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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.

Comprehensive measures for the estimation performance evaluation (EPE) has become increasingly prominent. This paper proposed a new radar chart evaluation method to measure the estimation performance. Firstly, the new radar chart index, which is composed of several popular incomprehensive measures, are presented, and the method of the weight of the each index is calculated based on vector ranking method. Secondly, the new comprehensive measures for the EPE is designed according to the fan area and the fan arc length. Finally, two cases study are provided to verify the effectiveness of this method.

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