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.

This paper proposes a moving source localization method that combines TDOA, FDOA and doppler rate measurements. First, the observation equations are linearized by introducing nuisance variables and an initial solution of all the variables is acquired using the weighted least squares method. Then, the Taylor expression and gradient method is applied to eliminate the correlation between the elements in the initial solution and obtain the final estimation of the source position and velocity. The proposed method achieves CRLB derived using TDOA, FDOA and doppler rate and is much more accurate than the conventional TDOA/FDOA based method. In addition, it can avoid the rank-deficiency problem and is more robust than the conventional method. Simulations are conducted to examine the algorithm's performance and compare it with conventional TDOA/FDOA based method.