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?