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Two modified multi-frequency GNSS approaches to estimate the pseudorange observable-specific signal bias for the CDMA and FDMA models

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Abstract

Pseudorange bias handling is essential in satellite positioning, navigation and timing (PNT) services and ionospheric modeling. Differential code bias (DCB) is commonly utilized and parameterized as the differential form of the pseudorange bias. To overcome the challenges of the inflexible and inconvenient extendable DCB calibration for the multi-frequency observations with multiple signal modulations, the pseudorange observable-specific signal bias (OSB) is used alternatively as the observation-specific individual bias representation. The study estimates the pseudorange OSBs of all the observation channels with two rigorous and modified multi-frequency approaches: multi-frequency modified carrier-to-code leveling (MFMCCL) and multi-frequency modified precise point positioning (MFMPPP) approaches. Both two approaches extract the slant ionospheric observables by considering the time-variant characteristic of the receiver pseudorange bias, after that estimating the pseudorange OSBs with certain reliability. After solving the various linear combinations of the pseudorange OSBs by two approaches, including the slant ionospheric observables and satellite-plus-receiver (SPR) pseudorange biases, all possible multi-frequency pseudorange OSBs are estimated simultaneously. Both two approaches are discussed for the GNSS observations with the code division multiple access (CDMA) and frequency division multiple access (FDMA) models. The two methods are validated with one-month data to estimate 31 types of pseudorange OSBs for the GPS, BDS, GLONASS and Galileo systems. Compared with the Chinese Academy of Sciences (CAS) pseudorange OSB product, the results indicated that both two proposed approaches can estimate the reliable multi-frequency multi-GNSS pseudorange OSBs with high stability and consistency.

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Data availability

The GNSS observation data used is provided by the MGEX network (ftp://igs.ign.fr/pub/igs/data/campaign/mgex/daily/rinex3/). The precise products are provided by the GFZ (ftp://ftp.gfz-potsdam.de/GNSS/products/mgex/).

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Acknowledgements

The authors would like to acknowledge the MGEX for providing the multi-GNSS observations.

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Authors and Affiliations

  1. Department of Space Information, Space Engineering University, No. 1 Bayi Road, Beijing, 101416, China

    Ke Su

  2. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, 200030, China

    Guoqiang Jiao

Authors
  1. Ke Su
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  2. Guoqiang Jiao
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KS initiated the main idea of the manuscript and design the experiment. KS wrote the manuscript. GJ revised the manuscript. All authors joined discussions throughout the development.

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Correspondence to Ke Su.

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Su, K., Jiao, G. Two modified multi-frequency GNSS approaches to estimate the pseudorange observable-specific signal bias for the CDMA and FDMA models. GPS Solut 27, 83 (2023). https://doi.org/10.1007/s10291-023-01417-5

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