I have a Kalman Filter working in a simulation environment, therefore allowing me to plot the estimates against the ground truth. One way I assess the performances of my filter is to ensure that the error (estimate - ground truth) always stays with the [-3sigma : +3 sigma] bounds.
Without divergence and the error staying in those bounds, I currently say that my filter is correctly tuned and work properly. I also check the observation residuals pre/post filtering as outlined here: How to verify Kalman filter performance without true data.
Is there any other method that could assess even further the filter performances? I briefly heard once a mention to the study of the information matrix. What conclusions can be drawn from it?