Modeling and estimation of multiscale stochastic processes

The authors introduce a class of multiscale stochastic processes which are Markov in scale and which are characterized by dynamic state models evolving in scale. The models for these processes are motivated by the theory of multiscale representations and the wavelet transform. The authors formulate an optimal estimation problem based on these models, which has potential applications to sensor fusion problems where there exist data from sensors of differing resolution, and provide an efficient algorithm based on the wavelet transform. They give examples applying these models to first-order Gauss-Markov processes