LOWER ORDER LINEAR FILTERING AND PREDICTION OF NONSTATIONARY RANDOM SEQUENCES.

Abstract

The method of Kalman and Bucy for the optimal linear filtering and prediction of nonstationary sample functions has been modified by Bryson and Johansen. They do not require all measurements to contain white noise. The observations without white noise and some of their derivatives are used to reduce the order of the optimal filter. An analogous philosophy is applied here in the discrete time case. The purpose is to specify a lower order optimal filter, in the presence of measurements free of white noise. In a self-contained derivation, the optimal filter is shown to consist of a dynamical part in the form of a difference equation, and a direct algebraic feed-forward path parallel to it. The order of the dynamical part is n-p, where n is the combined number of state variables of the observed signal and noise processes, and p is the number of measurements without white noise. The parameters of the optimal filter are specified by a set of recurrence equations, similar to those of the discrete-time Kalman filter.

Document Details

Document Type
Technical Report
Publication Date
Feb 10, 1967
Accession Number
AD0650641

Entities

People

  • K. G. Brammer

Organizations

  • United States Air Force Academy

Tags

DTIC Thesaurus Topics

  • Difference Equations
  • Equations
  • Filters
  • Filtration
  • Kalman Filters
  • Linear Filtering
  • Mathematical Analysis
  • Measurement
  • Noise
  • White Noise

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.