Huber’s M-estimation in GPS Positioning: Computational Aspects

When GPS signal measurements have outliers, using least squares (LS) estimation will likely give poor position estimates. One of typical approaches to handling this problem is to use robust estimation techniques. In this paper, we study the computational issues of Huber’s M-estimation applied to relative positioning. First for code based relative positioning, we use simulation results to show Newton’s method usually converges faster than the iteratively reweighted least squares (IRLS) method, which is often used in geodesy for computing robust estimates of parameters. Then for code and carrier phase based relative positioning, we present a recursive modified Newton method to compute Huber’s M-estimates of the positions. The structures of the model are exploited to make the method efficient. Numerical stability and storage issues are also taken into account in designing the numerical method. Simulation results are given to illustrate the effectiveness of the method.