Abstract
The proper choice of stochastic model is of great importance to global navigation satellite system (GNSS) data processing. Whereas extensive investigations into stochastic modeling are mainly based on the relative (or differential) method employing zero and/or short baselines, this work proposes an absolute method that relies upon a stand-alone receiver and works by applying the least-squares variance component estimation to the geometry-free functional model, thus facilitating the characterization of stochastic properties of multi-frequency GNSS observables at the undifferenced level. In developing the absolute method, special care has been taken of the code multipath effects by introducing ambiguity-like parameters to the code observation equations. By means of both the relative and absolute methods, we characterize the precision, cross and time correlation of the code and phase observables of two newly emerging constellations, namely the Chinese BDS and the European Galileo, collected by a variety of receivers of different types at multiple frequencies. Our first finding is that so far as the precision is concerned, the absolute method yields nearly the same numerical values as those derived by the zero-baseline-based relative method. However, the two methods give contradictory results with regard to the cross correlation, which is found (not) to occur between BDS phase observables when use has been made of the relative (absolute) method. Our explanation to this discrepancy is that the cross correlation found in the relative method originates from the parts (antenna, cable, low noise amplifier) shared by two receivers creating a zero baseline. The time correlation is only of significance when the multipath effects are present, as is the case with the short-baseline-based relative method; this correlation turns out to be largely weaker (or ideally absent) in the absolute (or zero-baseline-based relative) method. Moreover, with the absolute method, the stochastic properties determined for two receivers of the same type but subject to different multipath effects are virtually the same. We take this as a convincing evidence that the absolute method is robust against multipath effects. Hence, the absolute method proposed in the present work represents a promising complement to the relative method and appears to be particularly beneficial to GNSS positioning, navigation and timing technologies based on the undifferenced observables, typically the precise point positioning.
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Data availability statement
RINEX observation data of MGEX stations and broadcast ephemeris are obtained from the online archives of the Crustal Dynamics Data Information System, ftp://cddis.gsfc.nasa.gov; RINEX observation data collected in the Curtin university are accessed from the website of Curtin GNSS Research Center, http://saegnss2.curtin.edu.au/ldc/; RINEX observation data of Hong Kong CORS is downloaded from the Hong Kong Geodetic Survey Services, https://www.geodetic.gov.hk/en/index.htm. RINEX observation data collected in Wuhan is available at https://pan.baidu.com/s/1CYVPnWGvb0-_S8zS-VGD_A (Extraction code: rgex).
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Acknowledgements
This work was funded by the National Natural Science Foundation of China (Nos. 41774042, 41574015). The first author is supported by the CAS Pioneer Hundred Talents Program. The fourth author acknowledges the LU JIAXI International team program supported by the K.C. Wong Education Foundation and CAS. All this support is gratefully acknowledged.
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Baocheng Zhang proposed the method, designed the research and wrote the paper. Pengyu Hou developed the software, analyzed the data and wrote the paper. Teng Liu improved the computational efficiency of the software and revised the manuscript. Yunbin Yuan supervised the experimental analysis and revised the manuscript.
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Zhang, B., Hou, P., Liu, T. et al. A single-receiver geometry-free approach to stochastic modeling of multi-frequency GNSS observables. J Geod 94, 37 (2020). https://doi.org/10.1007/s00190-020-01366-8
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DOI: https://doi.org/10.1007/s00190-020-01366-8