A subspace fitting-like method for almost low rank models

Subspace fitting methods have grown popular for parameter estimation in many different application, for example sensor array signal processing, blind channel identification and identification of linear state space systems. Here we show that similar procedures can be used even for data models where the noise free signal gives a full rank contribution to the covariance matrix. A general weighting is introduced and the optimal weight matrix is given together with the resulting asymptotic covariance of the parameter estimates. The method works well when the number of dominating eigenvalues still is fairly small. As an example, we study estimation of direction and spread angle of a source subject to local scattering, using a uniform linear array of sensors. As the algorithm is computationally expensive, the results are not primarily intended for practical implementations, rather they show the theoretical limit for any estimation procedure that uses a low rank approximation of the covariance matrix.