Robustness of maximum likelihood frequency estimators under model errors

In this paper, the robustness of maximum likelihood (ML) constant frequency estimators is discussed. The motivation for the paper is to understand the performance of the hidden Markov model-maximum likelihood (HMM-ML) tandem frequency tracker where the signal´s frequency is assumed to be piecewise constant. For this purpose the frequencies of noisy linear FM signals are estimated under the wrong assumption that they have constant frequencies and the performance of the ML constant frequency estimator is analyzed at different signal-to-noise ratio (SNR) levels extending the techniques in Rife and Boorstyn (1974). The change of the threshold SNR with respect to the rate of the frequency variation is investigated and a simple rule of thumb is given for this change. The results are supported by simulations