Fixed-interval smoothing algorithm based on singular value decomposition

In this paper, a new fixed-interval smoothing algorithm based on singular value decomposition (SVD) is presented. The main idea of the new algorithm is to combine a forward-pass SVD-based square-root Kalman filter, developed recently by the authors, with a Rauch-Tung-Striebel backward-pass recursive smoother by using the SVD as a main computational tool. Similarly to the SVD-based square-root filter, the proposed smoother has good numerical stability and does not require covariance matrix inversion. It is formulated in a vector-matrix form, and thus is handy for implementation with parallel computers. A typical numerical example is used to demonstrate the performance of the new smoother