Polytopic model estimation using Dirichlet prior

A polytopic model (PM) structure is often used in the areas of automatic control and fault detection as an alternative multiple model approach that explicitly allows for interpolation among local models. The model that is valid, usually unknown, is represented by a weighed combination of models in a given model set. Proposed is a novel approach to PM estimation by modeling the set of PM weights as a random vector with the Dirichlet distribution (DD). A new approximate PM estimator, referred to as a Quasi-Bayesian (QB) Adaptive Kalman Filter (QBAKF) is derived and implemented. State and parameter estimation in the QBAKF is performed adaptively by a QB estimator for the weights and a single KF for the PM with the estimated weights. Since the PM estimation problem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developed and implemented. Simulation results are presented illustrating that the proposed algorithms have better estimation accuracy, design simplicity, and computational requirements for PM estimation than several other popular estimators.