The Kalman-Bucy Filter as a True Time-Varying Wiener Filter

Mrstract—The notion is exploded that to build a Kalman–Bucy filter, one needs to know tbe whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariwrces 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 tbe smoothing problem.