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Simultaneous Estimation of Filtered and Smoothed State Probability Density Functions by Multiple Distribution Estimation

机译：多重分布估计同时估计滤波态和平滑态概率密度函数

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摘要

This paper shows that for the multiple distribution estimation filter (MDEF)[1] [2], the one-step-behind (OSB) smoothed state probability density function (PDF) used for the estimation of the filtered state PDF is the key factor for the high filtering accuracy of the MDEF. The MDEF calculates the OSB smoothed state PDF prior to the calculation of the filtered state PDF at the current epoch and the filtered state PDF is estimated by the marginalization of the conditional state PDF with respect to this smoothed state PDF. Since the OSB smoothed state PDFs are obtained at every time step prior to the observation update, the MDEF can be regarded as providing the simultaneous estimation of the filtered and OSB smoothed state PDFs. In this paper, we numerically evaluate the estimation accuracy for the OSB smoothed state estimates by the MDEF using the benchmark filtering problems [3]-[5] and compare it with those for the particle and the Gaussian smoothers employed to the MDEF. We confirmed that the smoothing accuracy for the OSB smoothed state estimates was more accurate than that for the Gaussian smoother and almost comparable to that for the particle smoother, while the calculation cost was significantly lowered than that for the particle smoother.
机译：本文表明，对于多重分布估计滤波器（MDEF）[1] [2]，用于估计滤波状态PDF的一步一步（OSB）平滑状态概率密度函数（PDF）是关键因素MDEF的高过滤精度。 MDEF在计算当前时期之前的滤波状态PDF之前先计算OSB平滑状态PDF，并通过条件状态PDF相对于该平滑状态PDF的边缘化来估计滤波状态PDF。由于OSB平滑状态PDF是在观察更新之前的每个时间步获得的，因此MDEF可被视为同时提供了滤波后的OSB平滑状态PDF的估计。在本文中，我们使用基准滤波问题[3]-[5]对MDEF对OSB平滑状态估计的估计准确性进行了数值评估，并将其与MDEF中使用的粒子和高斯平滑器的估计准确性进行了比较。我们确认，OSB平滑状态估计的平滑精度比高斯平滑器更准确，并且几乎与粒子平滑器可比，而计算成本明显低于粒子平滑器。

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