Journal of Geodesy

, Volume 93, Issue 12, pp 2499–2514 | Cite as

Single-frequency PPP models: analytical and numerical comparison

  • Bofeng LiEmail author
  • Nan Zang
  • Haibo Ge
  • Yunzhong Shen
Original Article


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.


Single-frequency precise point positioning (SFPPP) Ionosphere-weighted (IW) model Ionosphere-corrected (IC) model Ionosphere-float (IF) model Estimability Solvability 



This study is sponsored by National Natural Science Funds of China (41874030, 41622401, 41574023 and 41730102), The Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee (18511101801), The National Key Research and Development Program of China (2017YFA0603102, 2016YFB0501802), and The Fundamental Research Funds for the Central Universities. The authors thank the efforts of the IGS MGEX campaign for providing multi-GNSS data and products.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Surveying and GeoInformaticsTongji UniversityShanghaiPeople’s Republic of China
  2. 2.Department of GeodesyGeoForschungZentrum (GFZ)PotsdamGermany

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