<p>Relativistic clock drift in Global Navigation Satellite Systems is typically simplified as a constant drift term and addressed through frequency pre-adjustment before satellite launch. However, this simplified approach fails to fully eliminate drift errors, necessitating refined modeling and compensation methods. This study provides a detailed analysis of the causes, characteristics, and dynamic changes of relativistic clock drift in satellites of different orbital types. The results reveal that relativistic clock drift exhibits significant orbital dependence and periodicity: deviations between the actual and nominal semi-major axes can lead to constant drift model errors exceeding 2&#xa0;ns/day; J<sub>2</sub>-induced relativistic clock drift periods primarily relate to orbital inclination; the J<sub>2</sub>,<sub>2</sub> term causes orbital resonance in high-altitude satellites, generating relativistic clock drift errors up to 160&#xa0;ns per orbital adjustment cycle. The relativistic clock drift residuals (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\it {\text{ddCon}}\)</EquationSource> </InlineEquation>) show semi-monthly (~ 14&#xa0;days) and semi-annual (~ 182&#xa0;days) cycles. Analysis indicates a negative correlation between&#xa0;<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\it {\text{ddCon}}\)</EquationSource> </InlineEquation>&#xa0;and the absolute value of lunar elevation angle: larger absolute lunar elevation corresponds to smaller&#xa0;<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\it {\text{ddCon}}\)</EquationSource> </InlineEquation>, and vice versa. Long-term trends also negatively correlate with the absolute solar elevation angle. When the absolute solar elevation is large,&#xa0;<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\it {\text{ddCon}}\)</EquationSource> </InlineEquation> is smaller overall, and vice versa. Notably, when solar and lunar elevations are low, relativistic clock drift induced by solar-lunar gravity can reach ~ 0.34&#xa0;ns/day for some satellites, exceeding the impact of the J<sub>2</sub> term. These findings highlight the limitations of relying solely on “constant compensation” models under real orbital conditions, underscoring the necessity of dynamic numerical integration for high-precision applications.</p>

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Revisiting relativistic clock drift in GNSS: from constant model to dynamic model

  • Shang Wu,
  • Yang Liu,
  • Yanxiong Liu,
  • Yikai Feng,
  • Huayi Zhang,
  • Dongxu Zhou,
  • Zejie Tu

摘要

Relativistic clock drift in Global Navigation Satellite Systems is typically simplified as a constant drift term and addressed through frequency pre-adjustment before satellite launch. However, this simplified approach fails to fully eliminate drift errors, necessitating refined modeling and compensation methods. This study provides a detailed analysis of the causes, characteristics, and dynamic changes of relativistic clock drift in satellites of different orbital types. The results reveal that relativistic clock drift exhibits significant orbital dependence and periodicity: deviations between the actual and nominal semi-major axes can lead to constant drift model errors exceeding 2 ns/day; J2-induced relativistic clock drift periods primarily relate to orbital inclination; the J2,2 term causes orbital resonance in high-altitude satellites, generating relativistic clock drift errors up to 160 ns per orbital adjustment cycle. The relativistic clock drift residuals ( \(\it {\text{ddCon}}\) ) show semi-monthly (~ 14 days) and semi-annual (~ 182 days) cycles. Analysis indicates a negative correlation between  \(\it {\text{ddCon}}\)  and the absolute value of lunar elevation angle: larger absolute lunar elevation corresponds to smaller  \(\it {\text{ddCon}}\) , and vice versa. Long-term trends also negatively correlate with the absolute solar elevation angle. When the absolute solar elevation is large,  \(\it {\text{ddCon}}\) is smaller overall, and vice versa. Notably, when solar and lunar elevations are low, relativistic clock drift induced by solar-lunar gravity can reach ~ 0.34 ns/day for some satellites, exceeding the impact of the J2 term. These findings highlight the limitations of relying solely on “constant compensation” models under real orbital conditions, underscoring the necessity of dynamic numerical integration for high-precision applications.