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Efficient estimation of the parameters in a sum of complex sinusoids in complex autoregressive noise

Although the periodogram maximizer has good asymptotic properties in the case of a single sinusoid in colored noise, in low SNR conditions and/or in the case of small sample size, the data need to be prewhitened in order for the periodogram maximizer be likely to occur near the true frequency. In this paper we derive an efficient least squares algorithm for estimating the frequencies, amplitudes, phases and autoregressive parameters for a sum of sinusoids in complex autoregressive noise. The procedure is seen to be a generalization of the Levinson-Durbin algorithm, an efficient technique for estimating the parameters in an autoregression.