WEIGHTED LS AND TLS APPROACHES YIELD ASYMPTOTICALLY EQUIVALENT RESULTS

The weighted least-squares (LS) and total-least-squares (TLS) solution s to a perturbed system of linear equations are shown to be asymptotic ally equivalent (as the perturbation level goes to zero). An immediate consequence of this fact is that an optimally weighted LS-ESPRIT meth od, recently proposed for bearing estimation, achieves the lowest poss ible asymptotic estimation error variance in the classes of weighted T LS-ESPRIT estimates as well, and hence it is statistically efficient f or Gaussian perturbations.