Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems

Abstract : The aim of this paper is to propose a new numerical approximation of the Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is based on the selection of typical trajectories of the driving semi-Markov chain of the process by using an optimal quantization technique. The main advantage of this approach is that it makes pre-computations possible. We derive a Lipschitz property for the solution of the Riccati equation and a general result on the convergence of perturbed solutions of semi-Markov switching Riccati equations when the perturbation comes from the driving semi-Markov chain. Based on these results, we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step. We employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the Kalman-Bucy filter and the Markovian linear minimum mean squares estimator.
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Contributor : Benoîte De Saporta <>
Submitted on : Wednesday, September 10, 2014 - 10:47:57 AM
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Benoîte De Saporta, Eduardo Costa. Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (8), pp.2035 - 2048. 〈〉. 〈10.1109/TAC.2015.2495578〉. 〈hal-01062618〉



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