A Generalized Autocovariance Least-Squares Method for Kalman Filter Tuning

Bernt Magnus Åkesson, John Bagterp Jørgensen, Niels Kjølstad Poulsen, Sten Bay Jørgensen

Research output: Contribution to journalJournal articleResearchpeer-review


This paper discusses a method for estimating noise covariances from process data. In linear stochastic state-space representations the true noise covariances are generally unknown in practical applications. Using estimated covariances a Kalman filter can be tuned in order to increase the accuracy of the state estimates. There is a linear relationship between covariances and autocovariance. Therefore, the covariance estimation problem can be stated as a least-squares problem, which can be solved as a symmetric semidefinite least-squares problem. This problem is convex and can be solved efficiently by interior-point methods. A numerical algorithm for solving the symmetric is able to handle systems with mutually correlated process noise and measurement noise. (c) 2007 Elsevier Ltd. All rights reserved.
Original languageEnglish
JournalJournal of Process Control
Issue number7
Pages (from-to)769-779
Publication statusPublished - 2008


  • Kalman filtering
  • covariance estimation
  • optimal estimation
  • state estimation
  • semidefinite programming

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