Optimal filtering and smoothing algorithms for linear distributed-parameter systems with pointwise observation

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7 Citations (Scopus)

Abstract

Sequential algorithms for filtering, fixed-interval, fixed-point and fixed-lag smoothing are developed for a class of linear distributed-parameter systems. The class of systems concerned is that involving noisy measurement data which are obtained from a finite number subdomain in the spatial domain, i.e. pointwise sensor. The basic tools of the development are the Wiener-Hopf equation, innovation theory and the fundamental value theory for the differential operator. The fixed-lag smoother obtained is new. Finally, for the numerical solution, the expansion method of eigen-functions in L2(D) and L2(D × D) is asserted, and it is shown that the results obtained here are general forms, which contain the results of the finite state space reported earlier.

Original languageEnglish
Pages (from-to)325-349
Number of pages25
JournalInternational Journal of Systems Science
Volume12
Issue number3
DOIs
Publication statusPublished - 1981
Externally publishedYes

Fingerprint

Optimal Filtering
Smoothing Algorithm
Distributed Parameter Systems
Innovation
Wiener-Hopf Equations
Sequential Algorithm
Sensors
Eigenfunctions
Differential operator
Smoothing
State Space
Filtering
Fixed point
Numerical Solution
Sensor
Interval
Class
Observation
Lag
Form

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Management Science and Operations Research

Cite this

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AB - Sequential algorithms for filtering, fixed-interval, fixed-point and fixed-lag smoothing are developed for a class of linear distributed-parameter systems. The class of systems concerned is that involving noisy measurement data which are obtained from a finite number subdomain in the spatial domain, i.e. pointwise sensor. The basic tools of the development are the Wiener-Hopf equation, innovation theory and the fundamental value theory for the differential operator. The fixed-lag smoother obtained is new. Finally, for the numerical solution, the expansion method of eigen-functions in L2(D) and L2(D × D) is asserted, and it is shown that the results obtained here are general forms, which contain the results of the finite state space reported earlier.

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