Ambiguity resolution and validation are perhaps the most popular GNSS-related research topics. A plethora of methods were developed for this purpose such as the popular ratio test, the difference test, the projector test, the W-test, etc. However, the techniques that worked for short-baseline RTK don’t perform as well for long-baseline RTK or PPP.
The main reason is the presence of the ionosphere. For short-baseline RTK, ambiguity residuals are only correlated with positioning errors. As the baseline length increases, satellite-dependent errors creep in and make the ambiguity validation process much more complex. Partial ambiguity resolution aimed at solving this problem, but knowing which satellites to select/discard is not always a simple task.
My preferred method for ambiguity resolution in kinematic applications is the so-called “BIE” approach. The first paper I know describing it was written by Blewitt , although it was deemed unpractical at the time because of the heavy computational load. The basic idea consists of computing a weighted average of integer vectors. The outcome can be summarized as:
- Poorly-defined solution = float solution
- Precise solution = fixed solution
- Otherwise = somewhere between the float and fixed solutions (generally!)
Hence, BIE offers a nice and smooth convergence to an ambiguity-fixed solution and is valid for short-baseline RTK or PPP. Be aware that BIE can go very wrong if your stochastic model is incorrect… but more on this topic in a subsequent post!
Blewitt, G. (1989). “Carrier-phase ambiguity resolution for the global positioning system applied to geodetic baselines up to 2000 km,” Journal of Geophysical Research, Vol. 94, No. B8, pp. 10187-10203. doi:10.1029/JB094iB08p10187.