Abstract
In this paper, the partitioned filtering problem is investigated for a class of stochastic distributed parameter systems. The partition theorem, which may be applicable to construct the adaptive distributed-type estimator in the Bayesian sense, is formally derived by using the smoothing property of expectation operator. With the aid of the above result, the distributed-type partitioned filter can be obtained in terms of each unique solution for the distributed parameter Kalman filter with nominal initial state, its fundamental solution matrix and the fixed-point smoother for the residual unknown initial perturbed state. It is discussed that these-type estimators are effective for the unsteady-state sequential state estimation problem of a system having the unknown initial state, and for the sensitivity analysis due to the initial data. Finally, the results obtained here are applied to the numerical solution method for the unsteadystate partial differential Riccati equation associated with a problem of distributed parameter filtering or a problem of optimal sensor locations, and then a “distributed partitioned-type numerical algorithm” (DPNA) is proposed.
