A BAYESIAN NON-PARAMETRIC APPROACH TO FREQUENCY ESTIMATION

Although frequency estimation is a nonlinear parametric problem, it can be cast in a non-parametric framework. By assigning a natural a priori probability to the unknown frequency, the covariance of the prior signal model is found to admit an eigenfunction expansion alike the famous prolate spheroidal wave functions, introduced by D. Slepian in the 1960's. This leads to a technique for estimating the hyperparameters of the prior distribution which is essentially linear. This is in contrast to standard parametric estimation methods which are based on iterative optimization algorithms of local nature. The approach seems to be new and quite promising.