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Evaluation of Bayesian Approaches for Bathymetry-based

Localization of Autonomous Underwater Robots

Jungseok Hong1, Michael Fulton2, and Junaed Sattar3 ∗

Abstract

This paper presents an evaluation of four probabilistic

algorithms for localization of autonomous underwater vehi-

cles (AUVs) using bathymetry data. The algorithms work

by fusing bathymetry information with depth and altitude

data from an AUV. Four different Bayes filter-based algo-

rithms are used to design the localization algorithms: the

Extended Kalman Filter (EKF), Unscented Kalman Filter

(UKF), Particle Filter (PF), and Marginalized Particle Filter

(MPF). We evaluate the performance of these four Bayesian

bathymetry-based AUV localization approaches on eight

real-world lake bathymetry maps of Minnesota lakes, with

both linear and mixed motion policies. The localization

algorithms overcome unique challenges of the underwa-

ter domain, including visual distortion and radio frequency

(RF) signal attenuation, which often make landmark-based

localization infeasible. Evaluation results on real-world

bathymetry data show the effectiveness of each algorithm

under a variety of conditions, with the MPF being the most

accurate.

1 Introduction

The field of underwater robotics has recently been ex-

periencing significant development, primarily driven by re-

search in AUVs. AUVs have seen applications in envi-

ronmental monitoring (e.g., [20, 6, 7]), bathymetry sur-

veys [10], and security [33], among others. These applica-

tions are enabling scientific breakthroughs, environmental

conservation and restoration work, and exploration of the

many underwater environments of our planet. For AUVs to

navigate and operate such missions successfully, the abil-

ity to localize accurately is essential. Underwater localiza-

tion is a challenging and open problem due to the unique

∗The authors are with the Department of Computer Science and En-

gineering, Minnesota Robotics Institute, University of Minnesota–Twin

Cities, 200 Union St SE, Minneapolis, MN, 55455, USA {1jungseok,2fulto081,

3junaed} at umn.edu.

(a) (b)

Figure 1: (1a) Visual representation of AUV location in a

body of water. The top of the figure is assumed to be the

surface. The surface and bottom of the body are indicated

by the dashed yellow lines. (1b) Representation of the AUV

(in blue) location against a lake profile.

circumstances AUVs face: GPS and other forms of RF-

based communications are either completely unavailable or

limited to extremely short ranges, and landmark-based lo-

calization using exteroceptive sensors can often be ham-

pered by environmental factors. Here, we present a novel,

low-cost approach for localizing AUVs in water bodies for

which bathymetry information is available.

Robot localization problems in many environments have

been studied extensively. The problem we address in this

paper is underwater-specific and a subset of Terrain-based

Navigation (TBN) [2], which is widely used across domains

and refers to a general localization problem using a priori

maps. In a broad sense, there are primarily three major tech-

niques to address the problem for underwater robots: using

inertial data combined with dead reckoning [19], acoustic

transponders [1], and landmark-based (also known as geo-

physical features) approaches (e.g., [4, 24]).

The first of these techniques uses an inertial measure-

ment unit (IMU) and velocity measurement (e.g., from a

Doppler velocity log (DVL)) to estimate the position of

the robot by correcting the IMU’s drift with velocity in-

formation. While this approach is widely adopted, it of-

ten struggles with accuracy drifting over time and requires

expensive, high-accuracy IMUs (e.g., [23, 12, 18]). Tech-

niques which use acoustic transponders include long base-

line (LBL) [27], ultra-short baseline (USBL) [21], and short

baseline (SBL) systems, all of which are highly accurate

and quite expensive (at least 10, 000 USD). However, most

of these techniques require either a surface ship carrying a

transponder or pre-installed beacons on the floor of the wa-

ter body in question. In many applications, it is impractical

or impossible to install these devices for localization pur-

poses due to the added cost and overhead, or environmen-

tal constraints. Lastly, landmark-based methods use visual

and acoustic sensors to detect known features in the ma-

rine environment, usually on the floor, which can be used

by AUVs to localize themselves relative to the landmarks.

However, optical distortions such as scattering, absorption,

and attenuation (e.g., arising from turbidity in the water)

can be extreme, resulting in features only being visible at

close range. A lack of clear visuals can make it challeng-

ing to use vision-based methods for broad-area localization.

Landmark-based methods with an acoustic sensor provide

practical means to tackle underwater localization problems;

however, landmarks must be precisely located via acoustic

means, which is not feasible due to environmental factors

and sensor limitations. In contrast, the methods presented in

this paper require only a depth (pressure) sensor and sonar

altimeter, which are both inexpensive (depth sensors gener-

ally less than 100USD and altimeters 300 - 500USD) Addi-

tionally, there is no installation of transponders or beacons.

This significantly reduces the cost of the required hardware

for AUV localization, as well as eliminating costly infras-

tructure requirements.

As an accurate, low-cost alternative to the previously dis-

cussed methods, we present four Bayes filter-based local-

ization methods which utilize bathymetry data. Bathymetry

data, a measurement of the height of the water column at

every (x, y) location on the surface of the water body, is

used as an a priori map. For the rest of this paper, the term

height will refer to the total depth of the water body from

the floor to the surface (shown as L(px,t, py,t) in Fig. 1b).

Although the depth of the robot can vary, the height of the

water column remains relatively constant (not considering

wave effects) at that specific grid location. An AUV would

need both a depth sensor and a sonar altimeter to determine

the total height of the water column at its location, along

with its position in the column.

In this paper, we present bathymetry-based AUV local-

ization algorithms using depth data from a pressure sen-

sor and altitude data from a single-beam sonar as inputs,

by applying four well-known Bayes filter-based methods:

the EKF, UKF, PF, and MPF. The EKF and UKF are

parametric implementations of the Bayes filter algorithm

with Gaussian assumptions, and the PF is a nonparamet-

ric implementation. The MPF, otherwise known as the

Rao-Blackwellized Particle Filter (RBPF), is a “hybrid”

approach that combines the Kalman Filter (KF) and the

PF [28].

Table 1: Selected existing localization algorithms

Sensors Parameters of

state vector sAlgorithms

Teixeira

et al. [31]

DVL,

Single-

beam

sonar

b = (bx, by)s = (x, y, b)

PF

Fairfield

and Wet-

tergreen

[5]

Multi-

beam

sonar

q =(φ, θ, ψ, x, y, z)s = (q, q, q)

PF

Ura et al.

[34]

Profiling

sonar

s = (x, y) PF

Williams

and

Mahon

[36]

Single-

beam

sonar

q = (x, y, z)s = (q, q)

PF

Meduna

et al. [17]

Single-

beam

sonar

s = (x, y) PMF

Kim and

Kim [15]

Single-

beam

sonar

p = (φ, θ, ψ)q = (u, v, w)s = (x, y, z, p, q)

MPF

Ours Single-

beam

sonar

s = (x, y, z) EKF,

UKF, PF,

MPF

The main contributions of this paper are the following:

• We propose four AUV localization algorithms using

low-cost sensors to estimate the position of an AUV

along all three axes (x, y, z) using bathymetry data.

• We compare and evaluate the performance of four lo-

calization algorithms with real-world bathymetry data

and different motion models.

• We discuss the benefits and drawbacks of each filter,

culminating in recommendations on when to use each

technique.

2 Related Work

Underwater localization using landmark-based methods

with acoustic sensors has been widely studied. For these

methods, ranging-type sonars including the single-beam

profiling, and multi-beam varieties have been used [24].

Multi-beam and profiling sonars collect multiple measure-

ments, and they can give more accurate results than single-

beam sonars. Table 1 summarizes selected existing local-

ization algorithms. (φ, θ, ψ) represents the Euler angles,

(u, v, w) is the AUV velocity in the body-fixed frame, and

(bx, by) is the velocity bias.

2

Although DVL, multi-beam sonar, and profiling sonar-

based methods yield better results than those with single-

beam sonar (e.g., [34, 5, 22, 31]), such sensors can be pro-

hibitively expensive.

Single-beam sonars use a narrow acoustic projection to

measure altitude and are thus vulnerable to noise. How-

ever, they have been widely adopted to solve localization

problems since they are among the most affordable acous-

tic sensors [18]. Williams and Mahon [36] proposed a lo-

calization algorithm based on the PF, but the computational

burden of the algorithm is heavy. Meduna et al. [17] pre-

sented a point mass filter (PMF)-based algorithm, but it is

limited to the (x, y) positions of an AUV. Kim and Kim [15]

used a single-beam sonar with the MPF and estimated the

6-DOF position and orientation of an AUV along with the

velocity. However, the algorithm requires a highly-accurate

IMU, which can be rather expensive.

Several Bayes filter-based methods have been used to

solve the localization problem [2] with sonar data. Among

Bayes filters, the EKF and UKF have seen the most use

in this domain (e.g., [9, 37]). Karimi et al. [12] showed

that the EKF can outperform the UKF in their particular

case. However, the UKF captures nonlinearity up to the

second-order term in the state transition process [24], which

in theory could outperform the EKF in similar applications.

We thus develop both EKF and UKF-based algorithms and

compare their performance in AUV localization. Although

the EKF and UKF can handle unimodal Gaussian distribu-

tions, they often fail to converge when the underlying dis-

tribution is multi-modal. The inherent nonlinearity of the

underwater terrain or nonlinear AUV motions underwater

makes it challenging for these methods to work reliably.

To address such issues, the PF has been widely used (e.g.,

[32, 13, 36, 25, 26, 34, 16, 22, 8, 29, 31]). However, the PF

is computationally expensive and thus can be prohibitive to

run on board AUVs for real-time localization. The MPF, on

the other hand, has a lower computational cost and provides

similar benefits to the PF, handling nonlinearity to some

extent [28], thus making it potentially useful for underwa-

ter localization (e.g., [14, 15]). However, localization with

bathymetry data considering 3-DOF state vectors and us-

ing four Bayes filter-based algorithms (EKF, UKF, PF, and

MPF) is yet to be extensively studied.

3 Problem Formulation

Bayesian filters require motion and measurement models

to estimate system state using the well-known propagate-

predict-update process. We propose two motion models for

updating the AUV position and a measurement model for

collecting the depth and height at each location, which are

subsequently used to get AUV state estimates.

3.1 Motion Model

A general discrete time state-space model can be repre-

sented as Eq. 1 to formulate the localization problem where

xt is a state vector, ut is a control input, and yt is a mea-

surement. As mentioned in Section 1, only the 3D position

of an AUV is included in the state vector. f and h can be

either linear or nonlinear functions. qt and rt represent the

noise from motion and measurements. The model in Eq.

1 is used for the EKF, UKF, and PF-based localization al-

gorithms. The model for the MPF-based localization algo-

rithm is introduced in Section 4.3.

{

xt = f(xt−1, ut) + qt

yt = h(xt) + rt(1)

The state vector and control inputs are defined as follows:

xt =[

px,t py,t pz,t]T

(2)

ut =[

vx,t vy,t vz,t]T

(3)

The AUV motion models are defined in Eqs. 4 and 5.

3.1.1 Linear motion model

All state variables are updated linearly.

f(xt, ut) = xt + ut ∗ dt (4)

3.1.2 Linear/Nonlinear mixed motion model

We propose a linear/nonlinear mixed motion model to im-

plement a motion showing nonlinearity without using the

Euler angles. Among the three state variables in the state

vector, px,t and py,t are updated based on the height of the

position (px,t, py,t), L(px,t, py,t). Therefore, the changes in

px,t and py,t are proportional to the height of the water body

at the position (px,t, py,t). In other words, the greater the

height of the water body at the given position, the greater

the change. Unlike the other two variables, the state vari-

able pz,t is updated linearly as in the linear motion model.

In Eq. 5, a, ad, aoff , b, bd, and boff are constants defined

for each water body such that the AUV navigates each lake

without collision.

f(xt, ut) =

px,t + a[

L(px,t,py,t)ad

+ aoff

]

dt

py,t + b[

L(px,t,py,t)bd

+ boff

]

dt

pz,t + vz,t ∗ dt

(5)

3

3.2 Measurement Model

The measurement function h is the same for both the lin-

ear and mixed models.

h(xt) =[

pz,t pz,a,t = L(px,t, py,t)− pz,t]T

(6)

L is bathymetry data (depths for each x and y location

on a grid), pz,t represents the depth of the vehicle from the

surface measured by the pressure sensor, and pz,a,t repre-

sents the altitude of the AUV measured by the single-beam

sonar. Therefore, the sum of pz,t and pz,a,t is the height

L(px,t, py,t) at the position (px,t, py,t) as shown in Fig. 1.

4 Methodology

Since the motion model in Eq. 5 and the measurement

model in Eq. 6 are nonlinear, it is necessary to use non-

linear Bayes filter algorithms to solve the localization prob-

lem. The EKF and UKF are widely used to handle nonlinear

state estimation with the assumption that the state variables

follow a Gaussian distribution, but they could fail when the

distribution is not Gaussian [30]. The PF [32] is resilient to

various types of noise, but it is computationally expensive.

The MPF [29] uses the PF for nonlinear state variables and

the KF for linear state variables because the KF is a filter

optimal for estimating linear state variables.

4.1 Kalman Filters

The EKF and UKF are directly applied without major

modification to Eq. 1 for linear and mixed motion cases to

localize AUVs using the depth and altitude measurements.

Readers are directed to Julier et al. [11] for a full description

of the EKF and to Wan et al. [35] for the UKF.

4.2 Particle Filter

We propose PF-based localization (PFL) in Algorithm

1. During the update process, the algorithm only assigns

weights if the particle is within the boundaries of the map.

Once the weights for the particles are calculated, they are

normalized to ensure that they sum to 1. Then, particles

are resampled based on their weights. To avoid a situation

where all the particles are trapped in incorrect positions in

similar environments, some of the N particles are sampled

randomly at each time step. Although this can degrade the

accuracy of the algorithm, it decreases the chance of incor-

rect estimation occurrences.

4.3 Marginalized Particle Filter

We separate the model in Eq. 1 into linear and nonlinear

state variables as shown in Eqs. 7 and 8. We then develop

Algorithm 1 PF-based Localization

1: PFL main

2: L = Bathymetry data of a target water body

3: N = The number of particles

4: xinit = Initial pose of an AUV

5: x1 = Initialize around pose(L,N)6: zt = Sensor measurements

7: ut = Control input

8: for t = 1, ..., T do

9: xp = xt10: for m = 1, ..., N do

11: x(m, :) = motion update(ut, xp(m, :), L)12: w(m) = sensor update(zt, x(m, :), L)13: end for

14: wtotal = sum(w)15: for m = 1, ..., N do

16: w(m) = w(m)/wtotal

17: end for

18: xt = resample particles(x(m, :), w, L, rand)19: wt = w20: est pose = PFL get pose(xt, wt)21: end for

22: return est pose

the MPF-based localization algorithm using the MPF [28]

and PFL. The motion model noise qnt , qlt and the measure-

ment model noise rt are assumed to be Gaussian with zero

mean. The matrices A,C, and G are determined by the

motion model. Additionally, the MPF requires covariance

matrices, Q and P , as described in [28].

In our case, the ratioN(k)NPF

is 1.1 whereN(k) is the num-

ber of particles that can be used for the MPF, and NPF is

the number of particles used for the standard PF. The ratio

means that the MPF can use 10% more particles than the

PF while retaining the same computational complexity as

the standard PF. However, the EKF and UKF are still faster

than the MPF, albeit less accurate.

xt =

[

xntxlt

]

(7)

xnt+1 = fnt (x

nt ) +An

t (xnt )x

lt +Gn

t (xnt )q

nt

xlt+1 = f lt(x

nt ) +Al

t(xnt )x

lt +Gl

t(xnt )q

lt

yt = ht(xnt ) + Ct(x

nt )x

lt + rt

(8)

5 Experimental Setup and Results

5.1 Bathymetry Data

The following lakes located in Minnesota, USA were

chosen as test locations: Lake Bde Maka Ska, Lake

Nokomis, Lake Hiawatha, Lake Harriet, Lake Turtle, Lake

4

Table 2: Model parameters

Parameter Value

No. of particles for the

PF, NPF

5000

No. of particles for the

MPF, NNPF

300

Motion noise cov.,Q (m) 0.01

v2x 0 00 v2y 00 0 (0.3048vz)

2

Measurement noise cov.,

R (m)

[

0.30482 00 0.30482

]

Initial uncertainty cov.,

P (m)

12 0 00 12 00 0 0.30482

Howard, Lake Waverly, and Lake Pulaski. The lakes were

chosen since they are large, well-studied, have an undulat-

ing floor, and are easy to access for future field studies. The

bathymetry data was acquired from the Minnesota Depart-

ment of Natural Resources (MN DNR) [3]. The size of grid

cells for each lake’s bathymetry data is 5m. The lake height

at each position is given in feet, which were converted to

meters for our study. In our experiments, we assume that

the grid size is 1m to simplify the calculations, and the

bathymetry data is scaled accordingly.

5.2 Simulation Settings

The goal of this study is to evaluate each algorithm with

real bathymetry data as a prerequisite to choosing a deploy-

able localization algorithm. Due to the unique challenges

of the underwater environment, it is extremely difficult, if

not impossible, to obtain the ground truth of the AUV’s po-

sitions. Thus, to quantify the accuracy and efficiency of

the algorithms, we simulate the ground truth position of the

AUV and evaluated the performances of each filter’s po-

sition estimates against the simulated AUV’s motion. The

linear and mixed motion models are designed to test the per-

formance of each localization algorithm on the bathymetry

data from different lake environments. Table 2 includes the

model parameters for the simulation. The control inputs for

each algorithm and lake are separately designed due to the

lakes’ different sizes and heights. The parameters are de-

fined for the linear motion in Eqs. 3 and 4, and the mixed

motion in Eq. 5. For the mixed model, x and y are non-

linear state variables, and z is a linear state variable. We

measure the performance of our algorithms on a 4.20GHz

Core i7-7700K processor running Ubuntu 18.04.2 LTS with

16GB of DDR3 memory with MATLAB R2018b. We con-

duct 100 trials with each filter for each combination of lake

and motion, accumulating to a total of 6, 400 trials.

5.3 Results and Discussions

The results of our trials are summarized in Table 3. We

use the root-mean-square error (RMSE) in Eq. 9 as a metric

to evaluate the performance for each axis of motion where

T is the number of steps, pg is the ground truth, and pe is

the estimated position.

RMSE =

√

∑T

t=1(pg − pe)2

T(9)

One trial in Lake Bde Maka Ska is shown in Figs. 2 and

3. For both the linear and nonlinear cases, the EKF gen-

erally shows the worst performance. The UKF performed

well in the linear case, but it deviates from the ground truth

in the nonlinear case. Notably, the PF and MPF mostly out-

perform the EKF and UKF for both the linear and mixed

motion cases. However, the PF occasionally diverges from

the ground truth and shows unstable performances. A likely

cause is that the randomly selected particles can make the

estimation diverge from the ground truth when a water

body’s bathymetry data does not have enough variations.

5.3.1 Linear motion case

The EKF performs the worst for most lakes, and the re-

sults are not reliable since the performance varies between

lakes. The UKF does not always perform best, but it gives

reliable and relatively accurate results with lower computa-

tional complexity. The PF shows the most accurate result

for some lakes, but it performs worst for Lake Nokomis.

This result is likely caused by the fact that Lake Nokomis

has a symmetrical structure and fewer variations in height.

The MPF generally gives accurate and reliable results, and

it is computationally cheaper than the PF. Overall, the MPF

is the most reliable and accurate filter based on the results

of these experiments. It is worth mentioning that the UKF

is a good option if an AUV does not have much computa-

tional power and high accuracy is not required. The PF can

be used for localization if the bathymetry data has enough

variation in height and has an asymmetrical structure, pro-

vided that an AUV has enough computational power.

5.3.2 Nonlinear motion case

As in the linear motion cases, the PF and MPF generally

perform better than the EKF and UKF. The UKF performs

poorly for some cases due to the high nonlinearity of the

motion. The PF displays the same issue that it has in the lin-

ear motion cases: the estimations diverge when there are not

enough variations in bathymetry data. Similar to the linear

cases, the MPF gives reliable and accurate results overall.

5

(a) Evaluation of linear motion estimations with bathymetry data of

Lake Bde Maka Ska (top view).

(b) Evaluation of mixed motion estimations with bathymetry data of

Lake Bde Maka Ska (top view).

(c) Evaluation of linear motion estimations with bathymetry data of

Lake Bde Maka Ska (zoomed-in view).

(d) Evaluation of mixed motion estimations with bathymetry data of

Lake Bde Maka Ska (zoomed-in view).

Figure 2: Localization performance of the four algorithms for an AUV with an altimeter and depth sensor within Lake Bde

Maka Ska using bathymetry data (Start:❍ End:✳).

5.3.3 Discussion

The MPF consistently shows reliable and accurate results

for both the linear and mixed motion cases while maintain-

ing relatively low computational costs. If an AUV needs

a well-rounded algorithm for the localization problem, the

MPF is the best filter among the four filters. However, if

the bathymetry data of a lake has enough variation and the

task requires high accuracy, then the PF is a better option.

Determining what constitutes “enough variation” is a com-

plicated question, one which should be explored in future

work. While PF and MPF have high accuracy, they require

memory to store the state of their estimated particles, mak-

ing them computationally expensive. The MPF is signifi-

cantly less computationally demanding than the PF, but still

requires more memory and processing power than the UKF.

Therefore, for an AUV with low computational power, the

UKF could be the best filter for localization if the AUV’s

motion is mostly going to be linear.

6 Conclusion

Using bathymetry data and the measurements from a

single-beam sonar altimeter and a depth sensor, we present

four localization algorithms based on the EKF, UKF, PF,

and MPF respectively. We evaluate the performance of

each filter in various aquatic environments and with mul-

tiple robot motions. The results demonstrate the feasibil-

6

0 5 10 15 20 25 30

Time (sec)

100

110

120

130

x (m

)

0 5 10 15 20 25 30

Time (sec)

150

200

250

y (m

)

0 5 10 15 20 25 30

Time (sec)

-4.5

-4

-3.5

-3

z (m

)

TruthEKFUKFPFMPF

(a) Evaluation of linear motion estimations on x,y,z axis.

0 5 10 15 20 25 30

Time (sec)

50

100

150

x (m

)

0 5 10 15 20 25 30

Time (sec)

190

200

210

220

y (m

)

0 5 10 15 20 25 30

Time (sec)

-5

-4

-3

z (m

)

TruthEKFUKFPFMPF

(b) Evaluation of mixed motion estimations on x,y,z axis.

Figure 3: Evaluation of each algorithm’s performance over time within Lake Bde Maka Ska.

Table 3: Localization performance evaluation for an AUV; bathymetry data from the MN DNR.

Lake

Number

of

steps

Linear motion model Mixed motion model

MethodRuntime

(s)

RMSE(m)Method

Runtime

(s)

RMSE(m)x y z x y z

Bde Maka Ska 50 EKF 90.15 4.09 12.43 0.42 EKF 90.13 2.25 5.01 0.53

Bde Maka Ska 50 UKF 52.33 3.07 3.26 0.40 UKF 53.92 4.07 9.02 0.55

Bde Maka Ska 50 PF 252.14 1.38 3.57 0.67 PF 279.03 4.18 9.56 1.32

Bde Maka Ska 50 MPF 94.02 2.88 2.32 0.74 MPF 103.70 4.18 3.90 1.15

Nokomis 50 EKF 57.77 3.92 5.60 0.43 EKF 59.84 4.96 7.12 0.49

Nokomis 50 UKF 29.72 3.05 3.98 0.42 UKF 29.47 12.74 12.70 0.46

Nokomis 50 PF 251.50 13.69 23.12 0.89 PF 291.11 11.90 18.60 0.98

Nokomis 50 MPF 79.42 2.84 3.10 0.76 MPF 79.87 4.12 4.80 0.76

Hiawatha 30 EKF 12.97 3.56 3.57 0.48 EKF 12.88 3.33 2.63 0.51

Hiawatha 30 UKF 6.95 3.07 2.93 0.53 UKF 7.32 3.03 3.00 0.57

Hiawatha 30 PF 137.52 1.66 2.57 1.13 PF 152.90 1.15 2.33 1.15

Hiawatha 30 MPF 37.82 3.10 3.51 0.97 MPF 42.73 3.33 3.47 0.90

Harriet 30 EKF 37.03 5.03 7.20 0.63 EKF 35.80 5.98 9.40 0.63

Harriet 30 UKF 19.43 3.09 3.09 0.59 UKF 18.01 4.08 6.03 0.54

Harriet 30 PF 149.71 1.77 3.72 1.13 PF 176.66 1.62 2.84 1.16

Harriet 30 MPF 51.71 2.93 2.42 1.10 MPF 54.39 3.13 2.75 1.09

Turtle 50 EKF 46.20 3.50 4.26 0.50 EKF 46.47 3.66 3.20 0.44

Turtle 50 UKF 24.81 3.00 3.19 0.47 UKF 25.04 3.16 5.38 0.44

Turtle 50 PF 213.86 2.10 3.03 1.21 PF 249.93 2.68 3.78 1.24

Turtle 50 MPF 45.31 2.82 2.75 0.92 MPF 48.24 3.09 3.25 0.92

Howard 50 EKF 88.94 2.98 3.29 0.38 EKF 89.33 3.08 3.90 0.43

Howard 50 UKF 46.00 3.18 3.37 0.47 UKF 46.00 6.53 7.12 0.48

Howard 50 PF 236.41 2.21 2.52 1.21 PF 282.78 3.26 3.34 1.23

Howard 50 MPF 58.75 2.68 2.71 0.89 MPF 61.76 3.50 4.38 0.91

Waverly 50 EKF 60.00 3.79 3.84 0.49 EKF 59.95 5.62 3.11 0.59

Waverly 50 UKF 31.59 3.15 2.64 0.48 UKF 32.57 6.05 4.24 0.47

Waverly 50 PF 227.69 1.61 1.20 1.30 PF 227.26 3.00 1.64 1.25

Waverly 50 MPF 49.60 2.46 2.45 0.96 MPF 53.39 5.67 3.30 0.99

Pulaski 50 EKF 72.03 3.02 3.20 0.39 EKF 71.81 3.54 3.34 0.49

Pulaski 50 UKF 37.51 3.08 3.11 0.48 UKF 37.48 4.55 4.06 0.49

Pulaski 50 PF 224.57 2.03 1.14 1.29 PF 278.01 2.68 2.86 1.30

Pulaski 50 MPF 53.87 3.00 3.00 0.91 MPF 56.99 4.18 3.30 1.05

7

ity of the Bayesian filter-based algorithms for localizing an

AUV with bathymetry information using two low-cost sen-

sors. The MPF-based localization generally performs best,

both in terms of accuracy and computational cost. However,

the UKF can be a good alternative to the PF and MPF at

the expense of accuracy if an AUV mostly actuates linearly

and has limited computational power. Additionally, the PF

seems to be the most accurate in water bodies with suffi-

cient terrestrial variations if an AUV possesses the neces-

sary computational power. Future work will focus on evalu-

ating the performance of the proposed algorithms with field

tests and analyzing the failures of particle filters on simple

bathymetry in more detail.

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