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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 sufficiently small and, accordingly, the filter converges.

Convergence Analysis of a Family of Robust Kalman Filters Based on the Contraction Principle