Equivalence analysis of two-domain combined adjustment solutions of pseudo-range single point positioning

The combined adjustment solutions of the linear observation model in the observation domain and in the adjustment range are completely equivalent. However, in practice, the observation models of the combined adjustment are mostly nonlinear, which always need to be linearized in parameter estimation, resulting in linearized model error. The influence of this error on the equivalence of the two-domain adjustment solutions remains to be discussed. Thus, taking pseudo-range single point positioning (SPP) as an example, the solution formulas of the combined adjustment in the adjustment range of the observation model are deduced in this paper, on which the reason why the two-domain combined adjustment cannot be completely equivalent under the SPP model is presented and a numerical analysis is carried out with the example data. Research shows, the two-domain adjustment solution of SPP cannot be equivalent because it is assumed that the initial value of each iteration solution of a single system is the same as that of the combined adjustment of the observation range. And under the same configuration, the two-domain adjustment position solutions of different Global Navigation Satellites System (GNSS) combined SPP are the same value on the order of millimeter, that is, for the application of SPP, the two-domain adjustment solutions can be considered the same. The content of this paper also has certain reference significance for some other GNSS applications.