Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables identification

The time domain maximum likelihood (TML) method and the sample maximum Likelihood (SML) method are two approaches for identifying errors-invariables models. Both methods may give the optimal estimation accuracy (achieve Cramér-Rao lower bound) but in different senses. In the TML method, an important assumption is that the noise-free input signal is modeled as a stationary process with rational spectrum. For SML, the noise-free input needs to be periodic. It is interesting to know which of these assumptions contain more information to boost the estimation performance. In this paper, the estimation accuracy of the two methods is analyzed statistically. Numerical comparisons between the two estimates are also done under different signal-to-noise ratios (SNRs). The results suggest that TML and SML have similar estimation accuracy at moderate or high SNR.