Development of a Simulation Environment for Evaluation of a Forward Looking Sonar System for Small AUVs

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Development of a Simulation Environment for

Evaluation of a Forward Looking Sonar System for

Small AUVs

Christopher Morency, Daniel J. Stilwell

Bradley Department of Electrical and Computer Engineering

Virginia Polytechnic Institute and State University

Blacksburg, VA, USA

{cmorency, stilwell}@vt.edu

Sebastian Hess

Atlas Elektronik GmbH

Bremen, Germany

sebastian.hess@atlas-elektronik.com

Abstract—This paper describes a high-ﬁdelity sonar model and

a simulation environment that implements the model. The model

and simulation environment have been developed to aid in the

design of a forward looking sonar for autonomous underwater

vehicles (AUVs). The simulator achieves real-time visualization

through ray tracing and approximation. The simulator facilitates

the assessment of sonar design choices, such as beam pattern and

beam location, and assessment of obstacle detection and tracking

algorithms. An obstacle detection model is proposed for which

the null hypothesis is estimated from the environmental model.

Sonar data is generated from the simulator and compared to

the expected results from the detection model demonstrating the

beneﬁts and limitations of the proposed approach.

I. INTRODUCTION

We describe a high-ﬁdelity sonar model that is well-suited

to evaluation of design choices for forward-looking sonar.

We present a complete set of equations that constitute the

model as well as approaches for implementing the model in a

numerical simulation. We are especially interested in assessing

the performance of forward-looking sonar systems that could

be used for object detection in small autonomous underwater

vehicle (AUV) applications. Our simulation combines a high-

ﬁdelity sonar model with the capability to simulate AUV

missions in a three dimensional environment in real time.

Many open source and commercial high-ﬁdelity sonar mod-

els and simulations are described in the literature [1], [2],

[3]. The Sonar Simulation Toolset (SST) [1] from APL-UW

is a high-ﬁdelity open-source sonar simulation toolset. The

SST simulates an ocean environment and the sound generated

by a sonar. Due to the complexity of the model, it is not

intended for use as a real time software. Espresso [2] was built

to evaluate NATO minehunting sonar performance. Espresso

makes a ﬂat and homogeneous seabed assumption and does

not include sonar motion in the model [4]. LYBIN [3] is an

acoustic ray-theoretical model for sonar performance. LYBIN

uses a high-ﬁdelity sonar model and runs in real time, however,

it is limited to two-dimensions. These simulations provide

the desired high-ﬁdelity sonar models and excel at modelling

sonar performance yet are not capable of evaluating sonar

performance through simulated AUV missions in real time.

AUV simulators [5], [6], [7] make up a separate class of

simulators, mainly focused on rapid protyping of AUVs by

simulating the dynamics and missions for AUVs. UWSim [5]

is a visualization and simulation tool which uses a range

camera to simulate sonar data, capturing the distance of

objects from the sensor. UUV Simulator [6] is a Gazebo-based

package for AUV simulation. The Gazebo-based simulation

provides a sensor model for a multi-beam echo sounders using

2D laser range ﬁnders, returning the distance of an object

from the sensor. Project Mako [7] describes an AUV simulator

(SubSim) built for an AUV competition. The SubSim sensor

model traces a ray from the sonar, only returning the distance

to the object. These simulators compute the distance to an

object, but they do not calculate the sound intensity returned to

the sonar. Therefore, they are unsuitable for assessing obstacle

detection/tracking algorithms.

To assess the performance of object detection algorithms,

we seek a high-ﬁdelity forward-looking sonar simulator that

can be integrated with an accurate AUV motion model. Our

sonar model calculates the sound intensity received by each

sonar transducer element, binned by distance, for the entire

range of each sonar ping. Our numerical simulation can be

used to test the various types of design choices, such as the

number and direction of beams for obstacle detection and

tracking.

Obstacle detection algorithms can be assessed using the

high-ﬁdelity simulated sonar model. We brieﬂy illustrate the

assessment of an obstacle detection approach based on the

Bayesian framework and employ a Bayesian detector to

construct decision rules. When all uncertain parameters are

known, our Bayesian detector is optimal. A similar framework

is presented in [8].

We consider a forward looking sonar with a limited number

of beams as a case study throughout this paper. This illustrative

example falls between forward looking imaging sonars, such

as the Blueview P450-15E [9] and DIDSON [10] sonars which

use a large number of ﬁxed beams, and a single beam forward

looking sonar that is stationary [11] or mechanically steered

such as the Imagenex 881L Proﬁling Sonar [12]. We assess the

accuracy of our numerical simulation by comparing the results

arXiv:2210.06535v1 [cs.RO] 12 Oct 2022

from the simulation to the theoretical results obtained through

our environmental model, which cannot be run in real-time.

Using a limited number of beams, the simulator provides a

real-time visualization capability. The number of beams used

in the simulator can be scaled up at the cost of additional

computational effort.

Organization of the paper is as follows. The equations used

to model sound propagation appear in Section II. The detection

model outlines approaches to compute the null and alternate

hypothesis in Section III. Discussion of the simulator and

results from illustrative test cases are presented in Sections

IV and V.

II. ENVIRONMENTAL MODEL

The environmental model is constructed such that the sound

energy returned to the sonar from reﬂections can be charac-

terized by a discrete set of distances, or equivalently, discrete

times. The energy returned to the sonar is discretized into a set

of equal length distance bins over the entire range of the sonar.

The environmental model consists of a set of equations that

model the acoustic propagation of the sonar. These equations

model the sound velocity, transmission loss, beam pattern loss,

backscatter, sonar resolution and noise. The transmission loss

is comprised of attenuation and spread loss. The backscatter

is the energy reﬂected back to the sonar from bottom, surface

and volume.

A. Sound Velocity

The speed of sound can be estimated with less than 0.1 m/s

error using the empirical formals in [13] and [14]. However,

the empirical formulas are difﬁcult to compute in real-time, so

we adopt a simpliﬁed approximation for the speed of sound,

described in [15]. Sound velocity in m/s is expressed

c= 1449.2+4.6T−0.055T2+ 0.00029T3

+(1.34 −0.010T)(S−35) + 0.016z(1)

where Tis temperature (°C), Sis salinity (ppt), and zis water

depth (m). The equation (1) is valid for 0≤T≤35,0ppt

≤S≤45 ppt, and 0m≤z≤1000m.

B. Attenuation

Attenuation is modeled using the Francois and Garrison

formulas [16], [17],

αw=A1P1f1f2

1+f2+A2P2f2f2

2+f2+A3P3f2dB/km

The boric acid coeﬁcients are

A1=8.696

c100.78pH−5

f1= 2.8rS

35104−1245

T+273

P1= 1

The magnesium sulphate coefﬁcients are

A2= 21.44S

c(1 + 0.025T)

f2=8.17 ×108−1990/(T+273)

1+0.0018(S−35)

P2= 1 −1.37 ×10−4zmax + 6.2×10−9×z2

max

The coefﬁcients for pure water viscocity are

A3=









4.937 ×10−4−2.59 ×10−5T+

9.11 ×10−7T2−1.5×10−8T3for T≤20°C

3.964 ×10−4−1.146 ×10−5T+

1.45 ×10−7T2−6.5×10−10T3for T > 20°C

P3= 1 −3.83 ×10−5zmax + 4.9×10−10 ×z2

max

where fis the frequency in kHz, Tis the temperature (°C),

Sis salinity (ppt), zmax is the maximum water depth (m), c

is the sound speed (m/s) and pH is the acidity (Moles/litre).

The total attenuation αtwith respect to distance d(m) is

αt=(2d−1) ×αw

1000 dB (2)

C. Spread Loss

Assuming spherical spreading with no cylindrical spreading,

the intensity of a sound wave is inversely proportional to the

distance d(m) [18]. Since the sound energy in an area is

computed with respect to the energy at 1meter, the two-way

loss due to spherical spreading for distance dis

SL= 40 log10(d)(3)

The total two-way transmission loss is

T L =SL+αt(4)

where αtis the attenuation at distance dfrom (2).

D. Beam Pattern

The beam pattern is calculated using the single-point-source

(SPS) approach [19]. The calculation takes into consideration

the wavelength λ(m), the transducer’s horizontal length LH

(m), the transducer’s vertical length LV(m), the horizontal

beam angle θ(radians), and vertical beam angle ψ(radians).

The beam pattern loss is

BP = 20 log10(αβ)dB

where

α= sinc sin(θ) cos(ψ)LH

λ(5)

and

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摘要：

DevelopmentofaSimulationEnvironmentforEvaluationofaForwardLookingSonarSystemforSmallAUVsChristopherMorency,DanielJ.StilwellBradleyDepartmentofElectricalandComputerEngineeringVirginiaPolytechnicInstituteandStateUniversityBlacksburg,VA,USAfcmorency,stilwellg@vt.eduSebastianHessAtlasElektronikGmbHBreme...

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Development of a Simulation Environment for Evaluation of a Forward Looking Sonar System for Small AUVs

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