Method of dummy measurements for multiple model estimation of processes in a linear stochastic system

We consider the estimation problem for the state vector of a linear stochastic discrete system some of whose components are constant parameters with Gaussian distribution and uncertain moments. Hypotheses regarding possible values of these moments are provided together with their prior probabilities. Instead of a classical multiple model solution that constructs Kalman filters for every hypothesis, we propose a less computationally intensive method that lets us compute posterior probabilities and estimate the state vector for individual hypotheses by the results of a single filter augmented with dummy measurements. The value and model of these measurements are defined by the possible values of the constant parameters' moments. We give examples of rational definition of the dummy measurement model. We compare the computational costs of the proposed approach and the classical one.