A minimum variance single frequency estimator using recursive least squares estimate of noise statistics

Abstract

This paper proposes a new minimum variance unbiased estimator (MVUE) for finding the frequency of a complex tonal signal corrupted by possibly coloured noise. The procedure employs unwrapping the phase of the measured samples of the signal and computing a weight vector such that the estimator is an MVUE. It is shown that when the noise is white, the estimator achieves CRLB (Cramer-Rao Lower Bound) and its performance matches that of Kay's estimator. In cases where the colouring process is unknown, we propose simultaneous estimation of unknown frequency as well as the unknown autocorrelation matrix using a recursive least square update procedure.