Multi-model system parameter estimation

We pose a multi-model system parameter estimation problem. A multi-model system is a linearly parameterized system H(z, p)=Σ_i=1^npp_iH_i(z). The parameter estimation problem is: given the set of systems {H_i(z)}_i=1^np, describing the multi-model system, find a causal system that assumes as an input the input/output signals of the multi-model system and produces as an output the parameter estimate. We propose an easy to implement suboptimal solution. The algorithm that realizes it selects the best linear combination of the estimates produced by the Kalman filters designed for the models {H_i(z)}_i=1^np. "Best" is defined in the sense of minimization of the output error of estimation covariance. The algorithm is appropriate for fault detection and can be viewed as an observer for the discrete state of a hybrid system.