Non-Linear Localization Algorithm Based on Newton Iterations

In order to improve the performance of time difference of arrival (TDOA) localization, a nonlinear least squares algorithm is proposed in this paper. Firstly, based on the criterion of the minimized sum of square error of time difference of arrival, the location estimation is expressed as an optimal problem of a non-linear programming. Then, an initial point is obtained using the semi-definite programming. And finally, the location is extracted from the local optimal solution acquired by Newton iterations. Simulation results show that when the number of anchor nodes is large, the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.