A Unitarily Constrained Total Least Squares Problem in Signal Processing

The problem addressed here is the determination of the total least squares solution, subject to a unitary constraint, of an overdetermined, inconsistent, linear system of equations. The problem arises in many signal processing applications, three of which are briefly presented and studied here. The solution to the constrained total least squares problem is seen to be the same as the solution to the orthogonal Procrustes problem.