Log-concave Observers
Author
Summary, in English
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.
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.
Department/s
Publishing year
2006
Language
English
Publication/Series
17th International Symposium on Mathematical Theory of Networks and Systems, 2006
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Document type
Conference paper
Topic
- Control Engineering
Keywords
- Event based control
- Observers
- Log-concave functions
Conference name
17th International Symposium on Mathematical Theory of Networks and Systems, 2006
Conference date
2006-07-24 - 2006-07-28
Conference place
Kyoto, Japan
Status
Published