基于Vondrák滤波1阶差分灰色模型的卫星钟差预报方法

为了提高卫星钟差预报的精度,提出基于Vondrák滤波1阶差分的灰色模型算法.首先,对原始钟差数据序列采用Vondrák滤波处理后,得到1组新的钟差数据序列.然后,对相邻历元的钟差数据序列作1阶差分处理.最后,基于Vondrák滤波后的1阶差分的钟差差值数据序列,建立了GPS钟差预报的灰色模型.此外,采用了IGS(International Global Navigation Satellite System Service)公布的精密卫星钟差数据进行了预报试验,通过与卫星钟差预报中常用的2次多项式模型和直接采用原始钟差数据建立灰色预报模型预报结果的对比分析,结果表明:该方法可以对GPS卫星钟差进行高精度的中短期预报.在12 h、16 h、20 h和24 h的平均预报精度分别为0.50 ns、0.85 ns、1.08 ns和1.27 ns,相比于2次多项式模型的平均预报精度分别提高了24.24%、15.84%、12.90%和11.81%;相比于直接采用原始钟差数据建立灰色预报模型的平均预报精度分别提高了56.14%、49.40%、48.82%和47.80%.     

基于GM(1,1)和MECM组合模型的GPS卫星钟差中短期预报

针对卫星钟差呈现趋势项和随机项变化的特点,提出了基于GM(1,1)(灰色预报模型)和修正指数曲线法(Modified Exponential Curve Method,MECM)的组合预报模型.该模型首先采用GM(1,1)预报钟差的趋势项,然后利用MECM模型对GM(1,1)残差序列进行建模和预报,最后将GM(1,1)和MECM模型的预报结果相加得到钟差的最终预报值.此外,采用IGS(International Global Navigation Satellite System Service)公布的精密卫星钟差进行预报试验,通过与卫星钟差预报中常用的二次多项式和MECM模型预报结果的对比分析,结果表明:该方法可以对GPS卫星钟差进行高精度的中短期预报.使用12 h钟差建模时,预报6 h、12 h、18 h和24 h的平均预报精度分别为0.43 ns、0.63 ns、0.74 ns和0.79 ns,相比于二次多项式的平均预报精度分别提高了57.43%、69.71%、80.47%和86.74%,相比于MECM模型的平均预报精度分别提高了50.57%、64.41%、76.80%和84.20%;使用24 h钟差建模时,预报6 h、12 h、18h和24 h的平均预报精度分别为0.57 ns、0.61 ns、1.02 ns和1.48 ns,相比于二次多项式的平均预报精度分别提高了32.94%、55.47%、55.07%和53.16%,相比于MECM模型的平均预报精度分别提高了92.98%、66.30%、65.42%和63.99%.     

北斗系统测站钟差短期预报模型比较及其在单星定轨中的应用

北斗卫星导航系统(BDS)地面跟踪站都配置有高精度的氢原子钟,并基于精密定轨数据处理与主站的时间基准进行同步.在卫星轨道机动以及机动恢复期间,通常采用几何法定轨以及单星定轨确定卫星的轨道.而在这两种定轨模式中,需要提供精确的测站钟差作为输入.为提高定轨的实时性,需要对测站钟差进行预报处理.分析了2次多项式模型、附加周期项模型、灰色模型3种模型对北斗地面跟踪站钟差短期拟合和预报的性能,并将钟差预报结果应用于单星定轨,同时还分析了不同预报钟差用于定轨的精度.试验发现,以上3种模型对6个测站钟差的平均拟合精度分别为0.14 ns、0.05 ns、0.27 ns,预报1 h的平均精度分别为1.17 ns、0.88 ns、1.28 ns,预报2 h的平均精度分别为2.72 ns、2.09 ns、2.53 ns.采用3种模型对测站钟差进行预报并用于单星定轨,采用附加周期项的钟差预报模型轨道3维误差最小,不同模型轨道径向精度差异在3 cm以内.以上结果表明,附加周期项的站钟拟合及预报模型在北斗系统机动期间的轨道恢复数据处理具有最好的效果.     

预报模型及建模序列长度对钟差短期预报精度影响研究

针对全球定位系统(Global Positioning System, GPS)星载原子钟在钟差预报时与不同模型的适应度不同的问题,采用二次多项式(Quadratic Polynomial, QP)模型、灰色(Grey Model, GM(1,1)模型和灰色+自回归(GM(1,1)+Autoregressive, GM(1,1)+AR)模型对不同类型原子钟的钟差进行预报,着重分析不同类型原子钟的预报精度、不同长度钟差序列建模预报效果以及钟差序列波动对预报结果的影响。实验结果表明:(1)钟差预报精度与建模序列长度有一定关系,二次多项式模型受影响最大,灰色+自回归模型受影响最小;(2)不同卫星原子钟在不同预报模型下最佳建模序列长度不同,铷钟受建模序列长度的影响小于铯钟;(3)二次多项式模型对铯钟预报效果较差,对铷钟预报效果可与灰色模型和灰色+自回归模型相当;(4)钟差序列波动时,建模预报精度降低,不同模型的预报结果受钟差波动幅度大小的影响不同。     

二次多项式模型和灰色理论模型在接收机钟差预报中的应用和比较

为了更好地对接收机钟差作科学、准确的预报,基于实验室解算出的接收机钟差数据,分别采用二次多项式模型和灰色理论模型对接收机钟差进行了预报和分析.预报结果及其比较表明,对于需要用少量接收机钟差数据建立预报模型时,灰色理论模型预报不论是单点预报还是多点(30个点)预报,其预报精度都优于二次多项式预报模型,可以在实际工作中应用.     

灰色模型修正及其在实时GPS卫星钟差预报中的应用研究

在GPS实时精密单点定位中,卫星钟差的实时可靠预报是实现GPS实时高精度单点定位的关键之一.星载GPS原子钟频率高,非常敏感,极易受到外界及其本身因素的影响,从而很难掌握其复杂细致的变化规律,这些属性符合灰色系统理论的特点.因此,考虑将钟差的变化过程看作一个灰色系统.在探讨二次多项式和灰色模型卫星钟差预报局限性基础上,提出了利用改进的灰色模型实时预报GPS卫星钟差的研究,最后利用3个不同时段的GPS卫星钟差资料进行不同采样间隔钟差预报精度分析、灰色模型指数系数与预报精度的关系、与二次多项式预报精度比较分析,总结不同卫星钟差类型与模型指数系数的一般关系,并与IGS最终钟差星历产品比较,验证本文提出的改进预报模型的可行性和有效性.为实时GPS动态精密单点定位提供较高精度的卫星钟差产品.     

基于ARMA模型的导航卫星钟差长期预报

卫星钟差长期可靠预报是实现卫星自主导航定轨所要解决的重要前提之一.针对多项式模型(PM)、灰色模型(GM)等常用的钟差预报方法存在的预报误差较大的情况,为了有效地进行卫星钟差预报和更好地反映卫星钟差变化特性,将ARMA(Auto-Regressive Moving Average)模型引入到卫星钟差预报中,利用IGS(International GNSS Service)提供的卫星钟差观测数据进行90 d的长期预报,根据各个卫星钟差的变化特性,对其进行模式识别、建模和预报,并与其它3种模型进行了较为细致的比较.计算结果表明,采用ARMA模型可以有效地提高卫星钟差的长期预报精度.     

泛函网络在导航卫星钟差中长期预报中的应用

为了更好地反映导航卫星钟差特性以及提高导航卫星钟差中长期预报精度,在对卫星原子钟差预报建模时,除考虑卫星原子钟频移、频漂和频漂率等物理性质外,还考虑了卫星钟差的周期性变化和随机性等特点.在传统多项式预报模型基础上,采用泛函网络对卫星钟差的周期项和随机项部分进行建模,利用GPS导航卫星钟差数据进行预报实验,并与传统的多项式模型、灰色系统模型、差分自回归滑动平均(ARIMA)模型以及Kalman滤波方法的预报结果进行比对,结果表明,基于泛函网络建立的混合预报模型能有效减小导航卫星钟差的中长期预报误差.     

一种改进钟差二次多项式模型的导航卫星钟差预报方法

为了更好地反映钟差特性并提高其预报精度,建立一种能够同时考虑星载原子钟物理特性、钟差周期性变化与随机性变化特点的钟差预报模型.首先采用附有周期项的二次多项式模型进行拟合提取卫星钟差(Satellite Clock Bias,SCB)的趋势项与周期项,然后根据拟合残差的特点采用时间序列ARIMA(Auto-Regressive Integrated Moving Average)模型对残差进行建模;最后将两种模型的预报结果结合得到最终钟差预报值.使用IGS(International GNSS Service)精密钟差数据进行预报试验,将新方法与二次多项式模型、灰色模型及ARIMA模型进行对比,证明了新方法能够更高精度地预报卫星钟差,且可以一定程度上改善ARIMA存在模型识别与定阶不准的不足.     

附有周期项的预报模型及其在GPS卫星钟差预报中的应用研究

为了有效进行GPS卫星钟差预报和更好地反映卫星钟差特性,除了考虑卫星原子钟频移、频漂和频漂率等物理性质外,还应考虑到卫星钟差的周期性变化特点.在二次多项式模型基础上,增加了周期项因素,构造了新的预报模型.选取部分GPS卫星铯钟(Cs.clock)和铷钟(Rb.clock)钟差资料,根据钟差变化趋势分3种情况,按不同时间长度进行钟差预报分析,并与二次多项式模型的预报结果比较分析,大量数据分析表明:附有周期项的二次多项式模型预报精度优于二次多项式模型,铷钟预报精度略优于铯钟.     

An Improved Grey Model and Its Application Research on the Prediction of Real-time GPS Satellite Clock Errors

In the work on the real-time GPS precise point positioning, the realtime and reliable prediction of the satellite clock error is one of the keys to the realization of the GPS real-time high accuracy point positioning. The satelliteborne GPS atomic clock has high frequency, is very sensitive and extremely easy to be influenced by the outside world and its own factors. Therefore, it is very difficult for one to know well its complicated and detailed law of change, with these attributes being in accordance with the characteristics of the theory of grey system. Thus, it is considered that the process of variation of the clock error is regarded as a grey system. On the basis of the exploration of the limitations of the quadratic polynomial and grey model satellite clock error predictions, the research on the real-time prediction of the GPS satellite clock error by taking advantage of the improved grey model is proposed. Finally, the materials of the GPS satellite clock error of 3 different time intervals are used to make the accuracy analysis of the clock error prediction of different sampling intervals, to study the relation between the grey model exponential coefficient and the prediction accuracy and to make the analysis of the comparison of the prediction accuracy with that of the quadratic polynomial method. The general relation between the different types of satellite clock errors and the model exponential coefficients is summarized and compared with the IGS final clock error ephemeris product to test and verify the feasibility and availability of the improved prediction model proposed in the present article so as to provide the higher-accuracy satellite clock error products for the real-time GPS dynamic precise point positioning.     

Long-term Clock Bias Prediction Based on An ARMA Model

The long-term and reliable prediction of satellite clock bias (SCB) is an important prerequisite for realizing the satellite autonomous navigation and orbit determination. Considering the shortcomings of the quadratic polynomial model (PM) and gray system model (GM) in the long-term prediction of SCB, a new prediction method of SCB based on an ARMA (Auto-Regressive Moving Average) model is proposed to represent the variation characteristics of SCB more accurately. In this paper, a careful precision analysis of the 90-day SCB prediction is made to verify the feasibility and validity of this proposed method by using the IGS (International GNSS Service) clock data. According to the variation characteristics of each satellite clock, the pattern recognition, modeling and prediction of SCB are conducted, and the detailed comparison is made with the other three models at the same time. The results show that adopting the ARMA model can effectively improve the accuracy of long-term SCB prediction.     

第三代卫星导航定位系统星载原子钟的新发展

传统铷原子钟和铯原子钟已在卫星导航定位系统中作为星载原子钟获得重要应用.卫星导航定位系统的更新和新发展要求更高精度更小型的新型星载原子钟.该文介绍采用新物理原理和先进技术在下-代卫星导航定位系统有应用前景的新原子钟的产生和发展以及它们目前的进展.     

Prediction of Clock Errors of Atomic Clocks Based on Modified Linear Combination Model†

The prediction of the clock errors of atomic clocks plays an important role in the work on time and frequency. Each of the prediction models often used at present has its own merits and shortages. A combination of the predicted results obtained by means of these models can be used to synthesize the characteristics of various kinds of prediction models. In the light of the problem which occurs when the linear combination model is used to make the prediction of clock errors, the concept of learning weight is proposed and the modified combination prediction model is made by taking advantage of various kinds of pieces of accuracy information. For verifying the efficiency of this method the clock error sequences of the IGS (International GNSS Service) of 4 GPS satellites are selected and the predicted results of the quadratic polynomial and grey model are combined. The result shows that the modified model can further improve the stability and accuracy based on the guarantee of the reliability.     

Comparison of BDS Station Clock Short-term Prediction Models and their Applications in Precise Orbit Determination

BDS (BeiDou Navigation Satellite System) ground tracking stations are equipped with high accuracy atomic clocks, and they are synchronized with the BDS time scale (BDT) via the Precise Orbit Determination (POD) processing. During the periods of satellite maneuver and post-maneuver, station clocks are kept fixed as known values in the POD processing. To improve the real-time POD capability, station clocks need to be predicted. In this paper, the performance of three clock prediction models is evaluated, including quadratic polynomial model (QP), periodical term model (PM), and grey model (GM). The precision of clock fitting and prediction, as well as the performance of the prediction models in POD are compared. Data of six stations are used for test, and the results show that: the mean fitting accuracy of quadratic polynomial model, periodical term model, and grey model is 0.14 ns, 0.05 ns, 0.27 ns, respectively; the 1 h and 2 h prediction precision of the three models is 1.17 ns, 0.88 ns, 1.28 ns, and 2.72 ns, 2.09 ns, 2.53 ns, respectively. Applying the 1 h and 2 h predicted station clocks in the POD, the 3D orbit accuracy reaches the best using the periodical term model, while the radial accuracy of satellite orbit is rather close for the three models with the difference within 3 cm.     

星载GPS自主定轨的长期稳定性

通过模拟长达100天的星载GPS伪距观测资料,进行卡尔曼滤波定轨仿真计算．重点研究：1)采用简化的动力学模型与简化状态转移矩阵,是否保证滤波的长期稳定性；2)模型误差矩阵Q的选取对滤波定轨精度的影响；3)与事后最小二乘批处理相比较,在简化模型下自主定轨的精度．同时给出了相应的结论．     

GPS近实时共视观测资料处理算法研究

GPS共视资料的高精度快速处理可实现近实时共视时间传递，常见的平滑方法不能满足近实时共视的要求。分析GPS共视资料特点，设计一种卡尔曼滤波算法，对共视资料进行近实时处理，以便削弱观测噪声，估计异地钟差，对相距2000多公里的中国科学院国家授时中心(NTSC)与日本通信综合研究所(CRL)，和相距1000多公里的CRL与韩国计量科学研究院(KRIS)的共视观测资料处理结果表明：卡尔曼滤波算法所得钟差与根据BIPMT公报所得钟差的均方根误差分别优于2．9ns和2．6ns，为进一步提高比对精度，最后对近实时共视应用于多站点间相互比对的情况，提出在卡尔曼滤波算法基础上使用间接观测平差处理技术，根据共视网络中站点间距离设置观测权值，通过解矛盾方程组得到两站钟差，以NTSC、CRL和KRIS3站比对为例，以BIPMT公报得到的钟差为标准，对间接观测平差处理前后的数据比较表明，近实时比对精度可进一步提高。