An Improved Method for Parametric Spectral Estimation

One important class of problems within spectral estimation is when the signal can be well represented by a parametric model. These kind of problems can be found in many applications such as radar, sonar and wireless communication, and has therefore been extensively investigated. The main problem is to estimate frequencies and their corresponding amplitudes and damping factors from noisy measurements. One approach to this problem is to form a matrix of measurements, and then find an approximation to the range space of the matrix, with requirements that the approximation is of low rank and have a Hankel structure. From the approximation, the signal parameters can be extracted. In this work, we investigate three different methods which follows this methodology. The main contribution will be an illustration of how the problem formulation and rank constraint management affects the accuracy of the estimate. Numerical simulations indicates that a method which formulates a single convex envelope of a least squares fit to the measurement matrix and to the rank constraint jointly is more accurate than the other two investigated methods.