Efficient time propagation of U-D covariance factors

Time propagation of the Kalman filter covariance matrix involves an operation of the form ФPФT where for many applications Ф is a sparse transition matrix. When the filter implementation employs U-D covariance factorization (i.e., recursions for U and D are used, where P = UDUT with U unit upper triangular and D diagonal) the corresponding time propagation involves W = ФU. Both the ФPФT and ФU computations can exploit transition matrix sparseness. If, however, the structure of W is not exploited, the computation involved with transforming W to an equivalent triangular form can be prohibitively expensive. The contribution of this paper is a streamlined Gram-Schmidt orthogonalization algorithm that can dramatically reduce UD time propagation computation costs.