Dey, Subhrakanti and Charalambous, Charalambos D.
(2001)
Discrete-time risk-sensitive filters with non-gaussian initial conditions and their Ergodic properties.
Asian Journal of Control, 3 (4).
pp. 262-271.
ISSN 1563-8625
Abstract
In this paper, we study asymptotic stability properties of risk-sensitive
filters with respect to their initial conditions. In particular, we consider a linear
time-invariant systems with initial conditions that are not necessarily Gaussian.
We show that in the case of Gaussian initial conditions, the optimal risksensitive filter asymptotically converges to a suboptimal filter initialized with
an incorrect covariance matrix for the initial state vector in the mean square
sense provided the incorrect initializing value for the covariance matrix results
in a risk-sensitive filter that is asymptotically stable, that is, results in a solution
for a Riccati equation that is asymptotically stabilizing. For non-Gaussian
initial conditions, we derive the expression for the risk-sensitive filter in terms
of a finite number of parameters. Under a boundedness assumption satisfied
by the fourth order absolute moment of the initial state variable and a slow
growth condition satisfied by a certain Radon-Nikodym derivative, we show
that a suboptimal risk-sensitive filter initialized with Gaussian initial conditions asymptotically approaches the optimal risk-sensitive filter for nonGaussian initial conditions in the mean square sense. Some examples are also
given to substantiate our claims.
| Item Type: |
Article
|
| Keywords: |
Risk-sensitive estimantion; asymptotic stability; non-Gaussian;
optimal filtering; |
| Academic Unit: |
Faculty of Science and Engineering > Electronic Engineering |
| Item ID: |
12731 |
| Depositing User: |
Subhrakanti Dey
|
| Date Deposited: |
09 Apr 2020 10:13 |
| Journal or Publication Title: |
Asian Journal of Control |
| Publisher: |
Wiley |
| Refereed: |
Yes |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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