Spectral factorization is a powerful tool in deriving the steady-state solution of Kalman filtering equations. It is an algebraic, nortrecursive method, thus economical in terms of computing cost, when compared with the conventional iterative algorithm. In this paper the technique is extended to time-varying systems having periodic coefficient matrices for both discrete and continuous systems. The tracking of low-thrust spacecraft from an Earth-based station is used as an example and a sensitivity study is performed using a computer program incorporating the algorithm.