Data-Selective Least Squares Methods for Elliptic Localization With NLOS Mitigation
Wenxin Xiong, Joan Bordoy, Christian Schindelhauer, Andrea Gabbrielli, Georg Fischer, Dominik Jan Schott, Fabian Hoeflinger, Stefan J. Rupitsch, Hing Cheung So
Abstract
In this letter, we consider the problem of 2-D elliptic localization, where multiple spatially separated sensors, including the transmitters and receivers, are exploited to locate the signal reflecting/relaying target in the mixed line-of-sight/nonline-of-sight (NLOS) environments. We begin by revisiting a plain closed-form linear least squares (LS) solution. As it is vulnerable to the existence of erroneous time-sum-of-arrival (TSOA) measurements under the NLOS conditions, we then devise two new data-selective LS methods, by which the outliers can be identified and mitigated and a higher level of resistance to the NLOS bias errors can be provided. To conduct data selection, the first algorithm combines the use of the traditional linear LS estimator and an additional cost function, whereas the second relies on the parameterization of the TSOA-defined ellipses and follows a nonlinear LS estimation criterion. Based on the simulations, we demonstrate the effectiveness of the proposed methods in NLOS error mitigation at acceptable computational costs.