Optimally Robust Kalman Filtering
- We present some optimality results for robust Kalman filtering. To this end, we introduce the general setup of state space models which will not be limited to a Euclidean or time-discrete framework. We pose the problem of state reconstruction and repeat the classical existing algorithms in this context. We then extend the ideal-model setup allowing for outliers which in this context may be system-endogenous or -exogenous, inducing the somewhat conflicting goals of tracking and attenuation. In quite a general framework, we solve corresponding minimax MSE-problems for both types of outliers separately, resulting in saddle-points consisting of an optimally-robust procedure and a corresponding least favorable outlier situation. Still insisting on recursivity, we obtain an operational solution, the rLS filter and variants of it. Exactly robust-optimal filters would need knowledge of certain hard-to-compute conditional means in the ideal model; things would be much easier if these conditional means were linear. Hence, it is important to quantify the deviation of the exact conditional mean from linearity. We obtain a somewhat surprising characterization of linearity for the conditional expectation in this setting. Combining both optimal filter types (for system-endogenous and -exogenous situation) we come up with a delayed hybrid filter which is able to treat both types of outliers simultaneously. Keywords: robustness, Kalman Filter, innovation outlier, additive outlier
Author: | P. Ruckdeschel |
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URN: | urn:nbn:de:hbz:386-kluedo-16505 |
Series (Serial Number): | Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (185) |
Document Type: | Report |
Language of publication: | English |
Year of Completion: | 2010 |
Year of first Publication: | 2010 |
Publishing Institution: | Fraunhofer-Institut für Techno- und Wirtschaftsmathematik |
Date of the Publication (Server): | 2010/07/21 |
Tag: | Kalman Filter; additive outlier; innovation outlier; robustness |
Faculties / Organisational entities: | Fraunhofer (ITWM) |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |