Overbounding the effect of uncertain Gauss-Markov noise in Kalman filtering

Steven Langel, Omar García Crespillo, Mathieu Joerger

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Prior work established a model for uncertain Gauss-Markov (GM) noise that is guaranteed to produce a Kalman filter (KF) covariance matrix that overbounds the estimate error distribution. The derivation was conducted for the continuous-time KF when the GM time constants are only known to reside within specified intervals. This paper first provides a more accessible derivation of the continuous-time result and determines the minimum initial variance of the model. This leads to a new, non-stationary model for uncertain GM noise that we prove yields an overbounding estimate error covariance matrix for both sampled-data and discrete-time systems. The new model is evaluated using covariance analysis for a one-dimensional estimation problem and for an example application in Advanced Receiver Autonomous Integrity Monitoring (ARAIM).

Original languageEnglish (US)
Pages (from-to)259-276
Number of pages18
JournalNavigation, Journal of the Institute of Navigation
Issue number2
StatePublished - Jun 1 2021


  • Gauss-Markov noise
  • Kalman filter
  • colored noise
  • covariance matrix
  • overbound
  • state augmentation

ASJC Scopus subject areas

  • Aerospace Engineering
  • Electrical and Electronic Engineering


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