Dey, Subhrakanti and Moore, John B. (1997) Risk-Sensitive Filtering and Smoothing via Reference Probability Methods. IEEE Transactions on Automatic Control, 42 (11). pp. 1587-1591. ISSN 0018-9286
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Abstract
In this paper, we address the risk-sensitive filtering problem
which is minimizing the expectation of the exponential of the squared
estimation error multiplied by a risk-sensitive parameter. Such filtering
can be more robust to plant and noise uncertainty than minimum
error variance filtering. Although optimizing a differently formulated
performance index to that of the so-called H1 filtering, risk-sensitive
filtering leads to a worst case deterministic noise estimation problem given
from the differential game associated with H1 filtering. We consider a
class of discrete-time stochastic nonlinear state-space models. We present
linear recursions in the information state and the result for the filtered
estimate that minimizes the risk-sensitive cost index. We also present
fixed-interval smoothing results for each of these signal models. In
addition, a brief discussion is included on relations of the risk-sensitive
estimation problem to minimum variance estimation and a worst case
estimation problem in a deterministic noise scenario related to minimax
dynamic games.
The technique used in this paper is the so-called reference probability
method which defines a new probability measure where the observations
are independent and translates the problem to the new measure. The
optimization problem is solved using simple estimation theory in the
new measure, and the results are interpreted as solutions in the original
measure.
Item Type: | Article |
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Keywords: | Estimation theory; optimal filtering; smoothing; |
Academic Unit: | Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute |
Item ID: | 14404 |
Identification Number: | 10.1109/9.649727 |
Depositing User: | Subhrakanti Dey |
Date Deposited: | 10 May 2021 14:05 |
Journal or Publication Title: | IEEE Transactions on Automatic Control |
Publisher: | IEEE |
Refereed: | Yes |
Related URLs: | |
URI: | https://mu.eprints-hosting.org/id/eprint/14404 |
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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