Details

Autor(en) / Beteiligte

• de Saporta, Benoite
• Costa, Eduardo F.

Titel

Approximate Kalman-Bucy Filter for Continuous-Time Semi-Markov Jump Linear Systems

Ist Teil von

• IEEE transactions on automatic control, 2016-08, Vol.61 (8), p.2035-2048

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2016

Quelle

IEL

Beschreibungen/Notizen

• 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.