A Variational Principle for the Linear Filter Matrix and an Interpretation for the Maximum Value of the Functional

A functional of a trial matrix and suitable correlation matrix is constructed which is an absolute maximum when the trial matrix satisfies the Wiener-Hopf equation for the filter matrix. mum value of the functional is essentially the sum of the squares of the minimum errors of the observations and is thus of interest in its own right. The maxi*Present address: Physics Department, Clark University, Worcester, MA, 01610. **Research sponsored by the Air Force Office of Scientific Research. Air Force Systems Command, USAF, under Grant No. AFOSR77-3169. and distribute reprints any copyright notation hereon. The United States Government is authorized to reproduce for Governmental purposes notwithstanding 163 Copyright