Optimal structurally partitioned filter for undisturbable stochastic systems Part I. Basic theory

An optimal structurally partitioned filtering theory is presented for continuous-time linear stochastic systems. A necessary and sufficient condition is given for the possibility of constructing such a partitioned filter, which consists of the well known reduced-order Kalman-type nominal filter and a reduced-order fixed point smoother, applying the Lainiotis' partition theorem. It is then shown that in an incompletely disturbable system, three kinds of partitioned filter can always be synthesized through the Kalman's disturbable canonical model. It is also indicated that the so called Friedland's bias correcting estimator can be obtained as an identity structurally partitioned filter. Furthermore, a partitioned filter based on the Jordan's canonical form is given for the case where there exists no system noise, i.e. a completely un-disturbable system. In comparison with the usual Kalman filtering method, the partitioned approach proposed here is able to deal with the lower order Riccati equation and hence necessitates less computational time per one update for a large-scale system, and moreover it can process the data in a highly parallel fashion with little communication between processors.