Abstract
The processing of stationary random sequences under nonparametric uncertainty is given by a filtering problem when the signal distribution is unknown. A useful signal (S n ) n≽1 is assumed to be Markovian. This assumption allows us to estimate the unknown (S n ) using only an observable random sequence (X n ) n≽1 .The equation of optimal filtering of such a signal has been obtained by A.V. Dobrovidov. Our result states that when the unobservable Markov sequence is defined by a linear equation with Gaussian noise, the equation of optimal filtering coincides with both the classical Kalman filter and the conditional expectation defined by the theorem on normal correlation.
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*The author appreciates the financial support provided within the Russian Foundation for Basic Research, grant 13-08-00744-A.
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Markovich, L.A. Inferences from optimal filtering equation*. Lith Math J 55, 413–432 (2015). https://doi.org/10.1007/s10986-015-9289-5
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DOI: https://doi.org/10.1007/s10986-015-9289-5