Least squares filtering and prediction of nonstationary sampled data

The design of a linear, least squares filter or predictor H for nonstationary sampled data is shown to entail the inversion of an n × n matrix for the nth row of the "transmission matrix" H which characterizes the device. By the use of an "ensemble-shaping" technique the computation required is reduced to tractable proportions. It is shown that even when the input data is stationary the filter which is optimum for all instants (and not only in the steady-state) is a time-varying device which approaches the optimum steady-state filter as the filtering time becomes infinite.