Passive Target Localization Based on TDOA Measurements in the Presence of NLOS Propagation Using a Hybrid Pufferfish–Differential Evolution Optimization Algorithm

The localization of a passive target based on time-difference-of-arrival (TDOA) measurements is a complex task in mixed line-of-sight/non-line-of-sight (LOS/NLOS) environments, where the NLOS propagation introduces additional positive range biases. Thus, the developed maximum likelihood (ML) objective function becomes highly nonlinear and multimodal. This paper formulates the passive target localization problem under a Gaussian-mixture LOS/NLOS measurement model and proposes a hybrid metaheuristic algorithm, named HPOADE, which combines the exploration mechanism of the Pufferfish Optimization Algorithm (POA) with the adaptive exploitation of differential evolution (DE) method. In addition, a closed-form constrained weighted least-squares (CWLS) estimator is derived and used for comparison. The optimization performance of HPOADE is first assessed on the CEC 2017 benchmark suite for D∈{10,30,50} against DE, PSO, POA, JADE and the state-of-the-art L-SHADE and jSO algorithms, with Wilcoxon rank-sum and Friedman tests and an ablation of its two components. HPOADE clearly outperforms POA and PSO, is competitive with JADE and DE, and trails the specialized CEC winners L-SHADE and jSO mainly on the hybrid functions at higher dimensions. Monte Carlo localization experiments over a wide range of NLOS noise levels, LOS probabilities and target geometries show that the metaheuristic ML estimators closely approach the Cramer-Rao lower bound while the closed-form estimators degrade, with proposed HPOADE method providing the best localization performance on majority of considered cases. Furthermore, the analysis has been performed which showed that the residual error under severe NLOS noise is a property of the mixture objective rather than of the optimizer.