Discrete-Time Least Squares, Minimum Mean Square Error, and Minimax Estimation

A discrete-time signal estimation problem in which the input signal is represented by an expansion in terms of linearly independent functions is considered. After a set of
r
noisy measurements of the signal are made, a linear estimator of the function and/or its derivatives at some point in time, τ, is required. Due to systems or physical considerations or some other a priori conditions, magnitude constraints or statistics associated with the input signal are known. The performance criteria considered in the solution to this problem include minimum mean square error, least squares, and minimization of the maximum mean square error. A unified approach to these problems is taken so that the relationship between the various performance criteria and their resultant accuracies is easily compared.