From the state predict equation: http://en.wikipedia.org/wiki/Kalman_filter#
$$P_{n+1}=AP_nA^T + Q$$
Suppose the $LDL^{T}$ ( http://en.wikipedia.org/wiki/Cholesky_decomposition#LDL_decomposition_2 ) factorization of $P_n$ is already available:
$$P_n = L_nD_nL_n^T$$
Is there an efficient way to obtain the updated decomposition
$$P_{n+1} = L_{n+1}D_{n+1}L_{n+1}^T$$
without having to multiply out and refactor $AP_nA^T + Q$?