fig. 20. Simulation results with a conventional DR navigation.

Therefore, the IMU-DVL-RA navigation system can reduce

initial position errors, and it can localize the underwater vehicle

to the true position with a known reference station.

VI. NUMERICALSIMULATION OFAUV NAVIGATION

A. IMU-DVL-RA With an AUV Dynamic Model

Numerical simulation was performed to demonstrate the ef-

fectiveness of the IMU-DVL-RA and its application to AUVs.

A 6-DOF mathematical model of the AUV [28], [29] was used

to generate accelerations, angular velocities, directional veloci-ties, heading angle, depth, and range data. The vehicle was sta-

tionary at first at the center of the navigation coordinate and went

forward to the north. We supposed that the AUV moved in a

lawn-mowing surveymode and changed depth 5 m in the middle

of the straight courses with a forward speed at 3.0 kn. The ve-

hicle changed depth 5 m at 30, 150, 270, and 390 second lapse,

and changed heading at 100, 120, 230, 250, 340, and 360 time

lapse to generate a boustrophedon trajectory. Depth and heading

controls were performed with a linear quadratic (LQ) controller.

Total simulation time was 500 s.

The sample rate of the IMU and the DVL was 100 and 2 Hz,

respectively, for the rotating arm experiment. The sample rate

of the range sonar was two samples per second. For range datageneration, we supposed that the reference station was located

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Fig. 21. Estimation error with the IMU-DVL-RA navigation system.

Fig. 22. Simulation results with the IMU-DVL-RA navigation system when

initial localization error exists. (a) Estimated trajectory. (b) Estimation error.

at (0, 50) m in the navigation coordinate. The bias and mea-

surement errors of the range sonar were set to 0.25 and 0.5 m, re-

spectively. After generating the constant bias errors and random

noises for each sensor, measurement signals were obtained by

adding them to the simulated data.

DR navigation was performed to check the validity of the

generated data and to compare the performance with the IMU-

DVL-RA navigation system. Fig. 20 shows the DR navigation

results. The moving path of the AUV is the dotted line and

the estimated position is the solid line in horizontal plane plot.

Fig. 20(a) and (b) shows the tracking errors with the DR navi-

gation. The navigation system appropriately estimates the AUV

position. The position estimation error is within 2.0 m for the500-s maneuvering.

Fig. 23. Estimated position error of IMU-DVL-RPA navigation system withthe water-track relative velocity measurement.

Fig. 21 shows the results of the IMU-DVL-RA navigation

system, where the moving path of the AUV is the dotted line

and the estimated position is the solid line, which is very similar

to those of the DR navigation. The IMU-DVL-RA navigation

systemfinely estimates the position of the AUV in general. The

position error is increased only when the AUV changes depth

5 m after 30-s lapse, where lateral bias is shown at this time

due to the range variation caused by the depth change. After

updating the range, the IMU-DVL-RA navigation system keeps

the error within 1.2 m evenly.

When we cannot set the initial position of the vehicle ex-

actly, the DVL-IMU-RA navigation system can regulate the ini-

tial error with the range information. On the other hand, the

DR navigation cannot exclude the error and the position of the

vehicle is biased all the way. Fig. 22 shows the results of the

IMU-DVL-RA navigation system of the vehicle with the initial

error. The IMU-DVL-RA navigation system updates the range

information and corrects the position. Fig. 22(a) shows the tra-

jectories of the AUV in the - plane. In this simulation, theinitial error converges within 2 m after 175 s and within 1.0 m

after 400 s as shown in Fig. 22(b).

The strong point of the IMU-DVL-RA navigation system is

that it is able to eliminate the initial position error and the error

accumulation of the conventional inertial acoustic navigation

system, which is unavoidable for the accelerometer and gyro

bias as well as scale effect of DVL.

B. IMU-DVL-RPA With the AUV Dynamic Model

Navigational simulation was performed to demonstrate the

effectiveness of the IMU-DVL-RPA. The integrated navigation

system with range and phase aiding can be extended to the casewhen only the relative velocity of the AUV is available. The

simulation conditions are all the same as those of the previous

section except the water-track relative velocity sensing and the

two range measurements. We assumed that the reference sta-

tion is located at (50, 50, 0) m in the global frame, and the

range transducers and are located at (0.5, 0, 0.3) and

( 0.5, 0, 0.3) m in the body-fixed frame of the AUV, respec-

tively. The range and and the incident angle were gen-

erated every 0.5 s considering the attitude and position of the

AUV and the offset of the range transducers and .

Fig. 23 shows the tracking errors of the integrated naviga-

tion system with two range transducers. The IMU-DVL-RPA

finely estimates the position of the AUV in general, even withthe water-tracked relative velocity measurement. Since the ref-

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erence station is at (50, 50, 0), the incident angle is nearzero when the AUV turns for the adjacent parallel track. When

the incident angle is small, the measurement error increases

and the navigation system cannot compensate the position error

exactly. Thus, the position estimation shows erroneous results

when the AUV turns around. After turning the AUV and keeping

the normal range of the incident angle, the navigation system

can stably estimate the position. In Fig. 23, the estimation error

is larger than those of the IMU-DVL-RA shown in Fig. 22, how-

ever, it can track the path with the 5-m accuracy for the 10-min

maneuvering by using the relative velocity of the AUV.

When the DVL cannot catch the bottom reflection and only

the water-track relative velocity is available, the range-phase

information can keep the navigation system from drifting andcorrect drift errors induced by the relative velocity information.

Therefore, we can extend the operational condition of the AUV

with the IMU-DVL-RPA.

VII. CONCLUSION

This paper presents an inertial acoustic underwater naviga-

tion system augmented with complementary range information.

Two measurement models of the range sensor were derived

and added to the conventional IMU-DVL navigation system

to improve the navigation performance. A multirate EKF was

adopted to propagate the error covariance with the inertial

sensors, where the filter updates the measurement errors andthe error covariance and corrects the system states when the

external measurements are available. The inertial acousticnavigation system with RA stably estimates the position of un-

derwater vehicles. Monte Carlo simulation with experimental

data and numerical model demonstrates the effectiveness of

the inertial acoustic navigation system with RA. This paper

simulates the influence of intermittent outliers, the short-dura-

tion dropouts of the range sensor and the DVL to the integrated

navigation system. This paper also examines the convergence

characteristics for the initial error removal. We can operate the

underwater vehicles by using the navigation system without a

special process for initialization. The strong point of the inertial

acoustic navigation system with range measurement is that it

is able to eliminate the error accumulation and remove initial

position errors and the dropout of acoustic signals.

APPENDIX

The system matrices of the navigation system error model

(26) are as shown in the equation at the top of the page.

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[22] P. Lee, S. Kim, B. Jeon, H. Choi, andC. Lee, Improvementon an iner-

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[28] S. Hong, P. Lee, Y. Lim, C. Lee, B. Jeon, J. Park, Y. Choi, S. Kim, andJ. Seo, Design and implementation of a dual use purpose semi-au-tonomous underwater vehicle,in Proc. Underwater Defense Technol.Conf., Jeju Island, Korea, 2002.

[29] B. H. Jeon, P. M. Lee, J. H. Li, S. W. Hong, Y. G. Kim, and J. Lee,Multivariable optimal control of an autonomous underwater vehiclefor steering and diving control in variable speed,in Proc. MTS/IEEEOCEANS Conf., San Diego, CA, 2002, pp. 26592664.

Pan-Mook Lee (A95M99) received the B.S. de-gree from Hanyang University, Seoul, Korea, and the

M.S. and Ph.D. degrees fromthe Korea Advanced In-stitute of Science and Technology (KAIST), Daejeon,Korea, in 1983, 1985, and 1998, respectively, all in

mechanical engineering.Since 1985, he has been a Principal Researcher

with the Maritime and Ocean Engineering ResearchInstitute, Korea Ocean Research and DevelopmentInstitute (KORDI), Daejeon, Korea. He was aVisiting Researcher with the University of Hawaii,

Manoa, in 1998. His research interests include navigation, guidance, control ofunderwater vehicles, and signal processing.

Dr. Lee is a member of the Korea Ocean Engineering Society (KSOE) andthe Institute of Control Automation System Engineers (ICASE) in Korea, and amember of the Oceanic Engineering, Automatic Control, Industrial Electronics,and Robotics and Automation Societies of IEEE.

Bong-Huan Junreceived the B.S. and M.S. degrees

in mechanical engineering from the Pukyong Na-tional University, Busan, Korea, in 1994 and 1996,respectively, and the Ph.D. degree in the Department

of Mechatronics Engineering, Chungnam NationalUniversity, Daejeon, Korea, in 2006.

He joined the Ocean System Development Labo-ratory of the Maritime and Ocean Engineering Re-search Institute, Korea Ocean Research and Develop-ment Institute (KORDI), in 1996 as a Research Sci-entist. His research interests include navigation guid-

ance and control of underwater vehicles, analysis and motion planning of un-derwater manipulators.

Dr. Jun is a member of the Korea Ocean Engineering Society (KSOE) andthe Institute of Control Automation System Engineers (ICASE) in Korea.

Kihun Kim received the B.S., M.S., and Ph.D.degrees in naval architecture and ocean engineering

from Seoul National University, Seoul, Korea, in1998, 2000, and 2005, respectively.

Since 2005, he has been a Researcher in theMaritime and Ocean Engineering Research Instituteof Ships and Ocean Engineering, Korea OceanResearch and Development Institute (KORDI),Daejeon, Korea. His research specializes in hydrody-namics, navigation and control, system identification,and estimation of hydrodynamic coefficients for

autonomous underwater vehicles.Dr. Kim is a member of the Society of Naval Architect of Korea.

Jihong Lee (M96) received the B.S. degree fromtheSeoul National University, Seoul, Korea, in 1983 and

theM.S. and Ph.D. degrees from theKoreaAdvancedInstitute of Science and Technology (KAIST), Dae-

jeon, Korea, in 1985 and 1991, respectively, all in

electrical and electronics engineering.Since 2001, he has been a Professor in the

Mechatronics Engineering Department, ChungnamNational University, Daejeon, Korea. His researchinterests include robotics, control system, and artifi-cial intelligence with neural network and fuzzy logic

system.Prof. Lee is a member of the Institute of Electronics Engineering of Korea

(IEEK) and the Institute of Control Automation System Engineers (ICASE) in

Korea, and a member of the Automatic Control and the Robotics and Automa-tion Societies of IEEE.

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Taro Aoki received the B.S. degree from the Uni-versity of Electro-communications, Tokyo, Japan, in1972.

Since 1978, he has been a Senior Researcherwith the Marine Technology Department of theJapan Agency for Marine-Science and Technology(JAMSTEC), Kanagawa, Japan, and he is currentlyProgram Director of the Marine Technology Re-

search and Development Program of JAMSTEC. Hehas a lot of experience in research and developmentof underwater vehicles in JAMSTEC. He has taken

charge of the development of Dolphin 3K, UROV7K, 11 000-m-depth-ratedROV KAIKO, a working AUV MR-X1, and a 3000-m-depth-rated AUV

URASHIMA.

Tadahiro Hyakudome received the B.S. degreefrom the Department of Computer Science and Sys-tems Engineering, Kyushu Institute of Technology,Kyushu, Japan, in 1995 and the M.S. and Ph.D.degrees from the Interdisciplinary Graduate Schoolof Engineering Sciences, Kyushu University, in 1997and 2000, respectively.

Since 2004, he has been a Researcher with the Ma-

rine Technology Research and Development Programof the Japan Agency for Marine-Science and Tech-nology (JAMSTEC), Kanagawa, Japan. His research

interests are the research and development of the navigation, control, and powersystems of a 300-km-long-range AUV, URASHIMA.

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