A Joint Estimation Algorithm for Multiple Sinusoidal Frequencies

Accurate estimation of sinusoidal frequencies from noisy observations is an important problem in many applications including radar, sonar, and data communications. Among many algorithms is the iterative filtering algorithm (IFA), proposed by Kay, which provides a computationally simple procedure yet capable of accurate frequency estimation especially at low signal-to-noise ratio (SNR). However, the convergence and other numerical/statistical properties of IFA have not been established beyond simulation. This paper makes several important contributions: (a) it shows that the poles of the AR filter must be reduced via a shrinkage parameter to accommodate possibly poor initial values; (b) it shows that the AR estimates in each iteration must be bias-corrected to produce more accurate frequency estimates; a closed-form expression is provided for bias correction; and (c) it shows that for a sufficiently large sample size, the resulting algorithm, called new IFA, or NIFA, converges to the desired fixed-point which constitutes a consistent frequency estimator. Numerical examples, including a radar data example, are provided to demonstrate the findings