Sequential Monte Carlo Filtering for Nonlinear GNSS Trajectories

The Kalman filter is supposed to be the optimal analytical closed-form solution for the Bayesian space-state estimation problem, if the state-space system is linear and the system noises are additive Gaussian. Unfortunately, except in the above mentioned cases, there is no closed-form solution to the filtering problem. So it is necessary to adopt alternative techniques in order to solve the Bayesian filtering problem. Sequential Monte Carlo (SMC) filtering - or commonly known as particle filter - is a well known approach that allows to reach this goal numerically, and works properly with nonlinear, non-Gaussian state estimation. However, computational difficulties could occur concerning the sufficient number of particles to be drawn. We present in this paper a more efficient approach, which is based on the combination of SMC filter and the extended Kalman filter. We identified the resulting filter as extended Kalman particle filter (EKPF). This filter is applied to a method for the direct geo-referencing of 3D terrestrial laser scans.