Super Efficient Frequency Estimation

In this paper we propose a modified Newton-Raphson method to obtain super efficient frequency estimators of sinusoidal signals in presence of stationary noise. It is observed that if we start from an initial estimator with convergence rate Op(n ) and use the NewtonRaphson algorithm with proper step factor modification, then it produces super efficient frequency estimator in the sense it has asymptotic variance which is lower than the asymptotic variance of the least squares estimator. The proposed frequency estimator is consistent and have the optimum rate of convergence, namely Op(n − 3 2 ), which is same as the least squares estimator. Monte Carlo simulations are performed to observe the performances of the proposed estimator for different sample sizes and for different models. The results are