A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modeling and estimation of multiscale stochastic processes
ICASSP '91 Proceedings of the Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference
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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.