GNSS星载原子钟质量评价及精密钟差算法研究
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摘要
时间系统是卫星导航定位的核心要素之一，导航定位实际是测时间。而卫星导航系统的时频由卫星所装载的原子钟所提供。星载原子钟作为导航系统测距的星上时间基准，又是卫星导航系统有效核心荷载之一，其性能直接决定着导航定位和时频传递的精度。目前GNSS系统特别是我国的北斗卫星导航系统（Beidou/COMPASS）的星载原子钟特性及其性能维护还有许多理论问题和实际问题值得研究。进行GNSS卫星导航系统星载原子钟的时频特性以及精密钟差研究的理论意义在于探索卫星钟系统的时变规律，进而为卫星钟动态特性预测、性能维护等提供理论依据；精密卫星钟差特性研究的实践意义在于为用户导航定位提供精确的时差，为提高卫星定轨精度、用户导航定位精度提供支持。于是，星载原子钟特性及其性能维护研究是国内外卫星导航理论探索与实践研究的热点问题之一。
鉴于此，本文利用GNSS钟差产品对星载原子钟的特性、模型以及预报方法等进行了系统的研究，主要内容包括：
（1）针对GNSS卫星钟差数据，设计了相应的星载原子钟状态监测和质量评价技术路线。以GPS为例，利用十年的IGS精密钟差产品研究了其星载原子钟的长期特性变化规律，比较了不同类型星载钟在稳定度、模型噪声、用户定位误差（URE）等方面的数值差异，推导了频率稳定度与钟差模型噪声水平之间的线性关系。
（2）利用阿伦方差和哈达码方差等度量方法，研究了顾及钟差随机噪声类型的标准卡尔曼滤波实时钟差算法，分析比较了GPS不同类型星载钟实时参数估计与短期预报精度的数值差异。
（3）针对卫星钟差实时参数估计和短期预报中的粗差和钟跳问题，研究提出了新型的基于开窗取样的分类因子抗差自适应序贯平差钟差算法，并将其进一步拓展成实时卡尔曼滤波卫星钟差算法，新算法能够显著提高实时钟差参数估计和预报的精度和稳健性。
（4）针对卫星钟差长期预报问题，研究提出了抗差最小二乘估计与滑动自回归模型相结合（RLS+ARIMA）的两步钟差预报算法，一方面兼顾了钟自身的钟速、钟漂特性，同时利用抗差最小二乘估计求解星钟参数时间序列，揭示了其长期变化规律，另外还利用滑动自回归（ARIMA）模型对星钟参数的随机性部分进行了有效预报。
（5）针对GPS和GLONASS的IGU-P实时钟差产品精度过低问题，研究提出了改进的自适应实时钟差预报模型。改进模型在处理周期项误差、自适应钟差模型选择、起点偏差以及观测随机模型调整等多个环节上都提出了新的处理策略。另外还通过钟差预报和实时精密单点定位（PPP）实例对新模型和IGU-P产品的预报精度和定位精度进行了对比，验证新模型的精度和可靠性。
（6）由于目前GLONASS实时钟差预报方法尚不成熟，IGS尚无实时的GLONASS预报钟差产品发布，对三家主要的IGS研究机构提供的GLONASS钟差产品进行了实时预报分析，并提出和比较了改进模型的有效性和精度，同时还利用谱分析方法求解了GLONASS卫星钟差存在的显著周期项。
（7）推导了不同误差源对GNSS单站精密授时解的数值影响公式。针对“天跳变”现象，构建了一种基于参数先验贝叶斯估计的连续CP时频传递算法，通过对单天观测数据附加合理的参数先验约束，从而平滑过渡不同天之间的钟差解。数值算例结果显示，新方法相比单天PPP法具有更好的连续性和更高的稳定性。
（8）通常，载波相位（CP）技术是单站观测，受环境天气等因素影响严重，其中短距离内比对结果和精度并不稳定，提出了一种基于单差模式的连续载波相位时间传递算法（DCP），该算法能够较好地削弱两测站间的共视误差，提高了测站间时频传递的精度和稳定性。同时还进一步将DCP算法拓展应用于精密定位领域，并通过实际的动静态精密定位算例进行测试，验证了该方法的有效性和精度。
（9）针对传统多模GNSS融合PPP算法运算效率较低、难以满足高精度实时、高频数据的实际解算需求，提出了一种基于参数等价约化原理的自适应GNSS融合PPP算法。新算法一方面运算效率大大提高，更适用于实时定位；另一方面还利用了验后方差因子自适应平衡不同系统间的贡献权比关系，提高了融合定位的精度和可靠性。
（10）提出了在用户端上利用融合PPP模型结合不同类型IGS产品进行GNSS时差监测的技术方法，并获得了包括真实系统时差、伪时差、系统间硬件延迟较差等产品，分析了这些产品的稳定性、精度以及变化规律等特征，并对这些产品在实际用户导航定位中的实用性进行了测试论证，最后指出伪时差的监测和预报工作对于导航定位用户而言具有更重要的实用价值。
Time system is one of the core elements of satellite navigation and positioning system. Time is the most basic observation of navigation system. Time-frequency observations of satellite navigation system are provided by the satellite atomic clocks. Satellite clocks which provide time scale of navigation systems directly determine the accuracy of navigation and positioning plus time-frequency transferring. Nowadays, for GNSS, especially China's BeiDou satellite navigation systems (COMPASS), there are many theoretical and practical problrms in the satellite clocks characteristics and performance maintenance. The theoretical significance of atomic clock's time-frequency characteristics and various satellite clock errors are for exploring the time-varying regularity of satellite clock system and providing theoretical basis for dynamic characteristics predicting of satellite clock and performance maintenance. The practical significance of the study on precise satellite clock characteristics is for providing accurate time offset and supporting to enhance the accuracies of the satellite orbit determination for user's navigation and positioning. Therefore, the research on characteristics and performance maintenance of satellite atomic clocks is one of the hot theoretical exploration and practical research issues in the field of satellite navigation..
In the research, GNSS clock products are used to study on clock characteristics, error models and prediction methods of the satellite clocks on orbit. The main work and contributions of this thesis are as follows:
(1) IGS clock products from2001to2010are used to analyze the GPS satellite clock qualities such as frequency stabilities and clock noise level. We find out that the frequency stabilities and clock noise of the clocks of Block IIA satellites are ten times worse than that of the Block IIR and IIR-M satellites. Moreover, the linear relationships between frequency stabilities and clock residuals have been deduced with an accuracy of better than0.02nanoseconds. Specially, it is noticed that the clock of the PRN27is instable and the relationship between the frequency stability and residuals can be described by a quadratic curve. Therefore, we suggested that GPS satellite clocks should be weighted by their quality levels in application, and the observations of the Block IIA should not be used for real-time positioning in the situation with required precision better than one meter.
(2) Through the analysis of GPS satellite clocks noise by Allan variance and Hadamard total variance, as well as the research on estimation and prediction of satellite clock errors by Kalman filter given stochastic model of satellite clock noise, precision abnormity was computed among different style of clock. Meanwhile, combined with satellite clock stability, some conclusions can be obtained:Stability and precision of GPS Block IIR-M Rb clock is better than that of Block IIR Rb clock, Stability and precision of GPS Block IIR Rb clock is better than that of Block IIA Rb clock, compared with Rb clock, Cs clock's stability and precision is worse by2-3times.
(3) In order to estimate the satellite clock offset in a real-time mode, a new algorithm of adaptively robust Kalman filter with classified adaptive factors for clock offset estimation is proposed. Compared with standard Kalman filter clock offset model, the new method can detect and control the influences of outliers and clock jumps automatically in real-time. Moreover, the clock model parameters, which contain the clock offset, clock speed and clock shift, are classified to decide the adaptive factors in the new model. Thus, clock jumps with different characteristics can be distinguished more effectively. Meanwhile, the dynamic noise characteristics of clock offset series are used for stochastic modeling. An actual numerical example is presented, which shows that the proposed filter can give a better performance than other commonly used filters.
(4) Based on the properties of clock velocity and shift, a robust quadratic polynomial model to fit single-day clock error and to mitigate the effect of exceptional data is provided firstly. Then we fuse the long-term clock parameters fitted from former clock time series and use the ARIMA model to predict the long-term clock parameters. This novel algorithm is tested to predict clock errors for100days, and the prediction accuracy is better than34ns, which is significantly better than other traditional algorithms.
(5) Improved prediction models for GPS and GLONASS satellite clocks are proposed in order to enhance the precision of predicted clock offsets. Firstly, the proposed prediction models are proposed, in which a few cyclic terms is added to absorb the periodic effects and a time adaptive function is used to adjust the weight of the observation in the prediction model. Secondly, initial deviations of the predictions are reduced by using a modified method to a constant term. The simulating results have shown that the proposed prediction model can give a better performance than that from IGU-P clock products. In addition, RTPPP method was chosen to testify the efficiency of the new model for real-time static and kinematic positioning.
(6) Because IGS has no useable products of GLONASS real-time clock prediction, real-time forecasting is studied based on the GLONASS clock products which offered by the three major IGS research institutions. The improved model is proposed and the validity and accuracy of the improved model are computed. In addition, the spectral analysis method is used to solve the significant periodic terms of the GLONASS satellite clock.
(7) Clock error sequence obtained by the traditional single-day PPP is not continuous, which exists day-boundary. This problem directly influences the popularization and application of PPP technique in the realm of precise time and frequency transfer. In this paper, parameter-based Bayesian estimation with prior information is proposed to solve the problem of day-boundary. Namely, by constraining the prior information with different parameters, the author realized continuous PPP solution or approximate PPP solution, which successfully suppresses the day-slip resulted from single-day solution. The simulation results show that the proposed new algorithm for timing accuracy and stability of the PPP algorithm is significantly superior to the traditional, and it can effectively solve the problems of day-boundary.
(8) The characteristic of GPS Common View (GPS CV) and GPS Carrier Phase time transfer (GPS CP) methods are introduced, and a new continuous time and frequency transfer algorithm based on GPS single Different Carrier Phase observations is proposed. This new algorithm uses ionosphere-free combination of single different observations from the same satellite, and its processing steps are also consistent with simple common GPS CP. In addition, the Bayesian estimation of prior information is proposed to smooth the day-boundaries of time transfer results. The simulation results, which compared to that of GPS CP method, show that the proposed new algorithm has a remarkable improvement in the precision and frequency stability of the time and frequency transfer results.
(9) The standard GNSS combined PPP algorithm cannot be used satisfactorily in the real-time and high frequency precise positioning because of its low compute efficiency. A new algorithm based on the parameter equivalent reduction principle is proposed. First, the observation equations and the normal equations which belong to the single navigation system can be solved independently. Second, the normal equations of overlapping parameters between the different systems can be obtained by using parameter equivalent reduction principle. At last, the combined PPP resolutions can be computed easily by using the least squares method. The proposed algorithm can improve the calculating efficiency immensely. In addition, an adaptively combined method which can automatically adjusts the contributed weight of different GNSS systems is also proposed.
(10) A new method of GNSS time offset monitoring is proposed based on the combined PPP model and the different IGS clock products. The real GNSS time offset, the hardware delay difference between different systems and the user time offset are obtained. Meanwhile, the stability, accuracy and variation characteristics of these products are analyzed. The practical application of these products in the real navigation and positioning is tested. In the end, it was concluded that the monitoring and forecasting of the user time offset has more important practical value for the users of navigation and positioning.
鉴于此，本文利用GNSS钟差产品对星载原子钟的特性、模型以及预报方法等进行了系统的研究，主要内容包括：
（1）针对GNSS卫星钟差数据，设计了相应的星载原子钟状态监测和质量评价技术路线。以GPS为例，利用十年的IGS精密钟差产品研究了其星载原子钟的长期特性变化规律，比较了不同类型星载钟在稳定度、模型噪声、用户定位误差（URE）等方面的数值差异，推导了频率稳定度与钟差模型噪声水平之间的线性关系。
（2）利用阿伦方差和哈达码方差等度量方法，研究了顾及钟差随机噪声类型的标准卡尔曼滤波实时钟差算法，分析比较了GPS不同类型星载钟实时参数估计与短期预报精度的数值差异。
（3）针对卫星钟差实时参数估计和短期预报中的粗差和钟跳问题，研究提出了新型的基于开窗取样的分类因子抗差自适应序贯平差钟差算法，并将其进一步拓展成实时卡尔曼滤波卫星钟差算法，新算法能够显著提高实时钟差参数估计和预报的精度和稳健性。
（4）针对卫星钟差长期预报问题，研究提出了抗差最小二乘估计与滑动自回归模型相结合（RLS+ARIMA）的两步钟差预报算法，一方面兼顾了钟自身的钟速、钟漂特性，同时利用抗差最小二乘估计求解星钟参数时间序列，揭示了其长期变化规律，另外还利用滑动自回归（ARIMA）模型对星钟参数的随机性部分进行了有效预报。
（5）针对GPS和GLONASS的IGU-P实时钟差产品精度过低问题，研究提出了改进的自适应实时钟差预报模型。改进模型在处理周期项误差、自适应钟差模型选择、起点偏差以及观测随机模型调整等多个环节上都提出了新的处理策略。另外还通过钟差预报和实时精密单点定位（PPP）实例对新模型和IGU-P产品的预报精度和定位精度进行了对比，验证新模型的精度和可靠性。
（6）由于目前GLONASS实时钟差预报方法尚不成熟，IGS尚无实时的GLONASS预报钟差产品发布，对三家主要的IGS研究机构提供的GLONASS钟差产品进行了实时预报分析，并提出和比较了改进模型的有效性和精度，同时还利用谱分析方法求解了GLONASS卫星钟差存在的显著周期项。
（7）推导了不同误差源对GNSS单站精密授时解的数值影响公式。针对“天跳变”现象，构建了一种基于参数先验贝叶斯估计的连续CP时频传递算法，通过对单天观测数据附加合理的参数先验约束，从而平滑过渡不同天之间的钟差解。数值算例结果显示，新方法相比单天PPP法具有更好的连续性和更高的稳定性。
（8）通常，载波相位（CP）技术是单站观测，受环境天气等因素影响严重，其中短距离内比对结果和精度并不稳定，提出了一种基于单差模式的连续载波相位时间传递算法（DCP），该算法能够较好地削弱两测站间的共视误差，提高了测站间时频传递的精度和稳定性。同时还进一步将DCP算法拓展应用于精密定位领域，并通过实际的动静态精密定位算例进行测试，验证了该方法的有效性和精度。
（9）针对传统多模GNSS融合PPP算法运算效率较低、难以满足高精度实时、高频数据的实际解算需求，提出了一种基于参数等价约化原理的自适应GNSS融合PPP算法。新算法一方面运算效率大大提高，更适用于实时定位；另一方面还利用了验后方差因子自适应平衡不同系统间的贡献权比关系，提高了融合定位的精度和可靠性。
（10）提出了在用户端上利用融合PPP模型结合不同类型IGS产品进行GNSS时差监测的技术方法，并获得了包括真实系统时差、伪时差、系统间硬件延迟较差等产品，分析了这些产品的稳定性、精度以及变化规律等特征，并对这些产品在实际用户导航定位中的实用性进行了测试论证，最后指出伪时差的监测和预报工作对于导航定位用户而言具有更重要的实用价值。
Time system is one of the core elements of satellite navigation and positioning system. Time is the most basic observation of navigation system. Time-frequency observations of satellite navigation system are provided by the satellite atomic clocks. Satellite clocks which provide time scale of navigation systems directly determine the accuracy of navigation and positioning plus time-frequency transferring. Nowadays, for GNSS, especially China's BeiDou satellite navigation systems (COMPASS), there are many theoretical and practical problrms in the satellite clocks characteristics and performance maintenance. The theoretical significance of atomic clock's time-frequency characteristics and various satellite clock errors are for exploring the time-varying regularity of satellite clock system and providing theoretical basis for dynamic characteristics predicting of satellite clock and performance maintenance. The practical significance of the study on precise satellite clock characteristics is for providing accurate time offset and supporting to enhance the accuracies of the satellite orbit determination for user's navigation and positioning. Therefore, the research on characteristics and performance maintenance of satellite atomic clocks is one of the hot theoretical exploration and practical research issues in the field of satellite navigation..
In the research, GNSS clock products are used to study on clock characteristics, error models and prediction methods of the satellite clocks on orbit. The main work and contributions of this thesis are as follows:
(1) IGS clock products from2001to2010are used to analyze the GPS satellite clock qualities such as frequency stabilities and clock noise level. We find out that the frequency stabilities and clock noise of the clocks of Block IIA satellites are ten times worse than that of the Block IIR and IIR-M satellites. Moreover, the linear relationships between frequency stabilities and clock residuals have been deduced with an accuracy of better than0.02nanoseconds. Specially, it is noticed that the clock of the PRN27is instable and the relationship between the frequency stability and residuals can be described by a quadratic curve. Therefore, we suggested that GPS satellite clocks should be weighted by their quality levels in application, and the observations of the Block IIA should not be used for real-time positioning in the situation with required precision better than one meter.
(2) Through the analysis of GPS satellite clocks noise by Allan variance and Hadamard total variance, as well as the research on estimation and prediction of satellite clock errors by Kalman filter given stochastic model of satellite clock noise, precision abnormity was computed among different style of clock. Meanwhile, combined with satellite clock stability, some conclusions can be obtained:Stability and precision of GPS Block IIR-M Rb clock is better than that of Block IIR Rb clock, Stability and precision of GPS Block IIR Rb clock is better than that of Block IIA Rb clock, compared with Rb clock, Cs clock's stability and precision is worse by2-3times.
(3) In order to estimate the satellite clock offset in a real-time mode, a new algorithm of adaptively robust Kalman filter with classified adaptive factors for clock offset estimation is proposed. Compared with standard Kalman filter clock offset model, the new method can detect and control the influences of outliers and clock jumps automatically in real-time. Moreover, the clock model parameters, which contain the clock offset, clock speed and clock shift, are classified to decide the adaptive factors in the new model. Thus, clock jumps with different characteristics can be distinguished more effectively. Meanwhile, the dynamic noise characteristics of clock offset series are used for stochastic modeling. An actual numerical example is presented, which shows that the proposed filter can give a better performance than other commonly used filters.
(4) Based on the properties of clock velocity and shift, a robust quadratic polynomial model to fit single-day clock error and to mitigate the effect of exceptional data is provided firstly. Then we fuse the long-term clock parameters fitted from former clock time series and use the ARIMA model to predict the long-term clock parameters. This novel algorithm is tested to predict clock errors for100days, and the prediction accuracy is better than34ns, which is significantly better than other traditional algorithms.
(5) Improved prediction models for GPS and GLONASS satellite clocks are proposed in order to enhance the precision of predicted clock offsets. Firstly, the proposed prediction models are proposed, in which a few cyclic terms is added to absorb the periodic effects and a time adaptive function is used to adjust the weight of the observation in the prediction model. Secondly, initial deviations of the predictions are reduced by using a modified method to a constant term. The simulating results have shown that the proposed prediction model can give a better performance than that from IGU-P clock products. In addition, RTPPP method was chosen to testify the efficiency of the new model for real-time static and kinematic positioning.
(6) Because IGS has no useable products of GLONASS real-time clock prediction, real-time forecasting is studied based on the GLONASS clock products which offered by the three major IGS research institutions. The improved model is proposed and the validity and accuracy of the improved model are computed. In addition, the spectral analysis method is used to solve the significant periodic terms of the GLONASS satellite clock.
(7) Clock error sequence obtained by the traditional single-day PPP is not continuous, which exists day-boundary. This problem directly influences the popularization and application of PPP technique in the realm of precise time and frequency transfer. In this paper, parameter-based Bayesian estimation with prior information is proposed to solve the problem of day-boundary. Namely, by constraining the prior information with different parameters, the author realized continuous PPP solution or approximate PPP solution, which successfully suppresses the day-slip resulted from single-day solution. The simulation results show that the proposed new algorithm for timing accuracy and stability of the PPP algorithm is significantly superior to the traditional, and it can effectively solve the problems of day-boundary.
(8) The characteristic of GPS Common View (GPS CV) and GPS Carrier Phase time transfer (GPS CP) methods are introduced, and a new continuous time and frequency transfer algorithm based on GPS single Different Carrier Phase observations is proposed. This new algorithm uses ionosphere-free combination of single different observations from the same satellite, and its processing steps are also consistent with simple common GPS CP. In addition, the Bayesian estimation of prior information is proposed to smooth the day-boundaries of time transfer results. The simulation results, which compared to that of GPS CP method, show that the proposed new algorithm has a remarkable improvement in the precision and frequency stability of the time and frequency transfer results.
(9) The standard GNSS combined PPP algorithm cannot be used satisfactorily in the real-time and high frequency precise positioning because of its low compute efficiency. A new algorithm based on the parameter equivalent reduction principle is proposed. First, the observation equations and the normal equations which belong to the single navigation system can be solved independently. Second, the normal equations of overlapping parameters between the different systems can be obtained by using parameter equivalent reduction principle. At last, the combined PPP resolutions can be computed easily by using the least squares method. The proposed algorithm can improve the calculating efficiency immensely. In addition, an adaptively combined method which can automatically adjusts the contributed weight of different GNSS systems is also proposed.
(10) A new method of GNSS time offset monitoring is proposed based on the combined PPP model and the different IGS clock products. The real GNSS time offset, the hardware delay difference between different systems and the user time offset are obtained. Meanwhile, the stability, accuracy and variation characteristics of these products are analyzed. The practical application of these products in the real navigation and positioning is tested. In the end, it was concluded that the monitoring and forecasting of the user time offset has more important practical value for the users of navigation and positioning.
引文
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