Sequential estimation of the sum of sinusoidal model parameters

Estimating the parameters of the sum of a sinusoidal model in presence of additive noise is a classical problem. It is well known to be a difficult problem when the two adjacent frequencies are not well separated or when the number of components is very large. In this paper we propose a simple sequential procedure to estimate the unknown frequencies and amplitudes of the sinusoidal signals. It is observed that if there are p components in the signal then at the kth (k⩽p) stage our procedure produces strongly consistent estimators of the k dominant sinusoids. For k>p, the amplitude estimators converge to zero almost surely. Asymptotic distribution of the proposed estimators is also established and it is observed that it coincides with the asymptotic distribution of the least squares estimators. Numerical simulations are performed to observe the performance of the proposed estimators for different sample sizes and for different models. One ECG data and one synthesized data are analyzed for illustrative purpose.