Joint estimation of the number and the frequencies of multiple sinusoids from very noisy data

We address the problem of the joint estimation of the number and frequencies of multiple sinusoids. Extremely severe noise conditions are dealt with; consequently, an approximation of the MLE must be employed. A closed loop detection and estimation system is studded, where the statistical information about the unknown frequencies is progressively refined using the results of the estimation algorithm, in such a way that the detection algorithm can exploit improved a priori information. Simulations have shown that this scheme achieves encouraging performance as for robustness towards noise.