Estimation of close sinusoids in colored noise and model discrimination

This paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown. Earlier attempts have assumed the additive noise to be independent. Next we develop decision rules for checking whether the observed signal has only one sinusoid or two close sinusoids. All of the earlier studies assumed that there are two close sinusoids in the signal. Another model discrimination problem considered is the determination of the causal structure of the observed periodicity. A rule is given to test whether the observation comes from a sinusoid plus additive noise, possible colored, or the observation comes from a stationary autoregressive model. We also present a numerical study showing the efficacy of the robust estimation procedure for estimating the two frequencies and the decision rules for checking the number of dominant frequencies and the causal mechanism. Finally, we compare the proposed method to well-known methods used for two close sinusoids in white noise.