A Joint TDOA/FDOA Localization Algorithm Using Bi-iterative Method with Optimal Step Length

In order to improve the estimation accuracy of multi-station joint Time difference of arrive / Frequency difference of arrive (TDOA/FDOA) location with Bi-Iterative method, a solution for the position of target with Gauss-Newton optimal step length is proposed in this paper. First, get the initial estimation of target based on Two-stage weighted least-squares (TSWLS) algorithm, and then alternately solve the position and velocity of the target with Bi-Iterative method. In this paper, Gauss-Newton method is applied to iteratively solve the target position, including the detailed equations of the descending direction and the optimal iterative step length in each iterative process. Simulations are carried out to examine the algorithm's performance by comparing it with TSWLS method and Gauss-Newton method regardless of the step length. The results show that when Gauss noise variance is small, the estimation accuracy is close to Cramer Rao lower bound (CRLB) and the proposed method performs better than the other two methods. In addition, because the model which includes the position and velocity of the observation station and the target is in line with the over-the-horizon reality scene in this paper, our research has certain practical value.