Multistage estimation of dynamical and weakly coupled states in continuous-time linear systems

In this paper we demonstrate that it is possible to extend Friedland´s [1] bias estimation technique, as derived in a constructive manner by Mendel and Washburn [8], to the problem of estimating dynamical and weakly coupled states. We have shown how to obtain an exact multistage decomposition not only for the state estimation equations, but also for the associated error covariance equations. Additionally, we have obtained a first- and second-order suboptimal multistage estimator, using perturbation techniques. Whereas a high-order matrix Riccati equation must be solved when the exact multistage solutions are used, a matrix Riccati equation, only of the dimension of the partitioned weakly coupled states, must be solved when the suboptimal results are used. Numerical comparisons between exact and suboptimal results are included.