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

Steve Langel, Omar GarcĂ­a Crespillo, Mathieu Joerger

Peer Reviewed

Abstract: 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).
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Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 68, Number 2
Pages: 259 - 276
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https://doi.org/10.1002/navi.419
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