基于GPS精密单点定位的时间比对与钟差预报研究
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摘要
GPS精密单点定位(PPP)的时间比对就是利用IGS精密轨道和精密星钟数据,对单台接收机所采集的测码伪距和载波相位观测数据进行解算,获得IGST时间尺度下的接收机钟差,实现纳秒至亚纳秒级精度的时间比对。
PPP方法观测灵活,与GPS共视比对(CV)相比,不需要同步观测,就可以实现任意时间和地点的时间传递,与GPS全视(AV)相比, PPP能充分利用载波相位观测精度高的特点,使得时间传递精度有较大的提高。与其它远程时间比对方法相比,PPP投入少,易实现。因此,PPP目前是国际时频界研究的热点问题。研究该方法对提高国际原子时(TAI)的计算精度,对建立我国综合地方原子时,对我国正在建设自主卫星导航系统,有着重要的意义。
本文深入研究了PPP技术,分析了PPP的各种误差的消除方法,实现了PPP时间比对算法,平滑了比对结果,讨论了钟差预报等相关问题。本文的主要研究内容包括:
(1)实现了PPP时间比对算法
欲使PPP钟差解算精度达到纳秒至亚纳秒级,因此必须采用完善的模型加以改正影响GPS时间比对的各项误差,并将改正后仍然无法忽略的残差作为未知数进行估计。本文详细地分析了相关误差源及其改正方法,选择了Kalman滤波模型求解参数,并用Helmert方差估计调整测码伪距和载波观测伪距的验前方差,使得两类观测值精度合理匹配。用Matlab软件实现了PPP时间传递的算法,并选择了短基线法和比测法研究了模型的特点,将相关的计算结果与IGS结果相比较,得到的结论是,本文算法稳定、精度可靠,可以用于时间实验室之间远程时间比对。
(2)比对数据的平滑
比对数据的平滑是数据处理中重要内容。讨论了Vondrak法平滑PPP比对结果,该法随着选取的ε的不同而有不同的结果,通过对四条典型链路的平滑研究,认为ε的经验取值为200～400为宜。顾及到PPP和AV的各自特点,讨论了Vondrak-Cepek组合平滑这两种时间比对的结果。为该法组合平滑不同时间比对结果提供了新的思路。鉴于Vondrak-Cepek法的优良特性,在文中也运用该法组合了氢铯钟钟差,得到了较为理想的结果。
(3)钟差预报方法
钟差预报在时间传递、守时和导航中起着重要的作用。本文简单地讨论了一些常用的钟差预报模型,包括多项式模型、灰色模型、谱分析模型和自回归模型。重点地研究了Kalman滤波(KF)模型,讨论了确定状态噪声协方差阵ΣW k和观测噪声的协方差阵Σk的方法。针对经典KF方程不能有效地抵抗粗差的影响,讨论了基于小波多尺度分析、基于残差预报的自适应和基于Sage自适应的KF模型。考虑到各种模型的预报优点和局限性,首次将组合预报理论用于钟差预报中,根据组合模型的特性不同将组合方法分为线性组合预报模型和非线性组合预报模型,对于前者,根据定权方法不同,讨论了经典权和最优权,对于后者以神经网络为例讨论了建模特点。在实际运用过程中,针对钟差预报特点,提出了修正线性组合预报模型,修正后模型能提高组合预报的可靠性和准确性。
GPS precise point positioning (PPP) which can be implemented only by one dual-frequency receiver can obtain the clock accuracy is about nanosecond or sub-nanosecond by using GPS precise satellite orbit and clock error data. Correspondingly, time comparison using PPP can attain this accuracy under the IGST.
Compared with GPS Common-View (CV), PPP need not observe the same satellites in the sky. Therefore, PPP can accomplish time compare in any time and in any place in theory. Compared with GPS All-in-View (AV), PPP uses carrier observation data which is more accurate than code observation. Moreover, PPP is more flexible and lower cost than other time transfer methods.
In this paper, we make intensive study on PPP, analysis the error elimination, realize the time comparison algorithm, smooth the result, and discuss the atomic clock prediction. The main content are as following:
(1) PPP time comparison algorithm realization
To achieve the centimeter accuracy for parameter estimation, more precise model must be used to correct the error while PPP is used to transfer time. And some residual error which are can not be neglected must be estimate as unknown parameter. The error resources and correction model are discussed in detail and Kalman filter (KF) model to estimate the parameter is chosed. Meantime, Helmert variance estimation is used to adjuste the variances from the two-type observations. Then time comparison algorithm is realized. To study the model precision, short baseline and comparison methods are employed. Results from the two methods show that the model precision is about 0.1ns. Meantime, time comparison is computed for the four time links and the results is compared with IGS outcome. Finally we get conclusion that this algorithm can be used in the time laboratory.
(2) Comparison data smoothing
Comparison data smoothing is one of the most important tasks in time transfer. Vondrak smooth method depends on the smooth parameterε. Through study on the four time links, we consider the empirical value ofεis about 200～400. Considering the characteristic of PPP and AV, we propose combining the result from these two methods by using Vondrak-Cepek which is available method to smooth the time comparison data. Just as Vondrak method, Vondrak-cepek is determined byεandε, so we propose the empirical values of these two parameters. Because the Vondrak-Cepek method is valid, the H-master and Cesium clock data is combined using this model and ideal result is obtained.
(3) Clock prediction
Clock prediction plays an important role in time transfer, time keeping and navigation. In this paper, the conventional methods for clock prediction including polynomial model, auto-regression model, spectrum analysis model and grey model are presented. Then we study the KF model in detail. Two methods to get the noise matrices are discussed. Classical KF is employed to predict the atomic clock; we find that classical KF is useful while there is no jump happened. But if there are jumps, KF become lower convergence, even more KF diverges. To deal with the problem from classical KF, wavelet KF and adaptive KFs are proposed. Finally, the combination models are studied which may improve the accuracy and stability. According to the combination characteristic, these models are divided into linear models and non-linear models. In the former, classic and optimal weight are present. In the latter, artificial neutral network is discussed as an example. Because IGS precise clock data has more accuracy, we use the data as example to confirm the models validation.
PPP方法观测灵活,与GPS共视比对(CV)相比,不需要同步观测,就可以实现任意时间和地点的时间传递,与GPS全视(AV)相比, PPP能充分利用载波相位观测精度高的特点,使得时间传递精度有较大的提高。与其它远程时间比对方法相比,PPP投入少,易实现。因此,PPP目前是国际时频界研究的热点问题。研究该方法对提高国际原子时(TAI)的计算精度,对建立我国综合地方原子时,对我国正在建设自主卫星导航系统,有着重要的意义。
本文深入研究了PPP技术,分析了PPP的各种误差的消除方法,实现了PPP时间比对算法,平滑了比对结果,讨论了钟差预报等相关问题。本文的主要研究内容包括:
(1)实现了PPP时间比对算法
欲使PPP钟差解算精度达到纳秒至亚纳秒级,因此必须采用完善的模型加以改正影响GPS时间比对的各项误差,并将改正后仍然无法忽略的残差作为未知数进行估计。本文详细地分析了相关误差源及其改正方法,选择了Kalman滤波模型求解参数,并用Helmert方差估计调整测码伪距和载波观测伪距的验前方差,使得两类观测值精度合理匹配。用Matlab软件实现了PPP时间传递的算法,并选择了短基线法和比测法研究了模型的特点,将相关的计算结果与IGS结果相比较,得到的结论是,本文算法稳定、精度可靠,可以用于时间实验室之间远程时间比对。
(2)比对数据的平滑
比对数据的平滑是数据处理中重要内容。讨论了Vondrak法平滑PPP比对结果,该法随着选取的ε的不同而有不同的结果,通过对四条典型链路的平滑研究,认为ε的经验取值为200～400为宜。顾及到PPP和AV的各自特点,讨论了Vondrak-Cepek组合平滑这两种时间比对的结果。为该法组合平滑不同时间比对结果提供了新的思路。鉴于Vondrak-Cepek法的优良特性,在文中也运用该法组合了氢铯钟钟差,得到了较为理想的结果。
(3)钟差预报方法
钟差预报在时间传递、守时和导航中起着重要的作用。本文简单地讨论了一些常用的钟差预报模型,包括多项式模型、灰色模型、谱分析模型和自回归模型。重点地研究了Kalman滤波(KF)模型,讨论了确定状态噪声协方差阵ΣW k和观测噪声的协方差阵Σk的方法。针对经典KF方程不能有效地抵抗粗差的影响,讨论了基于小波多尺度分析、基于残差预报的自适应和基于Sage自适应的KF模型。考虑到各种模型的预报优点和局限性,首次将组合预报理论用于钟差预报中,根据组合模型的特性不同将组合方法分为线性组合预报模型和非线性组合预报模型,对于前者,根据定权方法不同,讨论了经典权和最优权,对于后者以神经网络为例讨论了建模特点。在实际运用过程中,针对钟差预报特点,提出了修正线性组合预报模型,修正后模型能提高组合预报的可靠性和准确性。
GPS precise point positioning (PPP) which can be implemented only by one dual-frequency receiver can obtain the clock accuracy is about nanosecond or sub-nanosecond by using GPS precise satellite orbit and clock error data. Correspondingly, time comparison using PPP can attain this accuracy under the IGST.
Compared with GPS Common-View (CV), PPP need not observe the same satellites in the sky. Therefore, PPP can accomplish time compare in any time and in any place in theory. Compared with GPS All-in-View (AV), PPP uses carrier observation data which is more accurate than code observation. Moreover, PPP is more flexible and lower cost than other time transfer methods.
In this paper, we make intensive study on PPP, analysis the error elimination, realize the time comparison algorithm, smooth the result, and discuss the atomic clock prediction. The main content are as following:
(1) PPP time comparison algorithm realization
To achieve the centimeter accuracy for parameter estimation, more precise model must be used to correct the error while PPP is used to transfer time. And some residual error which are can not be neglected must be estimate as unknown parameter. The error resources and correction model are discussed in detail and Kalman filter (KF) model to estimate the parameter is chosed. Meantime, Helmert variance estimation is used to adjuste the variances from the two-type observations. Then time comparison algorithm is realized. To study the model precision, short baseline and comparison methods are employed. Results from the two methods show that the model precision is about 0.1ns. Meantime, time comparison is computed for the four time links and the results is compared with IGS outcome. Finally we get conclusion that this algorithm can be used in the time laboratory.
(2) Comparison data smoothing
Comparison data smoothing is one of the most important tasks in time transfer. Vondrak smooth method depends on the smooth parameterε. Through study on the four time links, we consider the empirical value ofεis about 200～400. Considering the characteristic of PPP and AV, we propose combining the result from these two methods by using Vondrak-Cepek which is available method to smooth the time comparison data. Just as Vondrak method, Vondrak-cepek is determined byεandε, so we propose the empirical values of these two parameters. Because the Vondrak-Cepek method is valid, the H-master and Cesium clock data is combined using this model and ideal result is obtained.
(3) Clock prediction
Clock prediction plays an important role in time transfer, time keeping and navigation. In this paper, the conventional methods for clock prediction including polynomial model, auto-regression model, spectrum analysis model and grey model are presented. Then we study the KF model in detail. Two methods to get the noise matrices are discussed. Classical KF is employed to predict the atomic clock; we find that classical KF is useful while there is no jump happened. But if there are jumps, KF become lower convergence, even more KF diverges. To deal with the problem from classical KF, wavelet KF and adaptive KFs are proposed. Finally, the combination models are studied which may improve the accuracy and stability. According to the combination characteristic, these models are divided into linear models and non-linear models. In the former, classic and optimal weight are present. In the latter, artificial neutral network is discussed as an example. Because IGS precise clock data has more accuracy, we use the data as example to confirm the models validation.
引文
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