Estimating frequencies of exponentials in noise using joint diagonalization

The problem of estimating frequencies of superimposed exponentials in white noise, collected by a single sensor, is considered. We discuss a solution based on a modification of an analytic algorithm that was recently proposed for separation of constant modulus signals received by an antenna array by Van der Veen and Paulraj. We show that with an appropriate implementation of certain constraints, the algorithm produces excellent super-resolution results. An advantage of the algorithm is that it does not require multidimensional search, and therefore, it is free from problems associated with search algorithms like convergence to local extremum or proper initialization. Another advantage is its applicability in nonuniform sampling conditions, where methods based on linear prediction cannot be applied. We carry out a detailed performance analysis under the assumption of long data record and derive conditions for estimating all the frequencies. The performance of the proposed algorithm compares favorably with the performance of the Tufts-Kumaresan method.