Here's another, very detailed 4-part "build your own GPS" article from the early 90s:

http://lea.hamradio.si/~s53mv/navsats/theory.html

No FPGAs, RPis, or SDRs --- it's mostly done in discrete logic with a 68000 doing the back-end processing. As a bonus, he also implemented GLONASS. Furthermore, the software takes up less than 32KB of ROM.

Note that while well explained, this is a very 90s way of implementing a GPS receiver. As I understand it modern receivers use FFT-based correlators that have much better cold-start performance than the old-fashioned design because they can test very large numbers of possible correlations at once (generally hundreds of thousands of them).