Improved subspace-based frequency estimation for real-valued data using angles between subspaces

A multitude of applications contain signals that can be well described as being formed as a sum of sinusoidal components corrupted by noise, and, as a result, the literature contains a large variety of estimation algorithms tailored for this problem. Many of these estimators assume a complex-valued signal model, typically formed using the discrete-time Hilbert transform. For a large number of observations, or with frequencies being neither too high nor too low, this approach works well, whereas it might well cause considerable problems otherwise. One way to handle these situations is to instead form the frequency estimation algorithm assuming a real-valued signal. In this paper, we show how the principle of angles between subspaces can be applied to this problem to alleviate some of the shortcomings of subspace-based frequency estimation using the MUSIC algorithm and demonstrate the resulting attractive properties via computer simulations.