How ellipsoidal validation gate is formed around a track in trackerGNN?

According to Introduction to Assignment Methods in Tracking Systems a validation gate is formed around a track using the threshold, . But this gate is formed using residual covariance . But is computed using . So if varies from detection to detection, then this changes and depending upon that the gate changes. In short, a different gate is established for the case of every detection.
But this fact is problematic because according to images given in the page accessed by link, there is just a single ellipsoidal gate. It may be the case that I am missing something and have not interpreted things correctly. Whichever is the case, it would be very helpful, if somebody clearly explains what is happening here.

Answer 1

[Elad Kivelevitch]

In tracking, gates are calculated based on the combination of tracks and detections, using the Mahalanobis distance (or negative likelihood distance in our case), so they depend on both track and detection.

It is virtually impossible to show that clearly in a drawing, so we opted to explain it more generally in the doc.

[Usman]

Now that definitely clears my confusion. Thanks

[Usman]

Can you please elaborate more on how to calculate this "Negative likelihood distance" ?