Bias reduced method for TDOA and AOA localization in the presence of sensor errors

We focus on the 3-dimensional (3D) source localization passively by using TDOA and AOA in the presence of sensor errors. Determining the position from the TDOA and AOA measurements is not an easy task because the relationship between them is nonlinear. We present a new WLS solution that the TDOA equation is simpler than relevant literature (Yin and Wan, A Simple and Accurate TDOA-AOA Localization Method Using Two Stations). However, the bias of the WLS solution is larger. Hence, we propose a bias reduced method by imposing a quadratic constraint so that the expectation of cost function can attain the minimum value at the true position. The simulation illustrates the method is effective and the performance of this method can achieve the Cramer-Rao Lower Bound (CRLB) when the noises are Gaussian and in small region.