一种无矩阵求逆的最优滤波计算方法

A New Kind of Inverse-of-matrix-free Kalman Filtering Algorithm

本文回顾了在改善卡尔曼滤波数值稳定性,提高计算效率等数值计算方面的主要研究与发展,包括平方根协方差、U-D分解、奇异值分解(SVD)等计算方法。这些算法都存在不同程度地通过牺牲计算效率换取数值稳定性的不足。本文提出了一种无矩阵求逆的最优卡尔曼滤波计算方法,该算法数值稳定性强,且计算量也比较小。

Focused on the numerical stability, computational efficiency of Kalman filtering algorithms, the development history of Kalman filtering algorithms are briefly reviewed and summarized, including Square Root Covariance Filtering (SRCF), U-D decomposition and Singular Value Decomposition (SVD). These algorithms all exist weakness in some certain degree that of low computational efficiency. In this paper, a new kind of inverse-of-matrix-free Kalman filtering algorithm is proposed, which has both high numerical robustness and good computational efficiency.