Approximate Nonlinear Filtering and Its Applications for GPS

In this report 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 particle filtering for an exponential family of densities. We prove that under certain conditions the approximated conditional density converges to the true conditional density. For the case where the conditional density does not lie in an exponential family but stays close to it, we show that under certain assumptions the error of the estimate given by this approximate nonlinear filtering, projection particle filtering, is bounded. In the simulation results we show the application of particle filtering to Global Position System (GPS).