### 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 |

State | 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 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

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

**A geometric interpretation of the linear set-valued estimator.** / Morrell, Darryl; Stirling, Wynn C.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*1990 IEEE Int Symp Inf Theor.*Publ by IEEE, Piscataway, NJ, United States, pp. 31, 1990 IEEE International Symposium on Information Theory, San Diego, CA, USA, 1/14/90.

}

TY - GEN

T1 - A geometric interpretation of the linear set-valued estimator

AU - Morrell, Darryl

AU - Stirling, Wynn C.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025682791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025682791&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025682791

SP - 31

BT - 1990 IEEE Int Symp Inf Theor

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -