Abstract
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.
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References
M. Loève: Probability Theory (Van Nostrand, Princeton 1955)
R. S. Liptser, A. N. Shiryayev: Statistics of Random Process I, General Theory, Applications of Mathematics, Vol. 5 (Springer, Berlin, Heidelberg, New York 1978)
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© 1985 Springer-Verlag Berlin Heidelberg
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Ruymgaart, P.A., Soong, T.T. (1985). A Theorem by Liptser and Shiryayev. In: Mathematics of Kalman-Bucy Filtering. Springer Series in Information Sciences, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96842-6_5
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DOI: https://doi.org/10.1007/978-3-642-96842-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-96844-0
Online ISBN: 978-3-642-96842-6
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