Single-frequency PPP models: analytical and numerical comparison

Ionosphere delay is a key factor in the single-frequency Precise Point Positioning (SFPPP). In tradition, two SFPPP models are applied, i.e., ionosphere-corrected (IC) and ionosphere-free-half (IFH) models. The ionospheric delays are directly corrected in IC model with external ionospheric products, while they are eliminated by forming the ionosphere-free combination with code and phase in IFH model. However, almost all studies focus on the numerical performance of these two models and lack the comprehensive study on the estimability and solvability of SFPPP model with either code division multiple access (CDMA) or frequency division multiple access (FDMA) system, respectively. In this paper, we dedicate to the analytical study on SFPPP models for both CDMA and FDMA systems. To assimilate the impact of ionospheric delays on positioning, a general SFPPP model, i.e., ionosphere-weighted (IW) model, is first formulated to identify the varying situations with the different uncertainties of ionospheric constraints. Then, we mathematically show how the IC, IFH and ionosphere-float (IF) models are reduced from IW model. The numerical comparison with GPS and GLONASS data with geodetic and cost-effective receivers effectively confirms our theoretical inference on the relationship of IC, IF and IW models and indicates the best results of IW model for all situations.