Kalman Filter Covariance
The covariance matrix of a Kalman filter is a function of the $ Q $ and $ R $ matrices of the model.
If you use a model where $ R $ and $ Q $ are time invariant or known in prior then the calculation of the covariance matrix $ P $ can be done offline and isn't a function of the measurements.

In some cases, advanced implementations of Kalman Filter estimate the covariances $ R $ and $ Q $ on line according to some data gathered in the process of calculating the result.