The space–time references of BeiDou Navigation Satellite System

Cheng, Han; Liu, Li; Cai, Zhiwu; Lin, Yuting

doi:10.1186/s43020-021-00044-0

Cited by 19 publications

(5 citation statements)

References 13 publications

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“…By making the above three equations equal to zero and the second derivative not zero, we can obtain the following: From Formulas (5), (7), and (8), the derivative of the difference between the elliptic anomaly E and the mean anomaly M with respect to the elliptic anomaly E, the mean anomaly M, and the true anomaly f can be obtained:…”

Section: Parametermentioning

confidence: 99%

New Methods of Series Expansions between Three Anomalies

Zhao,

Li,

Bian

et al. 2024

Applied Sciences

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The calculation of satellite orbit involves some very complex formula derivations and expansions, which are very difficult to manually derive and prone to errors. And the efficiency of manual derivation is not high. We can use computer algebra systems to derive complex formulas related to satellite orbits. This can avoid some of the drawbacks of manual derivation and significantly improve computational efficiency and accuracy. In the past, the relationship among three anomalies was generally represented in the form of a trigonometric series with the first eccentricity e as the parameter. In this paper, the trigonometric series with the parameter m=1−1−e2e is used, as determined by the Lagrange conjugate series. We can use the formula of the Lagrange conjugate series to derive the relationship between the true anomaly and elliptic anomaly. And the relationship between the elliptic anomaly and the mean anomaly is derived by using the symbolic iteration method. In this research paper, we calculated the accuracy of the trigonometric series expansion among three types of anomalies at the first eccentricity e equal to values of 0.01, 0.1, and 0.2. The calculation results indicate that the accuracy of the trigonometric series expansion with m as the parameter is better than 10−5. Moreover, in some cases, the trigonometric series expansion among the three anomalies with m as a parameter is simpler in form than the expansion expressed with parameter e. This paper also derived and calculated the symbolic expressions and extreme values of the difference among three anomalies and expressed the extreme values of the difference in the form of a power series of e. It can be seen that the extreme value increases with the increase in eccentricity e. And the absolute values of the extreme value of the difference between the elliptic anomaly and the mean anomaly, the true anomaly and the elliptic anomaly, and the true anomaly and the mean anomaly increase in this order. When the eccentricity is small, the absolute value of the extreme value of the difference between the true anomaly and the mean anomaly is about twice as large as the elliptic anomaly and the mean anomaly and the true anomaly and the mean anomaly.

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Section: Parametermentioning

confidence: 99%

New Methods of Series Expansions between Three Anomalies

Zhao,

Li,

Bian

et al. 2024

Applied Sciences

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“…Galileo relies on a contractual collaboration with 5 European NMIs and broadcasts a prediction of UTC without specifying the particular UTC(k) that it is based on [8]. BeiDou broadcasts a prediction of UTC built from UTC(NTSC) realized at the National Time Service Center of China [9] and UTC(NIM) realized at the China National Institute of Metrology [10].…”

Section: Predictions Of Utc Broadcast By the Gnssmentioning

confidence: 99%

“…In addition to disciplining the internal oscillator of the GNSS DO, decoding of the navigation message allows the receiver to obtain the calendar date and time-of day. The encoding of the required information is described in the GNSS ICDs [6][7][8][9][10][11]. Retrieval and dissemination of this data content is the most basic use of GNSS signals for timing, that many low-cost timing receivers employ to provide a source of time.…”

Section: Differentiation Between Types Of Usementioning

confidence: 99%

Achieving traceability to UTC through GNSS measurements

et al. 2022

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Coordinated Universal Time (UTC) is the international reference for time and frequency measurement, and the basis of civil timekeeping world-wide. The reception of signals from Global Navigation Satellite Systems (GNSS) as a source of time and frequency (synchronization and syntonization) has found widespread use in virtually all user sectors, including electrical power supply, telecommunications, and financial institutions. This paper summarizes the concept of metrological traceability and the practices employed in the time and frequency metrology community for achieving it. Practical steps are proposed to ensure that traceability to UTC from GNSS signal reception is available to a wide community of users, addressing different levels of required uncertainty in time and frequency offset from UTC. We suggest some practical measures that can be followed by users, and improvements to the services provided by National Metrology Institutes (NMIs).

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“…Set a GEO satellite as a reference "Q" the parameter to be estimated includes Q's clock offsets with respect to BDT, and others are the differences of zero value of L-band larger-diameter antennas. After that, the observation equations in the least square estimation are given as Equation (3).…”

Section: Estimation Of Clock Offsets With Respect To Bdtmentioning

confidence: 99%

High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Multi-Source Observations

et al. 2022

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Satellite clock offsets are the critical parameters for The Global Navigation Satellite Systems (GNSSs) to provide position and timing (PNT) service. Unlike other GNSSs, BDS-3 uses the two-way superimposition strategy to measure satellite clock offsets. However, affected by some deficiencies of the two-way superimposition strategy, the accuracy of BDS-3 clock offsets parameters is 1.29 ns (RMS), which is the main bottleneck for BDS-3 to improve its space signal accuracy. After analyzing problems in the clock offsets measurement process of BDS-3, the paper proposes a new strategy to real-time estimate high-accuracy satellite clock offsets. The clock offsets estimated by the new strategy show a good consistency with GBM clock offsets. The averaged STD of their differences in MEO is 0.14 ns, and the clock offsets estimated by the new strategy present less fluctuation in the 1-day fitting residuals. Applying the new clock offsets to prediction, BDS-3 can reduce its clock offsets errors from 1.05 ns to 0.29 ns (RMS), about 72%. The above results indicate that the new clock offsets estimated strategy can improve the accuracy of clock offsets parameters of BDS-3 effectively.

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The space–time references of BeiDou Navigation Satellite System

Cited by 19 publications

References 13 publications

New Methods of Series Expansions between Three Anomalies

New Methods of Series Expansions between Three Anomalies

Achieving traceability to UTC through GNSS measurements

High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Multi-Source Observations

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