The GPS filtering problem

The authors explore the possibility of both improved navigation accuracy and computational simplification by using nonlinear filters based on direct solutions to the GPS (Global Positioning System) equations. After reviewing results concerning the existence of sufficient statistics for the nonlinear GPS filtering problem, they introduce the notion of a two-stage estimator in which a direct solution is combined with a time-series smoothing algorithm, such as a constant-gain Kalman filter. This method provides a means for decoupling, in a sense, the spatial and temporal aspects of the GPS filtering problem. Experiments using real data suggest that the method has advantages over the extended filter, in terms of both computational burden and accuracy