On adaptive implementations of Pisarenko´s harmonic retrieval method

The problem of locating spectral lines (sinusoids) in white noise has been studied intensively in the past few years, especially since the work of Pisarenko who showed that unbiased estimates of the sinusoidal frequencies could be obtained from the λ0eigenvector (i.e. the eigenvector associated with the smallest eigenvalue) of the covariance matrix of the process. Recently, adaptive implementations of Pisarenko´s method have been developed in which the estimates can be updated as new data is observed, and so these algorithms have the ability to track slowly time-varying processes. In this paper, a new adaptive algorithm based on the inverse power method is developed and compared by simulation to other methods. Conclusions are drawn which affect any adaptive implementation of Pisarenko´s method.