Measurement-Error Controlled Iterative Least-Squares Solutions of Inverse Field Transformation Problems

Abstract

The inverse equivalent source problem related to near-field antenna measurements is typically ill-posed, i.e., the forward operator suffers from non-trivial null spaces. This issue is commonly tackled by pursuing a least-squares solution of the reconstructed near fields. We propose to find a solution of the normal error system of equations which minimizes the ℓ2-norm of the source-coefficients reconstruction deviation. In the scope of near-field to far-field transformations (NFFFTs), advantages are found in a slightly better iterative solver convergence, a reduced number of unknowns, and—most importantly—a more convenient control of the stopping criterion of the iterative solution process. Since the residual of the normal-error solution equals the reconstruction deviation, the proposed formulation includes a meaningful stopping criterion based on the measurement error. All these claims are corroborated by NFFFTs of synthetic and real-world measurement data.