Reflector-aided direct locations of multiple signals in the presence of small reflector position biases

Abstract

Direct position determination (DPD) is a single-step method that localizes transmitters from sensor outputs without computing intermediate parameters. It outperforms conventional two-step localization methods, especially under low signal-to-noise ratio conditions. This article proposes a reflector-aided DPD algorithm for multiple signals of known waveforms received by an array observer. In previous studies, reflector-aided localization has always required very precise locations of reflectors. Therefore, the localization performance depends sensitively on accurately knowing each reflector position. This study considers the presence of small biases in reflector locations. To make the problem tractable, we simplify the signal model through an approximation using the first-order Taylor expansion and then directly localize multiple sources in a decoupled manner. Unlike most DPDs that presume noise is spatially uncorrelated, our study imposes no restriction on the correlation structure of noise, allowing this algorithm to be used in more general scenarios. In addition, we derive the Cramér–Rao bound expression and perform an analysis of the direct locations of multiple signals when the reflector positions are assumed accurate but in fact have small biases. Simulation results corroborate the theoretical results and a good localization performance of the proposed algorithm in the presence of small reflector position biases.