The post left out the some important parts of the Kalman Filter, where you adjust your certainty in how well you're able to predict where the target will go and how accurate your sensors are in response to how they perform over time. So even if you're Gaussians are 10 klicks apart the variance for this prediction still shrinks, but your future Gaussians would be much wider. I think what was described in the post was more an alpha-beta filter.
Adjusting the measurement covariance to fit the residuals is not part of the Kalman filter algorithm. One could make the argument that any real-world implementation needs to address this problem, but as far as the algorithm is concerned, the measurement covariance is externally computed.
http://en.wikipedia.org/wiki/Kalman_filter
http://en.wikipedia.org/wiki/Alpha_beta_filter