A geometric interpretation of the linear set-valued estimator

Darryl Morrell, Wynn C. Stirling

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Summary form only given, as follows. Recently, a theory of discrete-time optimal estimation (filtering, smoothing, and prediction) based on convex sets of probability distributions has been developed. By restricting attention to the linear Gaussian problem, a set-valued estimator is obtained; the estimator is an exact solution to the problem of running an infinity of Kalman filters (and fixed-interval smoothers), each with different initial conditions. The philosophical basis underlying the theory of set-valued estimation is presented, and the estimator developed for the linear Gaussian problem is briefly reviewed. A geometrical interpretation of this estimator is presented; this interpretation provides a natural and informative framework in which the set-valued estimator can be understood. In addition, the geometric interpretation leads to a significant generalization in the sets that can be represented in the set-valued estimation algorithms.

Original languageEnglish (US)
Title of host publication1990 IEEE Int Symp Inf Theor
Place of PublicationPiscataway, NJ, United States
PublisherPubl by IEEE
Pages31
Number of pages1
Publication statusPublished - 1990
Event1990 IEEE International Symposium on Information Theory - San Diego, CA, USA
Duration: Jan 14 1990Jan 19 1990

Other

Other1990 IEEE International Symposium on Information Theory
CitySan Diego, CA, USA
Period1/14/901/19/90

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ASJC Scopus subject areas

  • Engineering(all)

Cite this

Morrell, D., & Stirling, W. C. (1990). A geometric interpretation of the linear set-valued estimator. In 1990 IEEE Int Symp Inf Theor (pp. 31). Piscataway, NJ, United States: Publ by IEEE.