@article {Langel259, author = {Steven Langel and Omar Garc{\'\i}a Crespillo and Mathieu Joerger}, title = {Overbounding the effect of uncertain Gauss-Markov noise in Kalman filtering}, volume = {68}, number = {2}, pages = {259--276}, year = {2021}, doi = {10.1002/navi.419}, publisher = {Institute of Navigation}, 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).}, issn = {0028-1522}, URL = {https://navi.ion.org/content/68/2/259}, eprint = {https://navi.ion.org/content/68/2/259.full.pdf}, journal = {NAVIGATION: Journal of the Institute of Navigation} }