Huber's M-estimation in relative GPS positioning: computational aspects

When GPS signal measurements have outliers, using least squares (LS) estimation is likely to give poor position estimates. One of the typical approaches to handle this problem is to use robust estimation techniques. We study the computational issues of Huber's M-estimation applied to relative GPS positioning. First for code-based relative positioning, we use simulation results to show that 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, and orthogonal transformations are used to ensure numerical reliability of the method. Economical use of computer memory is also taken into account in designing the method. Simulation results show that the method is effective.