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Navigation ground verification is an essential part of X-ray pulsar navigation (XPNAV) research. Aiming at the need of real and continuous pulsar signals for navigation algorithm verification, and to avoid the difficulties and high costs of X-ray modulation and detection, we propose an XPNAV ground verification system based on visible light source. In this system, the pulsar signal model at the solar system barycenter and the orbit information are used to establish the real-time photon arrival rate function at a spacecraft, and then the rate function is digitized and converted into voltage signal by the designed hardware system to drive a linear light source. After the processes of light attenuation, signal detection and pulse discrimination are experienced, the real-time photon time of arrivals (TOAs) at a spacecraft can be achieved. These photon TOAs contain characteristics of the pulsar profiles and frequency, the time propagation effect in the solar system, and cosmic X-ray background. The system uses semi-physical devices to modulate and attenuate visible light, and judges whether the spacecraft can observe the navigation pulsar according to the real position, thereby realizing the simulation of X-ray propagation in space. At present, the detection method of pulsar observation with single detector include detection of single pulsar, time division detection of multiple pulsars, and simultaneous detection of multiple pulsars. The system has four channels, each of which has three output modes mentioned above, and can support the verification of multiple navigation modes. This system consists of signal simulator and controller, single photon generator and detector, single photon screening and time tagging, and navigation algorithm verification. This paper presents the testing results of the system characteristics, the authenticity of the simulated photon arrival time series and the navigation verification. Monte Carlo experiments show that the recording accuracy of photon arrival time is 10 ns and the delays of the four channels are (11 ± 2), (15 ± 4), (14 ± 3), and (16 ± 4)
${\text{μ}}{\rm{s}}$ , respectively. The multi-physical properties of simulated photon arrival time series are introduced in detail, including photon flux, shape of observation profile, pulsar frequency characteristics and Doppler shift. The position and velocity errors of autonomous navigation algorithm test are 13.587 km and 14.277 m·s–1, respectively, with an orbital altitude 26610 km and within 10 h. The ground verification system adopts master-slave control mode, the master computer mainly implements parameter setting and navigation algorithm verification, and the slave computer mainly carry out pulsar signal simulation. The communication based on TCP/IP protocol is applied to realize parameter transmission and real-time control between the master and slave computers in navigation verification process. The results of performance and functional test show that the system is available to accomplish the simulation of photon TOAs of X-ray pulsars at a spacecraft in real time and implement the ground verification of XPNAV.-
Keywords:
- X-ray pulsar navigation /
- ground verification system /
- multi-physical properties /
- signal simulation
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Zhang H, Xu L P 2011 Journal of Optoelectronics · Laser 22 905 (in Chinese)
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Emadzadeh A A, Speyer J L (translated by Hou J W, Yang G, He L, Wu R) 2013 Navigation in space by X-ray Pulsars (Beijing: National Defend Industry Press) pp15−19 (in Chinese)
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[20] 毛悦 2009 博士学位论文(郑州: 解放军信息工程大学)
Mao Y 2009 Ph. D. Dissertation (Zhengzhou: The PLA Information Engineering University) (in Chinese)
[21] Margaret A L, Victoria M K 2011 Astrophys. J. 742 31
Google Scholar
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Google Scholar
Fang H Y, Liu B, Li X P, Sun H F, Xue M F, Shen L R, Zhu J P 2016 Acta Phys. Sin. 65 119701
Google Scholar
[23] de Jager O C, Swanepoel J W H, Raubenheimer B C 1989 Astron. Astrophys. 221 180
[24] Sheikh S I, Pines D J, Ray P S, Wood K S, Lovellette M N, Wolff M T 2006 J. Guid. Control Dyn. 29 49
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图 1 系统组成 (a)结构图; (b)实物图
Figure 1. Component of the system: (a) Structure diagram; (b) physical diagram.
图 2 导航验证系统软件框架
Figure 2. Framework of navigation verification platform.
图 3 航天器处光子序列实时模拟原理图
Figure 3. Principle flow diagram of real-time simulation of photon TOA at the spacecraft.
图 4 航天器处光子序列实时模拟流程图
Figure 4. Flow diagram of simulation of photon TOA at the spacecraft.
图 5 电压合成电路组成
Figure 5. Diagram of the voltage synthesis which consists of a FPGA and a DAC.
图 6 DAC输出信号频谱
Figure 6. Frequency spectrum analysis of the DAC output signal.
图 7 系统时间延迟测量原理
Figure 7. Principle of system time delay measurement.
图 8 面积归一化的观测轮廓
Figure 8. Observed profiles by area normalization.
图 9 频率缓变特性模拟
Figure 9. Simulation of slow changing frequency characteristics.
图 10 光子序列的多普勒频移
Figure 10. Doppler frequency of photon TOA at the spacecraft.
图 11 导航算法验证流程图
Figure 11. Flow diagram of navigation algorithm verification.
图 12 导航算法结果 (a)评估界面截图; (b)算法精度
Figure 12. Results of navigation algorithm: (a) Evaluation-interface screenshot; (b) algorithm precision.
表 1 脉冲星流量
Table 1. Flux of pulsars.
脉冲星 实际流量/
ph·m–2·s–1模拟流量/ph·m–2·s–1 ±
标准差B0531+21 15400 15410 ± 100 B1821–24 51.93 53 ± 6 B1937+21 50.499 51 ± 4 B1509–58 212 214 ± 10 B0833–45 65.9 66 ± 5 
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表 2 航天器初始参数
Table 2. Initial parameters of spacecraft.
参数 航天器初始状态 状态初始估计值 X/m –13305111.403 –13305111.403 + 10000 Y/m 13305111.403 13305111.403 + 10000 Z/m 18816268.995 18816268.995 + 10000 Vx/m·s–1 –2736.715 –5473.431 + 10 Vy/m·s–1 –2736.715 –5473.431 + 10 Vz/m·s–1 0 0 + 10 R/m 26610222.806 26610222.806 + 17320.508 V/m·s–1 3870.299 3870.299 + 17.321
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表 3 脉冲星参数
Table 3. Pulsars parameters.
Pulsar B1509–58 B0531+21 B0833–45 RAJ 15 13 55.598 5 34 31.972 8 35 20.591 DECJ –59 8 9.56 22 0 52.07 –45 10 35.35 MJD 49180.000000505 49368.000000239 49353.000000103 f (0)/s–1 6.6327493860874 29.9167641742573 11.1975539227276 f (1)/s–2 –6.75556 × 10–11 –3.76613 × 10–10 –1.55984 × 10–11 f (2) /s–3 1.96 × 10–21 4.28 × 10–21 1.72 × 10–22 Area/m2 1 1 1
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[1] Sheikh S I 2005 Ph. D. Dissertation (USA: University of Maryland)
[2] 苏哲, 许录平, 王婷 2011 物理学报 60 119701
Google Scholar
Su Z, Xu L P, Wang T 2011 Acta Phys. Sin. 60 119701
Google Scholar
[3] 贝晓敏, 帅平, 黄良伟, 孙海峰, 吴耀军, 张倩 2014 物理学报 63 219701
Google Scholar
Bei X M, Shuai P, Huang L W, Sun H F, Wu Y J, Zhang Q 2014 Acta Phys. Sin. 63 219701
Google Scholar
[4] 薛梦凡, 李小平, 孙海峰, 刘兵, 方海燕, 沈利荣 2015 物理学报 64 219701
Google Scholar
Xue M F, Li X P, Sun H F, Liu B, Fang H Y, Shen L R 2015 Acta Phys. Sin. 64 219701
Google Scholar
[5] 胡慧君, 赵宝升, 盛立志, 鄢秋荣 2011 物理学报 60 029701
Google Scholar
Hu H J, Zhao B S, Sheng L Z, Yan Q R 2011 Acta Phys. Sin. 60 029701
Google Scholar
[6] 刘利, 郑伟, 汤国建, 孙守明 2012 国防科技大学学报 34 10
Google Scholar
Liu L, Zheng W, Tang G J, Sun S M 2012 Journal of National University of Defense Technology 34 10
Google Scholar
[7] 周峰, 吴光敏, 赵宝升, 盛立志, 宋娟, 刘永安, 鄢秋荣, 邓宁勤, 赵建军 2013 物理学报 62 119701
Google Scholar
Zhou F, Wu G M, Zhao B S, Sheng L Z, Song J, Liu Y A, Yan Q R, Deng N Q, Zhao J J 2013 Acta Phys. Sin. 62 119701
Google Scholar
[8] 徐能, 盛立志, 张大鹏, 陈琛, 赵宝升, 郑伟, 刘纯亮 2017 物理学报 66 059701
Google Scholar
Xu N, Sheng L Z, Zhang D P, Chen C, Zhao B S, Zheng W, Liu C L 2017 Acta Phys. Sin. 66 059701
Google Scholar
[9] 张华, 许录平 2011 光电子·激光 22 905
Zhang H, Xu L P 2011 Journal of Optoelectronics · Laser 22 905 (in Chinese)
[10] 孙海峰, 谢楷, 李小平, 方海燕, 刘秀平, 傅灵忠, 孙海建, 薛梦凡 2013 物理学报 62 109701
Google Scholar
Sun H F, Xie K, Li X P, Fang H Y, Liu X P, Fu L Z, Sun H J, Xue M F 2013 Acta Phys. Sin. 62 109701
Google Scholar
[11] Li X P, Xue M F, Fang H Y, Liu B, Sun H F, Liu Y M 2017 IEEE Trans. Ind. Electron. 64 1486
Google Scholar
[12] Winternitz L M B, Mitchell J W, Hassouneh M A, Valdez J E, Price S R, Semper S R, Yu W H, Ray P S, Wood K S, Arzoumanian Z, Gendreau K C 2015 IEEE Aerospace Conference Big Sky, MT, USA, March 7−14, 2015 p1
[13] 孙海峰, 包为民, 方海燕, 李小平 2014 物理学报 63 069701
Google Scholar
Sun H F, Bao W M, Fang H Y, Li X P 2014 Acta Phys. Sin. 63 069701
Google Scholar
[14] 郑世界, 葛明玉, 韩大炜, 王文彬, 陈勇, 卢方军, 鲍天威, 柴军营, 董永伟, 冯旻子, 贺健健, 黄跃, 孔敏南, 李汉成, 李陆, 李正恒, 刘江涛, 刘鑫, 师昊礼, 宋黎明, 孙建超, 王瑞杰, 王源浩, 文星, 吴伯冰, 肖华林, 熊少林, 许寒晖, 徐明, 张娟, 张来宇, 张力, 张晓峰, 张永杰, 赵一, 张双南 2017 中国科学: 物理学 力学 天文学 47 120
Zheng S J, Ge M Y, Han D W, Wang W B, Chen Y, Lu F J, Bao T W, Chai J Y, Dong Y W, Feng M Z, He J J, Huang Y, Kong M N, Li H C, Li L, Li Z H, Liu J T, Liu X, Shi H L, Song L M, Sun J C, Wang R J, Wang Y H, Wen X, Wu B B, Xiao H L, Xiong S L, Xu H H, Xu M, Zhang J, Zhang L Y, Zhang L, Zhang X F, Zhang Y J, Zhao Y, Zhang S N 2017Scientia Sinica Physica, Mechanica & Astronomica 47 120 (in Chinese)
[15] 张大鹏, 王奕迪, 姜坤, 郑伟 2018 宇航学报 39 411
Zhang D P, Wang Y D, Jiang K, Zheng W 2018 Journal of Astronautics 39 411 (in Chinese)
[16] 徐延庭, 宫超林, 胡慧君, 张玉兔, 邵思霈, 史钰峰, 宋娟, 宋晓林 2018 航天器工程 27 114
Google Scholar
Xu Y T, Gong C L, Hu H J, Zhang Y T, Shao S P, Shi Y F, Song J, Song X L 2018 Spacecraft Engineering 27 114
Google Scholar
[17] Mitchell J W, Winternitz L M, Hassouneh M A, Price S R, Semper S R, Yu W H, Ray P S, Wolff M T, Kerr M, Wood K S 2018 41st Annual American Astronautical Society (AAS) Guidance and Control Conference Breckenridge, CO, United States, February 1−7, 2018 p1
[18] 艾玛德扎赫, 斯派尔 著 (侯建文, 阳光, 贺亮, 吴蕊 译) 2013 X射线脉冲星导航 (北京: 国防工业出版社) 第15−19页
Emadzadeh A A, Speyer J L (translated by Hou J W, Yang G, He L, Wu R) 2013 Navigation in space by X-ray Pulsars (Beijing: National Defend Industry Press) pp15−19 (in Chinese)
[19] Chen P T, Speyer J L, Bayard D S, Majid W A 2017 J. Guid. Control Dyn. 40 2237
Google Scholar
[20] 毛悦 2009 博士学位论文(郑州: 解放军信息工程大学)
Mao Y 2009 Ph. D. Dissertation (Zhengzhou: The PLA Information Engineering University) (in Chinese)
[21] Margaret A L, Victoria M K 2011 Astrophys. J. 742 31
Google Scholar
[22] 方海燕, 刘兵, 李小平, 孙海峰, 薛梦凡, 沈利荣, 朱金鹏 2016 物理学报 65 119701
Google Scholar
Fang H Y, Liu B, Li X P, Sun H F, Xue M F, Shen L R, Zhu J P 2016 Acta Phys. Sin. 65 119701
Google Scholar
[23] de Jager O C, Swanepoel J W H, Raubenheimer B C 1989 Astron. Astrophys. 221 180
[24] Sheikh S I, Pines D J, Ray P S, Wood K S, Lovellette M N, Wolff M T 2006 J. Guid. Control Dyn. 29 49
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