Multiscale Bayesian Estimation and Data Rectification
Most measured data contain features localized at multiple scales in time and frequency. Multiscale approaches to state estimation and data rectification offer attractive alternatives to traditional single scale methods by exploiting the ability of wavelets to approximately decorrelate many autocorrelated stochastic processes and extract deterministic features in a signal. This chapter describes several important features of the framework, (a) a Bayesian approach for efficiently fusing prior information with measured data subject to process model constraints, (b) the ability of wavelets to extract temporal dynamics in scale leading to efficient rectification methods for processes lacking accurate models, (c) multiscale linear models to describe the time—scale localized evolution of the system leading to adaptive estimation in time and scale and (d) parallelizable and computationally efficient algorithms. Most existing single scale methods as well their multiscale analogues are shown to be special cases of the general multiscale Bayesian approach.
KeywordsFine Scale Wavelet Coefficient Data Rectification Coarse Scale Single Scale
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