脉冲星角位置参数是诸多研究领域的重要基础，如参考架建立、脉冲星计时模型建模、引力波探测和脉冲星导航等。获取高精度的角位置参数将推动脉冲星方面的研究工作进入更具实际价值的工程应用阶段。地面甚长基线干涉测量精度在毫角秒至亚毫角秒量级，由于地球半径限制、大气扰动、基线长度和时延估计误差等因素的影响，其测量精度难以继续提高。本文针对现有测量手段对角位置参数测量精度不足的难题，研究了高精度的脉冲星角位置测量方法。

脉冲星角位置测量是在惯性空间基准下，利用脉冲星辐射信号解算出赤经和赤纬参数的过程。本文研究了基于光子聚束效应的X射线脉冲星角位置测量方法。所提方法是利用两颗或两颗以上航天器的皮秒量级的观测数据，根据光子聚束原理，采用统计方法高精度的反演脉冲星的赤经和赤纬参数。它涉及脉冲星信号模型、光子聚束、高精度光子到达时间、时间校正分析、空间基线误差分析、符合矩阵拟合处理和光子到达时间仿真等。本文从以上方面开展了研究。

首先提出了一种基于光子符合的脉冲星角位置测量方法，该方法利用光子聚束效应中光子符合数目与角位置参数精度成正相关的现象，通过相干性测量获取高精度脉冲星角位置。本文设计了二阶相干函数计算方法，利用实验数据分析了相干函数的展宽效应，提出了X射线脉冲星辐射场相干性测量方案。观测X射线脉冲星相干性，即符合光子的数目，需要高精度的角位置参数，据此设计了所提方法流程并给出了证明过程。为从符合光子中提取角位置参数，构造了符合矩阵，设计了符合矩阵最大元素所在位置的拟合方法，给出了符合矩阵中主要图像特征为椭圆或直线两种情况下的算法和约束方程。考虑脉冲星自行，推导了角位置变化速率公式，分析了观测时长的约束条件，给出了任意时刻脉冲星角位置拟合方法。并将所提方法与时延量测角方法进行比较，从理论上表明了所提方法不存在难以收敛的问题。

然后从时间校正、光子聚束比例、光子符合精度、位置误差和航天器轨道夹角等方面，分析了所提方法的影响因素，并进行了仿真。仿真结果表明：为实现亚皮秒量级的仿真精度需要采用全部航天器处到太阳系质心处的时间校正项；航天器处到参考位置处的时间校正公式只需使用几何、太阳和地球Shapiro时延项即可实现皮秒量级的时间校正；所提方法要求位置误差小于厘米量级，在高光子聚束比例下，光子符合精度提高1个数量级对应测角精度提高1个数量级，在低光子聚束比例下，为实现同样的测量精度需要适当降低光子符合精度；航天器轨道夹角和初始位置会影响符合矩阵主要特征图像的形状，最好采用三个航天器进行联合观测。

最后设计了高精度的数值仿真方法，实现了软件验证系统，并给出仿真结果。推导了含有自行速度参数的太阳系质心处脉冲星计时模型，通过仿真计算，在30天内传统计时模型的相位精度约在10-8量级。设计了一种亚皮秒量级的具有二阶相干特性的航天器处光子到达时间仿真方法。以可视化软件形式实现了数值仿真验证系统，可进行在轨实验前的地面验证。对光子符合角位置测量方法的仿真结果表明：在光子聚束比例为0.0001，光子符合精度为0.1 ns，总观测时长为10000 s，航天器和地球位置误差标准差均为1 cm，使用三个航天器且探测器有效面积均为100 cm2进行联合观测的情况下，实现了对Crab脉冲星赤经的测量误差小于5个微时秒和赤纬小于32个微角秒的高精度测量。

本文所提基于光子符合的测量方法实现了微角秒精度的脉冲星角位置测量目标，分析了影响因素并进行仿真验证。该方法比地面甚长基线干涉测量的精度高1到2个数量级。

Pulsar angular position parameters are the important basis of many research fields, such as reference frame establishment, pulsar timing modeling, gravitational wave detection and pulsar navigation. The parameter with high precision is essential part of the process from the research work on pulsars to practical engineering. The accuracy of very long baseline interferometry ranges from milliarcsecond to sub-milliarcsecond. Because of the limitation of Earth radius, atmospheric disturbance and estimation error of baseline length and time delay, it is difficult to improve the measurement accuracy. Aiming at the problem of inadequate accuracy of angular position by existing methods, this paper studies a high precision method for measuring the angular position of pulsars.

Pulsar angular position measurement is a process of calculating the right ascension and the declination by the radiation signal of the pulsar in the inertial space reference. In this paper, we study a method for measuring the angular position of pulsars. Based on photon coincidence principle, a new method is proposed which uses the observed picosecond data of two or more spacecraft to precisely retrieve the right ascension and the declination of pulsars by statistical method. This paper introduces pulsar signal model, high precision photon arrival time, time transfer analysis, spatial baseline error analysis, coincidence matrix fitting and simulation of photon time of arrival.

Firstly, we propose a method for measuring the angular position of pulsars based on photon coincidence. The method is based on the phenomenon that the number of photon coincidence in photon bunching effect is positively related to the accuracy of angular position parameters, so the high-precision pulsar angle position can be obtained through coherence measurement. We also design the calculation method of second-order coherence function, and analyze the broadening effect of this function by using experimental data, and propose the coherent measurement scheme for X-ray pulsars. Observing the radiation field coherence of X-ray pulsar, which is consistent with the number of photon coincidence, requires high accuracy angular position parameters. Based on this, this paper introduces the proof and flow of the method. In order to get angular position parameters from coincidence photons, we construct a coincidence matrix, and design a fitting method for the location of the largest element of the matrix, introducing constraint equation and algorithm when the main image features of the coincidence matrix are ellipse or straight line. Considering the self-motion of pulsars, we deduce the formula of angular position change rate, and analyze the constraints of observation time, and introduce the fitting method for obtaining the angular position at any time. The theoretical comparison between the proposed method and the angle measurement by time-delay method shows that the proposed method is convergent.

Then, the influence factors of the proposed method are analyzed by simulation, such as time transfer model, photon bunching ratio, photon coincidence accuracy, position error and spacecraft orbit angle. The sub-picosecond simulation accuracy can only be achieved by using all time transfer items from spacecraft to the center of mass of the solar system. In addition, time transfer formula from spacecraft to reference position can be realized in picosecond order merely using geometry, Sun and Earth Shapiro time delay items. And the proposed method demands that the position error is less than centimeter. In the case of high photon bunching ratio, increasing photon coincidence accuracy by one order of magnitude leads to an increase in angle measurement accuracy by one order of magnitude. Otherwise, in the case of low photon bunching ratio, the same measurement accuracy can be achieved by reducing the photon coincidence accuracy appropriately. The orbital angle of spacecraft will affect the shape of the main characteristic image of coincidence matrix, so it is best to use three spacecraft for observation.

Finally, we put forward a high-precision numerical simulation method and design a verification software. The timing model is deduced at the center of mass of the solar system containing pulsar velocity information, and the phase accuracy of the traditional timing model is about 10-8 orders of magnitude in 30 days. A method of simulating photon time of arrival at spacecraft is proposed, which has sub-picosecond accuracy and second-order coherence. So the software can be used for ground verification before on-orbit experiments. The simulation results show that the measurement error of Crab pulsar right ascension and declination is less than 5 μs and 32 μas respectively, in the case of ratio of photon bunching 0.0001, photon coincidence accuracy 0.1 ns, position error 1 cm, three spacecraft’s effective area 100 cm2 and total observation time length 10,000 s.

The method based on photon coincidence proposed in this paper achieves the target of micro-arcsecond accuracy of pulsar angular position. The influencing factors are analyzed and verified by simulation. The accuracy of this method is 1 to 2 orders of magnitude higher than that of very long baseline interferometry.

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