Fast least-squares polynomial approximation in moving time windows

Abstract

Only a few time series methods are applicable to signal trend analysis under real-time conditions. The use of orthogonal polynomials for least-squares approximations on discrete data turned out to be very efficient for providing estimators in the time domain. A polynomial extrapolation considering signal trends in a certain time window is obtainable even for high sampling rates. The presented method can be used as a prediction algorithm, e.g. in threshold monitoring systems, or as a trend correction possibility preparing the analysis of the remaining signal. In the theoretical derivation, the recursive computation of orthogonal polynomials allows the development of these fast algorithms for least-squares approximations in moving time windows.