Identification of nonstationary stochastic systems using parallel estimation schemes

The parallel (multiple-model) schemes for identification of nonstationary stochastic systems are considered. First, the form of the optimal-local Bayesian predictor is derived under the assumptions that system coefficients vary according to the random walk model and that the Kalman-filter-based algorithms are used for identification purposes. A rational extension of this strategy, which can be applied to identification algorithms of any form, is discussed. Specific suggestions are made concerning the possible choice of adaptation gains of the competitive adaptive filters. Computer simulation results, confirming the good estimation robustness properties of the parallel identification schemes, are presented. It is shown that the proposed scheme can significantly decrease sensitivity of the identification algorithm to the rate of nonstationarity of the analyzed system or (alternatively) to the choice of design parameters such as adaptation gains and forgetting factors