This paper considers a passive target localization problem based on the noisy time of arrival measurements obtained from multiple receivers and a single transmitter. The maximum likelihood (ML) estimator for this localization problem is formulated as a highly nonlinear and non-convex optimization problem, where conventional optimization methods are not suitable for solving such a problem. Consequently, this paper proposes an improved adaptive hybrid firefly differential evolution (AHFADE) algorithm, based on hybridization of firefly algorithm (FA) and differential evolution (DE) algorithm to estimate the unknown position of the target. The proposed AHFADE algorithm dynamically adjusts the control parameters, thus maintaining high population diversity during the evolution process. This paper aims to improve the accuracy of the global optimal solution by incorporating evolutionary operators of the DE in different searching stages of the FA. In this regard, an adaptive parameter is employed to select an appropriate mutation operator for achieving a proper balance between global exploration and local exploitation. In order to efficiently solve the ML estimation problem, this paper proposes the well-known semidefinite programming (SDP) method to convert the non-convex problem into a convex one. The simulation results obtained from the proposed AHFADE algorithm and well-known algorithms, such as SDP, DE and FA, are compared against Cramér–Rao lower bound (CRLB). The statistical analysis has been performed to compare the performance of the proposed AHFADE algorithm with several well-known algorithms on CEC2014 benchmark problems. The obtained simulation results show that the proposed AHFADE algorithm is more robust in high-noise environments compared to existing algorithms.

本文基于从多个接收器和单个发送器获得的噪声到达时间测量结果，考虑了被动目标定位问题。针对此定位问题的最大似然（ML）估计值公式化为高度非线性且非凸的优化问题，其中常规优化方法不适合解决此类问题。因此，本文提出了一种改进的自适应混合萤火虫差分进化算法（AHFADE），该算法基于萤火虫算法（FA）和差分进化算法（DE）的混合算法来估计目标的未知位置。提出的AHFADE算法动态调整控制参数，从而在进化过程中保持较高的种群多样性。本文旨在通过在FA的不同搜索阶段引入DE的进化算子来提高全局最优解的准确性。在这方面，采用自适应参数来选择适当的突变算子，以实现全球勘探与局部开采之间的适当平衡。为了有效地解决ML估计问题，提出了一种著名的半定规划（SDP）方法将非凸问题转化为凸问题。从提出的AHFADE算法和著名的算法（如SDP，DE和FA）获得的仿真结果与Cramér-Rao下界（CRLB）进行了比较。进行了统计分析，以比较拟议的AHFADE算法和针对CEC2014基准问题的几种著名算法的性能。