After a little discussion with @Turbinenreiter I have volunteered to clean up and publish his navigation board design. I suggested that it would probably be possible to arrange things to fit a footprint for this GPS Receiver
on the board as well- it is a fully integrated receiver module with a built-in antenna in a 16x16x5 mm package requiring essentially no external components to work; pretty much just provide it with 3.3V and put it out in the open and you will start receiving GPS location data from the UART in under a minute.
However, at $30 it would add substantially to the cost of the navigation board, so I would want to make it optional; however, while it is possible to hand-solder a module like this I expect that would be tricky for most users.
Any votes on including this? Possible alternative parts for GPS? I have some more questions for potential users, so I'll start another topic soon to discuss the navigation board, but I wanted to get a sense of peoples interest here.
Yes, quaternions aren't a topic I would want to have to tackle on my own (complex numbers with two more 'imaginary' components - fun!) but fortunately we probably don't have to; as you pointed out there is plenty of work already out there. Another issue if we include GPS would be figuring out how to integrate that data with the IMU data. The IMU should be very useful for small movements over short time scales, and GPS provides a solid reference for large movements over longer time scales, but it isn't obvious to me how to link them - however, @Turbinenreiter suggests that this is also a 'solved problem', so it should be possible to make use of prior work.