Approximate nonlinear filtering and its application in navigation

In this paper, we introduce for the first time particle filtering for an exponential family of densities. We prove that under certain conditions the approximated conditional density of the state converges to the true conditional density. In the realistic setting 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 an approximate nonlinear filter (which we call the projection particle filter), is bounded. We use projection particle filtering in state estimation for a combination of inertial navigation system (INS) and global positioning system (GPS), referred to as integrated INS/GPS. We illustrate via numerical experiments that projection particle filtering outperforms regular particle filtering in navigation performance, and extended Kalman filter as well when satellite loss-of-lock occurs.