Closed-form real single-tone frequency estimator based on a normalized IIR notch filter

A novel unbiased frequency estimator for a single real-valued sinusoid in white noise is proposed, which is based on a normalized second-order infinite impulse response (IIR) notch filter, and can be seen as an extension of the Pisarenko harmonic decomposer (PHD) estimator. The new estimator inherits the simplicity of the PHD estimator and the high accuracy and selectivity achieved by an IIR filter. As the coefficient determining the pole angle of the IIR notch filter depends on the unknown frequency value, an iterative scheme is proposed in which this coefficient is computed from the frequency estimate from the previous iteration. An analytic expression for the mean square error at each iteration is derived. Simulation results show that this iterative method can approach the Cramer–Rao lower bound in a few iterations under different signal to noise ratio levels, provided that the data record length is sufficiently large.