Statistical analysis of the least-squares autoregressive frequency estimator for random-amplitude sinusoidal signals

Abstract In this paper, we address the problem of estimating the frequency of a random-amplitude sinusoidal signal by means of least-squares autoregressive (AR) modelling. We provide formulas for the asymptotic bias and variance of the estimate. The influence of the lowpass envelope characteristics on the estimation performance is studied in detail. This paper includes a number of numerical studies and simulations which provide illustrations of the main theoretical results. They provide quantitative insights into the trade-offs associated with the use of the AR estimator for the data considered.

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