TRACK FITTING WITH LONG-TAILED NOISE - A BAYESIAN-APPROACH

If the measurement noise in a linear dynamic system is non-Gaussian, the optimal linear filter (Kalman filter) is not necessarily the one with minimum variance. We describe a non-linear filter, based on a Bayesian approach, which performs better than the linear filter. The relative efficiency of the non-linear filter in the context of track reconstruction is determined in a simulation study. As the filter presupposes a Gaussian mixture model of the measurement noise, we address the problem of approximating the distribution of the measurement errors by a Gaussian mixture. We also study the performance of the filter on some types of long-tailed distributions other than Gaussian mixtures. Finally, the filter is extended to cope with long-tailed process noise, for example a Gaussian mixture model of multiple scattering.