Log-concave Observers

Toivo Henningsson, Karl Johan Åström

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

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Abstract

The Kalman filter is the optimal state
observer in the case of linear dynamics and Gaussian noise.
In this paper, the observer problem
is studied when process noise and measurements
are generalized from Gaussian to log-concave. This
generalization is of interest for example in the case
where observations only give information that the
signal is in a given range. It turns out that the optimal
observer preserves log-concavity. The concept
of strong log-concavity is introduced and two new
theorems are derived to compute upper bounds on
optimal observer covariance in the log-concave case.
The theory is applied to a system with threshold
based measurements, which are log-concave but far
from Gaussian.
Original languageEnglish
Title of host publication17th International Symposium on Mathematical Theory of Networks and Systems, 2006
Publication statusPublished - 2006
Event17th International Symposium on Mathematical Theory of Networks and Systems, 2006: MTNS 2006 - Kyoto, Japan
Duration: 2006 Jul 242006 Jul 28
Conference number: 17

Conference

Conference17th International Symposium on Mathematical Theory of Networks and Systems, 2006
Country/TerritoryJapan
CityKyoto
Period2006/07/242006/07/28

Subject classification (UKÄ)

  • Control Engineering

Keywords

  • Event based control
  • Observers
  • Log-concave functions

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