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.