Force-directed hybrid PSO–SNTO algorithm for acoustic source localization in sensor networks

Abstract

As a smart combination of particle swarm optimization (PSO) and sequential number-theoretic optimization (SNTO), a new hybrid PSO–SNTO algorithm is proposed to handle the initialization dependence of basic PSO algorithm. We then apply the hybrid algorithm to the acoustic source localization problem in sensor networks, which is modeled as a maximum likelihood estimation problem. Furthermore, a heuristic method based on virtual force is used to direct the particles of PSO to the global optimum, which can efficiently speed up the algorithm convergence. Simulation results demonstrate that the hybrid algorithm can achieve robust convergence with sophisticated estimation performance, and the convergence rate can be largely enhanced with the assistance of the force-directed heuristics.

Introduction

Source localization is one of the key motivating applications for implementing sensor networks [1], [2], [3], [4]. Using the fact that acoustic signal intensity decreases as the distance from its source increases, maximum likelihood estimation (MLE) methods for source localization have been presented [3], [4]. The MLE approach involves minimizing the negative of a highly complicated multimodal log-likelihood function which has multiple local optima and saddle points [2], Fig. 1 especially when the acoustic source energy and the attenuation factor are unknown. In this case, the gradient based local optimization methods like Newton–Raphson algorithm may stagnate at one of these suboptimal solutions instead of converging to the optimal one. Some global optimization algorithms, such as particle swarm optimization (PSO) [5], [6] and sequential number-theoretic optimization (SNTO) [7], [8], have been used to handle likelihood optimization. PSO has shown outstanding ability in solving many benchmark and real-life optimization problems, with advantages of easy to implement and rapid convergence. But PSO tends to converge prematurely giving a suboptimal result and its performance is heavily dependent on the initialized positions of particles that are commonly generated by pseudo-random generators. SNTO is based on numeric theory and statistic theory, and is attractive because of its simplicity. But the lack of randomized operations may make SNTO easily trapped by local optima thus it needs a large number of sampling points to guarantee converging to global optimal solution [8]. Moreover, the convergence performance of both PSO and SNTO algorithms will deteriorate rapidly in complicated or high-dimension cases.

Inspired by SNTO, a hybrid PSO–SNTO algorithm is first constructed in this letter to enhance the robustness of PSO. The particles of PSO are initialized by number-theoretic method and the search space is sequentially contracted similar to SNTO. The hybrid algorithm is suitable for all types of optimization problems in which PSO can be used. Specifically, for energy-based acoustic source localization in sensor networks, a novel heuristic method based on virtual force is integrated into PSO algorithm to speed up convergence. Above two improvements can be combined to form the so-called force-directed hybrid PSO–SNTO algorithm, therefore steady and efficient estimation of source location and other related parameters can be guaranteed. Extensive simulations containing standard benchmark functions and localization problem are given to evaluate algorithm performance.