On the distributed parameter least-squares state estimation theory
Spyros G. Tzafestaş · International Journal of Systems Science · 1973
Some results concerning the state estimation problem of distributed-parameter systems corrupted by white, in time, stochastic disturbances and noises are presented. The least-squares technique is adopted throughout. First, the Gauss-Markov theorem is extended to the distributed-parameter ease and a dynamic estimator is derived governing the minimal variance linear unbiased estimate of the state of the system at hand. Second, the innovations approach to least-squares estimation is invoked and the filtering, fixed-interval, fixed-point, and fixed-lag smoothing problems are studied and solved. Finally, the stability properties of the optimal filter derived are studied by employing the controllability and observability properties of the system under consideration. The results of the paper provide new tools for dealing with distributed data, thus substantially enlarging the existing distributed-parameter estimation theory.