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2018 On the stability and the concentration of extended Kalman-Bucy filters
Pierre Del Moral, Aline Kurtzmann, Julian Tugaut
Electron. J. Probab. 23: 1-30 (2018). DOI: 10.1214/18-EJP188


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 and fully observable 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 $\chi $-square concentration inequalities and Laplace estimates with spectral and random matrices theory, and the non asymptotic stability theory of quadratic type stochastic processes.


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Pierre Del Moral. Aline Kurtzmann. Julian Tugaut. "On the stability and the concentration of extended Kalman-Bucy filters." Electron. J. Probab. 23 1 - 30, 2018.


Received: 22 August 2017; Accepted: 12 June 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 1401.93199
MathSciNet: MR3858919
Digital Object Identifier: 10.1214/18-EJP188

Primary: 60G25 , 60M20 , 93C55 , 93D20 , 93E11

Keywords: Concentration inequalities , extended Kalman-Bucy filter , Lyapunov exponents , non asymptotic exponential stability , Riccati equation


Vol.23 • 2018
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