修正钟差的脉冲星方位误差估计算法

doi:10.12305/j.issn.1001-506X.2021.03.24

摘要/Abstract

摘要：

为克服时钟钟差对脉冲星方位误差估计的影响, 设计了两步卡尔曼滤波(two-stage Kalman filter, TSKF)算法。首先, 分析时钟钟差对脉冲星方位误差估计的影响, 并通过仿真进行验证。其次, 结合脉冲星方位误差估计原理重新推得考虑时钟钟差的状态和观测方程。再次, 根据TSKF算法, 在估计方位误差的同时解耦估计时钟钟差。最后, 仿真结果显示, 当钟差导致传统算法估计偏差较大时, TSKF算法依然能有效抑制钟差的影响, 使赤经和赤纬误差估计精度均保持在0.1 mas以内。

关键词: 方位误差, 时钟钟差, 卡尔曼滤波, 两步滤波

Abstract:

In order to overcome the influence of clock error on pulsar position error estimation, a two-stage Kalman filter (TSKF) algorithm is designed. Firstly, the influence of the clock error on the estimation of pulsar position error is analyzed and verified by simulation. Secondly, combined with the principle of pulsar position error estimation, the state and observation equations of the clock error are considered again. Thirdly, according to the TSKF algorithm, when estimating the position error, the clock error is decoupled. Finally, the simulation results show that when the clock error causes the traditional algorithm to estimate a large deviation, the TSKF algorithm can still effectively suppress the influence of the clock error, so that the accuracy of right ascension and declination error estimation are both kept within 0.1 mas.

Key words: position error, clock error, Kalman filter, two-stage filtering

中图分类号:

肖永强, 王宏力, 冯磊, 由四海, 何贻洋, 许强. 修正钟差的脉冲星方位误差估计算法[J]. 系统工程与电子技术, 2021, 43(3): 789-795.

Yongqiang XIAO, Hongli WANG, Lei FENG, Sihai YOU, Yiyang HE, Qiang XU. Pulsar position error estimation algorithm with corrected clock error[J]. Systems Engineering and Electronics, 2021, 43(3): 789-795.

图/表 12

图1

图2

表1

表2

图3

图4

表3

图5

表4

图6

图7

表5

参考文献 34

1	EMADZADEH A , SPEYER J L . Relative navigation between two spacecraft using X-ray pulsars[J]. IEEE Trans.on Control Systems Technology, 2010, 19 (5): 1021- 1035.
2	SHEIKH S I , HANSON J E , GRAVEN P H , et al. Spacecraft navigation and timing using X-ray pulsars[J]. Navigation, 2011, 58 (2): 165- 186. doi: 10.1002/j.2161-4296.2011.tb01799.x
3	XIAO M L , ZHANG Y B , FU H M , et al. Nonlinear unbiased minimum-variance filter for Mars entry autonomous navigation under large uncertainties and unknown measurement bias[J]. ISA Transactions, 2018, 76 (3): 97- 109.
4	ZHANG H , JIAO R , XU L P . Formation of a satellite navigation system using X-ray pulsars[J]. Publications of the Astronomical Society of the Pacific, 2019, 131 (8): 24- 35.
5	XU Q , WANG H L , FENG L , et al. A novel X-ray pulsar integrated navigation method for ballistic aircraft[J]. Optik, 2018, 175 (9): 28- 38.
6	CHEN P T , SPEYER J L , BAYARD D S , et al. Autonomous navigation using X-ray pulsars and multirate processing[J]. Journal of Guidance, Control, and Dynamics, 2017, 40 (9): 2237- 2249. doi: 10.2514/1.G002705
7	XUE M F , SHI Y F , GUO Y F , et al. X-ray pulsar-based navigation considering spacecraft orbital motion and systematic biases[J]. Sensors, 2019, 19 (8): 18- 77.
8	WANG Y D , ZHENG W , AN X Y , et al. XNAV/CNS integrated navigation based on improved kinematic and static filter[J]. The Journal of Navigation, 2013, 66 (6): 899- 918. doi: 10.1017/S0373463313000301
9	CUI P Y , WANG S , GAO A , et al. X-ray pulsars/Doppler integrated navigation for Mars final approach[J]. Advances in Space Research, 2016, 57 (9): 1889- 1900. doi: 10.1016/j.asr.2016.02.001
10	YANG H F , WANG Z H , FU H M , et al. Integrated navigation for Mars final approach based on Doppler radar and X-ray pulsars with atomic clock error[J]. Acta Astronautica, 2019, 159 (7): 308- 318.
11	LI X Y , JIN J , SHEN Y . Modified unscented Kalman filter for X-ray pulsar-based navigation system in the presence of measurement outliers[J]. Proceedings of the Institution of Mechanical Journal of Aerospace Engineering, 2016, 232 (2): 260- 269.
12	GUO P B , SUN J , HU S L , et al. Multirate observation-based X-ray pulsar navigation technique[J]. Journal of Aerospace Engineering, 2017, 30 (2): 13- 22.
13	ZHANG H , JIAO R , XU L P . Orbit determination using pulsar timing data and orientation vector[J]. The Journal of Navigation, 2019, 72 (1): 155- 175. doi: 10.1017/S0373463318000632
14	LIU J , MA J , TIAN J W , et al. X-ray pulsar navigation method for spacecraft with pulsar direction error[J]. Advances in Space Research, 2010, 46 (11): 1409- 1417. doi: 10.1016/j.asr.2010.08.019
15	WANG Y D , ZHENG W , SUN S M , et al. X-ray pulsar-based navigation using time-differenced measurement[J]. Aerospace Science and Technology, 2014, 36 (10): 27- 35.
16	WANG Y D , ZHENG W , SUN S M , et al. Robust information filter based on maximum correntropy criterion[J]. Journal of Guidance, Control, and Dynamics, 2016, 39 (5): 1126- 1131. doi: 10.2514/1.G001576
17	刘劲. 基于X射线脉冲星的航天器自主导航方法研究[D]. 武汉: 华中科技大学, 2011.
	LIU J. Research on autonomous navigation method of spacecraft based on X-ray pulsar[D]. Wuhan: Huazhong University of Science and Technology, 2011.
18	孙守明, 郑伟, 汤国建. X射线脉冲星星表方位误差估计算法研究[J]. 飞行器测控学报, 2010, 29 (2): 57- 60.
	SUN S M , ZHENG W , TANG G J . Research on estimation of position error of X-ray pulsar[J]. Journal of Aircraft Measurement and Control, 2010, 29 (2): 57- 60.
19	XU Q , WANG H L , FENG L , et al. An improved augmented X-ray pulsar navigation algorithm based on the norm of pulsar direction error[J]. Advances in Space Research, 2018, 62 (11): 3187- 3198. doi: 10.1016/j.asr.2018.08.026
20	REN X B , NIE G G , LI L Y . An Improved augmented algorithm for direction error in XPNAV[J]. Symmetry, 2020, 12 (7): 165- 178.
21	XIONG K , WEI C L , LIU L D . Robust Kalman filtering for discrete-time nonlinear systems with parameter uncertainties[J]. Ae-rospace Science and Technology, 2012, 18 (1): 15- 24. doi: 10.1016/j.ast.2011.03.012
22	NING X L , GUI M Z , FANG J C , et al. Differential X-ray pulsar aided celestial navigation for Mars exploration[J]. Aerospace Science and Technology, 2017, 62 (7): 36- 45.
23	NING X L , GUI M Z , ZHANG J , et al. Impact of the Pulsar's direction on CNS/XNAV integrated navigation[J]. IEEE Trans.on Aerospace and Electronic Systems, 2017, 53 (6): 3043- 3055. doi: 10.1109/TAES.2017.2725518
24	GU L , JIANG X Q , LI S , et al. Optical/radio/pulsars integrated navigation for Mars orbiter[J]. Advances in Space Research, 2019, 63 (1): 512- 525. doi: 10.1016/j.asr.2018.09.005
25	王宏力, 许强, 由四海, 等. 考虑卫星位置误差的增广脉冲星方位误差估计算法[J]. 国防科技大学学报, 2018, 40 (5): 177- 182.
	WANG H L , XU Q , YOU S H , et al. Augmentation pulsar position error estimation algorithm considering satellite position error[J]. Journal of National University of Defense Technology, 2018, 40 (5): 177- 182.
26	孙守明, 郑伟, 汤国建. X射线脉冲星/SINS组合导航中的钟差修正方法研究[J]. 国防科技大学学报, 2010, 32 (6): 82- 86.
	SUN S M , ZHENG W , TANG G J . Research on clock error correction method in X-ray pulsar/SINS integrated navigation[J]. Journal of National University of Defense Technology, 2010, 32 (6): 82- 86.
27	LIU J , MA J , TIAN J W , et al. Pulsar navigation for interplanetary missions using CV model and ASUKF[J]. Aerospace Science and Technology, 2012, 22 (1): 19- 23. doi: 10.1016/j.ast.2011.04.010
28	王璐, 史晨曦, 李建勋, 等. 考虑钟差修正的脉冲星与多普勒差分组合导航[J]. 电波科学学报, 2018, 33 (2): 217- 224.
	WANG L , SHI C X , LI J X , et al. Pulsar and Doppler difference integrated navigation considering clock error correction[J]. Journal of Radio Science, 2018, 33 (2): 217- 224.
29	HAESSIG D , FRIEDLAND B . Separate-bias estimation with reduced-order Kalman filters[J]. IEEE Trans.on Automatic Control, 1998, 43 (7): 983- 987. doi: 10.1109/9.701106
30	李孝辉, 吴海涛, 高海军, 等. 用Kalman滤波器对原子钟进行控制[J]. 控制理论与应用, 2003, 28 (4): 551- 554. doi: 10.3969/j.issn.1000-8152.2003.04.014
	LI X H , WU H T , GAO H J , et al. Controlling atomic clock with Kalman filter[J]. Control Theory & Applications, 2003, 28 (4): 551- 554. doi: 10.3969/j.issn.1000-8152.2003.04.014
31	FRIEDLAND B . Treatment of bias in recursive filtering[J]. IEEE Trans.on Automatic Control, 1969, 14 (4): 359- 367. doi: 10.1109/TAC.1969.1099223
32	IGNAGNI M B . Separate bias Kalman estimator with bias state noise[J]. IEEE Trans.on Automatic Control, 1990, 35 (3): 338- 341. doi: 10.1109/9.50352
33	王奕迪, 郑伟, 孙守明, 等. 考虑系统偏差的脉冲星守时算法研究[J]. 国防科技大学学报, 2013, 35 (2): 12- 16.
	WANG Y D , ZHENG W , SUN S M , et al. Research on pulsar timekeeping algorithm considering system deviation[J]. Journal of National University of Defense Technology, 2013, 35 (2): 12- 16.
34	许强, 范小虎, 徐利国, 等. 脉冲星方位误差估计的TSKF算法[J]. 北京航空航天大学学报, 2020, 46 (4): 761- 768.
	XU Q , FAN X H , XU L G , et al. TSKF algorithm for estimating pulsar position error[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46 (4): 761- 768.

脉冲星参数	参数值
赤经/(°)	83.63
赤纬/(°)	22.01
距离/kpc	2.0
P/ms	33.4
W/ms	1.7
F_x/(ph·cm^-2·s^-1)	1.54
p_f/%	70

卫星轨道参数	参数值
半长轴/km	7 460
离心率	4.55×10^-16
轨道倾角/(°)	25
近地点幅角/(°)	45
升交点赤经/(°)	0
初始真近地点/(°)	30
起始时间	2015-7-1T12-00-00

钟差(×10^-6)/s	未修正钟差的估计偏差/mas	TSKF估计偏差/mas
1	(2.940, 21.090)	(0.002, 0.013)
2	(4.760, 34.070)	(0.005, 0.034)
3	(6.580, 46.870)	(0.007, 0.062)
4	(8.410, 59.960)	(0.008, 0.063)
5	(10.230, 74.920)	(0.010, 0.092)
6	(12.050, 85.890)	(0.012, 0.101)
7	(13.870, 98.890)	(0.014, 0.124)
8	(15.690, 111.790)	(0.015, 0.125)
9	(17.510, 124.740)	(0.019, 0.150)
10	(19.330, 137.660)	(0.020, 0.160)

钟差(×10^-6)/s	TSKF估计偏差/mas	ASKF估计偏差/mas
2	(0.005, 0.034)	(0.005, 0.031)
5	(0.010, 0.092)	(0.008, 0.086)
10	(0.020, 0.160)	(0.020, 0.139)

A₀(×10^-6)/s	B₀(×10^-6)/s	TSKF估计偏差/mas
1	1	(0.015, 0.048)
2	1	(0.021, 0.057)
1	2	(0.019, 0.061)
2	2	(0.036, 0.077)