Hybrid Descriptor System State Estimation through an IMM Approach

Liangquan Zhang (1) , Qinghua Zhang (1, 2)

1 I4S - Statistical Inference for Structural Health Monitoring
2 IFSTTAR/COSYS - Département Composants et Systèmes

Stochastic hybrid systems have been largely studied in the literature in the framework of Markov mode transitions and linear Gaussian state space mode models. In order to generalize such results to hybrid systems involving phenomena characterized by differential-algebraic equations, this paper studies the problem of state estimation for stochastic hybrid systems with modes described by descriptor equations. The proposed state estimation algorithm follows the interacting multiple model (IMM for short) approach, but the classical state space system Kalman filters are replaced by descriptor system Kalman filters. Because of the difficulty for computing the innovation of each descriptor system Kalman filter, a new method for likelihood evaluation is proposed, as one important step of the new IMM algorithm. Numerical examples are presented to illustrate the performance of the proposed algorithm.

Mots clés: Hybrid system; descriptor system; IMM estimator; descriptor system Kalman filter

Domaines: Automatique

Liangquan Zhang, Qinghua Zhang. Hybrid Descriptor System State Estimation through an IMM Approach. 17th IFAC Symposium on System Identification (SYSID), Oct 2015, Beijing, China. ⟨hal-01232174⟩