I'm trying to calculate the position of a multi-constellation GNSS receiver using GPS and GLONASS satellites using least-squares optimization. Sparing the details, I have 5 equations to solve for 5 unknowns: (x, y, z, r_gps, r_gal).
4 equations are for GPS satellites, taking the form:
sqrt((x - x1)**2 + (y - y1)**2 + (z - z1)**2) - (pr - r_gps) = 0
And 1 equation is for the sole GLONASS satellite, taking the form:
sqrt((x - x1)**2 + (y - y1)**2 + (z - z1)**2) - (pr - r_gal) = 0
When implemented in python, the LS method converge to the same x,y,z solution no matter whether all 5 equations are taken, or only the 4 GPS equations or used. I.e, the 1 equation having the term r_gal is ignored. Mathematically, why is this the case?