Least squares filtering and prediction of nonstationary sampled data

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)297-313
Number of pages17
JournalInformation and Control
Volume1
Issue number4
DOIs
StatePublished - Dec 1958
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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