Reparameterization of single difference and undifferenced kinematic GPS positioning models

A series of advantages of single difference (SD) and undifferenced (ZD) models are given as compared with the double difference (DD) model. However, rank defects exist in SD and ZD models. The reparameterization method is provided to resolve this rank defect problem by estimating some combinations of the unknowns rather than the unknowns themselves. The reparameterization of SD and ZD functional models is discussed in detail with their stochastic models. The theoretical confirmation of the equivalence of undifferenced and differenced models is described in a straightforward way. The relationship between SD and ZD residuals is given and verified for some special purposes, e. g. research on the stochastical properties of GPS observations.