Frequency-estimation error variance of an adaptive scheme based on structured AR modeling

An on-line version of a recently proposed frequency-estimation algorithm based on structured autoregressive (AR) modeling of data is derived for the special case of a single cisoid in noise. The adaptive notch filter utilizes a weighted sum-of-squares of the AR prediction error that is recursively minimized with respect to the frequency of the cisoid. The steady-state performance of the algorithm is characterized by aid of a linear filter-approximation technique, and design rules for the tuning variables are given. An excellent agreement is demonstrated between the results predicted by theory and the measured performance based on numerical simulations. The tracking ability and noise rejection is compared both with the performance of alternative algorithms and with the appropriate Cramer-Rao bound. It is shown that the algorithm is close to being statistically efficient.