On stability of a class of filters for nonlinear stochastic systems. (English) Zbl 1448.37061
Authors’ abstract: This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous- and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds.
Reviewer: Kaïs Ammari (Monastir)
MSC:
| 37H30 | Stability theory for random and stochastic dynamical systems |
| 37N35 | Dynamical systems in control |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93B05 | Controllability |
| 93B07 | Observability |
| 93D20 | Asymptotic stability in control theory |
| 93E15 | Stochastic stability in control theory |
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