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JOURNALS // Problemy Peredachi Informatsii // Archive

Probl. Peredachi Inf., 2008 Volume 44, Issue 1, Pages 59–79 (Mi ppi1266)

This article is cited in 5 papers

Large Systems

Kalman Filter and Quantization

A. I. Ovseevich

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: We give an interpretation of the problem of filtering of diffusion processes as a quantization problem. Based on this, we show that the classical Kalman–Bucy linear filter describes a flow of automorphisms of the Heisenberg algebra. We obtain new formulas for the unnormalized conditional density in the linear case, a new interpretation of the Mehler formula for the fundamental solution of the Schrödinger operator for a harmonic oscillator, and formulas for a regularized determinant of a Sturm–Liouville operator.

UDC: 621.391.1:519.2

Received: 15.10.2007


 English version:
Problems of Information Transmission, 2008, 44:1, 53–71

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