Approximate Nonlinear Filtering and Its Applications for GPS

Abstract

In this paper we address the problem of nonlinear filtering in the presence of integer uncertainty. In the simulation results we show that Particle Filtering is capable of resolving integer ambiguity in the given nonlinear setup. Motivated by these results, we introduce a new Particle Filtering algorithm that can reducethe computational complexity for a certain class of problems. In this class, it isassumed that the conditional density of the state of the system given the observations is close to a known exponential family of densities. The proof of convergence of the approximated density to the actual density is given, and the application for GPS positioning is stated.