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.     

脉冲星钟模型精度分析

毫秒脉冲星具有很高的自转稳定性,利用脉冲星自转极其稳定的特性可以开展许多应用研究,如:脉冲星时间标准的建立、宇宙背景引力波的探测、X射线脉冲星导航应用等等.利用国际脉冲星计时阵(International Pulsar Timing Array,IPTA)中J0437-4715和J1713+0743 2颗源的实测数据开展脉冲星钟模型参数精度分析和脉冲到达时间(Time Of Arrival,TOA)预报精度研究.通过研究得知,目前脉冲星自转频率测量精度为10-15Hz,频率1阶导数测量精度为10~(-23)s~(-2),且自转参数测量精度随观测时间跨度每4–5 yr提高1个量级.另外,利用J0437-4715 10 yr观测数据建立的钟模型,其脉冲到达时间预报偏差4.8 yr之内可保持在1μs之内.因此,利用该脉冲星建立时间标准用于校准原子时,可以使原子时相对于地球时(Terrestrial Time,TT)的偏差在4.8 yr之内小于1μs.     

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。     

X射线脉冲星导航可用目标源研究

脉冲星具有自转非常稳定的特性,在空间自主导航中有重要的应用前景.选择和研究一组适合于脉冲星导航使用的候选目标源非常重要,决定脉冲星导航精度的主要因素有:导航目标源X射线流量强度、目标源的位置精度和旋转参数精度.对可用于导航的一些X射线源进行了讨论研究,并对最适合做导航研究的转动能驱动的X射线脉冲星进行统计分析.     

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。     

计时观测测量脉冲星参数的数学模型与精度估计

脉冲星计时观测能够精确测量脉冲星自转参数和天体测量参数.概述了脉冲星计时模型和利用最小二乘拟合测量脉冲星各个参数并估计其方差的数学方法.在黄道坐标系导出了脉冲星各个参数误差与计时残差之间关系的数学表达式.给出了脉冲星黄经、黄纬和周年视差测量精度与脉冲星黄纬绝对值之间的关系曲线.讨论了脉冲星各个天体测量参数测量精度与脉冲星纬向参数本身的关系.     

关于脉冲星脉冲到达时间转换方程

较详细地介绍了脉冲星脉冲到达时间（TOA）转换方程,讨论了脉冲星TOA转换方程在航天器导航算法中的具体应用问题。同时,对导航用的脉冲星脉冲TOA转换方程与地面射电计时观测用的脉冲星脉冲TOA转换方程进行了比较研究。     

关于X射线脉冲星自主导航的位置观测方程

在X射线脉冲星自主导航(XNAV)中,位置观测方程表达了X光子到达航天器的时刻(TOA)和航天器位置的关系.具体讨论时,一般用TOA和"时间基准"的差值代替TOA,用太阳系质心系中的位置矢量表示航天器的位置."时间基准"可以取X光子到达太阳系质心(SSB)的真实时间,也可以取X光子到达SSB的"等效时间".讨论了基于这两种时间基准的位置观测方程,给出了时间精度为0.1 ns的位置观测方程,分析了其中各项的物理意义.     

几何因素对脉冲星自转参数的影响

脉冲星自转参数是脉冲星最重要的参数之一,能反映脉冲星本身的物理性质.根据计时观测所得的自转参数除了包含脉冲星本身固有的部分,还受到几何因素的影响,例如地球自转参数、岁差章动模型、行星历表误差、脉冲星相对于太阳系质心(solar system barycenter,SSB)的速度和加速度.通过分析脉冲星计时观测模型,从而推导出这些因素与脉冲星自转参数的关系,进一步估计了这些因素对自转参数影响的量级大小.在现有的观测精度下,地球自转参数和岁差章动模型的误差对计时观测的影响可忽略,可以认为脉冲星自转参数不受其影响.行星历表误差对自转参数的影响远小于自转参数本身,同样可以忽略.脉冲星相对于太阳系质心的视向速度影响到脉冲星周期,该影响比脉冲星本身周期约小4个量级.值得注意的是,脉冲星横向速度和脉冲星相对于太阳系质心的视向加速度对周期变率的影响不可忽略,特别是对于周期变率较小的毫秒脉冲星来说,这两个因素的影响可能是脉冲星视周期变率中的主要成分.     

地球自转角速度的变化与脉冲星的周期变率

本文分析了地球自转角速度的变化对脉冲星的周期变率P的影响,得出以下结果:(1)地球自转角速度的变化对每一脉冲星的脉冲周期和周期变率都存在影响,因此,在把地球上所测量的脉冲星脉冲到达时间归算到太阳系质心时,必须考虑地球自转角速度变化的影响。(2)地球自转角速度的变化对脉冲星的周期影响不大,但对周期变率的影响必须引起注意,特别是对于P较小的脉冲星,这种影响甚至可大于本体的周期变化。(3)地球自转角速度的变化对脉冲星周期变率影响的数值,取决于脉冲星的赤纬和观测台站的纬度;赤纬越大,纬度越高,其值越小。(4)在上、下中天观测,地球自转角速度的变化对脉冲星的周期变率的影响较大。     

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.     

On the Equation of Position Measurement of XNAV

The equation of position measurement of XNAV (X-ray pulsar-based autonomous navigation) reveals the relation between the time of arrival (TOA) of an X-ray photon and the spacecraft position at this moment. In specific dis- cussions of navigation, the TOA is generally replaced by the difference between the TOA and a preset “time reference”, and the spacecraft position is expressed by the position vector in the barycentric system of the solar system. The “time reference” may be the true TOA at the solar-system barycenter (SSB), or an “equivalent TOA” at SSB. As the true TOA at SSB is difficult to obtain, the “equivalent TOA” is more convenient for navigation. The equations of position measurement based on the two kinds of “time reference” are discussed, the equa- tion based on the “equivalent TOA”, which has the time accuracy of 0.1 ns, is given, and the physical meanings of the every term in which are analyzed.     

Autonomous optical navigation using nanosatellite-class instruments: a Mars approach case study

This paper examines the effectiveness of small star trackers for orbital estimation. Autonomous optical navigation has been used for some time to provide local estimates of orbital parameters during close approach to celestial bodies. These techniques have been used extensively on spacecraft dating back to the Voyager missions, but often rely on long exposures and large instrument apertures. Using a hyperbolic Mars approach as a reference mission, we present an EKF-based navigation filter suitable for nanosatellite missions. Observations of Mars and its moons allow the estimator to correct initial errors in both position and velocity. Our results show that nanosatellite-class star trackers can produce good quality navigation solutions with low position (\(<300\,\text {m}\)) and velocity (\(<0.15\,\text {m/s}\)) errors as the spacecraft approaches periapse.     

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.     

A new method for resolving phase ambiguity in radio interferometry using Earth rotation synthesis

As a key technique in deep space navigation, radio interferometry can be used to determine the accurate location of a spacecraft in the plane-of-sky by measuring its signal propagation time delay between two remote stations. To improve the measurement accuracy, differential phase delay without phase ambiguity is usually desired. Aiming at the difficulties of resolving phase ambiguity with few stations and narrowband downlink signals, a new method is proposed in this work by taking advantage of the Earth rotation. The high accurate differential phase delay between the spacecraft and a calibrator can be achieved not only in the in-beam observation mode but also in the out-of-beam observation mode. In this paper we firstly built the model of phase ambiguity resolution. Then, main measurement errors of the model are analyzed, which is followed by tests and validations of the model and method using the tracking data of the Cassini mission and Chang'E-3 mission. The results show that the phase ambiguities can be correctly resolved to generate a 10-picosecond level accuracy differential phase delay. Angular measurement accuracy of the Cassini reaches the milli-arc-second level, and the relative position accuracy between the Chang'E-3 rover and lander reaches the meter level.     

A Review for the Thermophysics and the Yarkovsky and YORP Effects of Asteroidstwo

The thermophysics of asteroids has become an important frontier for the research of asteroids in recent years. In this paper, we have introduced the thermophysical models commonly used in this field, by using these thermophysical models and combining with the data observed by the space or ground-based IR telescopes, some thermophysical parameters of asteroids, such as the thermal inertia, geometric albedo, effective diameter, surface roughness, and surface temperature, etc., can be derived. We have mentioned also the shape model and IR observation of asteroids, as well as the obtained thermophysical parameters for a part of asteroids. These thermophysical parameters can be further applied to studying the asteroids’ Yarkovsky effect, YORP effect, and so on, even can provide the relevant information for the spacecraft landing on the asteroid surface and the return mission of a spacecraft after the asteroid sampling.     

Creation of light-emitting diode optical beacons for spacecraft

A successful development of the semiconductor light-emitting diode (LED) technology made it possible to design efficient high-power light emission sources with small weight-and-size parameters. The technical characteristics of these LEDs allow one to use them as optical beacons on spacecraft. The application of LED optical beacons jointly with other equipment is intended to improve navigation support of space programs.     

Control of chaos in the vicinity of the Earth‐Moon L5 Lagrangian point to keep a spacecraft in orbit

The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi, and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L₅ of the Earth‐Moon system. We have determined the escape rate of the trajectories in the general three‐ and four‐body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L₅ point of the Earth‐Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L₅. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit‐keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time, and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L₅. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)