# Formula to calculate DGPS correction factors

I am trying to implement a differential GPS algorithm. During my research, I found a paper at https://opus.bibliothek.uni-wuerzburg.de/opus4-wuerzburg/frontdoor/deliver/index/docId/11361/file/144_Ali_TransNav.pdf which is pretty easy to understand for me. However, on page 5, there are the following formulae:

ρ = r + c.(dtr - dts + dT)

r = √((Xs-Xr)2 + (Ys-Yr)2 + (Zs-Zr)2)

CF = r - ρ + (dtr - dts + T) * c

where CF is the correction factor I want to calculate and ρ is the pseudorange.

Since the tropospheric delay T is not used in the algorithm according to the paper and and dT corresponds to 'other biases' which I for simplicity assume to be 0, the part c(dtr - dts) is the same in both the equation for ρ and CF. If I now substitute ρ with its equation, these parts cancel out each other and I get:

CF = r - rρ

Therefore, the correction factor would just be the difference of the geometric position. However, as far as I understood, differential GPS has to use more parameters to calculate the correction factor. What did I do wrong?

• As far as i read the article they assume that the correction factor is the same for basestation and rover when they are not to far away from each other. So the correction factor is calculated with trophospheric delay at the basestation, but not at the rover. The 0,78m positional error they achieve is in the range of a good L1 reciever with SBAS. It sounds a bit as they invented another form of wide area augmentation and not a high precision differential correction one you may think of. – Matte Jul 27 '18 at 7:31