Estimation and smoothing for data sets of deterministic and random values using linear control

A unified approach to constructing estimators for problems in which there is a mixture of deterministic and stochastic data is presented. The procedure is based on Hilbert space methods and is very simple conceptually. We show that a very large variety of problems can be reduced to the problem of finding a point on an affine variety nearest to a given point. This technique has applications in economics, trajectory planning for robots, mapping and many other areas where there is data to be approximated or interpolated.