Elephant Herding Optimization for Energy-Based Localization

1. Introduction

Localization of a source in wireless sensors networks (WSNs) has been commonly used in several real life applications, such as explorations (deep water, outer space, underground), surveillance and monitoring. [ 1 4 ]. In general, source localization algorithms can be categorized as range-free and range-based [ 5 8 ]. The former ones consider only information about connectivity and usually require a training phase in which a database is constructed [ 9 10 ]. Although less demanding in terms of computational burden, accuracy obtained by range-free methods is generally lower than the accuracy attained by the latter methods [ 9 13 ]. Range-based methods make use of the received signal in order to estimate the distance between the source and the receiving sensor node [ 14 ]. The distance information can be extracted from different measurements of the received signal, such as time of arrival, or time difference of arrival and received signal strength [ 15 19 ]. Nowadays, these different measurements are commonly integrated together, or combined with angle of arrival observations in order to enhance the localization accuracy [ 20 22 ].

Recently, energy-based localization has gained much attention in the signal processing community [ 23 29 ]. This localization approach considers averaging energy information of received acoustic signal data samples [ 30 ]. Energy-based acoustic localization, when considered for targets such as moving objects, has the property of varying slowly with time, thus, the acoustic energy signal can be sampled at a much lower rate. Therefore, the energy consumption for data transmission on individual sensor nodes will be reduced and the demand of communication bandwidth over wireless channels will also be lower [ 31 ]. By modeling the energy decay of an acoustic signal, transmitted within a WSN with one or more sources, a non-convex optimization problem arises. To deal with the non-convexity, several methods have been proposed in the literature. In [ 26 ], a weighted direct least-squares method with correction (WDC) was presented. This method is submissive to a correction technique leading to further performance gains, but its performance is degraded in high noise environments as the second-order noise terms are ignored. Wang and Yang showed in [ 29 ] that the non-convex problem can be relaxed as a convex semidefinite programming (SDP). Similarly, Beko showed in [ 24 ] that the originally non-convex problem can be solved by applying second-order cone programming (SOCP) relaxations. Although the methods in [ 24 29 ] perform well, even in noisy environments, their main drawback is their high computational complexity which increases significantly with the size of the network.

All of the above algorithms are based on applying certain approximations or relaxations to the original problem, causing discrepancies between the obtained and true solutions. These disparities might be large in the case where the applied relaxations are not sufficiently tight, resulting in high estimation errors. In order to circumvent this issue, this work proposes an entirely different approach. Instead of approximating the original localization problem, we tackle it directly, by resorting to a nature-inspired method, called the elephant herding optimization algorithm (EHO). This method was initially proposed by Wang et al. [ 32 ] applied to several benchmark functions. Essentially, it is a swarm based metaheuristic search method for solving optimization problems. The algorithm emulates the herding behavior of elephants in group. In nature, elephants belonging to different clans live together under the leadership of a matriarch, and the male elephants will leave their family group when reaching adulthood.

EHO has been applied to several optimization benchmark problems [ 33 ] and real life applications showing promising results in finding optimal solutions [ 34 35 ]. To the best of our knowledge, this method has not been used to solve energy based localization problems. Hence, in this work, EHO is adjusted and applied for energy-based positioning. While the main idea is preserved, optimal parameter tunning is sought through extensive simulations in order to capture the energy decay of acoustic signals between two sensor nodes. In this way, higher convergence rates are achieved together with near-optimal solutions. Since EHO does not resort to any type of relaxations, but rather tackles the original localization problem directly, its performance is less vulnerable to noise, thus, EHO outperforms the state of the art methods in high-level noise environments.

The paper is organized as follows. In Section 2 the energy decay model is introduces and the localization problem is formulated. Section 3 describes in detail the proposed EHO algorithm and the tunning procedure of its key parameters. Section 4 provides a performance analysis based on complexity and simulation results, and Section 5 summarizes the main conclusions and offers possible directions for future work.