A summary, by illustrations, of least-squares filters with constraints

Several methods of combining a number of time series into a single series are discussed. They are all individual filtering followed by summation and are somewhat like Wiener filtering in that a least squares criterion is used to define the filter coefficients. They differ from Wiener filtering in that signal information is given in the form of various linear constraints on the filter coefficients rather than being given as a signal correlation function. The formulas are worked out explicitly for the case of two time series and three filter points and presented in such a way as to make generalization clear. Accepted for the Air Force Franklin C. Hudson Chief, Lincoln Laboratory Office