Improved Two-Step Weighted Least Squares Algorithm for TDOA-Based Source Localization

The two-step weighted least squares (2WLS) is a classic method for time difference of arrival (TDOA) based source localization problem because of its computational efficiency. However, 2WLS method suffers from the sign ambiguity resulting from square root operation in the second WLS step. Although the sign of final solution can be roughly determined according to the estimate in the first WLS step, the localization accuracy will be degraded, since the position estimate in the first WLS step is not accurate enough. In this paper, an improved 2WLS method is proposed to circumvent this problem. The main strategy is to make proper transformation of the constraint relation, and keep only the linear items at the left side of the equation in the second WLS step. Simulation results show that the proposed method has better performance than the classic 2WLS algorithm, especially when the source is close to the reference receiver.