An AI based frequency weighted least-squares filter

An artificial intelligence (AI) based robust algorithm to extract, a posteriori, the rational signal model from a noisy measurement, with little a priori information, is proposed. The spectrum and the statistics of the signal and of the corrupting noise are assumed unknown except that the signal is assumed to have a rational spectrum. An algorithm based on both system and signal theory, and on heuristics is derived to select a set of frequencies where the SNR is high from a given measurement spectrum. A relative weighting which indicates the importance of the measurement at each frequency is also obtained. An estimate of the signal model is obtained from the best weighted least squares fit to the measurement spectrum at the selected frequencies. The proposed scheme has applications to control and signal processing, and is evaluated with a number of simulated examples, and on a physical system. The results are compared with conventional adaptive filter techniques.