Partitioned estimators based on the perturbed kalman filter equations

In this paper, the generalized partitioned filter, predictor and smoother formulae for continuous time linear systems in which the partitioned initial states are mutually correlated are derived by using the perturbed Kalman filter equations. It is shown that the results obtained here are extensions of recent results (Lainiotis 1971, Ljung and Kailath 1977) to more general cases, and that the works of Lainiotis and Andrisani II (1979) can be approached without using the partition theorem based on the Bayes estimation theory. Finally, the bias correcting estimators are briefly discussed in order to show the applicability of the formulae.