TY - RPRT
A1 - Ruckdeschel, P.
T1 - Optimally Robust Kalman Filtering
N2 - 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
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 185
KW - robustness
KW - Kalman Filter
KW - innovation outlier
KW - additive outlier
Y1 - 2010
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2208
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-16505
ER -