Preface
During my application to KairoSpace company, I went through number of interviews and tests. One of the tests was dedicated for designing a solution for usage GPS as navigation source for high orbit satellites.
Global Positioning System
Most of you probably know, what GPS technically is.
In a nutshell, this is a constellation of satellites on MEO orbits (orbital altitude of approximately 20180 km), equipped with very precise atomic clocks. These clocks additionally regularly corrected from Earth, so they are keeping extremely precise time. The satellites are also equipped with relatively directional antennas, and they transmit to Earth signals containing data about their orbital position and a precise timestamps.
On the receiver side a GPS chip (typically, embedded into most of modern devices, from smartphone to battle drone), via relatively simple mathematical operations synchronizes its local time with GPS time, and then performs multilateration to determine its position. From this, we can calculate velocity, direction, altitude etc.
Space application of GPS
But can we use GPS for position determination in space? At first glance – why not? Just plug GPS chip into a satellite and let it do its work. After a deeper consideration you starting to understand that this approach will cost troubles. Satellite speed is tremendously high – 10 times faster than bullet and 30 times faster than commercial aircraft. Its altitude is too high, and at some point it will just appear higher than GPS satellites themselves. And there… Antennas of GPS satellites pointed towards Earth, so your satellite will be outside of their signal cone. How to build a navigation solution in such harsh conditions?
I studied this question in more detail. And found out that, actually, there are ways to do this. And this have even been implemented in practice. On high altitudes you can detect your position, using antenna side lobes and advanced Kalman filtering techniques. High speeds can be detected using measurement of the Doppler shift of GPS signals. And even attitude (orientation!) of satellite can be detected this way, if you place multiple GPS antennas on your spacecraft. A combination of these methods allows you to determine your spacecraft position even beyond GEO, half way to the Moon.
If you need more technical details – you can find them in a file attached to this post.