Analysis of Threshold Effect of Dual-tone Frequency Estimation Based on Method of Interval Errors

Dual-tone signals are widely used in ranging. Dual-tone signal frequency estimation is the primary problem to be solved in its application. There is a threshold effect on the maximum likelihood estimator (MLE) for frequency estimation of dual-tone signals, and the thresholds of MUSIC and the maximum expectation (EM) algorithm are both close to the MLE. The threshold for predicting the threshold effect is of great significance to the practical application of the algorithm. In this paper, the approximate mean square error (MSE) of the MLE for dual-tone frequency estimation is derived using the method of interval errors. The simulation results show that the approximate MSE derived in this paper can well analyze and predict the threshold of MUSIC and the ME algorithm.