A Robustly Convergent Algorithm for Source LocalizationUsing Time Difference of Arrival and Frequency Difference of Arrival

To pursue accurate source location and velocity, this paper proposes a method based on the Regularization theory to solve the source localization problem utilizing Time-Difference-Of-Arrival (TDOA) and Frequency-Difference-Of-Arrival (FDOA). The proposed algorithm determines the objective function using the maximum likelihood estimator, and then uses classical Newton method to estimate the source position and velocity in an iterative way. It is known that the Newton method requires a good initial value, and a bad initial value can cause an ill-posed Hess matrix which leads to the iteration divergence. This paper introduces the Regularization theory to modify the Hess matrix to make it more proper, which ensures the iteration convergence. The experiment results show that compared with the classical Newton method, the proposed algorithm is robust to the initial value, and is still able to ensure its convergence even with an inaccurate initial value of large error. Compared with some other closed-form source location methods, the proposed algorithm has better location accuracy in large noise levels which can achieve the Cramer-Rao bound. The proposed algorithm can be widely applied in practice.