Discrete-Time Filtering for Linear Systems in Correlated Noise with Non-Gaussian Initial Conditions: Formulas and Asymptotics

Richard B. Sowers, Armand M. Makowski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the one-step prediction problem for discrete-time linear systems in correlated plant and observation noises, and non-Gaussian initial conditions. Explicit representations are obtained for the MMSE and LMMSE (or Kalman) estimates of the state given past observations, as well as for the expected square of their difference. These formulae are obtained with the help of the Girsanov transformation for Gaussian white noise sequences, and display explicitly the dependence of the quantities of interest on the initial distribution. With the help of these formulae, we completely characterize the asymptotic behavior of the error sequence in the scalar time-invariant case.
Original languageEnglish (US)
Title of host publicationRobust Control of Linear Systems and Nonlinear Control
Subtitle of host publicationProceedings of the International Symposium MTNS-89, Volume II
EditorsM A Kaashoek, J H van Schuppen, A C M Ran
PublisherBirkhauser Boston
Pages407-419
Number of pages13
ISBN (Electronic)978-1-4612-4484-4
ISBN (Print)978-1-4612-8839-8, 978-0-8176-3470-4
DOIs
StatePublished - 1990

Publication series

NameProgress in Systems and Control Theory
Volume4

Keywords

  • Probability Measure
  • Noise Sequence
  • Observation Noise
  • Correlate Noise
  • Prediction Problem

Fingerprint

Dive into the research topics of 'Discrete-Time Filtering for Linear Systems in Correlated Noise with Non-Gaussian Initial Conditions: Formulas and Asymptotics'. Together they form a unique fingerprint.

Cite this