Can GPT generate GPS data?

I am currently working on an orbit determination software. Everything is going well. The software seems to be working fine on a real dataset we got from the satellites that our customers own. Yet, we are not entirely sure if the software is doing a great job because of how little amount of data that we tested our software on. I was searching for any kind of open source GPS satellite data, but I wasn't able to.

So, I have come up with this idea. How about training a pre-trained GPT on the GPS data that we currently have and having the model generate GPS data that are reasonable.

I am not really knowledgeable in LLM or deep learning in general. Can Generative Pre-trained Transformers generate GPS data? or can you train one to generate GPS data?

Thanks!