Advanced

Log-concave Observers

Henningsson, Toivo LU and Åström, Karl Johan LU (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:
author
organization
publishing date
type
Contribution to conference
publication status
published
subject
keywords
Event based control, Observers, Log-concave functions
conference name
17th International Symposium on Mathematical Theory of Networks and Systems, 2006
language
English
LU publication?
yes
id
0d881dbf-c2b9-4408-bf4c-a044a554766f (old id 942410)
date added to LUP
2008-01-22 10:51:48
date last changed
2016-06-21 16:00:59
@misc{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},
  keyword      = {Event based control,Observers,Log-concave functions},
  language     = {eng},
  title        = {Log-concave Observers},
  year         = {2006},
}