NDLI: Real time solution of Duncan-Mortensen-Zakai equation without memory

Content Provider	IEEE Xplore Digital Library
Author	Yau, S.S.-T. Shing-Tung Yau
Copyright Year	2008
Description	Author affiliation: Dept. of Math., Harvard Univ., Cambridge, MA, USA (Shing-Tung Yau) \|\| Inst. of Math., East China Normal Univ., Shanghai, China (Yau, S.S.-T.)
Abstract	It is well known that the nonlinear filtering problem has important applications in both military and commercial industries. The central problem of nonlinear filtering is to solve the DMZ equation in real time and memoryless manner. The purpose of this paper is to show that, under very mild conditions (which essentially say that the growth of the observation \|h\| is greater than the growth of the drift \|f\|), the DMZ equation admits a unique nonnegative weak solution u which can be approximated by a solution $u_{R}$ of the DMZ equation on the ball $B_{R}$ with $u_{R}\|_{¿BR}$ = 0. The error of this approximation is bounded by a function of R which tends to zero as R goes to infinity. The solution $u_{R}$ can in turn be approximated efficiently by an algorithm depending only on solving the observation-independent Kolmogorov equation on $B_{R}.$ In theory, our algorithm can solve basically all engineering problems in real time manner. Specifically, we show that the solution obtained from our algorithms converges to the solution of the DMZ equation in $L^{1}-sense.$ Equally important, we have a precise error estimate of this convergence which is important in numerical computation.
Starting Page	5086
Ending Page	5091
File Size	216415
Page Count	6
File Format	PDF
ISBN	9781424431236
ISSN	01912216
DOI	10.1109/CDC.2008.4739506
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-12-09
Publisher Place	Mexico
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Nonlinear equations Nonlinear filters Filtering theory Mathematics Sonar navigation Defense industry H infinity control Convergence of numerical methods Maximum likelihood detection Aircraft navigation
Content Type	Text
Resource Type	Article

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