Credibility Test for Frequency Estimation of Sinusoid Using Chebyshev’s Inequality

Estimation of sinusoid frequency is a key research problem related to radar, sonar, and communication systems. The results of numerous investigations on frequency estimation have been reported in the literature. Nevertheless, to the best of our knowledge, none of them have dealt with credibility evaluation, which is used to decide whether an individual frequency estimate of the sinusoid is accurate or not. In this study, the credibility problem is modeled as a hypothesis test based on Chebyshev’s inequality (CI). The correlation calculated from the received signal and the reference signal generated according to the frequency estimate is used as a test statistic. A threshold is determined based on CI, and the analytical expression for the frequency estimation credibility detection performance is derived. Simulations show that the proposed method performs well even at low signal-to-noise ratios.