On-line multiscale filtering of random and gross errors without process models

Darn Rectification by univariate filtering is popular for processes lacking an accurate model. Linear filters are most popular for online filtering; h owever they are single-scale best suited for rectifying data containing fea tures and noise that are at the same resolution in time and frequency. Cons equently, for multiscale data, linear filters are forced to tr ade off the extent of noise removal with the accuracy of the features retained. In cont rast nonlinear filtering methods, such as FMH and wavelet thresholding, are multiscale, but they cannot be used for online rectification A technique i s presented for online nonlinear filtering based on wavelet thresholding. O LMS rectification applies wavelet thresholding to data in a moving window o f dyadic length to remove random errors. Gross errors are removed by combin ing wavelet thresholding with multiscale median filtering. Theoretical anal ysis shows that OLMS rectification using Haar wavelets subsumes mean filter s of dyadic length, while rectification with smoother boundary corrected wa velets is analogous to adaptive exponential smoothing. If the rectified mea surements are not needed online, the quality of rectification can be furthe r improved by averaging the rectified signals in each window, overcoming th e boundary effects encountered in TI rectification. Synthetic and industria l data show the benefits of the online multiscale and boundary corrected tr anslation invariant rectification methods.