Log-concave Observers
(2006) 17th International Symposium on Mathematical Theory of Networks and Systems, 2006- 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... (More) - 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/942410
- author
- Henningsson, Toivo LU and Åström, Karl Johan LU
- organization
- publishing date
- 2006
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Event based control, Observers, Log-concave functions
- host publication
- 17th International Symposium on Mathematical Theory of Networks and Systems, 2006
- conference name
- 17th International Symposium on Mathematical Theory of Networks and Systems, 2006
- conference location
- Kyoto, Japan
- conference dates
- 2006-07-24 - 2006-07-28
- language
- English
- LU publication?
- yes
- id
- 0d881dbf-c2b9-4408-bf4c-a044a554766f (old id 942410)
- date added to LUP
- 2016-04-04 14:23:36
- date last changed
- 2018-11-21 21:32:40
@inproceedings{0d881dbf-c2b9-4408-bf4c-a044a554766f,
abstract = {{The Kalman filter is the optimal state<br/><br>
observer in the case of linear dynamics and Gaussian noise. <br/><br>
In this paper, the observer problem<br/><br>
is studied when process noise and measurements<br/><br>
are generalized from Gaussian to log-concave. This<br/><br>
generalization is of interest for example in the case<br/><br>
where observations only give information that the<br/><br>
signal is in a given range. It turns out that the optimal<br/><br>
observer preserves log-concavity. The concept<br/><br>
of strong log-concavity is introduced and two new<br/><br>
theorems are derived to compute upper bounds on<br/><br>
optimal observer covariance in the log-concave case.<br/><br>
The theory is applied to a system with threshold<br/><br>
based measurements, which are log-concave but far<br/><br>
from Gaussian.}},
author = {{Henningsson, Toivo and Åström, Karl Johan}},
booktitle = {{17th International Symposium on Mathematical Theory of Networks and Systems, 2006}},
keywords = {{Event based control; Observers; Log-concave functions}},
language = {{eng}},
title = {{Log-concave Observers}},
url = {{https://lup.lub.lu.se/search/files/26761902/8865396.pdf}},
year = {{2006}},
}