Worst-case centre-frequency estimation

Abstract

This paper analyzes the centre-frequency estimator proposed by Lank, Reed, and Pollon [1]. This estimator is popular in practical applications due to its robustness and computational simplicity. The estimator's behaviour when applied to sinusoidal signals has previously been studied. The behaviour for non-sinusoidal signals is analysed here. Under general conditions the estimator is shown to be statistically consistent and asymptotically normally distributed as the number of samples of the signal grows. The asymptotic variance is shown to depend upon the spectrum of the underlying signal, and in particular its band-width. Sinusoidal signals are shown to minimise this variance and so represent the best-case behaviour. Under a bandwidth constraint, the worst-case behaviour is shown to occur when the underlying signal consists of two sinusoids separated by the bandwidth. This worst-case behaviour provides upper bounds on the error and corresponding confidence intervals when the underlying signal is unknown. The upper bounds are useful in applications such as electronic support where the specific form of received signals may not be known.