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.
Original languageEnglish
Article number52
Issue number2
Early online date18 Apr 2022
Publication statusPublished - 30 Apr 2022

Bibliographical note

Funding Information:
Funding: This research was funded by both the UK Natural Environment Research Council (NERC) and Engineering and Physical Sciences Research Council (EPSRC) grant number NE/N012070/1. This research was partially funded by CMMI Cyprus Marine and Maritime Institute. CMMI was established by the CMMI/MaRITeC-X project as a “Center of Excellence in Marine and Maritime Research, Innovation and Technology Development” and has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 857586 and matching funding from the Government of the Republic of Cyprus.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.


  • marine swarm robotics
  • particle swarm optimisation
  • source localisation
  • wavefield correlation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Control and Optimization
  • Artificial Intelligence


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