A new reduction scheme for Gaussian Sum Filters

In many signal processing applications it is required to estimate the unobservable state of a dynamic system from its noisy measurements. For linear dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum Filters (GSF) provide the MMSE state estimate by tracking the GM posterior. However, since the number of the clusters of the GM posterior grows exponentially over time, suitable reduction schemes need to be used to maintain the size of the bank in GSF. In this work we propose a low computational complexity reduction scheme which uses an initial state estimation to find the active noise clusters and removes all the others. Since the performance of our proposed method relies on the accuracy of the initial state estimation, we also propose five methods for finding this estimation. We provide simulation results showing that with suitable choice of the initial state estimation (based on the shape of the noise models), our proposed reduction scheme provides better state estimations both in terms of accuracy and precision when compared with other reduction methods.