Abstract
This paper considers a passive target localization problem in Wireless Sensor Networks (WSNs) using the noisy time of arrival (TOA) measurements, obtained from multiple receivers and a single transmitter. The objective function is formulated as a maximum likelihood (ML) estimation problem under the Gaussian noise assumption. Consequently, the objective function of the ML estimator is a highly nonlinear and nonconvex function, where conventional optimization methods are not suitable for this type of problem. Hence, an improved algorithm based on the hybridization of an adaptive differential evolution (ADE) and Nelder-Mead (NM) algorithms, named HADENM, is proposed to find the estimated position of a passive target. In this paper, the control parameters of the ADE algorithm are adaptively updated during the evolution process. In addition, an adaptive adjustment parameter is designed to provide a balance between the global exploration and the local exploitation abilities. Furthermore, the exploitation is strengthened using the NM method by improving the accuracy of the best solution obtained from the ADE algorithm. Statistical analysis has been conducted, to evaluate the benefits of the proposed modifications on the optimization performance of the HADENM algorithm. The comparison results between HADENM algorithm and its versions indicate that the modifications proposed in this paper can improve the overall optimization performance. Furthermore, the simulation shows that the proposed HADENM algorithm can attain the Cramer-Rao lower bound (CRLB) and outperforms the constrained weighted least squares (CWLS) and differential evolution (DE) algorithms. The obtained results demonstrate the high accuracy and robustness of the proposed algorithm for solving the passive target localization problem for a wide range of measurement noise levels.
Highlights
Determining the position of a passive target using time of arrival (TOA) measurements has become an important issue for a number of different applications, such as radar, sonar, telecommunications, mobile communications, and navigation [1, 2]
To further increase the exploitation ability, the NM method is employed with the aim to enhance the accuracy of the best solution previously obtained by the adaptive differential evolution (ADE) algorithm (iii) The experiments are carried out to evaluate the benefits of the proposed modifications on the optimization performance of the proposed HADENM algorithm
The Cramer-Rao lower bound (CRLB) is obtained from the diagonal elements of the inverse of the Fisher information matrix (FIM) [26], denoted by IðxÞ, which is based on the probability density function f ðrjxÞ, defined in Equation (6), and is represented as ln ð f ðrjxÞÞ∂ ∂x ln ð f ðrjxÞÞT ∂x
Summary
Determining the position of a passive target using time of arrival (TOA) measurements has become an important issue for a number of different applications, such as radar, sonar, telecommunications, mobile communications, and navigation [1, 2]. Various efficient optimization algorithms have been derived to overcome these types of difficulties and to answer the challenges of complex optimization problems [10] Motivated by these facts, this paper proposes evolutionary algorithms (EAs) and their hybrid variants to overcome these drawbacks and improve the localization performance [11]. The purpose of this paper is to propose a robust optimization algorithm for the passive target localization problem for a wide range of measurement noise levels. (ii) An improved HADENM algorithm, as the hybridization of the ADE and NM algorithms, is proposed in order to efficiently solve the passive target localization problem. To further increase the exploitation ability, the NM method is employed with the aim to enhance the accuracy of the best solution previously obtained by the ADE algorithm (iii) The experiments are carried out to evaluate the benefits of the proposed modifications on the optimization performance of the proposed HADENM algorithm.
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