Precise Point Positioning with low-cost GNSS receivers is attractive for numerous applications, as it can provide centimeter-level positioning without the exchange of raw measurements from a reference station. However, pseudorange multipath has to be accurately considered for a reliable ambiguity fixing. In this paper, we derive a precise model for the pseudorange multipath from the received signal, the correlator and discriminator function. We consider multiple reflections with individual amplitudes, phasings, Doppler shifts and code delays. We estimate a pseudorange multipath parameter for each satellite in our precise position solution to exploit the temporal correlation of multipath and to prevent a mapping of multipath to other state parameters. The method was tested with real measurements from a low-cost receiver and SSR corrections and showed that a millimeter-level positioning accuracy is achievable.