Process Noise Covariance Design in Kalman Filtering via Bounds Optimization

Manuel Salvoldi, Daniel Choukroun

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This note presents new results on the design of the process noise covariance matrix in Kalman filtering. The proposed design belongs to the realm of worst case methods: the optimal covariance is sought such as to maximize an upper bound on the estimation error matrix under a total budget constraint. Optimality conditions are derived along with a numerical algorithm for iterative approximation of the optimal solution. The optimal solution features a few time points and the associated covariances. Broadly speaking, the process noise is only 'active' at the time points that enhance its controllability. The importance of the method is that it bounds from above the performance of any Kalman filter with a different design. Monte Carlo simulations on a double harmonic system numerical example illustrate the good convergence, performance, and low sensitivity to initial guesses of the proposed method. Moreover, in terms of estimation accuracy, the Kalman filter with the optimal design outperforms a robust H-2 filter designed to cope with an equivalent uncertainty.

Original languageEnglish
Article number8360949
Pages (from-to)834-840
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - 1 Feb 2019


  • Covariance matrices
  • Kalman filters (KF)
  • optimization methods
  • performance analysis
  • process modeling

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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