Optimal autoregressive modelling of a measured noisy deterministic signal using singular-value decomposition

A new simple method using singular-value decomposition (SVD) to find the optimal order for an autoregressive (AR) model of a deterministic time series is proposed. The method is particularly effective when the signal is contaminated with additive noise, and it is shown that the choice of sampling rate is also important when the signal is contaminated with noise. In this paper, the signal of interest is the impulse response of a second-order differential system, and various levels of white noise are also added to the signal, to show the robustness of the method. Simulation results show the method to be very reliable even when the noise level is high (e.g. a signal-to-noise ratio of 6 dB). To validate the method on experimental data the method is applied to the impulse response of a cantilever beam contaminated with additive white noise. (C) 2003 Elsevier Science Ltd. All rights reserved.