Abstract
The differential inter-frequency biases (DIFB) caused by the differential code phase biases (DCPB) between inhomogeneous stations are correlated with the ambiguity parameters and are difficult to estimate in GLONASS FDMA precise positioning. Without known DIFB, the double difference (DD) ambiguity cannot be fixed or only partial ambiguity resolution is achievable. The Monte Carlo-based method can estimate DIFB with sampled values where if only some samples are close enough to the true value, the unknown phase bias parameter can be estimated successfully and thus enable high precision positioning. This study implements the Markov chain Monte Carlo (MCMC) method to refine the sample distribution in DCPB estimation with GLONASS-only single-epoch observations. As a result, the procedure enables GLONASS-only FDMA ambiguity fixing and achieves single-epoch precise positioning even though the baseline and DIFB are unknown in advance. Also, the computation load of MCMC procedure is further reduced by merging the common computations of different samples in the ambiguity fixing step. The experiments with baselines OHI3_OHI2, WTZ2_WTZZ and TLSE_TLSG on 30 days show that the fix rates reach 93.6%, 89.1% and 85.0%, respectively, with baseline solution errors within [0.025, 0.025, 0.050]m. The positioning computation at each epoch takes only tens of milliseconds.
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Data availability
The GLONASS data were obtained from the International GNSS Services (IGS) and can be accessed at ftp://igs.ign.fr/pub/igs/data/2020/.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 42274032, 41804022), Science and Technology Innovation Project of Southwest Jiaotong University (No. XJ2021KJZK011), Sichuan Provincial Science and Technology Program (No. Q113521S09004). The authors thank IGS for providing GNSS data.
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Tian, Y., Liu, Z. & Li, K. Markov chain Monte Carlo-based DCPB estimation for ambiguity fixing of GLONASS-only FDMA single-epoch positioning. GPS Solut 27, 46 (2023). https://doi.org/10.1007/s10291-022-01383-4
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DOI: https://doi.org/10.1007/s10291-022-01383-4