A Novel Method for the Computation of the Deterministic Maximum Likelihood Estimator of Multiple Real Sinusoids

Abstract

In this manuscript a novel computationally efficient method for implementing the Deter- ministic Maximum Likelihood estimator of multiple superimposed real sinusoids is derived. This method is an adaptation of a recently proposed algorithm for the estimation of undamped exponentials and offers two significant advantages in terms of complexity with respect to various alternatives available in the technical literature. First, the dependence of the computational complexity on the snapshot length is the same as that of the Fast Fourier Transform. Consequently, increasing the snapshot length does not have a substantial impact on the overall computational burden. Second, the proposed method exploits the ability of the periodogram estimator to coarsely locate the global maximum of the Deterministic Maximum Likelihood cost function, thereby eliminating the need for a global search on this last function. Our numerical results show that it achieves a better accuracy-complexity trade-off than various estimators available in the literature.

Keywords

• Amplitude estimation
• array signal processing
• direction-of-arrival estimation
• discrete Fourier transforms
• Fourier transforms
• frequency estimation