### 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 language | English (US) |
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Title of host publication | 1990 IEEE Int Symp Inf Theor |

Place of Publication | Piscataway, NJ, United States |

Publisher | Publ by IEEE |

Pages | 31 |

Number of pages | 1 |

Publication status | Published - 1990 |

Event | 1990 IEEE International Symposium on Information Theory - San Diego, CA, USA Duration: Jan 14 1990 → Jan 19 1990 |

### Other

Other | 1990 IEEE International Symposium on Information Theory |
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City | San Diego, CA, USA |

Period | 1/14/90 → 1/19/90 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*1990 IEEE Int Symp Inf Theor*(pp. 31). Piscataway, NJ, United States: Publ by IEEE.