Maximum likelihood identification of multiscale stochastic models using the wavelet transform and the EM algorithm

The authors address the problem of estimating the parameters of a class of multiscale stochastic processes that can be modeled by state-space dynamic systems driven by white noise in scale rather than in time. They present a maximum likelihood identification method for estimating the parameters of the multiscale stochastic models given data which are based on the wavelet transform and the expectation-maximization algorithm. Numerical examples are provided for identifying the parameters of the state-space models based on synthesized data to demonstrate the accuracy and the efficiency of the algorithm. In the examples the effects of performing system identification are illustrated based on data at both multiple and single scales. The single-scale case can be viewed as the standard problem of fitting model parameters to data, where here the model is not standard.<>