An Efficient Gaussian Sum Filter Based on Prune-Cluster-Merge Scheme

The main problem for the state estimation with Gaussian mixture model is the exponentially growing number of Gaussian components. To solve this problem, an efficient Gaussian sum filter (GSF) based on the prune-cluster-merge (PCM) scheme-based Gaussian mixture reduction method is proposed. First, an adaptive weight-censored pruning strategy named as the j-th order statistical technique is presented to delete components with little contributes to the posterior distribution. Then, the Gauss clustering method is proposed to partition the remainder components into clusters based on the newly defined distribution similarity criterion. Integrating the acquired clusters with the covariance intersection algorithm, the components in the same cluster are merged into a standard Gaussian component by keeping the shape of the original distribution. Meanwhile, an extended integral square error cost function is constructed to optimize the performance of the cluster-merge operation. Finally, an efficient Gaussian sum filter is derived by combining the PCM scheme with extended Kalman filters. Numerical results show that the proposed filter can not only keep a better approximation to the original distribution with fewer Gaussian components comparing with the number-limited GSF and Runnalls's GSF, but achieve a higher cost-effectiveness than the particle filter.