The below rtk-gps measures position to about 1.5inches
for $1500 and an update rate of 5Hz on gps, and it measures
12.6mm x 4.6mm so that it would easily fit inside of
a 20mm-diameter tube-shaped rocket-robot.
Do people sell cheaper ones that are faster, say 60Hz instead of 5Hz,
but still meet the above or similar gps-accuracy and still fit inside
a 20mm-diameter tube? Something in the vicinity of $200-ish or less.
It is very complicated to find GPS that updates the data so fast, they usually have updates between 1-10Hz. I leave you some options that might interest you, you must verify that being inside the tube locks the system and finds signal. For the GPS to work properly should have free vision of the sky (ideally), you must perform tests.
As you probably already know, RTK is a complex process on top of regular GPS signals to enhance the accuracy of the system. And as you can guess more complex usually means more expensive.
We do offer RTK options, but I think none of them would fit your size requirements.
A quick search online reveals that the fastest commercial systems seem to be around 20 Hz and worth tens of thousands of dollars! Oh, and they are huge, too.
If you need a faster position update than GPS & RTK can provide at a reasonable cost you may want to look into making your own localization system with beacons on the ground (at least 3 must be visible for a 3D position). Of course, that is no trivial task!