A Theorem by Liptser and Shiryayev
A relatively complete mathematical development of the Kalman-Bucy filter has been presented in Chap. 4. One of the results that emerged in this discourse is the fact that success of the filter depends on the contamination of observation by white noise, much like dimming the light to see more clearly. The purpose of this short chapter is to shed some light on this self-contradictory phenomenon through a theorem by Liptser and Shiryayev.
KeywordsWhite Noise Orthonormal Base Orthogonal Projection Spectral Representation Variance Estimator
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