Robot Localization - Is it good practice to continually update sensor covariance matricies?

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Does the Robot Localization package need/benefit from:

1. The variances in sensor message variance-covariance matrices being updated in real-time from the sensors readings?
2. Likewise, populating the covariances in the covariance-matrix with real-time values?
3. If real-time sensor covariances (not variances) are not available, is it preferred that the covariances in the sensor topic/message are set to zero or some static pre-calculated non-zero value?

Background: We have a setup where each sensor (wheel encoders, IMUs) is interfaced via an Arduino; so calculating running/streaming variances, on the microprocessor, before passing each sensor topic/message to robot-localization is not an issue. Real-time covariances are more difficult so we'd prefer just to pass zeroes or a static non-zero value.