Approximate nonlinear filtering and its applications for GPS

We address the problem of nonlinear filtering in the presence of integer uncertainty. This setup is specially important for the case of differential GPS with carrier phase measurements. In 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 reduce the computational complexity for a certain class of problems. In this class, it is assumed that the conditional density of the state of the system given the observations is close to a known exponential family of densities