Robust weighted subspace fitting in the presence of array model errors

Model error sensitivity is an issue common to all high resolution direction of arrival estimators. Much attention has been directed to the design of algorithms for minimum variance estimation taking only finite sample errors into account. Approaches to reduce the sensitivity due to array calibration errors have also appeared in the literature. Herein, a weighted subspace fitting method for a wide class of array perturbation models is derived. This method provides minimum variance estimates under the assumption that the prior distribution of the perturbation model is known. Interestingly enough, the method reduces to the WSF (MODE) estimator if no model errors are present. On the other hand, when model errors dominate, the proposed method turns out to be equivalent to the “model-errors-only subspace fitting method”. Unlike previous techniques for model errors, the estimator can be implemented using a two-step procedure if the nominal array is uniform and linear, and it is also consistent even if the signals are fully correlated.