2016/06/27 by Pierre Del Moral, Del Moral, Pierre, Aline Kurtzmann +3 · 1 citation
Decision Sciences · Engineering · #60G25 #60M20 #93C55 #93D20 #93E11 #Control and Stability of Dynamical Systems #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1606.08251
openalex publication_date 2016/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially observed signals are derived in terms of the stability properties of the filters. These non asymptotic exponential inequalities allow to design confidence interval type estimates in terms of the filter forgetting properties with respect to erroneous initial conditions. For uniformly stable signals, we also provide explicit non-asymptotic estimates for the exponential forgetting rate of the filters and the associated stochastic Riccati equations w.r.t. Frobenius norms. These non asymptotic exponential concentration and quantitative stability estimates seem to be the first results of this type for this class of nonlinear filters. Our techniques combine χ-square concentration inequalities and Laplace estimates with spectral and random matrices theory, and the non asymptotic stability theory of quadratic type stochastic processes.