导航卫星原子钟时频特性分析理论与方法研究
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摘要
在卫星导航定位中，精确位置测量实际上是精确时间的测量。原子钟作为导航系统测距的星上时间基准，是卫星导航系统有效载荷的核心部分，其性能直接决定用户的导航定位精度。因此，对导航卫星原子钟时频特性进行分析具有重要意义。本文主要研究了导航卫星原子钟时频特性分析的理论与方法，主要内容和创新点概括如下：
1、分析了原子钟数据特征，主要包括系统性变化和随机性变化两部分。其系统性变化可用时差、频差和频漂以及周期变化分量来表示，而随机性变化可用七种独立的能量谱噪声来描述，并分析了这几种噪声的产生机制及其时频域特性。在分析原子钟数据特征的基础上，总结了原子频标时频特性主要技术参数的测试分析方法。
2、针对原子钟数据预处理，指出了数据绘图表示的重要性，给出了粗差探测方法，特别强调剔除粗差前要结合原子钟运行条件进行分析，断定异常点是粗差还是频标噪声。给出了相位跳变、频率跳变以及数据间断处理方法，详细分析了不同噪声情况下的频差、频漂估计方法。
3、对实验室真空状态三台Rb钟约60天的频率数据以及GPS Rb钟和Cs钟651天的五分钟精密钟差数据进行了预处理，结果表明：真空状态Rb钟的日漂移率和频率偏差比GPS Block IIR Rb钟约低两个数量级，此外，所有钟还受到明显的周期变化影响。
4、对原子钟时域频率稳定性分析方法进行了系统研究。详细分析了时域频率稳定性分析的各种方差，重点研究了其等效自由度，得出一些有意义的结论：重叠估计和相应的总方法估计对高频噪声等效自由度的提高优于低频噪声，而非重叠估计与之相反。从频域角度揭示了时域频率稳定性分析方法的本质，推导了各种方差的传递函数，并在此基础上分析了各种方差与能量谱噪声的关系，进一步明确各种方差的适用范围。提出了一种分段拟合的噪声水平估计方法。
5、对原子钟频域稳定性分析方法进行了系统研究。比较分析了几种常用的功率谱密度模型，提出了能量谱分析法，该方法能明确地确定原子钟受周期性环境因素影响情况。推导了时频域稳定性分析的严格转换公式，给出由时域稳定性分析计算噪声水平系数的精确公式。
6、重点研究了影响时域稳定性的主要因素，给出了相应的改正方法，并用模拟数据验证了方法的有效性。这主要包括能量谱噪声、频率漂移、相位跳变和频率峰值、无数据段、测量分辨率噪声、周期性环境因素影响以及能量渗漏误差和截断误差等。
7、对实验室真空状态的三台Rb钟和GPS Rb钟、Cs钟进行了时频域稳定性分析，结果表明：所有钟都受到明显的周期变化影响，但不同类型原子钟对环境变化敏感程度不同；Rb钟都有明显的频漂，且受到甚低频噪声影响，Block IIR Rb钟还受到测量噪声引起的调相噪声影响；Rb钟应采用哈达玛系列方差分析其频率稳定性，Cs钟应采用阿仑系列方
Measuring of precise distances and positions is really measuring of precise time in a satellite navigation system. The atomic clock is the on-board time datum for measuring the distance in satellite navigation. And it is also one of the key navigation payloads of the satellite navigation system. The performance of the on-board clock affects the navigation and position directly. Therefore, It is very important to study the time and frequency characterization of the on-board atomic clocks. This dissertation mainly focuses on the analysis theories and algorithms of the time and frequency characterization for the atomic clocks of navigation satellites. The main works and contributions are summarized as follows:
1. It is shown that the time deviation (or time error) and frequency-offset of atomic clock can be modeled by a deterministic part and a random part by analyzing its data. The deterministic part is quantified by the addition of a constant time offset, constant frequency offset, constant linear frequency drift and periodic components induced by environmental changes. The random part is characterized by seven independent power-law noises whose characterizations and noise mechanisms are also analyzed. Furthermore, the methods of testing and evaluating the time and frequency characterization of frequency standards are summarized and analyzed.
2. Data plotting is one of the most important steps in preprocessing the measurement data for atomic clocks. A simple and effective technique for recognizing and removing outliers is presented. It is important to explain all outliers with the help of running environment of the frequency standard, thereby determining whether they are noise or the abnormal data caused by measurement process. Methods for dealing with phase steps, frequency steps and gaps are also developed. Additionally, the frequency offset and frequency drift are estimated and compared in the case of different kinds of noises.
3. The data series of 6-months frequency offsets of three Rb clocks in the vacuum sampled with 100-seconds and the 651-day time errors of GPS Rb clocks and Cs clocks sampled with 5-minutes are processed. It is shown that the daily frequency drifts and the frequency offsets of the Rb clocks in the vacuum are more than 2 orders in magnitude than those of GPS Block IIR Rb clocks and all clocks are obviously affected by the periodic components.
4. The methods for time-domain stability analysis of atomic clocks are discussed and their equivalent degrees of freedom (EDF) are studied in detail. The interesting results show that the improvement on the EDF of high frequency noise is more than that of low frequency noise for the overlapped estimators and the total estimators of stability variances, but the inverse
1、分析了原子钟数据特征，主要包括系统性变化和随机性变化两部分。其系统性变化可用时差、频差和频漂以及周期变化分量来表示，而随机性变化可用七种独立的能量谱噪声来描述，并分析了这几种噪声的产生机制及其时频域特性。在分析原子钟数据特征的基础上，总结了原子频标时频特性主要技术参数的测试分析方法。
2、针对原子钟数据预处理，指出了数据绘图表示的重要性，给出了粗差探测方法，特别强调剔除粗差前要结合原子钟运行条件进行分析，断定异常点是粗差还是频标噪声。给出了相位跳变、频率跳变以及数据间断处理方法，详细分析了不同噪声情况下的频差、频漂估计方法。
3、对实验室真空状态三台Rb钟约60天的频率数据以及GPS Rb钟和Cs钟651天的五分钟精密钟差数据进行了预处理，结果表明：真空状态Rb钟的日漂移率和频率偏差比GPS Block IIR Rb钟约低两个数量级，此外，所有钟还受到明显的周期变化影响。
4、对原子钟时域频率稳定性分析方法进行了系统研究。详细分析了时域频率稳定性分析的各种方差，重点研究了其等效自由度，得出一些有意义的结论：重叠估计和相应的总方法估计对高频噪声等效自由度的提高优于低频噪声，而非重叠估计与之相反。从频域角度揭示了时域频率稳定性分析方法的本质，推导了各种方差的传递函数，并在此基础上分析了各种方差与能量谱噪声的关系，进一步明确各种方差的适用范围。提出了一种分段拟合的噪声水平估计方法。
5、对原子钟频域稳定性分析方法进行了系统研究。比较分析了几种常用的功率谱密度模型，提出了能量谱分析法，该方法能明确地确定原子钟受周期性环境因素影响情况。推导了时频域稳定性分析的严格转换公式，给出由时域稳定性分析计算噪声水平系数的精确公式。
6、重点研究了影响时域稳定性的主要因素，给出了相应的改正方法，并用模拟数据验证了方法的有效性。这主要包括能量谱噪声、频率漂移、相位跳变和频率峰值、无数据段、测量分辨率噪声、周期性环境因素影响以及能量渗漏误差和截断误差等。
7、对实验室真空状态的三台Rb钟和GPS Rb钟、Cs钟进行了时频域稳定性分析，结果表明：所有钟都受到明显的周期变化影响，但不同类型原子钟对环境变化敏感程度不同；Rb钟都有明显的频漂，且受到甚低频噪声影响，Block IIR Rb钟还受到测量噪声引起的调相噪声影响；Rb钟应采用哈达玛系列方差分析其频率稳定性，Cs钟应采用阿仑系列方
Measuring of precise distances and positions is really measuring of precise time in a satellite navigation system. The atomic clock is the on-board time datum for measuring the distance in satellite navigation. And it is also one of the key navigation payloads of the satellite navigation system. The performance of the on-board clock affects the navigation and position directly. Therefore, It is very important to study the time and frequency characterization of the on-board atomic clocks. This dissertation mainly focuses on the analysis theories and algorithms of the time and frequency characterization for the atomic clocks of navigation satellites. The main works and contributions are summarized as follows:
1. It is shown that the time deviation (or time error) and frequency-offset of atomic clock can be modeled by a deterministic part and a random part by analyzing its data. The deterministic part is quantified by the addition of a constant time offset, constant frequency offset, constant linear frequency drift and periodic components induced by environmental changes. The random part is characterized by seven independent power-law noises whose characterizations and noise mechanisms are also analyzed. Furthermore, the methods of testing and evaluating the time and frequency characterization of frequency standards are summarized and analyzed.
2. Data plotting is one of the most important steps in preprocessing the measurement data for atomic clocks. A simple and effective technique for recognizing and removing outliers is presented. It is important to explain all outliers with the help of running environment of the frequency standard, thereby determining whether they are noise or the abnormal data caused by measurement process. Methods for dealing with phase steps, frequency steps and gaps are also developed. Additionally, the frequency offset and frequency drift are estimated and compared in the case of different kinds of noises.
3. The data series of 6-months frequency offsets of three Rb clocks in the vacuum sampled with 100-seconds and the 651-day time errors of GPS Rb clocks and Cs clocks sampled with 5-minutes are processed. It is shown that the daily frequency drifts and the frequency offsets of the Rb clocks in the vacuum are more than 2 orders in magnitude than those of GPS Block IIR Rb clocks and all clocks are obviously affected by the periodic components.
4. The methods for time-domain stability analysis of atomic clocks are discussed and their equivalent degrees of freedom (EDF) are studied in detail. The interesting results show that the improvement on the EDF of high frequency noise is more than that of low frequency noise for the overlapped estimators and the total estimators of stability variances, but the inverse
引文
1．陈俊勇．GPS现代化和Galileo运行准备的进展．测绘通报，2005(3)．
2．丁月蓉，郑大伟．天文测量数据的处理方法．南京大学出版社，1990．
3．高星伟．全球导航卫星系统(GLONASS)．测绘通报，2001(3)．
4．高玉平，GPS导航电文中时间参数的变化特点．陕西天文台台刊，2001(2)．
5．过静珺，卢建刚，吴为峰，曾润国．欧洲伽利略导航系统的发展．测绘通报，2002(2)．
6．何海波．高精度GPS动态测量及质量控制．解放军信息工程大学博士论文．2002．
7．管仲成，狄青叶，于洪喜，空间用原子频率标准．空间电子技术，1999(4)．
8．郭春梅，频率稳定度时域表征的测量不确定度．实用测试技术，2000(5)．
9．郭海荣，焦文海．地心运动对大地坐标的影响及其抗差谱分析．解放军测绘研究所学报，2002(3)．
10．郭海荣，杨元喜，焦文海．地心运动时间序列的抗差谱分析．测绘学报，2003(4)．
11．郭海荣，杨生，杨元喜，何海波，基于卫星双向时间频率传递进行钟差预报的几种方法．武汉大学学报信息科学版．
12．韩春好．相对论框架中的时间计量．天文学进展，2002(2)．
13．胡锦伦，共视法和综合法的GPS时间同步精度分析．中国科学院上海天文台台刊，2000(21)．
14．胡锦伦，氢钟守时应用．中国科学院上海天文台台刊，2000(21)．
15．胡锦伦，李树洲，李大志，国际原子时进展中的原子钟．宇航计测技术，2002(5)．
16．季善标，朱文耀，熊永清，精密GPS卫星钟差的改正和应用．空间科学学报，2001(1)．
17．柯熙政，原子钟噪声的时—频尺度分析及算法研究．中国科学院陕西天文台博士学位论文，1996．
18．李孝辉，张慧君，边玉敬，一种频率源噪声频谱拟合方法的研究．陕西天文台台刊，2002(2)．
19．李孝辉，边玉敬，用状态空间模型递推模拟振荡器噪声．时间频率学报，2003(1)．
20．刘利．相对论时间比对理论与高精度时间同步技术．解放军信息工程大学，2004．
21．刘利．GPS卫星钟噪声类型分析．全球定位系统，2005(2)．
22．刘铁新，原子频标发展的最新动向—第55届国际频率控制年会有关情况简介．天文学进展，2001(4)．
23．刘宇红，张立新，邓晓慧，原子频标与卫星导航定位系统．空间电子技术，1999(4)．
24．帅平，导航星座的自主导航技术—卫星自主时间同步．飞行器测控学报，2004(4)．
25．卫国，原子钟噪声模型分析与原子时算法的数学原理．中国科学院陕西天文台博士学位论文．1991．
26．卫国，原子钟相位与频率估计的误差特性．计量学报，1995(3)．
27．时间统一技术．国防工业出版社．2004．
28．王庆华，翟造成，原子钟和空间实验．宇航计测技术，1998(3)．
29．王淑芳，王礼亮．卫星导航定位系统时间同步技术．全球定位系统，2005(2)．
30．王万斌译．欧洲全球导航卫星系统(GNSS-2)比较研究(四)—轨道测定与时间同步协定．中国空间技术研究院，2002．
31．吴晓进等译．GPS理论与应用，第1卷(下)．西安导航技术研究所，1999．
32．徐进军，付孙钟．频谱分析在周期拟合中的应用．测绘信息与工程，2001．3：20～22．
33．许其凤．空间大地测量学—卫星导航与精密定位．解放军出版社，2001．
34．许其凤．区域卫星导航系统的卫星星座．测绘工程，2001(1)．
35．徐士良，C常用算法程序集．清华大学出版社，1996．
36．徐月青，姜东伟．两种方差在铷原子频标长稳测量中的比较分析．宇航计测技术，2004(1)．
37．杨廷高，仲崇霞，脉冲星稳定度及可能应用．时间频率学报，2004(2)．
38．杨元喜，抗差估计理论及其应用(专著)，八一出版社出版，1993，北京．
39．杨元喜，相关观测抗差估计，抗差估计论文集，测绘出版社，1992，14-21。
40．仲崇霞，杨廷高，脉冲星时间稳定度的估计方法．时间频率学报，2006(1)．
41．周宇昌，李孝强，下一代导航星—GPS IIF．空间电子技术，2002(1)．
42．张慧君，李孝辉，边玉敬．用总方差进行频率稳定度的估计．时间频率学报，2003(1)．
43．庄楚强，吴亚森．应用数理统计基础，华南理工大学出版社，2000．
44. Allan D. W., Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. UFFC-34, No. 6, 1987.
45. Allan D. W. and Barnes J. A., A modified "Allan Variance" with increased oscillator characterization ability. In Proceedings of the 35th IEEE Frequency Control Symposium, 1981.
46. Allan D. W., Hellwig H., and et al., Standard terminology for fundamental frequency and time metrology. In Proceedings of the 42th IEEE Frequency Control Symposium, 1988.
47. Allan D. W. and Weiss M. A., The variance of predictability of Hydrogen masters and primary Cesium standards in support of a real time prediction of UTC. Contribution of the US Government, not subject to copyright, 1994.
48. Allan D. W., Weiss M. A. and Jespersen J. L., A frequency-domain view of time-domain characterization of clocks and time and frequency distribution systems. In Proceedings of the 45th IEEE Frequency Control Symposium, pages 667-678, May 1991.
49. Ascarrunz F. G., Jefferts S. R., Parker T. E., Environmental Effects on Errors in Two-Way Time and Frequency Transfer. IEEE CPEM 1996 Conf. Dig, 1996, 518-519.
50. Ascarrunz F. G, Jefferts S. R, Parker T. E, Earth Station Errors in Two-Way Time and Frequency Transfer. IEEE T. Instrum. Meas, 1997,46: 205-208.
51. Ascarrunz F. G, Jefferts S. R, Parker T. E., A Delay Calibration System for Two-Way Time and Frequency Transfer. IEEE Intl. Freq. Cont. Symp, 1998,250-253.
52. Audoin C. and Guinot B., The measurement of time - time, frequency and the atomic clock. Cambridge University Press, 2001.
53. Azoubib J. Nawrocki J. and Lewandowski W., Independent atomic timescale in Poland-organization and results. Metrologia 40: 245-248,2003.
54. Barnes J. A, The measurement of linear frequency drift in oscillators. In Proceedings of the 15th Annual Precise Time and Time Interval (PTTI) Meeting, 1983.
55. Barnes J. A. and Allan D. W, Variances based on data with dead time between the measurements. NIST Technical Note 1318, 1990.
56. Barnes J. A, Chi A. R. and et al. Characterization of frequency stability. IEEE Transactions on Instrumentation and Measurement, 1971.
57. Baugh R.A, "Frequency Modulation Analysis with the Hadamard Variance", Proc. 25th Frequency Control Symposium, April 1971, pp. 222-225.
58. Beard R, Buisson J, and et. al, GPS block IIR Rubidium frequency standard life test results. 2002 IEEE International Frequency Control Symposium and PDA Exhibition, 2002.
59. Bernier L. G, Metrology of clocks & timescales. METAS 2002.
60. Bernier L. G, Application of the GSF-1 algorithm to the near-optimal timescale prediction of the hydrogen master. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
61. Block M, Mancini O. and McClelland T, Performance of Rubidium and Quartz clocks in space. 2002 IEEE International Frequency Control Symposium and PDA Exhibition, 2002.
62. Bourga C, Lobert B. and Brunet M, Experiment assessment of Galileo clocks performance in space. ION GPS 2002.
63. Breakiron L. A, A Kalman filter for atomic clocks and timescales. In Proceedings of the 33th Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
64. Breakiron L. A, Kalman filter characterization of cesium clocks and hydrogen masters. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
65. Bregni S. Generation of Pseudo-Random Power-Law Noise Sequences by Spectral Shaping. http://www.elet.polimi.it/～bregni. 2001.
66. Broderbauer V. and Weber R, Results of modeling GPS satellite clocks. 2003.
67. Busca G, Frelechoz C. and et al. Space Clocks for Navigation Satellites. Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 2003a.
68. Busca G and Wang Q., Time prediction accuracy for a space clock. Metrologia 40: 265-269, 2003b.
69. Carrillo F. J. M., Sanchez A. A. and Alonso L. B., Hybrid synthesizers in space Galileo's CMCU, 1999.
70. CCIR, Characterization of frequency and phase noise. Report 580 of the CCIR, 1986.
71. Coffer J. G and Camparo J. C, Long-term stability of a rubidium atomic clock in geosynchronous orbit. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
72. Crater D. T. and Mobbs H. S., The Impact of Operating GPS with More Rubidium frequency standards. ION GPS 1998.
73. Davis J. A., Harris P. M. and et al., Least-squares analysis of two-way satellite time and frequency transfer measurements. In Proceedings of the 33th Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
74. Davis J. A., Greenhall C. A. and Stacey P. W., A Kalman filter clock algorithm for use in the presence of flicker frequency modulation noise. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
75. DeYoung J. A., Discrete simulated power law data in the time-domain using the Kasdin and Water (1992). http://tycho.usno.naw.mil/powerlaw.html.
76. Delporte J., Vernotte F., Brunet M. and Tournier T., Modelization and extrapolation of time deviation of USO and atomic clocks in GNSS-2 context. In Proceedings of the 32th Annual Precise Time and Time Interval (PTTI) Meeting, 2000.
77. Delporte J, Vernotte F, Tournier T and Brunet M, Modelisation and extrapolation of time deviation: Application to the estimation of the datation stability of a navigation payload. 15th European Frequency and Time Forum, 2001.
78. Doug's Atomic Clocks, Doug Hogarth's Home Page.
79. Dow J. M., Summary of Galileo technical status. Hessischer Informationstag zu Galileo- Anwendungen 30.8.2004
80. Emery W. J., Thomson R. E.. Data analysis methods in physical oceanograph. PERGAMON, 1997: 391—395.
81. Epstein M. and Dass T., Management of phase and frequency for GPS IIR satellites. In Proceedings of the 33th Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
82. Epstein M., Freed G and Rajan J., GPS IIR Rubidium clocks: in-orbit performance aspects. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
83. Ferre-Pikal E. S., Vig J. R., Camparo J. C. and et al., Draft revision of IEEE STD 1139-1988 Standard definitions of physical quantities for fundamental frequency and time metrology -random instabilities. 1997 IEEE International Frequency Control Symposium, 1997.
84. Galindo F. J. and Palacio J., Post-processing ROA data clocks for optimal stability in the ensemble timescale. Metrologia 40: 237-244, 2003.
85. Galleani L., Sacerdote L., Tavella P. and Zucca C., A mathematical model for the atomic clock error. Metrologia 40: 257-264, 2003.
86. Galleani L. and Tavella P., Instantaneous spectrum of clock errors. Metrologia 40: 319-325, 2003.
87. Galleani L. and Tavella P., On the use of the Kalman filter in timescales. Metrologia 40: 326-334,2003.
88. Greenhall C. A., Removal of drift from frequency stability measurements. TDA progress report 42-65,1981.
89. Greenhall C. A., Frequency stability review. TDA progress report 42-88,1983.
90. Greenhall C. A., Estimating the modified Allan variance. 1995 IEEE International Frequency Control Symposium, 1995.
91. Greenhall C. A., Does Allan variance determine the spectrum? 1997 IEEE International Frequency Control Symposium, 1997.
92. Greenhall C. A., Forming stable timescales from the Jones-Tryon Kalman filter. Metrologia 40(2003)S335-341,2003.
93. Greenhall C. A., Howe D. A. and Percival D. B., Total variance, an estimator of long-term frequency stability. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 46, No. 5, September 1999.
94. Greenhall C. A. and Riley W. J., Uncertainty of Stability Variances based on finite differences. Hamilton Technical Services, In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
95. Grewal M. S., Brown W., Lucy R. and Hsu P., Geo Uplink Subsystem (GUS) clock steering algorithms performance and validation results. ION GPS 1999.
96. Hahn J. H., Graglia G. and et al., Timekeeping for GalileoSat. ION GPS 2000.
97. Hansen A., Walter T. and Enge P., GPS Satellite Clock Event on SVN 27 and its impact on augmented navigation systems. ION GPS 1998.
98. Harris P. M., Davis J. A., Cox M. G. and Schemar S. L., Least-squares analysis of time series data and its application to two-way satellite time and frequency transfer measurements. Metrologia 40: 342-347, 2003.
99. Hein G. W. and Eissfeller B., Galileo design options for the European GNSS-2. ION GPS 2001.
100.Howe D. A., Measurements, Modeling and Time-error prediction. PPT
101.Howe D. A., Frequency stability cookbook: frequency noise measurements and their measurement in oscillators. 2000a.
102.Howe D. A., The Total Deviation Approach to Long-Term Characterization of Frequency Stability. IEEE Trans. Ultrasonics,... 2000b.
103.Howe D. A., Interpreting oscillatory frequency stability plots. 2002 IEEE International Frequency Control Symposium and PDA Exhibition.
104.Howe D. A., Allan D. W. and Barnes J. A., Properties of signal sources and measurement methods. Proceedings of the 35th Annual Symposium on Frequency Control, 1981.
105.Howe D., Beard R. and et al., A Total estimator of the Hadamard function used for GPS operations. Proc. 32nd Annual PTTI Systems and Applications Meeting, 2000c, 28 (30): 255-268.
106.Howe D., Beard R. and et al., Total Hadamard variance: application to clock steering by Kalman filtering. 2001a.
107.Howe D., Beard R. and et al., Enhancements to GPS operations and clock evaluations using a "Total" Hadamard deviation. IEEE transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 52, No. 8, August 2005.
108.Howe D. A. and Greenhall C. A., Total variance: a progress report on a new frequency stability characterization, In Proceedings of the 29th Annual Precise Time and Time Interval (PTTI) Meeting, 1997.
109.Howe D. A. and Lainson K. J., Simulation study using a new type of sample variance. Proc. 27st Annual PTTI Systems and Applications Meeting, 1995.
110.Howe D. A. and Peppier T. K., Definitions of "total " estimators of common time-domain variances. 2001 IEEE International Frequency Control Symposium and PDA Exhibition, 2001b.
111 .Howe D. A. and Vernotte F., Generalization of the total variance approach to the modified Allan variance. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
112.Hutsell S. T, Relating the Hadamard variance to MCS Kalman filter clock estimation, in Proc. 27th Annu. PTTI Syst. Applications Meeting, San Diego, CA, Nov. 29 - Dec. 1, 1995, pp. 291-301.
113.Hutsell S.T., Reid W. G. and et al., "Operational Use of the Hamamard Variance in GPS", Proc. 28th PTTI Meeting, pp. 201-213, December 1996.
114.Jeanmaire A., Rochat P. and et al., Rubidium atomic clock for Galileo. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
115.Jespersen J., Introduction to the time domain characterization of frequency standards. In Proceedings of the 23th Annual Precise Time and Time Interval (PTTI) Meeting, 1991.
116.Jong G. and Kroon E., Analysis of one year of GPS and two-way time transfer results between PTB, NPL, and VSL. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002a.
117.Jong G. and Kroon E., Analysis of one year of zero-baseline GPS common-view time transferr and direct measurement using two co-located clocks. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002b.
118.Kasdin N. J. and Walter T., Discrete simulation of power law noise. 1992 IEEE Frequency Control Symposium, 1992.
119.Lance A. L., Seal W. D. and Labaar F., Phase Noise and AM Noise Measurements in the Frequency Domain. Infrared and Millimeter Waves, Vol. II, 1984.
120.Lesage P. and Audoin C., Characterization and measurement of time and frequency stability. Radio Science, 1979.
121.Lesage P. and Ayi T., Characterization of frequency stability: Analysis of the modified allan variance and properties of its estimate. IEEE Transactions on Instrumentation and Measurement, 1984.
122.Levine J. Introduction to time and frequency metrology. Review of Scientific instruments, 1999(6).
123.Li M., Peng H. and Liao C., MTIE and TDEV analysis of unevenly spaced time series data and its application to telecommunications synchronization measurements. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
124.Manning D. M., NGA GPS monitor station high-performance Cesium frequency standard stability: from NGA kalman filter clock estimators. In Proceedings of the 37th Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
125.Matsakis D., Miranian M. and Koppang P., Steering the U.S. Naval Observatory (USNO) Master clock. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
126.Mattioni L., Belloni M. and et al., The development of a passive hydrogen master clock for the Galileo navigation system. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
127.McCaskill T. B., Reid W.G., Buisson J. A. and Warren H. E., Analysis of the frequency stability of on-orbit GPS Navstar clocks. 1993 IEEE International Frequency Control Symposium, 1993.
128.McCaskill T. B., Analysis of the frequency stability history of GPS Navstar clocks. 1997 IEEE International Frequency Control Symposium, 1997.
129.McCaskill T. B., Oaks O. J. and Largay M. M., Performance of global Positioning System Block II/IIA/IIR on-orbit Navstar clocks. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
130.Merino M. M. R., Garcia A. M. and Medel C. H., GSTB-V1: The First Step Towards the development of Galileo navigation algorithms, www.gmv.com. 2004.
131.Moudrak A., Bruyninx C. and et al., Determination of GPS-Galileo Time Offset to support system interoperability. GNSS04.
132.Nuth V., Feess W. A. and Wu C., An evaluation of various space clocks for GPS IIF. In Proceedings of the 33~(rd) Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
133.Oaks J., McCaskill T. B. and Largay M. M., Performance of global Positioning System Block II/IIA/IIR on-orbit Navstar clocks. In Proceedings of the 33~(rd) Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
134.Oaks J., Largay M. M. and et al., Comparative analysis of clock performance using both code-phase and carrier-derived pseudorange observations. In Proceedings of the 36th Annual Precise Time and Time Interval (PTTI) Meeting, 2004.
135.Oaks J., Senior K. and Largay M. M., Global positioning system constellation clock performance. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
136.Oaks J., Senior K. and et al., NRL analysis of GPS on-orbit clocks. In Proceedings of the 37th Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
137.Parker T. E. and Zhang V. S., Investigation of instabilities in two-way time transfer. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
138.Percival D. B., Stochastic models and statistical analysis for clock noise. Metrologia 40: 289-304, 2003.
139.Petit G., Towards an optimal weighting scheme for TAI computation. Metrologia 40: 252-256, 2003.
140.Petzinger J., Reith R. and Dass T., Enhancements to the GPS Block IIR timekeeping system. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
141.Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P., Numerical Recipes in C : The Art of Scientific Computing, Second edition. Cambridge University Press, 1992.
142.Ray J. and Senior K., IGS/BIPM pilot project: GPS carrier phase for time/frequency transfer and timescale formation. Metrologia 40: 270-288, 2003.
143.Reid W., Mccaskill T., Largay M., Oaks O. J. and Buisson J, Performance of GPS Block IIR Rubidium clocks. ION GPS 2000, 19-22 September 2000, Salt Lake City, UT.
144.Riley W. J., Application of the 3-cornered hat method to the analysis of frequency stability. Hamilton Technical Services, 2003 a.
145.Riley°W. J., A test suite for the calculation of time domain frequency stability. 1995 IEEE Frequency Control Symposium, 1995.
146.Riley W. J., Confidence Intervals and Bias Corrections for the stable32 variance functions. Hamilton Technical Services, 2003b.
147.Riley W. J., Gaps, outliers, dead time, and uneven spacing in frequency stability data. Hamilton Technical Services, 2003e.
148.Riley W. J., Methodologies for time domain frequency stability measurement and analysis. Hamilton Technical Services, 2002a.
149.Riley W. J., The calculation of time domain frequency stability. Hamilton Technical Services, 2002b.
150.Riley W. J., The Hadamard variance. Hamilton Technical Services, 2002c.
151.Riley W. J., Techniques for frequency stability analysis. IEEE International Frequency Control Symposium, Tampa, FL, May 4, 2003c.
152.Riley W. J., Use of the Autocorrelation Function for frequency stability analysis. Hamilton Technical Services, 2003 d.
153.Riley W. J., The basics of frequency stability analysis. Hamilton Technical Services, 2004a.
154.Riley W. J. and Greenhall C. A., Power law noise identification using the lag 1 autocorrelation. The 18th European Frequency and Time Forum, University of Surrey, Guildford, UK. 5-7 April 2004b.
155.Rochat P, Droz F. and et al., The onboard Galileo Rubidium and Passive Maser, status and performance. Frequency Control Symposium and Exposition, 2005.
156.Rutman J., Oscillator Specification: A review of Classical and New Ideas, Proc. 31st Frequency Control Symposium, June 1977, pp. 291-301.
157.Schmidt L. S., Atomic clock models using fractionally integrated noise processes. Metrologia 40: 305-311, 2003.
158.Senior K., Beard R. and White J., CANVAS: Clock Analysis, Visualization, and Archiving System - A new software package for the efficient management of clock oscillator data. In Proceedings of the 37th Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
159.Shmaliy Yu. S., Ibarra-Manzano O. and Arceo-Miquel L., A Numerical Comparison of the Unbiased FIR and Kalman filters in applications to GPS-based timekeeping. In Proceedings of the 37st Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
160.Shmaliy Yu. S., Marienko A. V. and Savchuk A. V, GPS-based optimal Kalman estimation of time error, frequency offset and aging. In Proceedings of the 31st Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
161. Stein S. R., Frequency and time - their measurement and characterization. Precision Frequency Control, Volume 2, Chapter 12, 1985.
162.Stein S. R., Kalman filter analysis of precision clocks with real-time parameter estimation. 43~(rd) Annual Frequency Control Symposium, 1989.
163.Stein S. R. and Evans J., The application of Kalman filters and ARIMA models to the study of time prediction errors of clocks for use in the defence communication system (DCS). 44th Annual Frequency Control Symposium, 1990.
164.Stein S. R. and Filler R. L., Kalman filter analysis for real time applications of clocks and oscillators. 42~(nd) Annual Frequency Control Symposium, 1988.
165.Su W. and Filler R. L., Application of Kalman filtering techniques to the precision clock with non-constant aging. 1992 IEEE Frequency Control Symposium, 1992.
166.Su W. and Filler R. L., A new approach to clock modeling and Kalman filter time and frequency prediction. 1993 IEEE Frequency Control Symposium, 1993.
167.User manual - Stable32 frequency stability analysis. Hamilton Technical Services, 2005.
168.Vernotte F., Estimation of uncertainty in time error estimation. In Proceedings of the 31st Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
169.Vernotte F., Application of the Moment Condition to Noise simulation and to stability analysis. IEEE TRANS. ON UFFC, 2002.
170.Vernotte F., Incertitude Sur Les Coefficients D'interpolation Lineaire ET Les residus. Private Communication, 2006.
171.Vernotte F., Delporte J., Brunet M. and Tournier T., Uncertainties of drift coefficients and extrapolation errors: application to clock error prediction. Metrologia, vol.38, no.4 , 2001.
172.Vernotte F., Lantz E., Groslambert J. and Gagnepain J. J., A new multi-variance method for the oscillator noise analysis. 1992 IEEE Frequency Control Symposium, 1992.
173.Vernotte F., Zalamansky G. and Lantz E., Time stability characterization and spectral aliasing, Part I: a time-domain approach. Metrologia, 1998a, 35, 723-730.
174.Vernotte F., Zalamansky G. and Lantz E., Time stability characterization and spectral aliasing, Part I: a frequency-domain approach. Metrologia, 1998b, 35, 731-738.
175. Vig J. R., Quartz Crystal Resonators and Oscillators For Frequency Control and Timing Applications - A Tutorial. U.S. Army Communications-Electronics Command, Attn: AMSEL-RD-C2-PT, Fort Monmouth, NJ 07703, USA, 2000.
177. Walls F. L., Percival D. B. and Irelan W. R., Biases and variances of several FFT spectral estimators as a function of noise type and number of samples. In Proceedings of the 43th IEEE Frequency Control Symposium, 1989.
178. Weiss M. A., Allan D. W. and Howe D. A., Confidence on the second difference estimation of frequency drift - A study based on simulation. 1992 IEEE Frequency Control Symposium, 1992.
179.Weiss M. A. and Howe D. A., Total TDEV. 1998 IEEE International Frequency Control Symposium, 1998.
180.Weiss M. A., Time domain representation of oscillator performance. 27th Annual time and frequency metrology seminar, 2002.
181.Winkler G. M. R., Introduction to robust statistics and data filtering. Hamilton Technical Services, 1998.
182.Yang Y., Robust estimation for dependent observations, Manuscripta geodaetica, 1994 (19): 10-17.
183.Yang Y., Estimators of covariance matrix at robust estimation based on influence functions. Zeitschrift fuer Vermessungswesen. 122. Heft 4,1997: 166～174.
184.Yang Y. Some Numerical Prediction Methods for the Wind Speed in the Sea Based on ERS-1 Scatterometer Wind Data [J]. Survey Review, 2001, (36): 121-131.
185.Yang Y., Robust Estimation of Geodetic Datum Transformation [J]. Journal of Geodesy, 1999a (73): 268-264.
186.Yang Y. An optimal adaptive Kalman filtering, Journal of Geodesy, 2006, 80: 177-183.
187.Yang Y., Cheng M.K., Shum C.K., Tapley B.D.., Robust estimation of systematic errors of satellite laser range, Journal of Geodesy, 1999(73):345-349.
188.Yang Y, Cui X and Gao W. Adaptive integrated navigation for multi-sensor adjustment outputs. The Journal of Navigation, 2004, 57(2): 287-285.
189.Yang Y and Gao W. Comparison of adaptive factors in Kalman filters on navigation results, The Journal of Navigation, 2005, 58(3):471-478.
190.Yang Y and Gao W, A new learning statistic for adaptive filter based on predicted residuals. Progress in Natural Science, 2006,16(8): 833-837.
191.Yang Y, He H and Xu G. Adaptively robust filtering for kinematic geodetic positioning, Journal of Geodesy, 2001b, 75(2/3): 109-116.
192.Yang Y, Song L and Xu T. Robust estimator for correlated observations based on bifactor equivalent weights, Journal of Geodesy. 2002, 76(6-7), 353-358.
193.Yang Y., Tang Y., Li Q and Zou Y. Experiments of adaptive filters for kinematic GPS positioning applied in road information updating in GIS, International Symposium on Inertial Navigation Technology and Intelligent Traffic, Nanjing, China, 2004b.
194.Yang Y and Wen Y. Synthetically adaptive robust filtering for satellite orbit determination, Science in China, Series D, 2004, Vol. 47, No. 7, 585-592.
195.Yang Y, Xu T and He H. On adaptively kinematic filtering, Selected Papers for English of Acta Geodetica et Cartographica Sinica, 2001, 25-32.
196.Yang Y and Xu T. An adaptive Kalman filter based on Sage windowing weights and variance components, The Journal of Navigation, 2003, 56(2), 231-240.
197.Yang Y and Zhang S. Adaptive fitting for systematic errors in navigation, Journal of Geodesy, 2005, 79: 43-49.
2．丁月蓉，郑大伟．天文测量数据的处理方法．南京大学出版社，1990．
3．高星伟．全球导航卫星系统(GLONASS)．测绘通报，2001(3)．
4．高玉平，GPS导航电文中时间参数的变化特点．陕西天文台台刊，2001(2)．
5．过静珺，卢建刚，吴为峰，曾润国．欧洲伽利略导航系统的发展．测绘通报，2002(2)．
6．何海波．高精度GPS动态测量及质量控制．解放军信息工程大学博士论文．2002．
7．管仲成，狄青叶，于洪喜，空间用原子频率标准．空间电子技术，1999(4)．
8．郭春梅，频率稳定度时域表征的测量不确定度．实用测试技术，2000(5)．
9．郭海荣，焦文海．地心运动对大地坐标的影响及其抗差谱分析．解放军测绘研究所学报，2002(3)．
10．郭海荣，杨元喜，焦文海．地心运动时间序列的抗差谱分析．测绘学报，2003(4)．
11．郭海荣，杨生，杨元喜，何海波，基于卫星双向时间频率传递进行钟差预报的几种方法．武汉大学学报信息科学版．
12．韩春好．相对论框架中的时间计量．天文学进展，2002(2)．
13．胡锦伦，共视法和综合法的GPS时间同步精度分析．中国科学院上海天文台台刊，2000(21)．
14．胡锦伦，氢钟守时应用．中国科学院上海天文台台刊，2000(21)．
15．胡锦伦，李树洲，李大志，国际原子时进展中的原子钟．宇航计测技术，2002(5)．
16．季善标，朱文耀，熊永清，精密GPS卫星钟差的改正和应用．空间科学学报，2001(1)．
17．柯熙政，原子钟噪声的时—频尺度分析及算法研究．中国科学院陕西天文台博士学位论文，1996．
18．李孝辉，张慧君，边玉敬，一种频率源噪声频谱拟合方法的研究．陕西天文台台刊，2002(2)．
19．李孝辉，边玉敬，用状态空间模型递推模拟振荡器噪声．时间频率学报，2003(1)．
20．刘利．相对论时间比对理论与高精度时间同步技术．解放军信息工程大学，2004．
21．刘利．GPS卫星钟噪声类型分析．全球定位系统，2005(2)．
22．刘铁新，原子频标发展的最新动向—第55届国际频率控制年会有关情况简介．天文学进展，2001(4)．
23．刘宇红，张立新，邓晓慧，原子频标与卫星导航定位系统．空间电子技术，1999(4)．
24．帅平，导航星座的自主导航技术—卫星自主时间同步．飞行器测控学报，2004(4)．
25．卫国，原子钟噪声模型分析与原子时算法的数学原理．中国科学院陕西天文台博士学位论文．1991．
26．卫国，原子钟相位与频率估计的误差特性．计量学报，1995(3)．
27．时间统一技术．国防工业出版社．2004．
28．王庆华，翟造成，原子钟和空间实验．宇航计测技术，1998(3)．
29．王淑芳，王礼亮．卫星导航定位系统时间同步技术．全球定位系统，2005(2)．
30．王万斌译．欧洲全球导航卫星系统(GNSS-2)比较研究(四)—轨道测定与时间同步协定．中国空间技术研究院，2002．
31．吴晓进等译．GPS理论与应用，第1卷(下)．西安导航技术研究所，1999．
32．徐进军，付孙钟．频谱分析在周期拟合中的应用．测绘信息与工程，2001．3：20～22．
33．许其凤．空间大地测量学—卫星导航与精密定位．解放军出版社，2001．
34．许其凤．区域卫星导航系统的卫星星座．测绘工程，2001(1)．
35．徐士良，C常用算法程序集．清华大学出版社，1996．
36．徐月青，姜东伟．两种方差在铷原子频标长稳测量中的比较分析．宇航计测技术，2004(1)．
37．杨廷高，仲崇霞，脉冲星稳定度及可能应用．时间频率学报，2004(2)．
38．杨元喜，抗差估计理论及其应用(专著)，八一出版社出版，1993，北京．
39．杨元喜，相关观测抗差估计，抗差估计论文集，测绘出版社，1992，14-21。
40．仲崇霞，杨廷高，脉冲星时间稳定度的估计方法．时间频率学报，2006(1)．
41．周宇昌，李孝强，下一代导航星—GPS IIF．空间电子技术，2002(1)．
42．张慧君，李孝辉，边玉敬．用总方差进行频率稳定度的估计．时间频率学报，2003(1)．
43．庄楚强，吴亚森．应用数理统计基础，华南理工大学出版社，2000．
44. Allan D. W., Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. UFFC-34, No. 6, 1987.
45. Allan D. W. and Barnes J. A., A modified "Allan Variance" with increased oscillator characterization ability. In Proceedings of the 35th IEEE Frequency Control Symposium, 1981.
46. Allan D. W., Hellwig H., and et al., Standard terminology for fundamental frequency and time metrology. In Proceedings of the 42th IEEE Frequency Control Symposium, 1988.
47. Allan D. W. and Weiss M. A., The variance of predictability of Hydrogen masters and primary Cesium standards in support of a real time prediction of UTC. Contribution of the US Government, not subject to copyright, 1994.
48. Allan D. W., Weiss M. A. and Jespersen J. L., A frequency-domain view of time-domain characterization of clocks and time and frequency distribution systems. In Proceedings of the 45th IEEE Frequency Control Symposium, pages 667-678, May 1991.
49. Ascarrunz F. G., Jefferts S. R., Parker T. E., Environmental Effects on Errors in Two-Way Time and Frequency Transfer. IEEE CPEM 1996 Conf. Dig, 1996, 518-519.
50. Ascarrunz F. G, Jefferts S. R, Parker T. E, Earth Station Errors in Two-Way Time and Frequency Transfer. IEEE T. Instrum. Meas, 1997,46: 205-208.
51. Ascarrunz F. G, Jefferts S. R, Parker T. E., A Delay Calibration System for Two-Way Time and Frequency Transfer. IEEE Intl. Freq. Cont. Symp, 1998,250-253.
52. Audoin C. and Guinot B., The measurement of time - time, frequency and the atomic clock. Cambridge University Press, 2001.
53. Azoubib J. Nawrocki J. and Lewandowski W., Independent atomic timescale in Poland-organization and results. Metrologia 40: 245-248,2003.
54. Barnes J. A, The measurement of linear frequency drift in oscillators. In Proceedings of the 15th Annual Precise Time and Time Interval (PTTI) Meeting, 1983.
55. Barnes J. A. and Allan D. W, Variances based on data with dead time between the measurements. NIST Technical Note 1318, 1990.
56. Barnes J. A, Chi A. R. and et al. Characterization of frequency stability. IEEE Transactions on Instrumentation and Measurement, 1971.
57. Baugh R.A, "Frequency Modulation Analysis with the Hadamard Variance", Proc. 25th Frequency Control Symposium, April 1971, pp. 222-225.
58. Beard R, Buisson J, and et. al, GPS block IIR Rubidium frequency standard life test results. 2002 IEEE International Frequency Control Symposium and PDA Exhibition, 2002.
59. Bernier L. G, Metrology of clocks & timescales. METAS 2002.
60. Bernier L. G, Application of the GSF-1 algorithm to the near-optimal timescale prediction of the hydrogen master. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
61. Block M, Mancini O. and McClelland T, Performance of Rubidium and Quartz clocks in space. 2002 IEEE International Frequency Control Symposium and PDA Exhibition, 2002.
62. Bourga C, Lobert B. and Brunet M, Experiment assessment of Galileo clocks performance in space. ION GPS 2002.
63. Breakiron L. A, A Kalman filter for atomic clocks and timescales. In Proceedings of the 33th Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
64. Breakiron L. A, Kalman filter characterization of cesium clocks and hydrogen masters. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
65. Bregni S. Generation of Pseudo-Random Power-Law Noise Sequences by Spectral Shaping. http://www.elet.polimi.it/～bregni. 2001.
66. Broderbauer V. and Weber R, Results of modeling GPS satellite clocks. 2003.
67. Busca G, Frelechoz C. and et al. Space Clocks for Navigation Satellites. Proceedings of the 2003 IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, 2003a.
68. Busca G and Wang Q., Time prediction accuracy for a space clock. Metrologia 40: 265-269, 2003b.
69. Carrillo F. J. M., Sanchez A. A. and Alonso L. B., Hybrid synthesizers in space Galileo's CMCU, 1999.
70. CCIR, Characterization of frequency and phase noise. Report 580 of the CCIR, 1986.
71. Coffer J. G and Camparo J. C, Long-term stability of a rubidium atomic clock in geosynchronous orbit. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
72. Crater D. T. and Mobbs H. S., The Impact of Operating GPS with More Rubidium frequency standards. ION GPS 1998.
73. Davis J. A., Harris P. M. and et al., Least-squares analysis of two-way satellite time and frequency transfer measurements. In Proceedings of the 33th Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
74. Davis J. A., Greenhall C. A. and Stacey P. W., A Kalman filter clock algorithm for use in the presence of flicker frequency modulation noise. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
75. DeYoung J. A., Discrete simulated power law data in the time-domain using the Kasdin and Water (1992). http://tycho.usno.naw.mil/powerlaw.html.
76. Delporte J., Vernotte F., Brunet M. and Tournier T., Modelization and extrapolation of time deviation of USO and atomic clocks in GNSS-2 context. In Proceedings of the 32th Annual Precise Time and Time Interval (PTTI) Meeting, 2000.
77. Delporte J, Vernotte F, Tournier T and Brunet M, Modelisation and extrapolation of time deviation: Application to the estimation of the datation stability of a navigation payload. 15th European Frequency and Time Forum, 2001.
78. Doug's Atomic Clocks, Doug Hogarth's Home Page.
79. Dow J. M., Summary of Galileo technical status. Hessischer Informationstag zu Galileo- Anwendungen 30.8.2004
80. Emery W. J., Thomson R. E.. Data analysis methods in physical oceanograph. PERGAMON, 1997: 391—395.
81. Epstein M. and Dass T., Management of phase and frequency for GPS IIR satellites. In Proceedings of the 33th Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
82. Epstein M., Freed G and Rajan J., GPS IIR Rubidium clocks: in-orbit performance aspects. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
83. Ferre-Pikal E. S., Vig J. R., Camparo J. C. and et al., Draft revision of IEEE STD 1139-1988 Standard definitions of physical quantities for fundamental frequency and time metrology -random instabilities. 1997 IEEE International Frequency Control Symposium, 1997.
84. Galindo F. J. and Palacio J., Post-processing ROA data clocks for optimal stability in the ensemble timescale. Metrologia 40: 237-244, 2003.
85. Galleani L., Sacerdote L., Tavella P. and Zucca C., A mathematical model for the atomic clock error. Metrologia 40: 257-264, 2003.
86. Galleani L. and Tavella P., Instantaneous spectrum of clock errors. Metrologia 40: 319-325, 2003.
87. Galleani L. and Tavella P., On the use of the Kalman filter in timescales. Metrologia 40: 326-334,2003.
88. Greenhall C. A., Removal of drift from frequency stability measurements. TDA progress report 42-65,1981.
89. Greenhall C. A., Frequency stability review. TDA progress report 42-88,1983.
90. Greenhall C. A., Estimating the modified Allan variance. 1995 IEEE International Frequency Control Symposium, 1995.
91. Greenhall C. A., Does Allan variance determine the spectrum? 1997 IEEE International Frequency Control Symposium, 1997.
92. Greenhall C. A., Forming stable timescales from the Jones-Tryon Kalman filter. Metrologia 40(2003)S335-341,2003.
93. Greenhall C. A., Howe D. A. and Percival D. B., Total variance, an estimator of long-term frequency stability. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 46, No. 5, September 1999.
94. Greenhall C. A. and Riley W. J., Uncertainty of Stability Variances based on finite differences. Hamilton Technical Services, In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
95. Grewal M. S., Brown W., Lucy R. and Hsu P., Geo Uplink Subsystem (GUS) clock steering algorithms performance and validation results. ION GPS 1999.
96. Hahn J. H., Graglia G. and et al., Timekeeping for GalileoSat. ION GPS 2000.
97. Hansen A., Walter T. and Enge P., GPS Satellite Clock Event on SVN 27 and its impact on augmented navigation systems. ION GPS 1998.
98. Harris P. M., Davis J. A., Cox M. G. and Schemar S. L., Least-squares analysis of time series data and its application to two-way satellite time and frequency transfer measurements. Metrologia 40: 342-347, 2003.
99. Hein G. W. and Eissfeller B., Galileo design options for the European GNSS-2. ION GPS 2001.
100.Howe D. A., Measurements, Modeling and Time-error prediction. PPT
101.Howe D. A., Frequency stability cookbook: frequency noise measurements and their measurement in oscillators. 2000a.
102.Howe D. A., The Total Deviation Approach to Long-Term Characterization of Frequency Stability. IEEE Trans. Ultrasonics,... 2000b.
103.Howe D. A., Interpreting oscillatory frequency stability plots. 2002 IEEE International Frequency Control Symposium and PDA Exhibition.
104.Howe D. A., Allan D. W. and Barnes J. A., Properties of signal sources and measurement methods. Proceedings of the 35th Annual Symposium on Frequency Control, 1981.
105.Howe D., Beard R. and et al., A Total estimator of the Hadamard function used for GPS operations. Proc. 32nd Annual PTTI Systems and Applications Meeting, 2000c, 28 (30): 255-268.
106.Howe D., Beard R. and et al., Total Hadamard variance: application to clock steering by Kalman filtering. 2001a.
107.Howe D., Beard R. and et al., Enhancements to GPS operations and clock evaluations using a "Total" Hadamard deviation. IEEE transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 52, No. 8, August 2005.
108.Howe D. A. and Greenhall C. A., Total variance: a progress report on a new frequency stability characterization, In Proceedings of the 29th Annual Precise Time and Time Interval (PTTI) Meeting, 1997.
109.Howe D. A. and Lainson K. J., Simulation study using a new type of sample variance. Proc. 27st Annual PTTI Systems and Applications Meeting, 1995.
110.Howe D. A. and Peppier T. K., Definitions of "total " estimators of common time-domain variances. 2001 IEEE International Frequency Control Symposium and PDA Exhibition, 2001b.
111 .Howe D. A. and Vernotte F., Generalization of the total variance approach to the modified Allan variance. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
112.Hutsell S. T, Relating the Hadamard variance to MCS Kalman filter clock estimation, in Proc. 27th Annu. PTTI Syst. Applications Meeting, San Diego, CA, Nov. 29 - Dec. 1, 1995, pp. 291-301.
113.Hutsell S.T., Reid W. G. and et al., "Operational Use of the Hamamard Variance in GPS", Proc. 28th PTTI Meeting, pp. 201-213, December 1996.
114.Jeanmaire A., Rochat P. and et al., Rubidium atomic clock for Galileo. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
115.Jespersen J., Introduction to the time domain characterization of frequency standards. In Proceedings of the 23th Annual Precise Time and Time Interval (PTTI) Meeting, 1991.
116.Jong G. and Kroon E., Analysis of one year of GPS and two-way time transfer results between PTB, NPL, and VSL. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002a.
117.Jong G. and Kroon E., Analysis of one year of zero-baseline GPS common-view time transferr and direct measurement using two co-located clocks. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002b.
118.Kasdin N. J. and Walter T., Discrete simulation of power law noise. 1992 IEEE Frequency Control Symposium, 1992.
119.Lance A. L., Seal W. D. and Labaar F., Phase Noise and AM Noise Measurements in the Frequency Domain. Infrared and Millimeter Waves, Vol. II, 1984.
120.Lesage P. and Audoin C., Characterization and measurement of time and frequency stability. Radio Science, 1979.
121.Lesage P. and Ayi T., Characterization of frequency stability: Analysis of the modified allan variance and properties of its estimate. IEEE Transactions on Instrumentation and Measurement, 1984.
122.Levine J. Introduction to time and frequency metrology. Review of Scientific instruments, 1999(6).
123.Li M., Peng H. and Liao C., MTIE and TDEV analysis of unevenly spaced time series data and its application to telecommunications synchronization measurements. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
124.Manning D. M., NGA GPS monitor station high-performance Cesium frequency standard stability: from NGA kalman filter clock estimators. In Proceedings of the 37th Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
125.Matsakis D., Miranian M. and Koppang P., Steering the U.S. Naval Observatory (USNO) Master clock. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
126.Mattioni L., Belloni M. and et al., The development of a passive hydrogen master clock for the Galileo navigation system. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
127.McCaskill T. B., Reid W.G., Buisson J. A. and Warren H. E., Analysis of the frequency stability of on-orbit GPS Navstar clocks. 1993 IEEE International Frequency Control Symposium, 1993.
128.McCaskill T. B., Analysis of the frequency stability history of GPS Navstar clocks. 1997 IEEE International Frequency Control Symposium, 1997.
129.McCaskill T. B., Oaks O. J. and Largay M. M., Performance of global Positioning System Block II/IIA/IIR on-orbit Navstar clocks. In Proceedings of the 31th Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
130.Merino M. M. R., Garcia A. M. and Medel C. H., GSTB-V1: The First Step Towards the development of Galileo navigation algorithms, www.gmv.com. 2004.
131.Moudrak A., Bruyninx C. and et al., Determination of GPS-Galileo Time Offset to support system interoperability. GNSS04.
132.Nuth V., Feess W. A. and Wu C., An evaluation of various space clocks for GPS IIF. In Proceedings of the 33~(rd) Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
133.Oaks J., McCaskill T. B. and Largay M. M., Performance of global Positioning System Block II/IIA/IIR on-orbit Navstar clocks. In Proceedings of the 33~(rd) Annual Precise Time and Time Interval (PTTI) Meeting, 2001.
134.Oaks J., Largay M. M. and et al., Comparative analysis of clock performance using both code-phase and carrier-derived pseudorange observations. In Proceedings of the 36th Annual Precise Time and Time Interval (PTTI) Meeting, 2004.
135.Oaks J., Senior K. and Largay M. M., Global positioning system constellation clock performance. In Proceedings of the 35th Annual Precise Time and Time Interval (PTTI) Meeting, 2003.
136.Oaks J., Senior K. and et al., NRL analysis of GPS on-orbit clocks. In Proceedings of the 37th Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
137.Parker T. E. and Zhang V. S., Investigation of instabilities in two-way time transfer. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
138.Percival D. B., Stochastic models and statistical analysis for clock noise. Metrologia 40: 289-304, 2003.
139.Petit G., Towards an optimal weighting scheme for TAI computation. Metrologia 40: 252-256, 2003.
140.Petzinger J., Reith R. and Dass T., Enhancements to the GPS Block IIR timekeeping system. In Proceedings of the 34th Annual Precise Time and Time Interval (PTTI) Meeting, 2002.
141.Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P., Numerical Recipes in C : The Art of Scientific Computing, Second edition. Cambridge University Press, 1992.
142.Ray J. and Senior K., IGS/BIPM pilot project: GPS carrier phase for time/frequency transfer and timescale formation. Metrologia 40: 270-288, 2003.
143.Reid W., Mccaskill T., Largay M., Oaks O. J. and Buisson J, Performance of GPS Block IIR Rubidium clocks. ION GPS 2000, 19-22 September 2000, Salt Lake City, UT.
144.Riley W. J., Application of the 3-cornered hat method to the analysis of frequency stability. Hamilton Technical Services, 2003 a.
145.Riley°W. J., A test suite for the calculation of time domain frequency stability. 1995 IEEE Frequency Control Symposium, 1995.
146.Riley W. J., Confidence Intervals and Bias Corrections for the stable32 variance functions. Hamilton Technical Services, 2003b.
147.Riley W. J., Gaps, outliers, dead time, and uneven spacing in frequency stability data. Hamilton Technical Services, 2003e.
148.Riley W. J., Methodologies for time domain frequency stability measurement and analysis. Hamilton Technical Services, 2002a.
149.Riley W. J., The calculation of time domain frequency stability. Hamilton Technical Services, 2002b.
150.Riley W. J., The Hadamard variance. Hamilton Technical Services, 2002c.
151.Riley W. J., Techniques for frequency stability analysis. IEEE International Frequency Control Symposium, Tampa, FL, May 4, 2003c.
152.Riley W. J., Use of the Autocorrelation Function for frequency stability analysis. Hamilton Technical Services, 2003 d.
153.Riley W. J., The basics of frequency stability analysis. Hamilton Technical Services, 2004a.
154.Riley W. J. and Greenhall C. A., Power law noise identification using the lag 1 autocorrelation. The 18th European Frequency and Time Forum, University of Surrey, Guildford, UK. 5-7 April 2004b.
155.Rochat P, Droz F. and et al., The onboard Galileo Rubidium and Passive Maser, status and performance. Frequency Control Symposium and Exposition, 2005.
156.Rutman J., Oscillator Specification: A review of Classical and New Ideas, Proc. 31st Frequency Control Symposium, June 1977, pp. 291-301.
157.Schmidt L. S., Atomic clock models using fractionally integrated noise processes. Metrologia 40: 305-311, 2003.
158.Senior K., Beard R. and White J., CANVAS: Clock Analysis, Visualization, and Archiving System - A new software package for the efficient management of clock oscillator data. In Proceedings of the 37th Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
159.Shmaliy Yu. S., Ibarra-Manzano O. and Arceo-Miquel L., A Numerical Comparison of the Unbiased FIR and Kalman filters in applications to GPS-based timekeeping. In Proceedings of the 37st Annual Precise Time and Time Interval (PTTI) Meeting, 2005.
160.Shmaliy Yu. S., Marienko A. V. and Savchuk A. V, GPS-based optimal Kalman estimation of time error, frequency offset and aging. In Proceedings of the 31st Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
161. Stein S. R., Frequency and time - their measurement and characterization. Precision Frequency Control, Volume 2, Chapter 12, 1985.
162.Stein S. R., Kalman filter analysis of precision clocks with real-time parameter estimation. 43~(rd) Annual Frequency Control Symposium, 1989.
163.Stein S. R. and Evans J., The application of Kalman filters and ARIMA models to the study of time prediction errors of clocks for use in the defence communication system (DCS). 44th Annual Frequency Control Symposium, 1990.
164.Stein S. R. and Filler R. L., Kalman filter analysis for real time applications of clocks and oscillators. 42~(nd) Annual Frequency Control Symposium, 1988.
165.Su W. and Filler R. L., Application of Kalman filtering techniques to the precision clock with non-constant aging. 1992 IEEE Frequency Control Symposium, 1992.
166.Su W. and Filler R. L., A new approach to clock modeling and Kalman filter time and frequency prediction. 1993 IEEE Frequency Control Symposium, 1993.
167.User manual - Stable32 frequency stability analysis. Hamilton Technical Services, 2005.
168.Vernotte F., Estimation of uncertainty in time error estimation. In Proceedings of the 31st Annual Precise Time and Time Interval (PTTI) Meeting, 1999.
169.Vernotte F., Application of the Moment Condition to Noise simulation and to stability analysis. IEEE TRANS. ON UFFC, 2002.
170.Vernotte F., Incertitude Sur Les Coefficients D'interpolation Lineaire ET Les residus. Private Communication, 2006.
171.Vernotte F., Delporte J., Brunet M. and Tournier T., Uncertainties of drift coefficients and extrapolation errors: application to clock error prediction. Metrologia, vol.38, no.4 , 2001.
172.Vernotte F., Lantz E., Groslambert J. and Gagnepain J. J., A new multi-variance method for the oscillator noise analysis. 1992 IEEE Frequency Control Symposium, 1992.
173.Vernotte F., Zalamansky G. and Lantz E., Time stability characterization and spectral aliasing, Part I: a time-domain approach. Metrologia, 1998a, 35, 723-730.
174.Vernotte F., Zalamansky G. and Lantz E., Time stability characterization and spectral aliasing, Part I: a frequency-domain approach. Metrologia, 1998b, 35, 731-738.
175. Vig J. R., Quartz Crystal Resonators and Oscillators For Frequency Control and Timing Applications - A Tutorial. U.S. Army Communications-Electronics Command, Attn: AMSEL-RD-C2-PT, Fort Monmouth, NJ 07703, USA, 2000.
177. Walls F. L., Percival D. B. and Irelan W. R., Biases and variances of several FFT spectral estimators as a function of noise type and number of samples. In Proceedings of the 43th IEEE Frequency Control Symposium, 1989.
178. Weiss M. A., Allan D. W. and Howe D. A., Confidence on the second difference estimation of frequency drift - A study based on simulation. 1992 IEEE Frequency Control Symposium, 1992.
179.Weiss M. A. and Howe D. A., Total TDEV. 1998 IEEE International Frequency Control Symposium, 1998.
180.Weiss M. A., Time domain representation of oscillator performance. 27th Annual time and frequency metrology seminar, 2002.
181.Winkler G. M. R., Introduction to robust statistics and data filtering. Hamilton Technical Services, 1998.
182.Yang Y., Robust estimation for dependent observations, Manuscripta geodaetica, 1994 (19): 10-17.
183.Yang Y., Estimators of covariance matrix at robust estimation based on influence functions. Zeitschrift fuer Vermessungswesen. 122. Heft 4,1997: 166～174.
184.Yang Y. Some Numerical Prediction Methods for the Wind Speed in the Sea Based on ERS-1 Scatterometer Wind Data [J]. Survey Review, 2001, (36): 121-131.
185.Yang Y., Robust Estimation of Geodetic Datum Transformation [J]. Journal of Geodesy, 1999a (73): 268-264.
186.Yang Y. An optimal adaptive Kalman filtering, Journal of Geodesy, 2006, 80: 177-183.
187.Yang Y., Cheng M.K., Shum C.K., Tapley B.D.., Robust estimation of systematic errors of satellite laser range, Journal of Geodesy, 1999(73):345-349.
188.Yang Y, Cui X and Gao W. Adaptive integrated navigation for multi-sensor adjustment outputs. The Journal of Navigation, 2004, 57(2): 287-285.
189.Yang Y and Gao W. Comparison of adaptive factors in Kalman filters on navigation results, The Journal of Navigation, 2005, 58(3):471-478.
190.Yang Y and Gao W, A new learning statistic for adaptive filter based on predicted residuals. Progress in Natural Science, 2006,16(8): 833-837.
191.Yang Y, He H and Xu G. Adaptively robust filtering for kinematic geodetic positioning, Journal of Geodesy, 2001b, 75(2/3): 109-116.
192.Yang Y, Song L and Xu T. Robust estimator for correlated observations based on bifactor equivalent weights, Journal of Geodesy. 2002, 76(6-7), 353-358.
193.Yang Y., Tang Y., Li Q and Zou Y. Experiments of adaptive filters for kinematic GPS positioning applied in road information updating in GIS, International Symposium on Inertial Navigation Technology and Intelligent Traffic, Nanjing, China, 2004b.
194.Yang Y and Wen Y. Synthetically adaptive robust filtering for satellite orbit determination, Science in China, Series D, 2004, Vol. 47, No. 7, 585-592.
195.Yang Y, Xu T and He H. On adaptively kinematic filtering, Selected Papers for English of Acta Geodetica et Cartographica Sinica, 2001, 25-32.
196.Yang Y and Xu T. An adaptive Kalman filter based on Sage windowing weights and variance components, The Journal of Navigation, 2003, 56(2), 231-240.
197.Yang Y and Zhang S. Adaptive fitting for systematic errors in navigation, Journal of Geodesy, 2005, 79: 43-49.