Identification of ARX models with markovian parameters

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Abstract
Many different recursive identification methods for time-varying systems have been suggested in the literature. An assumption that the variations in the system parameters are slow is common for all the methods. When using the methods on systems with faster variations, one is forced to compromise between alertness to parameter variations on one hand and noise sensitivity on the other. The topic of this paper is to investigate if this compromise can be avoided for a special class of systems. The systems considered are such that their dynamic changes between some different typical modes. The philosophy behind the approach taken in the paper is to separate the observations into different sets corresponding to the different modes. The parameters of the different modes can then be estimated using the separated data sets. Technically, this parallel modelling is achieved by describing the system parameters as the realizations of a Markov chain. A parameter-identification algorithm for time-varying ARX models is then given in the paper. The behaviour of the algorithm is then investigated using simulations and some analysis. The analysis and the simulations show that a major problem is the initialization of the algorithm. Based on the analysis, modifications are made to the algorithm that improve the convergence properties.