covariance evaluation wrt localization lost

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Hello all,

I'm sorry it's not a question about ROS, but about state estimation problem.

When a localization system estimate its position and orientation in a prebuilt map, it always output its covariance, a 6*6 symmetric matrix. If we see its pose's covariance in rviz, we can see its shape is small or big intuitively. When localization lost, we can judge from the localization residual error if it bigger than our threshold, or from the diagonal fields of covariance if some field exceeds the threshold we set.

Is there any material or paper describing covariance evaluation wrt localization lost? Thanks for your help!