A geometric interpretation of the linear set-valued estimator

Darryl Morrell, Wynn C. Stirling

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


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
Number of pages1
StatePublished - 1990
Event1990 IEEE International Symposium on Information Theory - San Diego, CA, USA
Duration: Jan 14 1990Jan 19 1990


Other1990 IEEE International Symposium on Information Theory
CitySan Diego, CA, USA

ASJC Scopus subject areas

  • General Engineering


Dive into the research topics of 'A geometric interpretation of the linear set-valued estimator'. Together they form a unique fingerprint.

Cite this