Detection of sinusoids in unknown coloured noise using ratios of AR spectrum estimates

This paper is an introductory exposition of the application of the ratio of the 2p-th order autoregressive (AR) power spectrum estimate to the p-th order AR power spectrum estimate to the problem of detecting sinusoids of unknown frequency in additive coloured noise with unknown power spectral density (PSD). The resulting threshold test is independent of a priori knowledge of both the sinusoid's parameters and the PSD of the additive noise. Simulations are presented for the Gaussian case, focusing primarily on the SNR thresholding behaviour of the scheme. These simulations illustrate the power of the technique when highly resonant background noise is present, such as is often the case in rotating machinery, for example. Significant threshold extension, and slightly superior sub-threshold performance compared to the energy detector is observed in these cases. The paper also examines the application of the technique to the problem of identifying tones in diesel engine vibration data.