Passive multiple disjoint sources localization using TDOAs and GROAs in the presence of sensor location uncertainties

Passive source localization has been the focus of considerable research efforts due to its usefulness in various applications. This paper performs a fundamental investigation of whether the gain ratios of arrival (GROAs) can be utilized in conjunction with the time differences of arrival (TDOAs) to improve the multiple sources localization accuracy with erroneous sensor positions. It´s an urgent need to find a closed-form solution with good localization accuracy for this challenging problem. This paper takes the advantage that the TDOAs and GROAs from different sources have the same sensor position displacements and proposes an estimator that jointly estimates the unknown sources and sensor positions. In order to establish an closed-form solution for multiple sources location estimates using GROAs and TDOAs, we use the idea of hypothesized source locations in the algorithm development to enable the formulation of pseudo-linear equations. The proposed algebraic solution does not require initialization and does not have divergence problem. Our conclusion is that the improvement from GROAs is obvious for multiple sources localization compared with methods only using TDOAs. Numerical simulations are included to support and corroborate the theoretical developments.