基于奇异值分解的固定区间平滑新方法

A New Fixed-Interval Smoothing Algorithm Based on Singular Value Decomposition

本文提出一种基于奇异值分解（SVD）的固定区间平滑新方法，该方法基于RanchTung－Striebel固定区间平滑方法，利用奇异值分解作为计算工具，将原算法中协方差阵进行奇异值分解，不仅具有很好的数值稳定性和鲁棒性，而且避免了矩阵的求逆，此外，采用SVD分解，具有明显的物理意义．仿真计算结果证明了本文方法的有效性和优越性．

In this paper, a new fixed-interval smoothing algorithm based on singular value decomposition(SVD) technique is proposed. Based on Daunch-Tung-Strebel smoothing algorithm, the new smoothermakes use of the singular value decomposition as a main computation tool. The presented algorithm not onlyhas anexcellent numerical stability but also does not necessitate the inversion of system transition matrix.The algorithm is formulated in the form of vector-matrix operations, so it is useful for parallel computers. Atypical numerical example is used to demonstrate the performance of the new smoother.