An Integrated Navigation Systems for Underwater Vehicles Based on
Inertial Sensors and Pseudo LBL Acoustic Transponders
Pan-Mook Lee, Bong-Huan Jun, Hyun Taek Choi and Seok-Won Hong
Korea Research Institute of Ships and Ocean Engineering, KORDI, Republic of Korea

Abstract - This paper presents an integrated underwater navigation system for underwater vehicles using inertial sensors and range sonar. We supposes that two acoustic transponders, called pseudo long baseline (LBL) system, are installed at two reference stations on sea bottom or below surface and/or ice.
The navigation system is based on a strap-down inertial measurement unit (SD-IMU) mounted on an underwater vehicle and assisted with auxiliary navigation sensors, such as Doppler velocity log (DVL), depth, and heading sensors. Range measurement transducers are additional auxiliary navigation sensors. Using the two range measurements, the proposed navigation system will be able to improve the performance of conventional IMU-DVL navigation systems for long-time operation of underwater vehicles, and useful even without DVL information. An extended Kalman filter was adopted to propagate the error covariance, to update the measurement errors, and to correct the state equation when the external measurements are available. Simulations were conducted with the 6-d.o.f. nonlinear numerical model of an AUV in lawn-mowing survey mode under current flow condition.
Navigation performance is surveyed for the cases when the bottom reflected DVL information is unavailable. Simulations illustrate the effectiveness of the integrated navigation system assisted by the additional range measurements and robustness on initial position error.

I. INTRODUCTION
Strap-down inertial navigation systems (INS) composed of three accelerometers and three gyros are fascinating sensors for the localization and navigation of underwater vehicles, because it can be self-contained in a pressure vessel.
The errors of inertial measurement units (IMU), however, increase with time elapse due to the inherent bias errors of gyros and accelerometers. Inertial navigation systems give accurate position information for short time period, while the bias error accumulates with time. This accumulation leads to very large position error [1]. Additional sensors are needed to compensate the position errors of INS.
Surface navigation systems have been developed by integrating global positioning system (GPS) with inertial sensors in successful. However, introducing GPS to underwater navigation system is limited to the case of shallow water vehicle that repeats surfacing regularly to update the position information using GPS [2]-[4]. GPS is a good positioning sensor for air, land and maritime vehicles, but it is available only at surface and air.
An inertial navigation system, especially a directional gyro, cooperating with a Doppler velocity log (DVL) is a successful navigation system for underwater vehicles [5][10]. Even if the gyro is highly precise, the navigation

system still needs additional reference sensors, such as GPS, long baseline (LBL), ultra-short baseline (USBL), etc., when it is operated in long-term, because of the scale effects of velocity sensors. Furthermore, the initial localization of underwater vehicles equipped with inertial navigation system, even accompanied by DVL, is difficult to set exact position under sea without additional range information, LBL or USBL. The acoustic positioning systems have no accumulative error, while they have high frequency error and the update rate is usually low. LBL is limited to application of the artic undersea survey because of difficulties in launching and recovering the transponders under ice. On the other hand, USBL is hard to be used alone for the accurate positioning and control of underwater vehicle [11].
Larsen [5], [6], Beiter et al. [12], Uliana [13] successfully proposed a hybrid navigation system based on inertial sensor combined with acoustic velocity sensors.
Kinsey and Whitcomb [7]-[9] proposed integrating DVL signal to LBL system for the enhancement of the position accuracy in deep sea. The error sources of the DVL based navigation system are misalignment, environmental noises, scale effects, and acceleration drifts, which are directly reflected to the navigation performance. Lee et al. [10] proposed an inertial navigation algorithm assisted by DVL, depth and heading sensors. The IMU-DVL navigation system gave slowly drift in estimated position because of the integration of inherent errors from the sensors.
Recently, Lee et al. [14] and [15] proposed new hybrid underwater navigation systems based on a strap-down IMU accompanied by one and two range sonar sensors as well as
DVL, depth sensor, and magnetic compass, respectively.
The main ideas of those papers were to improve the performance of the IMU-DVL navigation system with the complementary range and phase information.
This paper presents an integrated underwater navigation system for underwater vehicles using inertial sensors and two range measurements from two reference stations.
We supposes that two acoustic transponders, called pseudo
LBL system, are installed at two reference stations on sea bottom or below surface and/or ice. The navigation system is based on a strap-down IMU (SD-IMU) mounted on an underwater vehicle and assisted with auxiliary navigation sensors, such as Doppler velocity log, depth, and heading sensors. Range measurement transducers are additional auxiliary navigation sensors. Using the two range measurements, the proposed navigation system will be able to improve the performance of conventional
IMU-DVL navigation systems for long-time operation of underwater vehicles, and useful even without DVL information. transponders.
InX this paper, a measurement model for the integrated navigation system including two range models is designed to implement an extended Kalman filter, where the order of the navigation system states is 22. The navigation system
USBL
Cable predicts the errors of the state variables based on the IMU sensor information with the extended Kalman filter, while
,, , . " the bias and scale errors of the state equation are updated indirectly whenever external measurements are available.
Numerical simulations were conducted with the 6-d.o.f. s' L
\
equations of motion of an AUV in lawn-mowing survey
Range Sonar 1
%'
Transponder mode under current flow condition. The performances of the integrated navigation system assisted by the pseudo LBL j/USB ' ~ > " is surveyed for the cases when the bottom reflected DVL information is unavailable. This paper also demonstrates i ,
-i; .
--._.
" the convergence of the initial position error with the
*',Rusanger 2 navigation system.
Simulation results illustrate the
_t-'
effectiveness of the integrated navigation system assisted by
AUV
Transponder the additional range measurements and robustness on initial
F/V

'

%

,-.L

position error.

ROV
Fig. 1. Configuration of the navigation system of the deep-sea unmanned undeirwater vehicle

11. PSEUDO LBL NAVIGATION SYSTEM
A. Strap-down Inertial Navigation System

For a strap-down inertial navigation system (SDINS) the
Here, authors briefly introduce the hybrid navigation navigation equation of a vehicle based on the system of the UUV under developing in KORDI-KRISO,~~earth-center-earth fixed reference coordinates can be
111 an which will be composed of an 111 underwater launcher
ROV,Xo Twr 1 1 1 obtained with the differential equations from the instrument and an AUV. The navigation system of the UUV will be designed with USBL, IMU, DVL, depth, heading sensors, coordinates, considering the frame rotation and acceleration, and two range transponders installed at sea-bed fixed station coordinate transformation, sensor error dynamics [1], [10]. and the moving launcher, as shown in Fig. . The USBL In the navigational frame mechanism, the ground speed is transponders will be installed at all the vehicles, and we can expressed in the navigation coordinates to give Vn. The

monitor the positions and set initial positions of the vehicles via fiber optic communication or acoustic modem.
Localization of the UUV will be performed using the USBL when the vehicles are in sndition. Without
USB
nry additional navigation sensors however, the sor e s p o
The ROV and the AUV estimate the position with the interal inertial navigation system composed of SD-IMU and auxiliary sensors. The estimated position error, however, will be accumulated due to bias error of the navigation sensors. We introduce range sensors to improve the navigational performance of the vehicles. Two acoustic transponders will be mounted at the fixed mooring station and the moving launcher, respectively. The range sonar of each of the ROV and AUV will transmit acoustic signal and the transponders of the launcher and the fixed station respond with interrogation signals to the vehicles. The ROV and the
AUV can get the range information with transponders.
Although the launcher moves up and down due to ship motion and laterally due to current, we could get the quasi-stationary position of the launcher in horizontal plane with the USBL. In case of AUV, the position information obtained by the USBL can be transmitted to the AUV via an acoustic link. Thus, we can roughly monitor the vehicles' position at surface with USBL, and we will be able to estimate the precise position with the SD-IMU based navigation system assisted by the pseudo LBL acoustic e p s

pen

ican

rate of change of Vn with respect to navigation axes may be expressed in terms of its rate of change in inertial axes, and the rate of change in latitude and longitude can be expressed in terms of the Earth radius and the speed of the vehicle in navigation coordinate. the Perturbation method is used to derive the error

equation

of the SDINS algorithm. The perturbation method analyzes the navigation system by defining the error as the difference between the estimated and true values. For a non-linear system, this method can be applied when the error is small.
Assuming the errors exist in the position, velocity, and attitude error, the perturbation method induces the following

differential equations.

PERmm

AJL di K5h

R ±h m pNsecL tanL-_

L

PE

1

h
Rm h A R±VN secL dL _
LEV
Ah + de
±
R+h) RD+h
Rt,+h
-'VD

)
6Vn = -(2n CX 5Vn + (cbnf') X ) + Cbnf b - (2Cojn + Cojn ) X vn

(2)

q5 =-con x 4-b(9h + 8co],,7

(3)

where

random noise [1], [10]. The output errors of accelerometers b can and (4D]T and
(4) and gyrosas of strap-down IMU, jf b variables and be expressed the summation of random

Vn =4VN Vr VnT=[V
[vE
°
_ie [Q0 QD ]T =[Qcos L 0 - Q sin L]T

go

white

=

n = PN PE PD ]T = [cosL -L

en~

-isinL]T

noise vector as (7) and (8).

=
PEPD
~~~~~~~~~~~~~~ A =P t,

~~

w()

7

(,

(7) fb nV±W(t), wa(t>-N(O,
Here Rm =OR./L=6RoesinLcosL, R, =0a1/0L=2ROesinLcosL,
V=O, V=[V. vy VZ], V(OyN(O,Ia)
Rm R (I-2e+3esin2L) ' Rt= RQ(±+esin2L) , Ro is the earth radius, e is the earth eccentricity, and the variables L and w 3iC) 6 ±+Wg(t)
W(t) N(O,Qg)
(8)
I represent the latitude and the longitude, respectively.
£(0) N(O,Pg).
£ = []x
£0
C]
Ty
0 =[N, E, D]
N OE, and D are the attitude errors of the vehicle with respect to the navigation coordinate in north, east, and downward direction, respectively. s denotes the
Here, the bias errors of the accelerometer and gyro, v variation of the components. f b and 3fb are the accelerometers and the accelerometer errors of the vehicle in and £, are assumed to be random walks, which are irregular the body coordinate, respectively. VN, VE, and VD are values decided when the sensors are turned on. The velocity components of the vehicle with respect to the measurement errors, , and w, are assumed to be white navigation coordinate in north, east, and downward direction noise.
Auxiliary navigation sensors can improve the navigation rate of the Earth, respectively. n is the Earth's ^- * r with
1
/ie1 *p e by c respect to the inertial frame, and Q is the Earth's rotation p v rformance b correcting the state variables in the navigation equation. The errors by the auxiliary navigation iS the turn rate of then rate. respect to the Earth, and PN PE and PD are the sensors, i.e. depth sensor, Doppler velocity log, and magnetic compass, can be modeled as the sum of random variables and components of Con in north, east, and downward direction,
The superscript n and b denote the white noise like the accelerometers and the gyros. Then, respectively. components are described in the navigation coordinate and the differences of the estimated information by strap-down the bodyacoordinate,respectively.
IMU and the measured values by the depth, DVL, and
By taking variation of (4), we can obtain the following heading sensors are expressed as follows: relations: -

gC

h-hmeas = (h+,8h)-(h+hb) = ah-hb
~~~~~~~~~~~~~Vn-,,a (Vn + gVn _-Cn, (Vn + Vh

0
-QNdL]
61), [Qt,dL°
_N,LYT

n

S
VE- PN ah
QD PVRtt ) L +
Rt +h
Rt+h
KDRt+h)

V

I

PER+ L-

Rn,

in

h

± NP
I-CQ psec2 L+ en in n=n+n

Rm + h

Rm, 1+h

PLRttPL± h
+±h) PNtanLah
Rt +
Rt

ie

_

bC, nV (9)

(1I0)
10
(11)

where is the bias error of the depth sensor, Vb is the bias error of the DVL cause by the scale factor error and misalignment of the sensor. A denotes the estimated value and the subscript 'mean' means measured data

tanL

Rt +h h B. Range Measurement Modelfor Two Reference Stations

(5)

This paper introduces additional measurement of two ranges to improve the navigation performance of the
SD-IMU navigation system. We sends interrogation signal installed at an underwater vehicle suppose that a transducer and a transponder installed at two known reference stations respond after receiving the interrogation signal. The vehicle can measure the distances from the vehicle to the reference stations with calculating each travel time.
Fig. 2 shows operational concept that the range sonar of an AUV transmit acoustic signal and the transponders of two reference stations, i.e. the launcher and the fixed station, respond with individual signals to the AUV. We suppose that the fixed station is located at (Xrl, Zri)l and the launcher is at (x2 y2Zr2). Let the AUV position is
( ,y ,z) and the transducer is at p = o, ,p) in the body fixed coordinate. If the measured distances are RI and R2 respectively, we can induce the following relations

The direction cosne matrix nbetween the navigaton coordinate and the body coordinate systems can be expressed as

-bQrnCbn b= CbQ = CbQz,

'mea= -O /

-Vx
Vn

(6)

where 91b is a skew-symmetric matrix described by the is a skew-symmetric matrix gyro measurement band ib [1]. The quarternion attitude composed Of C and representation is adopted to calculate the direction cosine matrix C in the navigation algorithm.
We can indirectly estimate the position of the vehicle by integrating the variations of the accelerations and gyros when the inertial sensors give exact changes of the body frame.
The measured inertial errors, however, include additional bias errors as well as the change ofthe frame.
The errors of inertial sensors and gyros of a strap-down
IMU can be modeled as the combination of random bias and n 1

12)
R1= R1 bp( j2-R +C
2
3

/ ^' R \~ ~ R 2
Reference
Station 2
[Transponder]

Station 1

Xri

[Transponder]

the time delay of acoustic measurement, multi-path in acoustic propagation, and so on. If the random noise and the bias error in range measurement are VR and Rb, respectively, the measured ranges Rmeas for two reference stations can be expressed as

Xr2

Zr2

\
Rl,,,Reas

20

\ ~

Range Sonar
Y"A_

R

R2meas

[Transducer]

=Rl + Rlb + VRI

(16)

-R+
= 2
2b + VR2

From (15) and (16), the measurement error models for the ranges from the two reference stations are obtained as
~

~~~~

y

z

y
Y,
RZ
~~~~ |hiz,Rlmeas9 xL (5X + RI 'R + z A- Rlb -VRI
RI
RI
~~~~x z
R2-Rmeas =~ 2X+ y22y 2Z-R2b VR2.
R2

Fig. 2. Coordinates of the range measurement of an AUV for two reference

stations

(1l7)

R2

2

C. Integrated Navigation System with Pseudo LBL

The ilter, whic atimalgprformane extended
Kma integrated navigation algorithm utilizes thefor linea
Kalman filter, which has optimal performance for linear systems. Equations (1)-(3) and (5) for the variations of velocity, - cos sin + sin sinOcos sin sin + cos sinOcos~ position, sensor attitude, and angular velocities, and the cos0 cos inertial output errors (7) and (8) constitute the
- sin cos + cs sn s
C'=Cossin
cos cos + sin sin sin b s s c j navigational system error model. Equations (9)-(I 1) and
(17) are used as the measurement for the Kalman filter.
The system error model where 0, o, V/ are roll, pitch and yaw angle of the AUV. . . ...........ssstem with pseudo LBL can beof the integrated navigation reduced as follows:
:
: '....... . y Measurement error model is required to implement the range information for the navigation system. The range RIl
(18)
(t) = F(t)x(t) + w(t), w N(O, and R2 are given as

The subscript 'O' means range from the center of the AUV, an the transformation mari and th trnfrmto matrix Cn is gie as inS given as b Q())

R=
Iv +Z12
R1=VX12 +yl2 ±z

2R

±Z,a
2 X± ~ ~ where 2~

~

~

~

~

X - Xr + CIIP + CL3PZ
YI YYrl +C21PA + C23PA
Z1 =Z Zri + C31Px + C33Pz

We can calculate the two ranges from the estimated position of the AUV with the SD-IMU system and the known reference stations. There exist range errors due to the estimation error of the SD-IMU navigation system. If the range errors are MRI and 5W2, the estimated ranges RI and can be

R
R= +5R

lRb R2b ~b

a

YI,(19) b =

=

R +

Yk =

Y + RI18'Z

23X± 22jy~ 22sz.
RX+ 6 R+

RI1 - Rlea imeas - R2meas
R2
I

expressed as

AX + R'
Rh R±+ MI RR + ~~~~RII
R
11

V; ab O1x3 Ox3 Wa j 0
0013o
O1x3 the components of the system matrix F(t) are described in
[1] and [10], and it is the time-varying system matrix well derived from the differential equation of the SD-IMU for the calculation of position, velocity and attitude. The state variable x(t) has 22 error states, where a is the scale factors of DVL. The system error w(t) includes the random noises of accelerometers and gyros, which has mean zero and error covariance Q(t).
The measurement difference at time tk may be
The measurementdierence atime tk may be expressed in terms of the error state variables as follows:

(14)

=

X2 =x-xr2+ CIIPx+A,iC3Pz
Y2 =Y - Yr2 + C21Px + C23P
Z2 =Z-Zr2 + C31A, +C33P.

R2

nV,

~ ~ ~ ~~hr
I

where

X

where

(1)
(13)

I

(20)

h-hmeas

VnVmeas
D 0 0I3
1D °X -1meas

(15)

2

0
°X6

O1X3

016

D2

01X3

I3 ORi (tk)

1
0

10 O°13

0

VR2 (tk)

=D3 O1X3 O1X3 O1X6 0 0 -1 O1X3 °X(tk)±tvh (tk)
°3X3 I1X3 - V X 0°3X6 0 0 0 -C °
V(L
_°3X1 O1X3 O1X2 -1 °1X6 0 0 0 O1X3 -1 _
Vag(tk)

On the other hand, the measured ranges also include measurement errors mixed of random error and bias error.
The bias errors are mainly induced by the AUV motion while
4

Generated Data for 2ReflTr: Relative Velocity of AUV against Tide

TABLE 1

SENSOR MODEL IN THE PSEUDO LBL NAVIGATION SYSTEM

Accelerometer
Gyro
DVL

Magnetic Compass
Depth-meter

Bias Error
1.0 mg
1.0 deg/h
0.01 m/s
10.0 deg
0.5 m

1O m

RangeoSonar

Random Noise (std)--50.0 mg
0.3 deg/s
0
0.5
0.1 m/s
1.0 deg
1) 0
0.5 m
0.5m

°5

where

DI= [X/R,

0/RI

ZI/R,]

N

300

40

500

60 0

100

200

aiO

400

WO

W00

5O

600

°

o

i
1,

1oo

i

200

mo
3
time [seo]

o400

Fig. 3. Simulated relative velocities of the AUV against current flow.

v(tk) denotes the measurement noise, and the subscripts R, h,
V, and ang, denote each measurement.

We can implement the extended Kalman filter [16] with the system error model (18) and the measurement model (20).
The dynamic system errors propagate forward with integrating the signals from the inertial sensors, and they are updated and corrected with the difference between the measurements and the estimated values.
III. NUMERICAL SIMULATION

200

''
0
0. I~L

D2 = [X2 /R2 Y2/R2 Z2 /R2 ]ii
D3 =

0

100

Generated Data for 2ReflTr: Range Data

300

25-E

A l r
X

A. A UVMotion Simulation
This paper evaluated the navigational performance of the integrated navigation system using the simulated motion dataX of an AUV. We generated the measurement data by adding the bias and random noises to the simulated motion data.
We supposed the vehicle loaded an inertial sensor made by
Honeywell Inc., HG1700AG1 1 IMU, and RD Instruments'
WHN300 DVL. The sampling rates are 1OOHz for the IMU, and 2 Hz for the DVL. We selected noise characteristics according to their sensor specifications. Table 1 shows the specifications of the sensors used in simulation.
The error of range measurement will increase due to vehicles motion and environmental noises. We suppose the sample rate of the range sensor is selectable between 0.5 and
4.0 seconds. The range error will vary according to time delay in acoustic wave propagation and vehicle speed.
Since the AUV speed is 3 knots, maximum range error is
3.Om in the worst. We set the bias of the range at 1.Om and the random error at 0.5m. Magnetic compass gives heading reference but it is apt to be contaminated by magnetic filed changes. The bias and random error of the heading sensor are 10.0 and 1.0 degrees, respectively. Both of the bias and random error of a depth sensor are 0.5m.
A 6-d.o.f. mathematical model of the AUV [17] was used to generate accelerations, angular velocities, directional velocities, heading angle, depth data and range data. We integrated the differential equation of the AUV with Euler method and time increment is 0.01 seconds. Total simulation time was 600 seconds. The vehicle was stationary at first at the origin of the navigation coordinate and went forward to
North. We supposed that the AUV moves in a lawn-

.

. -------------1 0

50

200 l 400

6tm

800

i

1000

j2W

1200

Fig. 4. Simulated measurement of Range 1 (red dotted line) and Range 2
(blue solid line) for the AUV motion.

mowing survey mode, forward speed is 3.0 knots, and changes depth 5 meters in the middle of straight courses.
We suppose the AUV moves in current flow, 0.2 m/s in speed and -30 degrees in the north direction (flow from the north-west direction) We considered that two conditions:
(l) the altitude of the AUV was less than 100 meters and it could get DVL signals every time step, (2) the DVL could not get bottom reflection and it measured the relative velocity of the AUV against the current. The vehicle changed depth i5m at 30, 150, 270, 390 second lapse, and changed heading at 100, 120, 230, 250, 340, 360 time lapse to make lawn mowing mode. Forward speed, depth and heading were controlled with a LQ controller. The AUV controlled to keep constant forward speed to 1.5 mes in the current. Fig 3 shows the generated measurement of the
DVL when onlydrelativevelocities are available.
For range data generation, we supposed that the reference station 1 and 2 were located at (0, -50, 0) and (-50, 50, 20) meters, respectively, in the navigation coordinate. After generating the constant bias errors and random noises for each sensor, the measurement signals were obtained adding them to the simulated AUV motion data. Fig. 4 shows the simulated range measurements for two reference stations
5

SAUV IM U-DVL-20th: X-Y plane view

250

F

2

ImuDvIR S 2ReflTr: w/ DVL-cur [0,0,0], RSrate=0.2 HzX-Y plane view

610

T

5 0 - - - - - -- - - --1

- - -

t~~~40-L

-

- - - - ------- ---------120
---

---------

20

/

15so c1 o U - - -4-1- - - t- - - -t 1 S X
-0--50 050

s

-50
-50

Fig. 5.

0

I
5n0 East
Y:

L

X 1 x o

1 00

1 50

20

100

150

-0

2

t: : :--:----------: - - --------: : :.l:

with ~

200

~

~ ~

-o

~

K0

'

0

~~

40I

[in]
Estimated X-Y trajectory of the AUV with a conventional IMUpropose
Before~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2 (a)
------------

20

!

-- ------- --- -- ------- - ----------

~ ~~~ ~~
~
~

50

~~~ ~~~~~0 --------seconds ot

100

[in]
X-Y plane trajectory
East

-'
150

200

------------------

DVL navigation system: solid line

trajectory.

-

estimated, dotted line

with 0.5 seconds of update rate.
B. Review

on

-

AUV

I

muDvIRS

2Hefl1T r wl DVL -cu r [0, 0,0] RSrate =. 25HzLooaIizat ion E rror

r

IMU-DVL Navigation

L 0_|

Before conducting performance test of the proposed interate navgatin sytem,we checked the navigation performance of the conventional IMU-DVL navigation system when DVL measures only the relative velocity of the
AUV against current flow. Simulation was performed with integrating (18) and updating the state variables of (1t9)

AVginstegratednavowiguationwsysteromedih|1],

_ 100

AS__________ 400
200
300 time [seo]

KW

2

eno

600

L diI1l ,

reangeinomtheveon.tmeasurements whenever shows tracking ofwereh available otisteifrain oi ie-etmtd otdln Urjecoy V external mesrdwtthe V navigation F 6.Smuain_eutsoth _sud_B_nvgainsytmit_ except the

(b) Estimation errors400
200
300
500
60 time[seo] Simulation solid of - pseudo LBL navigation system with DVL
Fig. 6. information:results linetheestimated, dotted line - AUV trajectory. nvgto ytmi ln,weeDLmaue measure navigeation sysotem in htheX-Y plaine,wheeDVLen

lineFig. the trajectory of the AUV, andIMU-DVLthe is the is the solid
X-Y plane, where DVL measures line system the current velocityinofthevelocity measured with the navigation relative dotted estimatedthethe AUV against IMU-DVL flow. contains the position with the bias of the DVL Thesystem.
Because the current flow, the effect of estimated position continuously increases as time elapses. Therefore, we
5

result

0

uanle sste DVLget bottomrefDLecaigtiont measurem theven abslues vhelct ofLunerwather vehicreles, o t

100

The proposed navigation system can estimate the position of the vehicle stably with the auxiliary two range measurements, even under the relative velocity from the DVL. The error is within 3.Om in all the time of the simulation, and does not increase as time elapses. The sampling rate of the two ranges is 4 seconds in this simulation. We can further reduce the estimation error with faster sample rate of the two ranges measurement.
For the second case, we simulated the integrated pseudo
LBL navigation using the nominal velocity without DVL.
Fig. 7 (a) and (b) shows the tracking result and the estimation errors of the proposed navigation system in the X-Y plane, respectively, where the nominal velocity is 1.5 mls in forward direction only. When the AUV changes its attitude to turn heading or depth, the velocity drops to half of the nominal velocity in maximum. In these regions, the estimated position increases in error, however, it is within 4m error bound and it is reduced right after recovering the vehicle velocity to nominal velocity. Simulation result

eaue

C. Pseudo LBL Navigation Performance
Since the proposed navigation system can correct the position of the AUV by using the two ranges information, it is possible to estimate the position without DVL measurement. This paper surveys two case studies with and without DVL. In the case without DVL, we use nominal velocity of the AUV in forward direction. As shown in Fig.
3, the AUV velocity changes according to the relative heading angle from the flow direction, and it also decreases when the vehicle changes its attitude. In this paper, we set the nominal velocity at 1.5 mls in forward direction only and choose its error covariance corresponding to the standard

deviation,

For the first case, we simulated the integrated pseudo
LBL navigation with the AUV motion data. Fig. 6 shows the tracking result and the estimation errors of the proposed
6

2 O . t . _ 2 O X , t ~ ~1 S

ImuDvIRS 2ReflTr-Rlrate-NV Vx=1.5 [O,O,O],H0, RSrate=0.25Hz, X-Y plane view

14016]I F

T

ImuDvIRS; 2ReflTr: wl DVL-ur [10,20,5],H30, RSrate=0.25Hz, X-Y plane view

1E1I

2
120

120

-0
40---

---0
----

50--

TA

T

1 60

100

150-I-

200-- 20
40

--

40----00

(a) X-Y plane trajectory
-401

xJ 5

500

time

[nec]

400

100

500
1

,,

--

0

200

200

500

00

Y: East [in]

40

-------

500

(a) X-Y plane trajectory

-4~~~~E01-1

ImuDvIRS; 2ReflTr-RSrate-V Vx 1 5 [0,0,0],HO, HSrate=U 25-Hz, Localization Error

100

T

0-4-1

Y: East [in]

0

1

F

ImuOvIRS 2HellTr-llSrate-NV Vx 1 5 [10 20 5],HH31 HSrate=0 25Hz, Localization Error

100
5000
600
2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2 0 -----------------------200------------,-----------0 0 time [nec]

-~~
0

30

,x

500

0

time[seo]

------L-. 600
~ ~ ~~+
-

100

500

1

200

500

400

500

500

time[seo]

(b) Estimation errors
Fig. 7. Simulation results of the pseudo LBL navigation system without
DVL information: solid line - estimated, doffed line - AUV trajectory. (b) Estimation errors
Fig. 8. Convergence of initial position error for the pseudo LBL navigation system without DVL information: solid line -estimated, dotted line
- AUV trajectory.

shows better results the other normal cruising region, because we control the vehicle to keep the speed 1.5m/s. In general, the pseudo LBL navigation system with DVL is better than the usage of nominal velocity without DVL.
From the simulations, we demonstrated the performance of the integrated navigation system with the pseudo LBL transponders and checked the possibility to eliminate DVL usage in underwater navigation,

position and heading error is 30 degrees. Simulation conditions are the same as the previous simulation using nominal velocity without DVL. We can find the position is corrected with the two ranges measurement every 4 seconds in Fig. 8 (a). In Fig. 8 (b), the error converges to near the
AUV position within 20 seconds. After the initial position error converges to zero, the estimation is similar to the previous simulation, where the error increases only when the
AUV changes its attitude and speed.
By introducing two ranges measurement, i.e. pseudo LBL transponders, therefore, we can improve the navigation performance of the conventional IMU-DVL navigation system. Especially, the navigation system is robust to the initial position error.

D. Pseudo LBL Navigation with Initial Position Error
We will set the initial position of the vehicles with USBL as mentioned in the introduction. Since the UBSL could not give exact position tot the vehicles, there should exist initial position error that propagates next position estimation in the navigation system. This paper checks the error convergence of the integrated navigation system with the pseudo LBL having the initial position error.
Monte Carlo simulation was performed for random initial errors. Fig. 8 shows one of the simulation results, where the initial position error is (10, 20, 5) meters from the AUV

IV. CONCLUSIONS
This paper proposed an integrated underwater navigation system using SD-IMU and additional two ranges information, called pseudo LBL system. We modeled the two range
7

transducers mathematically and augmented them to the state

variables of the conventional IMU-DVL navigation system.
The extended Kalman fillter was adopted to the navigation algorithm. Simulations were conducted with the 6-d.o.f.

[4]

P. E. An, A. J. Healey, S. M. Smith and S. E., "New experimental

results on GPS/INS navigation for Ocean Voyager II AUV," in Proc.
AUV '96, pp. 249-255.
[5] M. B. Larsen, "Synthetic long baseline navigation of underwater

vehicles," in Proc. Oceans 2000 Conf., vol. 3, pp. 2043-2050.
[6] M. B. Larsen, "High performance Doppler inertial navigation nonlinear numerical model of an AUV in lawn-mowing experimental results," in Oceans 2000 Conf., vol. 2, pp. 1449-1456.
Simulation
survey mode under current flow condition.
[7] J. C. Kinsey and L. L. Whitcomb, "Preliminary field experience with results illustrate the effectiveness of the integrated navigation integrated navigation system system assisted measurementsandthe DVLNAV Control Engineering Practice, vol.for12, oceanographic system assistedI by the additional range measurements and by the addilltional submersibles," issue 12, pp.
1541-1549, 2004. robustness on initial position error. Using the two range
[8] J. C. Kinsey and L. L. Whitcomb, "Toward in-situ calibration of gyro measurements, the proposed navigation system will be able and Doppler navigation sensors for precise underwater vehicle to eliminate the DVL usage without degrading navigation range performance. We can improve the long-term drift of the conventional IMU-DVL navigation system by introducing the pseudo LBL transponders. Especially, the navigation system is robust to the initial position error.
ACKNOWLEDGMENTS

This work was supported in part by the Ministry of

Marine Affairs and Fisheries (MOMAF) of Korea for the

development of a deep-sea unmanned undeirwater vehicle underwater development a deep-sea and KORDI for the hydrothermal vent exploration using
UUV. Authors would like to Mr. Andrew Bowen and Dr.
Dana Yoerger of WHOI (Woods Hole Oceanographic
Institution) for their technical support on the development of the UUV and valuable comments on the navigation system.
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