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Revisiting Doppler positioning performance with LEO satellites

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Abstract

Recently, the Doppler shifts from Low Earth Orbit (LEO) satellites have been used to augment GNSS and provide navigation services. We propose a Doppler-only point-solution algorithm for GNSS-like navigation systems operated in LEO. The proposed algorithm can simultaneously estimate the receiver clock drift, position and velocity. Then, we analyze the main error sources in Doppler positioning. To achieve the meter-level positioning accuracy, the satellite position and velocity errors should be within several meters and several centimeters per second, respectively. The ionospheric delay rates of C-band signal will cause about 1 m error in Doppler positioning, which can be eliminated using the ionosphere-free combination. The Doppler positioning accuracy will deteriorate sharply by dozens of meters if there are no corrections for the tropospheric errors. Subsequently, we analyze the Doppler positioning performance. The undifferenced Doppler positioning accuracy is at meter level, which is comparable with the pseudorange-based positioning in GNSS. To ensure convergence in the LEO-based Doppler positioning, the initial receiver position error should be less than 300 km when the satellites orbit is at an altitude of 550 km.

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Data availability

All ephemeris and observations used in this study are simulated. The Starlink orbital parameters are obtained from the SpaceX non-geostationary satellite system Attachment A: technical information to supplement Schedule S (https://www.fcc.report/IBFS/SAT-MOD-20181108-00083/1569860.pdf.) and verified using TLE files and SGP4 model (https://celestrak.org/norad/elements/table.php?GROUP=starlink&FORMAT=tle) in our early work (Zhang et al. 2022). The ai0, ai1 and ai2 coefficients used in NeQuick-G model are obtained from the Galileo navigation broadcast message.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 41931075, Grant No.42204033). The authors are grateful to CelesTrak for providing TLE files and the International GNSS Service (IGS) for providing Galileo navigation broadcast messages.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road, Beijing, 100191, China

    Chuang Shi & Yulu Zhang

  2. Key Laboratory of Navigation and Communication Fusion Technology, Ministry of Industry and Information Technology, 37 Xueyuan Road, Beijing, 100191, China

    Chuang Shi, Yulu Zhang & Zhen Li

  3. Research Institute for Frontier Science, Beihang University, 37 Xueyuan Road, Beijing, 100191, China

    Chuang Shi & Zhen Li

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  1. Chuang Shi
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Contributions

All authors contributed to the conception and design of the study. Material preparation, data collection and analysis were performed by CS, YZ and ZL. The first draft of the manuscript was written by YZ, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Zhen Li.

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Shi, C., Zhang, Y. & Li, Z. Revisiting Doppler positioning performance with LEO satellites. GPS Solut 27, 126 (2023). https://doi.org/10.1007/s10291-023-01466-w

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