2010/04/22 by Peter Ruckdeschel, Ruckdeschel, Peter
Mathematics · #62F35 #93E11 #Computation (stat.CO) #FOS: Computer and information sciences #msc:62F35 #msc:93E11 #stat.CO
paper · pdf · doi:10.48550/arxiv.1004.3895
arxiv created 2010/04/22 · arxiv updated 2010/04/23
We take up optimality results for robust Kalman filtering from Ruckdeschel[2001,2010] where robustness is understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods, allowing for outliers which in our context may be system-endogenous/propagating or -exogenous/non-propagating, inducing the somewhat conflicting goals of tracking and attenuation. Correspondingly, the cited references provide optimally-robust procedures to deal with each type of outliers separately, but in case of IO-robustness does not say much about the implementation. We discuss this in more detail in this paper. Most importantly, we define a hybrid filter combining AO- and IO-optimal ones, which is able to treat both types of outliers simultaneously, albeit with a certain delay. We check our filters at a reference state space model, and compare the results with those obtained by the ACM filter Martin and Masreliez[1977], Martin[1979] and non-parametric, repeated-median based filters Fried et al.[2006,2007].