This paper considers the problem of estimating the position of a target based on the time of arrival (TOA) measurements from a set of receivers whose positions are known. The weighted least square (WLS) technique is applied as an efficient existing approach. The optimization problem is formulated by the minimization of the sum of squared residuals between estimated and measured data as the objective function. The hybrid Genetic Algorithm-Nelder-Mead (GA-NM) method is proposed that combines the global search and local search abilities in an effective way in order to improve the performance and the solution accuracy. The corresponding Cramer-Rao lower bound (CRLB) on the localization errors is derived as a benchmark. Simulation results show that the proposed hybrid GA-NM method achieves a significant performance improvement compared to existing methods
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.
This paper addresses the problem of time difference of arrival (TDOA) based passive target localizationand proposes an improved chaos-driven hybrid differential evolution (DE) algorithm and butterfly optimization algorithm (BOA), named ICDEBOA, to solve this complex optimization problem. The proposed algorithm consists of a new mutation strategy with the mechanisms of the BOA algorithm incorporated into the DE algorithm. To boost optimization effectiveness, chaos theory is employed to adjust the control parameter values. The considered localization problem is formulated using the maximum likelihood estimator. To perform the accuracy comparison, the convex constrained weighting least squares algorithm is applied to the considered localization problem as the widely used method in literature. The statistical analysis shows that the proposed modifications to the ICDEBOA algorithm improve its optimization performance, as demonstrated by the improved performance on the CEC2014 benchmark problems. The ICDEBOA algorithm is also shown to be more robust than existing algorithms in noisy environments. Numerical simulation results show that the proposed ICDEBOA algorithm meets the CRLB and achieves better performance than the CWLS, DE, and BOA algorithms.
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