A singular value decomposition based Kalman filter algorithm

A novel Kalman filter algorithm for the discrete linear filtering problem has been developed. The crucial component of the algorithm involves the computation of the singular value decomposition of an unsymmetric matrix without explicitly forming its left factor which has a high dimension. The proposed algorithm has good numerical stability and can handle correlated measurement noise without any additional transformations. This algorithm is formulated in the form of vector-matrix and matrix-matrix operations, so that it is also useful for parallel computers. Details of the algorithm are provided, and a numerical example is given