A Robust Semidefinite Source Localization TDOA/FDOA Method with Sensor Position Uncertainties

Abstract

Source localization in a wireless sensor network (WSN) is sensitive to the sensors' positions. In practice, due to mobility, the receivers' positions may be known inaccurately, leading to non-negligible degradation in source localization estimation performance. The goal of this paper is to develop a semidefinite programming (SDP) method using time-difference-of arrival (TDOA) and frequency-difference-of-arrival (FDOA) by taking the sensor position uncertainties into account. Specifically, we transform the commonly used maximum likelihood estimator (MLE) problem into a convex optimization problem to obtain an initial estimation. To reduce the coupling between position and velocity estimator, we also propose an iterative method to obtain the velocity and position, by using weighted least squares (WLS) method and SDP method, respectively. Simulations show that the method can approach the Cramér-Rao lower bound (CRLB) under both mild and high noise levels.