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MMSE-Based Filtering in Presence of Non-Gaussian System and Measurement Noise

机译：存在非高斯系统和测量噪声的基于MMSE的滤波

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摘要

The problem of sequential Bayesian estimation in linear non-Gaussian problems is addressed. In the Gaussian sum filter (GSF), the non-Gaussian system noise, the measurement noise, and the posterior state densities are modeled by the Gaussian mixture model (GMM). The GSF is optimal under the minimum-mean-square error (MMSE) criterion, however it is impractical due to the exponential model order growth of the system probability density function (pdf). The proposed recursive estimator, named the Gaussian mixture Kalman filter (GMKF), combines the GSF and the model order reduction procedure. The posterior state density at each iteration is approximated by a lower order density. This model order reduction procedure minimizes the estimated Kullback-Leibler divergence (KLD) of the reduced order density from the original density at each step. The estimation performance of the proposed GMKF is compared with the interactive multiple modeling (IMM), particle filter (PF), Gaussian sum PF (GSPF), and the GSF with mixture reduction (MR) method via simulations. It is shown in several examples that the proposed GMKF outperforms the other tested algorithms in terms of estimation accuracy. The superior estimation performance of the GMKF is obtained at the expense of its computational complexity, which is higher than the IMM and the MR algorithms.
机译：解决了线性非高斯问题中的顺序贝叶斯估计问题。在高斯和滤波器（GSF）中，非高斯系统噪声，测量噪声和后态密度通过高斯混合模型（GMM）建模。 GSF在最小均方误差（MMSE）准则下是最佳的，但是由于系统概率密度函数（pdf）的指数模型阶数增长，因此GSF不切实际。拟议的递归估计器，即高斯混合卡尔曼滤波器（GMKF），结合了GSF和模型降阶程序。每次迭代的后态密度由一个较低阶的密度近似。模型降阶过程在每个步骤中将降阶密度与原始密度的估计Kullback-Leibler散度（KLD）最小化。通过仿真，将提出的GMKF的估计性能与交互式多重建模（IMM），粒子滤波器（PF），高斯和PF（GSPF）和带混合约简（MR）方法的GSF进行了比较。在几个示例中显示，在估计精度方面，拟议的GMKF优于其他测试算法。 GMKF的优越估计性能是以其计算复杂度为代价获得的，该计算复杂度高于IMM和MR算法。

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