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

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