Inferences from optimal filtering equation*

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• 作者：Liubov A. Markovich
• 关键词：60G35 ; 60A05 ; Markov sequence ; theorem on normal correlation ; Kalman filter ; optimal filtering ; Toeplitz matrix
• 刊名：Lithuanian Mathematical Journal
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：55
• 期：3
• 页码：413-432
• 全文大小：411 KB
• 参考文献：1.O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models, Springer, New York, 2005.MATH
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  15.R.A. Usmani, Inversion of Jacobi’s tridiagonal matrix, Comput. Math. Appl., 27(8):59-6, 1994.MathSciNet View Article MATH
  
• 作者单位：Liubov A. Markovich (1)
  
  1. Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya 65, 117997, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Statistics
  Algebra
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8825

文摘

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? is assumed to be Markovian. This assumption allows us to estimate the unknown (S n ) using only an observable random sequence (X n ) n? .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.