Citation: Rossides, G.; Hunter, A.;
Metcalfe, B. Source Localisation
Using Wavefield Correlation-
Enhanced Particle Swarm
Optimisation. Robotics 2022, 11, 52.
https://doi.org/10.3390/
robotics11020052
Academic Editors: Jacopo Aguzzi,
Giacomo Picardi, Damianos
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Weiss and Daniel Mihai Toma
Received: 20 March 2022
Accepted: 11 April 2022
Published: 18 April 2022
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Article
Source Localisation Using Wavefield Correlation-Enhanced
Particle Swarm Optimisation
George Rossides
1,2
, Alan Hunter
3
and Benjamin Metcalfe
2,
*
1
Marine Robotics Innovation Centre, Cyprus Marine and Maritime Institute, Larnaca 6023, Cyprus;
george.rossides@cmmi.blue or g.rossides@bath.ac.uk
2
Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK
3
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK; a.j.hunter@bath.ac.uk
* Correspondence: b.w.metcalfe@bath.ac.uk
Abstract:
Particle swarm optimisation (PSO) is a swarm intelligence algorithm used for controlling
robotic swarms in applications such as source localisation. However, conventional PSO algorithms
consider only the intensity of the received signal. Wavefield signals, such as propagating underwater
acoustic waves, permit the measurement of higher order statistics that can be used to provide
additional information about the location of the source and thus improve overall swarm performance.
Wavefield correlation techniques that make use of such information are already used in multi-
element hydrophone array systems for the localisation of underwater marine sources. Additionally,
the simplest model of a multi-element array (a two-element array) is characterised by operational
simplicity and low-cost, which matches the ethos of robotic swarms. Thus, in this paper, three
novel approaches are introduced that enable PSO to consider the higher order statistics available in
wavefield measurements. In simulations, they are shown to outperform the standard intensity-based
PSO in terms of robustness to low signal-to-noise ratio (SNR) and convergence speed. The best
performing approach, cross-correlation bearing PSO (XB-PSO), is capable of converging to the source
from as low as
−
5 dB initial SNR. The original PSO algorithm only manages to converge at 10 dB and
at this SNR, XB-PSO converges 4 times faster.
Keywords:
particle swarm optimisation; source localisation; marine swarm robotics; wavefield
correlation
1. Introduction
Swarm robotics is the discipline of cooperative robotics, concerned with developing
emergent collaborative behaviour in large numbers of robots. Robotic swarms are char-
acterised by flexibility, scalability and robustness [
1
], as well as simplicity and low-cost,
making them well suited for use in large, unexplored environments where semi-disposable
systems are needed. For this reason, they have been applied to marine robotic applications
including environmental monitoring [
2
], source detection of underwater oil spills [
3
] and
exploration [4].
Robotic swarms are typically controlled using swarm intelligence algorithms (SIAs) [
5
].
One of the most common SIAs is particle swarm optimisation (PSO), which was inspired
by the collective motion of birds and fish [
6
] and operates by assigning a fitness or cost
to different locations. The robots are then drawn towards those locations. There have
been numerous studies on the characteristics of PSO, leading to variants that address
different limitations, depending on the application. Other SIAs include glowworm swarm
optimisation (GSO) [
7
], which assigns a fitness value on each robot of the swarm, instead of
locations in space; ant colony optimisation (ACO) [
8
], which mimics the foraging strategies
employed by ants through the use of pheromones; and the firefly algorithm (FA), [
9
] which
is similar to GSO, but each robot is attracted to all other robots and the strength of the
attraction depends on the distance between robots.
Robotics 2022, 11, 52. https://doi.org/10.3390/robotics11020052 https://www.mdpi.com/journal/robotics
