Convergence analysis of a family of robust Kalman filters based on the contraction principle. (English) Zbl 1374.60074
Summary: 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.
MSC:
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 93B35 | Sensitivity (robustness) |
| 93E11 | Filtering in stochastic control theory |
Keywords:
block update; contraction mapping; Kalman filter; Riccati equation; Thompson’s part metric; risk-sensitive filteringReferences:
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