Efficient iteratively reweighted algorithms for robust hyperbolic localization

Hyperbolic localization utilizes the time-difference-of-arrival (TDOA) measurements obtained from multiple coordinated sensors to locate an emitting source. A challenge in such an area, is that ad-erse factors like the non-line-of-sight propagation in typical environments may lead to outlying sensor observations and therefore deteriorated positioning performance. To mitigate the negative effects of outliers in the raw TDOA-based range-difference (RD) data on localization accuracy, the conventional l(2)-norm based RD linear least squares (RD-LLS) location estimator is robustified here using the Geman-McClure (GM) and correntropy-induced loss functions, respectively. Two soft-redescending M-estimators are consequently developed, whereafter two iterative algorithms are presented to handle the corresponding optimization formulations. The first method applies the iteratively reweighted least squares to implement GM loss minimization, whereas the second employs the technique of half-quadratic optimization, through which the correntropy loss is maximized in an alternating manner. Either way the problem comes down to updating a series of weight-like variables and tackling a simplifed formulation that is closely related to RD-LLS at each iteration, thereby leading to fairly computationally efficient iterative solutions. Numerical results confirm the capabilities of the proposed schemes to outperform several existing hyperbolic positioning approaches. (c) 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.