GPS Solutions

, 22:59 | Cite as

A sequential network approach for estimating GPS satellite phase biases at the PPP-AR producer-side

  • Omid Kamali
  • Marc Cocard
  • Rock Santerre
Original Article


Ambiguity resolution (AR) in precise point positioning (PPP) requires precise satellite orbit, clocks, and phase biases corrections. Satellite phase biases are fractional hardware corrections which help to retrieve the un-differenced integer carrier phase ambiguities. Satellite corrections can be obtained from the international GNSS service (IGS) or estimated by correction providers called producer-side. We introduce a new PPP-AR observation model and a new sequential network algorithm (SNA) to estimate satellite phase biases. The new model is fully compatible with standard IGS satellite correction products, and it takes advantage of currently available IGS global ionosphere maps to improve the stability of corrections estimation. Furthermore, the proposed model is full-rank per-frequency and per-site and this method simplifies the integration of any additional frequency or site observables in the system of equations. The per-site satellite phase biases method allows users to customize their network solution. In many cases, users only have to estimate the phase biases of a few satellites estimated by few stations to resolve ambiguities of their observed satellites. The novel two-step algorithm provides a good balance between the computational burden, the computer memory load, the efficiency of handling parameters, and the precise estimation of correction parameters. The proposed PPP-AR model and the SNA performance is then validated by estimating satellite phase biases with 1 year of GPS data from a sub-network of IGS stations. A rigorous a posteriori statistical test is performed using data from an independent GPS network. As a result, the precision of WL and L1 ambiguities was improved significantly with the confidence level of P > 99.99% by applying the estimated phase bias corrections to phase observables.


Satellite phase biases GPS-PPP PPP-AR Producer-side Sequential network solution 



Several organizations have contributed to financing this research: The Canadian GEOIDE (GEOmatics for Informed DEcisions) Network phase III, the Natural Sciences and Engineering Research Council of Canada (NSERC) attributed to Rock Santerre, Fond de soutien de Faculté de Foresterie, de Géographie et de Géomatique (FFGG) from Laval University, and Centre de Recherche en Géomatique (CRG-REGARD Laboratory) for the access to their computer cluster. All these supports are gratefully acknowledged. The authors also acknowledge the availability of IGS data and products to this research, which is the result of the efforts of individuals and organizations that provide an invaluable service to the scientific and professional communities. Thanks to Ken MacLeod for proofreading this article.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Research in Geomatics (CRG)Laval University, Pavillon Louis-Jacques-CasaultQuebec CityCanada

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