As I promised in my previous post, I am sharing more information about my work with GPS navigation in space. In my previous post I mentioned that several technical limits, prevent GPS from being used in space the same way it is used on the Earth’s surface.

Two main limitations are:

• high spacecraft velocity
• limited visibility of GPS satellites

Therefore, conventional GPS positioning methods do not work well in space. Instead, the designer of GNSS navigation system should switch to more strategic approach, treating position determination as continuous, a dynamic Bayesian estimation process. You must not “fix your position” – you must “integrate your state”.

Technically, this means implementing an Extended Kalman Filter (EKF), which processes positions, velocities, pseudoranges and Doppler shifts of known (visible) GPS satellites from the entire constellation. The filter maintains the “spacecraft-and-environment” “state”, which then allow you to calculate your current position (in a way explained in my previous publication) and (what is more important) estimate the position determination error (from a covariance matrix of EKF filter).

This approach provides a stable and reliable method to integrate state of your spacecraft in Earth orbit between roughly 120 km and 70,000 km altitude and between 1 to 11 km/s velocity. I have not yet calculated error levels for different altitudes yet. But by initial estimation they are low enough for precise position determination at LEO and still acceptable near GEO. Beyond GEO the accuracy of the GPS solution gradually degrades, but as backup navigation system it can be used even there (especially for velocity determination using Doppler shift measurement).

Same as in previous post, I attached more detailed description of the concept of such a navigation system to this post. Inside you will find detailed explanation of the system, mathematics of EKF and algorithm of functioning.