Performance of the Maximum Likelihood Constant Frequency Estimator for Frequency Tracking

In this paper, the performance of maximum likelihood (ML) estimators for an important frequency estimation problem is considered when the signal model assumptions are not valid. The motivation for this problem is to understand the robustness of the hidden Markov model-maximum likelihood (HMM-ML) tandem frequency estimator [1], where the signal is divided into time blocks, and the frequency in each time block is estimated using the ML approach under the assumption that the signal has a constant frequency in each time block. In order to analyze the sensitivity of ML estimators to the model assumptions, the mean frequency of a discrete complex tone that has a time-varying (ramp) frequency is estimated under the incorrect assumption that it has a constant frequency. In particular, the behavior of the threshold region with respect to different chirp rates is analyzed, and a simple rule is given. The mean squared error above the threshold region is shown to be constant even at very high SNR levels. These results are supported by simulations.