In section 3 of your reference, it states
The EROS-A legacy pass-file contains all metadata in one file, but requires a lot of exceptional processing associated with [sic] customized coordinate system (so-called Q-frame).
Satellites usually have many frames associated with different aspects of the body of the satellite. For instance, there will be at least one star-tracker reference frame, so that star measurements can be easily computed in that frame. If the satellite is pointing a laser towards earth, there will be another frame associated with the direction of the laser. There will be another frame associated with the ACS, and indeed every other portion of the satellite from which calculations need to be made. For sharing data between different components of the satellite, everything is usually converted into one frame that is of primary importance. Going back to the laser, if the primary mission for the satellite dealt with the laser, the laser reference system would probably be the most important frame, and thus most measurements would be converted to that.
Simply put, this "q-frame" is almost certainly just a reference frame associated with an important part of the satellite. All measurements are represented in it to limit ambiguity.