This paper considers the worst–case estimation problem in the presence of unknown but bounded *** to stochastic approaches, the goal here is to confine the estimation error within a bounded set. Previous work dealing...
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This paper considers the worst–case estimation problem in the presence of unknown but bounded *** to stochastic approaches, the goal here is to confine the estimation error within a bounded set. Previous work dealing with the problem has shown that the complexity of estimators based upon the idea of constructing the state consistency set(e.g. the set of all states consistent with the a-priori information and experimental data) cannot be bounded a-priori, and can, in principle, continuously increase with time. To avoid this difficulty in this paper we propose a class of boundedcomplexity filters, based upon the idea of confining r–length error sequences(rather than states) to hyperrectangles. The main result of the paper shows that this can be accomplished by using Linear Time Invariant(LTI) filters of order no larger than r. Further, synthesizing these filters reduces to a combination of convexoptimization and line search.
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