"The Rasperry Pi" is not space worthy in general. It depends on the model. RPis are built based on various chips. The RPi B+, for example, got a LAN9514 which is qualified for an operating temperature range of 0°-70°C, so it's not exactly space worthy unless you make sure to have an adapted operating environment in the cubesat. It's also not radiation hardened, which might not be a problem for short missions in LEO, but since you mentioned GPS (which is in MEO) it could be prone to errors or even failure caused by radiation.
My recommendation for you:
First, get to know the mission specifications. How long should the satellite stay operable? What kind of orbit will the satellite be in? What kind of inputs, outputs and other specs do you require?
After that, I'd look at microcontrollers rather than single-board computers. There are space-grade microcontrollers that are being used on a professional level without being prohibitively expensive, but they might be hard to come by.
A good alternative would be looking for other cubesat projects. A lot of them might've been created for research reasons just like yours, so their components might've been partially published.