In this paper, we analyze the convergence of a family of robust Kalman filters. For each filter of this family, the model uncertainty is tuned according to the so-called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the N-fold composition of the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is suficiently small and, accordingly, the filter converges.
Convergence analysis of a family of robust Kalman filters based on the contraction principle
ZORZI, MATTIA
2017
Abstract
In this paper, we analyze the convergence of a family of robust Kalman filters. For each filter of this family, the model uncertainty is tuned according to the so-called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the N-fold composition of the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is suficiently small and, accordingly, the filter converges.
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