The Kalman-Bucv Filter as a True Time- varying wiener Filter

The notion is exploded that to build a Kalman-Bucy filter, one needs to know the whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariance~ required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these covariances. Performance of the Kalman-Bucy filter does depend on the models, however. Results are also obtained for the smoothing problem. Manuscript received June 22, 1970; revised November 13, 1970. This work was supported by the Australian Research Grants Committee, the Australian-American Educational Foundation, and the Air Force Office of Scientific Research under Contract F44620-68C-0023. Part of this work is based on research conducted by Dr. Anderson while at the Information and Control Sciences Center, Institute of Technology, Southern Methodist University, Dallas, Texas. The authors are with the Department of Electrical Engineering, University of Newcastle, New South Wales 2308, Australia.