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A Multiscale, Bayesian And Error-In-Variables Approach For Linear Dynamic Data Rectification, Sridhar Ungarala, Bhavik R. Bakshi

Chemical & Biomedical Engineering Faculty Publications

A multiscale approach to data rectification is proposed for data containing features with different time and frequency localization. Noisy data are decomposed into contributions at multiple scales and a Bayesian optimization problem is solved to rectify the wavelet coefficients at each scale. A linear dynamic model is used to constrain the optimization problem, which facilitates an error-in variables (EIV) formulation and reconciles all measured variables. Time-scale recursive algorithms are obtained by propagating the prior with temporal and scale models. The multi-scale Kalman filter is a special case of the proposed Bayesian EIV approach.