Algorithm Analysis of Autonomous Navigation of Spacecraft Based on X-ray Pulsars

A pulsar has the very stable rotation and can be used as the time standard. The astrometric parameters and astrophysical parameters of many pulsars, such as the spatial position, proper motion, distance, rotation period and its derivative, etc., can be all accurately determined. Since the pulsar can provide the time signal and the coordinates of its spatial position simultaneously, the pulsar navigation system installed on a spacecraft enables the autonomous navigation of the spacecraft to be realized. Firstly, the position of the spacecraft is predicted based on the equation of orbit dynamics of the spacecraft and then the Kalman filtering is applied to calculating the estimation error of the spacecraft position through the difference between the pulse arrival time observed on the spacecraft and the predicted pulse arrival time, thereby modifying the position of the spacecraft. Finally, the effects of the initial error, measuring accuracy of the pulse arrival time and number of pulsars on the navigation accuracy are analyzed.     

基于脉冲星的星载钟时间修正算法研究

讨论了一种对长期在轨运行的星载钟的钟差进行修正的方法,该方法以导航用毫秒脉冲星作为高稳定度频率源,采用卡尔曼最优估计算法对星载钟进行控制。仿真计算表明,该方法可以有效提高星载钟的长期频率稳定度,增强星载钟的长期自主运行能力。     

基于双谱滤波的综合脉冲星时算法研究

毫秒脉冲星的自转频率非常稳定,提供了一种独立的基于遥远自然天体并能持续数百万乃至数十亿年的时间基准,具有稳定性强、运行时间长、服务范围广等特点.为了减弱毫秒脉冲星计时观测中各种高斯噪声对脉冲星时的影响,研究了一种基于双谱滤波的综合脉冲星时构建算法,处理分析了国际脉冲星计时阵(International Pul-sar Timing Array,IPTA)最新发布的4颗毫秒脉冲星(PSR J0437-4715、J0613-0200、J1713+0747和J1909-3744)的观测数据,分析了不同时间尺度综合脉冲星时的稳定性,并与构成国际原子时(International Atomic Time,TAI)的4家授时单位原子钟稳定性进行了比较.结果表明:双谱滤波算法能够较好地抑制观测噪声,提高综合脉冲星时的稳定性.相比于经典加权算法,综合脉冲星时1 yr、10 yr稳定度从7.77×10^-14、8.56×10^-16分别提高到1.50×10^-14、3.50×10^-16,单脉冲星时稳定性的提升也类似.同时发现,综合脉冲星时稳定性在5 yr及以上时间尺度上优于原子钟稳定性,可用于改善当前原子时的长期稳定性.     

Real-time Solution of Atomic Clock Operating Parameters Based on Adaptive Kalman Filtering

The real-tine and accurate knowledge of the operation of an atomic clock is of great significance to satellite navigation and time keeping. In the light of the problems which exist in the real-time solution of the atomic clock operating parameters by means of the standard Kalman filtering, the method for applying the adaptive Kalman filtering model based on the prediction residual to the real-time solution of the clock parameters is proposed. An adaptive factor is constructed by the model based on the standard Kalman filtering model so that the accurate and reliable estimates of the operating parameters may be given rather fast after the frequency modulation or phase modulation of the atomic clock. Finally, in combination with the 3 computational examples of the work on the navigation and time keeping, the effectiveness of the method is verified.     

一种新的守时型原子钟综合时间尺度方法研究

在这篇文章中, 提出了一种基于改进的指数平滑和Vondrak_Cepek联合平滑的氢铯综合时间尺度产生方法. 以最小误差方法为理论基础, 动态估计氢原子钟频率漂移参数, 提升氢原子钟钟差预测准确度; 基于改进的二次指数平滑产生氢原子钟组时间尺度、加权平均方法产生铯原子钟时间尺度, 同时设计Vondrak_Cepek滤波器以结合两类时间尺度长短期稳定度优势, 提升综合时间尺度性能. 实验结果表明, 所提方法产生的氢铯综合时间尺度时稳可达1.60x10^-15,天稳可达3x10^-15,优于ALGOS、AT1和Kalman滤波3种经典方法产生的时间 尺度性能.     

基于卡尔曼滤波的脉冲星计时研究

脉冲星是高速自转的中子星,其自转周期稳定,不受人为干扰破坏,可作为绝对时间的参考量.论文提出一种基于卡尔曼滤波算法的脉冲星授时方法,以太阳某同步轨道为例,对基于卡尔曼滤波的钟差控制以及脉冲星星表误差和脉冲到达时间(TOA)测量精度对授时精度的影响进行了仿真分析.结果表明,该方法可以有效消除星载时钟钟差并抑制其随时间的增加,解决了航天器搭载低成本时钟精度不能满足要求的问题.     

四种综合脉冲星时算法比较

由单颗脉冲星定义的脉冲星时受多种噪声源的影响,其短期和长期稳定度都不够好.为了削弱这些噪声源对单脉冲星时的影响,可以采取合适的算法对多个单脉冲星时进行综合得到综合脉冲星时,从而提高综合脉冲星时的长期稳定度.文中介绍4种综合脉冲星时算法:经典加权算法、小波分析算法、维纳滤波算法和小波域中的维纳滤波算法,将这4种算法分别应用于Arecibo天文台对两颗毫秒脉冲星PSR B1855+09和PSRB1937+21观测得到的计时残差并作出比较.     

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。     

一种转发式卫星授时新方法

为了减少对GPS提供的高精度授时服务的依赖,建设拥有自主知识产权的且具有投入成本低、精度高的授时系统。提出了一种利用地面高稳定度原子钟作为时频基准,通过通信卫星转发实现卫星广播授时的新方法。详细研究了利用地面高稳定度原子钟和通信卫星组成的导航星座进行多星授时、单星授时的原理和测量方法,分析研究了影响授时精度的原因。由于转发式卫星授时系统的时频基准源稳定度高,其测距精度也会相应的提高。只要精确扣除时延误差,同样可以实现高精度授时。粗码的授时精度可达20ns以内,短精码的授时精度可达10ns左右。总之该系统具有组建灵活简便、应用面广等优势和特色。     

脉冲星在空间飞行器定位中的应用

利用脉冲星钟模型能高精度地预报脉冲星脉冲到达太阳系质心的时间。基于脉冲星时、空参考架可实现各类空间飞行器的自主导航。讨论了脉冲星钟的模型和脉冲星导航系统的框架结构,描述了脉冲星导航的基本原理和算法。指出脉冲星导航系统对脉冲星脉冲到达探测器时刻的测量精度,是决定空间飞行器位置解算精度的关键因素。脉冲星导航观测采用的原子钟如果足够稳定,则空间飞行器位置的解算方法可以简化。在脉冲星导航系统计时观测精度达到或优于几十微秒量级时,脉冲星视差、相对论效应的影响是不可忽略的。对脉冲星导航系统开发设计中的关键技术和进一步研究的主要问题进行了初步分析和讨论。     

An Orbital Prediction Algorithm for LEO Satellites Based on Optical Observations of Short Arcs at Single Station

The forecasting technique of the target tracking based on the short arcs at single station is an important way to guarantee that high-precision photoelectric theodolites can normally track and capture the targets in unconventional environments. We construct the tracking prediction algorithm based on nonlinear filter, which can provide the guiding data for the closed loop tracking under normal circumstances. At the same time we also construct the target prediction algorithm based on the nonlinear transformation, without valid observational data, which can provide a track guidance for the theodolite and ensure that the targets will not be lost. It is demonstrated that the nonlinear filtering is more effective than the EKF (extended Kalman filter) in the tracking prediction algorithm of the short arcs at single station. The results indicate that the nonlinear filter designed in this paper can be used as the guiding algorithm for the optical tracking equipments. And its guiding accuracy is in the same order of magnitude of the theodolite's random measurement accuracy. When the systematic error of the equipments reaches 50″, the accuracy can achieve 20″ for predictions in 60 s. This still satisfies the requirement of the field of view of the tracking equipments.     

A Comparison of the Four Algorithms of Ensemble Pulsar Time

The pulsar time defined by a single pulsar is affected by many kinds of noise sources. Its short-term and long-term degrees of stability are both not good enough. In order to weaken the influence of these noise sources on the single pulsar time, an appropriate algorithm can be adopted to make a synthesis of many single pulsar times, then the ensemble pulsar time is obtained, thereby increasing the long-term degree of stability of the ensemble pulsar time. In this article four kinds of algorithms of the ensemble pulsar time are introduced, i.e., the classical weighting algorithm, wavelet analysis algorithm, Wiener filtering algorithm and Wiener filtering algorithm in wavelet domain. These four algorithms are respectively applied to the timing residuals obtained from the observation of two millisecond pulsars, PSR B1855+09 and PSR B1937+21 made at the Arecibo Astronomical Observatory, and comparisons are carried out.     

Analysis of the Precision of Pulsar Time Clock Modeltwo

Millisecond pulsars have a very high rotation stability, which can be applied to many research fields, such as the establishment of the pulsar time standard, the detection of gravitational wave, the spacecraft navigation by using X-ray pulsars and so on. In this paper, we employ two millisecond pulsars PSR J0437-4715 and J1713+0743, which are observed by the International Pulsar Timing Array (IPTA), to analyze the precision of pulsar clock parameter and the prediction accuracy of pulse time of arrival (TOA). It is found that the uncertainty of spin frequency is 10^?15 Hz, the uncertainty of the first derivative of spin frequency is 10^?23 s^?2, and the precision of measured rotational parameters increases by one order of magnitude with the accumulated observational data every 4～5 years. In addition, the errors of TOAs within 4.8 yr which are predicted by the clock model established by the 10 yr data of J0437-4715 are less than 1 μs. Therefore, one can use the pulsar time standard to calibrate the atomic clock, and make the atomic time deviate from the TT (Terrestrial Time) less than 1 μs within 4.8 yr.     

Optimal filters for the construction of the ensemble pulsar time

An algorithm of the ensemble pulsar time based on the optimal Wiener filtration method has been constructed. This algorithm allows the separation of the contributions to the post-fit pulsar timing residuals of the atomic clock and the pulsar itself. Filters were designed using the cross- and auto-covariance functions of the timing residuals. The method has been applied to the timing data of millisecond pulsars PSR B1855+09 and B1937+21 and allowed the filtering out of the atomic-scale component from the pulsar data. Direct comparison of the terrestrial time TT(BIPM06) and the ensemble pulsar time PT_ens revealed that the fractional instability of TT(BIPM06)−PT_ens is equal to  σ _z = (0.8 ± 1.9) × 10⁻¹⁵  . Based on the  σ _z   statistics of TT(BIPM06)−PT_ens, a new limit of the energy density of the gravitational wave background was calculated to be equal to  Ω_g h ²∼ 3 × 10⁻⁹  .     

用脉冲星钟作航天器时间标准

在介绍参考坐标系和时间标准的基础上,讨论了用脉冲星为航天器导航的时间标准问题。利用X射线脉冲星实现航天器自主导航,星载钟的任何误差都会直接影响航天器位置测量。脉冲星钟具有较高的长期频率稳定度,适合用作各类航天器的时间标准。重点讨论了时间标准误差对航天器定位的影响;给出了用脉冲星钟作航天器时间标准的物理实现方法。     

大规模脉冲星候选体信号的无监督聚类分析研究

随着500 m口径球面射电望远镜(Five-hundred-meter Aperture Spherical radio Telescope, FAST)等大型射电望远镜的建设和使用,脉冲星巡天数据进入PB时代.为解决如此大量高速采样的标量数据挖掘问题,促进新天文现象的发现,提出一种基于无监督聚类的脉冲星候选体筛选方案.该方案采用基于密度层次、划分方法的混合聚类算法,结合MapReduce/Spark并行计算模型和基于滑动窗口的分组策略,进而提高大量候选体信号筛选的效率.通过在脉冲星数据集HTRU2 (High Time Resolution Universe)上的对比实验,结果表明该算法能取得较高的精确度和召回率,分别是0.946和0.905,并且当并行节点足够时,该算法的时间复杂度相比串行执行明显下降.可见,该方法为脉冲星观测大数据的分析挖掘提供一种可行思路.     

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.     

毫秒脉冲星在时间计量中的可能应用

在分析射电脉冲星的自转和时间尺度的基本特征及其相互之间的关系的基础上，讨论了毫秒脉冲星在时间工作中的可能应用。基于毫秒脉冲星的到达时间的测量，经过必要的时空转换、改正及参数拟合，可以建立脉冲星时及综合脉冲星时。虽然脉冲星时及综合脉冲星时对原子有所依赖，但它们，特别是综合脉冲星时，可以用来将原子时的准确度从一个时段传递到另一个时段，并可用来分析原子时的长期稳定度。另外，可以利用双星脉冲星的轨道运动的相位来定义一种动力学时间尺度－－双星脉冲星时。     

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.     

Research on Ensemble Pulsar Time Based on Observed Data

The applications of pulsar timing to several important aspects are introduced and a skeletal definition of the pulsar time scale is given. By taking advantage of the observational timing data of millisecond pulsars obtained at the Parkes Astronomical Observatory, Australia, the ensemble pulsar time based on 4 millisecond pulsars is built up, the comparison of its stability σz, with that of the atomic time is made, and finally a few of important factors which affect the ensemble pulsar time, as well as their influences on the pulsar timing accuracy and application are analyzed.