%0 Journal Article
%A Langel, Steven
%A Crespillo, Omar GarcĂa
%A Joerger, Mathieu
%T Overbounding the effect of uncertain Gauss-Markov noise in Kalman filtering
%D 2021
%R 10.1002/navi.419
%J NAVIGATION: Journal of the Institute of Navigation
%P 259-276
%V 68
%N 2
%X 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).
%U https://navi.ion.org/content/navi/68/2/259.full.pdf