Unscented Particle Filter for GPS Control Segment Precision Estimation

We propose to develop and apply an unscented particle filter for Global Positioning System (GPS) operations to improve Control Segment (CS) estimation and short-term prediction. GPS satellite orbital dynamics and GPS measurements are highly nonlinear. In the current implementation of GPS CS, both the state dynamics and measurements are linearized around a pre-computed reference trajectory in order to apply the Kalman filter for the state estimation and prediction. Instead of truncating the nonlinear functions to the first order as in the Kalman filter, the proposed unscented particle filter approximates the distribution of the state with a finite set of points (i.e., the particles) and then propagate these particles through the true nonlinear functions. Because the nonlinear functions are used without approximation, it is much simpler to implement and can generate better result. In Phase I, the proposed unscented particle filter will be formulated with the computational algorithms developed. We will use a computer simulation program consisting of the GPS constellation, the network of monitor stations, and the detailed models of orbital dynamics and GPS measurements to evaluate the algorithms. In Phase II, the recommended architecture and the validated algorithms will be implemented to process real GPS data for demonstration.