星载光纤陀螺随机漂移建模及滤波方法研究
|
摘要
传统的机械陀螺和激光陀螺捷联惯导系统具有体积大,重量大,可靠性低等缺点,而光纤陀螺捷联惯导系统正好弥补了上述不足,广泛的应用在了卫星导航系统上,而影响系统导航精度的主要因素之一是随时间积累而积累的光纤陀螺漂移。
为了提高卫星姿态确定精度,本文对光纤陀螺噪声源进行了分析,并对光纤陀螺随机漂移数据进行了统计检验,这些统计检验包括平稳性检验、周期性检验、正态检验,并对数据进行预处理,采用时间序列分析法建立了自回归模型和自回归滑动平均模型,对光纤陀螺随机漂移进行了kalman滤波。
此外,小波分析是一种具有多分辨分析能力的时频分析方法,适合对非平稳信号进行分析。小波分析也是用来分析光纤陀螺随机漂移的常用方法。本文研究了小波理论并对光纤陀螺随机漂移进行了小波分析。并用Allan方差法评定了两种滤波效果,Allan方差法评的结果表明,采用小波滤波省去了对光纤陀螺随机漂移数据的统计检验的工作,不用建立时间序列模型,仿真结果表明小波滤波能有效地减小光纤陀螺随机漂移,并且滤波效果优于kalman滤波。
针对对地定向三轴稳定卫星,采用四元数法,基于扩展kalman滤波理论,设计了“光纤陀螺+星敏感器”模式的姿态确定系统,仿真结果表明光纤陀螺随机漂移的减小有利于卫星姿态估计精度的提高,进一步肯定了光纤陀螺随机漂移的滤波对提高系统精度的意义。
Traditiona l mecha nical gyro SINS and laser gyro SINS have disad vantages suchas bulky, heavy, low reliability, and so on. FOG SINS can make up for thesedeficiencies, so it is used widely in satellite navigation system. One of the ma infactors affecting the accuracy of the system is that the drift of FOG increase s withtime.
In order to improve the precision of satellite attitude determination, the paperanalyzes the noise source of FOG, and inspects the data of the random drift throughstatistica l test including stability test, period ic test and norma l test. After the datapretreatment, the regression model and the auto-regression moving model isestablished through the time series analysis theory. And then, the data of the FOGrandom drift is processed by Kalma n filter.
In addition, wavelet analysis is a time-frequency analysis method with multiresolutionanalysis capability, which is suitable for non-sta tionary signa l analysis.Also, it is the usua l method to analyze the random drift of FOG. The paper studies thewavelet theory, by which analyzing the FOG random drift. Besides, the papercompares the results of the two filter methods with the Allan varia nce. The resultsshow that the wavelet filter method don’t need the statistica l test and the datapretreatment. Howev er, it can minish the FOG random drift effectively and the effectis better than Kalman filter method.
The paper designs an attitude determination system of“FOG + Star sensor”using extended Kalman filter theory for the Earth-oriented three-axis stabilizedsatellite, basing on the quaternion method. The simulation results show the system isfeasible, with a high precision of attitude estimate. It also show minishing the FOGrandom drift can improve the precision of attitude estimate , proving the mea ning ofthe filter of FOG random drift to improve the system precision.
为了提高卫星姿态确定精度,本文对光纤陀螺噪声源进行了分析,并对光纤陀螺随机漂移数据进行了统计检验,这些统计检验包括平稳性检验、周期性检验、正态检验,并对数据进行预处理,采用时间序列分析法建立了自回归模型和自回归滑动平均模型,对光纤陀螺随机漂移进行了kalman滤波。
此外,小波分析是一种具有多分辨分析能力的时频分析方法,适合对非平稳信号进行分析。小波分析也是用来分析光纤陀螺随机漂移的常用方法。本文研究了小波理论并对光纤陀螺随机漂移进行了小波分析。并用Allan方差法评定了两种滤波效果,Allan方差法评的结果表明,采用小波滤波省去了对光纤陀螺随机漂移数据的统计检验的工作,不用建立时间序列模型,仿真结果表明小波滤波能有效地减小光纤陀螺随机漂移,并且滤波效果优于kalman滤波。
针对对地定向三轴稳定卫星,采用四元数法,基于扩展kalman滤波理论,设计了“光纤陀螺+星敏感器”模式的姿态确定系统,仿真结果表明光纤陀螺随机漂移的减小有利于卫星姿态估计精度的提高,进一步肯定了光纤陀螺随机漂移的滤波对提高系统精度的意义。
Traditiona l mecha nical gyro SINS and laser gyro SINS have disad vantages suchas bulky, heavy, low reliability, and so on. FOG SINS can make up for thesedeficiencies, so it is used widely in satellite navigation system. One of the ma infactors affecting the accuracy of the system is that the drift of FOG increase s withtime.
In order to improve the precision of satellite attitude determination, the paperanalyzes the noise source of FOG, and inspects the data of the random drift throughstatistica l test including stability test, period ic test and norma l test. After the datapretreatment, the regression model and the auto-regression moving model isestablished through the time series analysis theory. And then, the data of the FOGrandom drift is processed by Kalma n filter.
In addition, wavelet analysis is a time-frequency analysis method with multiresolutionanalysis capability, which is suitable for non-sta tionary signa l analysis.Also, it is the usua l method to analyze the random drift of FOG. The paper studies thewavelet theory, by which analyzing the FOG random drift. Besides, the papercompares the results of the two filter methods with the Allan varia nce. The resultsshow that the wavelet filter method don’t need the statistica l test and the datapretreatment. Howev er, it can minish the FOG random drift effectively and the effectis better than Kalman filter method.
The paper designs an attitude determination system of“FOG + Star sensor”using extended Kalman filter theory for the Earth-oriented three-axis stabilizedsatellite, basing on the quaternion method. The simulation results show the system isfeasible, with a high precision of attitude estimate. It also show minishing the FOGrandom drift can improve the precision of attitude estimate , proving the mea ning ofthe filter of FOG random drift to improve the system precision.
引文
1胡静珍.光纤陀螺在小卫星上的应用研究.传感器技术. 2003, 17(3), 17-22
2 Spahlingeret G. Error compensation via signa l correla tion in high precisionclosed-loop fiber optic gyros SPIE, 1996, 2837: 218-227
3张桂才.光纤陀螺原理与技术.国防工业出版社, 2005. 28-29
4 Vali V, Shorthill R W, Fiber Ring Interferomerer. Applied Optics, 1996,15:1099-1100
5周海波,刘建业,赖际舟,李荣冰.光纤陀螺仪的发展现状.传感器技术.2005, 24(6): 1-3
6毛奔,林玉荣.惯性器件测试与建模.哈尔滨工程大学出版社, 2008. 98-114
7 USUI R, OH NO A. Recent Progress of Fiber Optic Gyroscopes and APPlica tionsat JAE(A). Optical Fiber Sensors Conference Techniea l Digest. USA. OFS 2002:11-14
8 Sanders G A, Za franiec B S, Liu R Y, et al. Fiber optic gyros for space marine andaviation applica tions. High-Performa nce Fiber Optic Gyros. 1996, 2837: 61-7l
9 Honeywell To Acquire Smiths Industries Fiber Optic Gyroscope Technology AndProducts Business Wire, March 14, 1996, 20-23
10 Culter C C, Show H J, Bergh R A. Source statistics and Kerr effe ct in fiber opticgyroscopes. Optics Letts, 1982, Vol.7: 563-565
11 ZHANG Fu-xue, WANG Hong-wei, ZHANG Nan. The structure principle ofsilicon micromachined driven by the rotating carrier. Internationa l Journal ofInformation Acquisition, 2005, 2(3): 11-18
12 Davis J L, Ezek iel S, Closed loop, high sensitivity fiber optic gyroscope. Fiber-Optic RotationSensors, Ezek iek S. Arditty H. J. Springs-Verla g, Berlin, 2002, 5(3):297-301
13冷宗圣.光纤陀螺的研究发展及其应用.光学技术. 2006, 5(6): 12-16
14 Sanders S J, Strandjord L K. Fiber optic gyro technology trendsa Honeywellperspective. Optica l Fiber Sensors Conference Technica l Digest, 2002(1): 5-8
15杨亭鹏,高亚楠,陈家斌.光纤陀螺仪零漂信号的Alla n方差分析.光学技术.2005, 31(1): 85-90
16 Tehrani M M, Ring Laser Gyro Data Analysis with Cluster Sampling Technique,SPIE, 1993, 412: 207-220
17 Seong SM, Lee J G, Park C G. Equivalent ARMA model representation for RL Grandom errors. IEEE Transactions on Aerospace and Electronics Systems, 2000,36(1): 286-290
18汤霞清,宗艳桃,郭理彬,贺勇.光纤陀螺随机漂移分析与建模方法.火力与指挥控制. 2008(33): 14-16
19 Hornby G S, Pollack J B. Creating high-level homponents with a generativerepresentation for body-brain evolution. Artificia l Life, 2002, 8(3): 8-12
20 IEEE Standard Specification Format Guide and Test Procedure for Single-AxisInterferometric Fiber Optic Gyros IEEE Std 952-1997
21 Sylvain S. Minima x threshold for denoising complex signa lwithwave shrink.IEEE Transactions on Signal Processing, 2000, 48(4): 422-428
22 Tuckenss M. Analysis of optica l navigation error during mass enery appliedmathematics and computation. J. of metrry and Remote Sensing, 2004, 80(1):1-22
23张晓峰,张桂才,巴晓艳.闭环消偏光纤陀螺输出数据Alla n方差分析的改进方法研究导航与控制. 2006(1): 53-57
24 G.koulouras, K. Kontkaos, I. Stavrakas. Embedded ComPact Flash. CcriultDeviees, EIEE, 2005, 1(4): 27-34
25 Randy Alla n. Compiling High-level Languages to DSPs. Signal Procesing, IEEE,2005, 22(3): 47-56
26祝树生,任建新,张安峰.光纤陀螺随机游走分析方法研究.应用光学. 2009 .30(6): 1003-1006
27朱奎宝,张春熹,张小跃.光纤陀螺随机漂移ARMA模型研究.宇航学报. 2006. 27(5): 1118-11120
28 PepperD M, Wang HTM. Nuclear Magnetic Resona nce Gyroscopes: AD -A 1249
25, 2004, 18(2): 10-13
29 Ng L C and Pines D J. Characterization of ring laser gyro performa nce using theallan varia nce mothod. Journal of Guidance, Control, and Dynamics, 2003, 20(1):16-20
30周海波,刘建业,赖际舟.干涉型光纤陀螺随机噪声的分析研究.传感器与微系统, 2006, 25(11): 73-76
31 Chen Xi-yuan. Modeling random gyro drift by time series neura l net works andbytraditiona l. method. IEEE. Int. Conf. Neutra l. Networks&Signal. Processing,Nanjing, Ch-ina. December, 2003: 14-17
32 Aboelma gd Noureld in, Dave Irvine-Halllday. New technique for reducing theangle random walk at the output of fiber optic gyroscopes during alignmentprocesses of inertia l navigation systems. 2001 Society of Photo-OpticalInstrumentation Engineers, 2001
33李晓峰,徐军,张胜修.光纤陀螺随机误差建模与滤波方法研究.光学技术.2008. 34. 179-180
34王雪平,李俊,张福斌.基于时间序列分析方法的FOG随机漂移建模与辨识.鱼雷技术, 2007, 15(4): 34-37
35 MIAO Ling-jua n, ZHANG Fang-sheng, SHENG Jun, LIU Wei. Data analysis andmodeling of fiber optic gyroscope drift. Journal of Beijing institute of technology,2002, 11(1)
36王新龙,陈涛,杜宇.基于ARMA模型的光纤陀螺漂移数据建模方法研究.弹箭与制导学报, 2006, 20(1): 5-7
37侯青剑,缪栋,彭云辉.激光陀螺随机漂移数据建模与滤波.中国惯性技术学报, 2005, 13(4): 39-42
38 Simon D, Chizeck H J. Kalman Filtering with Statistica l State Constraints.Control and Intelligent Systems (S1480-1752), 2006, 34(1): 73-79
39 Hornby G S, Pollack J B. Creating high-level homponents with a generativerepresentation for body-brain evolution. Artificia l Life, 2002, 8(3), 26-29
40王海,陈家斌. FOG随机漂移测试及分析.光学技术. 2004, 30(5): 623-625
41 Hao Wang, TIAN Weifeng. Modeling the random drift of micro-machinedgyroscope with neura l network. Neural Processing Letters, 2005, 22(3): 234-238
42缪玲娟.小波分析在光纤陀螺信号滤波中的应用.宇航学报. 2006. 21(1): 42-46
43 Sweldend W. The lifting scheme: A custom-design construction of biorthogoa nlwavelets. Applied and Computaion Harmonic Analysis, 2006, 3(2): 186-200
44秦前清,杨宗凯.实用小波分析.西安电子科技大学出版社. 1995: 112-134
45 Cohen A, Daubechies I. Orthonormal bases of compactly supported wavelets.Bette frequency resolution. SIAM J. Math. Anal. 2004, 24(2): 517-529
46刘镇平,张春熹,王妍.小波分析在捷联惯导陀螺信号中的应用.中国惯性技术学报. 2005, 2(1): 74-86
47袁瑞铭,韦锡华,李自怡,袁瑞雪.基于小波阈值滤波的光纤陀螺信号消噪算法.中国惯性技术学报. 2003, 12(5): 43-47
48 Daubechiesi. orthonorma l bases of compactly supported wavelets. variations on atheme. SIAM J. Math. Anal. 2005, 24(2): 490-524
49黄文梅,熊桂林,杨勇.信号分析与处理MATLAB语言及应用.国防科技大学出版社. 2007: 99-107
50屠善澄.卫星姿态动力学与控制.北京:宇航出版社, 1998, 4-8
51黄圳奎.航天器姿态动力学.长沙:国防科技大学出版社,1997, 3-9
2 Spahlingeret G. Error compensation via signa l correla tion in high precisionclosed-loop fiber optic gyros SPIE, 1996, 2837: 218-227
3张桂才.光纤陀螺原理与技术.国防工业出版社, 2005. 28-29
4 Vali V, Shorthill R W, Fiber Ring Interferomerer. Applied Optics, 1996,15:1099-1100
5周海波,刘建业,赖际舟,李荣冰.光纤陀螺仪的发展现状.传感器技术.2005, 24(6): 1-3
6毛奔,林玉荣.惯性器件测试与建模.哈尔滨工程大学出版社, 2008. 98-114
7 USUI R, OH NO A. Recent Progress of Fiber Optic Gyroscopes and APPlica tionsat JAE(A). Optical Fiber Sensors Conference Techniea l Digest. USA. OFS 2002:11-14
8 Sanders G A, Za franiec B S, Liu R Y, et al. Fiber optic gyros for space marine andaviation applica tions. High-Performa nce Fiber Optic Gyros. 1996, 2837: 61-7l
9 Honeywell To Acquire Smiths Industries Fiber Optic Gyroscope Technology AndProducts Business Wire, March 14, 1996, 20-23
10 Culter C C, Show H J, Bergh R A. Source statistics and Kerr effe ct in fiber opticgyroscopes. Optics Letts, 1982, Vol.7: 563-565
11 ZHANG Fu-xue, WANG Hong-wei, ZHANG Nan. The structure principle ofsilicon micromachined driven by the rotating carrier. Internationa l Journal ofInformation Acquisition, 2005, 2(3): 11-18
12 Davis J L, Ezek iel S, Closed loop, high sensitivity fiber optic gyroscope. Fiber-Optic RotationSensors, Ezek iek S. Arditty H. J. Springs-Verla g, Berlin, 2002, 5(3):297-301
13冷宗圣.光纤陀螺的研究发展及其应用.光学技术. 2006, 5(6): 12-16
14 Sanders S J, Strandjord L K. Fiber optic gyro technology trendsa Honeywellperspective. Optica l Fiber Sensors Conference Technica l Digest, 2002(1): 5-8
15杨亭鹏,高亚楠,陈家斌.光纤陀螺仪零漂信号的Alla n方差分析.光学技术.2005, 31(1): 85-90
16 Tehrani M M, Ring Laser Gyro Data Analysis with Cluster Sampling Technique,SPIE, 1993, 412: 207-220
17 Seong SM, Lee J G, Park C G. Equivalent ARMA model representation for RL Grandom errors. IEEE Transactions on Aerospace and Electronics Systems, 2000,36(1): 286-290
18汤霞清,宗艳桃,郭理彬,贺勇.光纤陀螺随机漂移分析与建模方法.火力与指挥控制. 2008(33): 14-16
19 Hornby G S, Pollack J B. Creating high-level homponents with a generativerepresentation for body-brain evolution. Artificia l Life, 2002, 8(3): 8-12
20 IEEE Standard Specification Format Guide and Test Procedure for Single-AxisInterferometric Fiber Optic Gyros IEEE Std 952-1997
21 Sylvain S. Minima x threshold for denoising complex signa lwithwave shrink.IEEE Transactions on Signal Processing, 2000, 48(4): 422-428
22 Tuckenss M. Analysis of optica l navigation error during mass enery appliedmathematics and computation. J. of metrry and Remote Sensing, 2004, 80(1):1-22
23张晓峰,张桂才,巴晓艳.闭环消偏光纤陀螺输出数据Alla n方差分析的改进方法研究导航与控制. 2006(1): 53-57
24 G.koulouras, K. Kontkaos, I. Stavrakas. Embedded ComPact Flash. CcriultDeviees, EIEE, 2005, 1(4): 27-34
25 Randy Alla n. Compiling High-level Languages to DSPs. Signal Procesing, IEEE,2005, 22(3): 47-56
26祝树生,任建新,张安峰.光纤陀螺随机游走分析方法研究.应用光学. 2009 .30(6): 1003-1006
27朱奎宝,张春熹,张小跃.光纤陀螺随机漂移ARMA模型研究.宇航学报. 2006. 27(5): 1118-11120
28 PepperD M, Wang HTM. Nuclear Magnetic Resona nce Gyroscopes: AD -A 1249
25, 2004, 18(2): 10-13
29 Ng L C and Pines D J. Characterization of ring laser gyro performa nce using theallan varia nce mothod. Journal of Guidance, Control, and Dynamics, 2003, 20(1):16-20
30周海波,刘建业,赖际舟.干涉型光纤陀螺随机噪声的分析研究.传感器与微系统, 2006, 25(11): 73-76
31 Chen Xi-yuan. Modeling random gyro drift by time series neura l net works andbytraditiona l. method. IEEE. Int. Conf. Neutra l. Networks&Signal. Processing,Nanjing, Ch-ina. December, 2003: 14-17
32 Aboelma gd Noureld in, Dave Irvine-Halllday. New technique for reducing theangle random walk at the output of fiber optic gyroscopes during alignmentprocesses of inertia l navigation systems. 2001 Society of Photo-OpticalInstrumentation Engineers, 2001
33李晓峰,徐军,张胜修.光纤陀螺随机误差建模与滤波方法研究.光学技术.2008. 34. 179-180
34王雪平,李俊,张福斌.基于时间序列分析方法的FOG随机漂移建模与辨识.鱼雷技术, 2007, 15(4): 34-37
35 MIAO Ling-jua n, ZHANG Fang-sheng, SHENG Jun, LIU Wei. Data analysis andmodeling of fiber optic gyroscope drift. Journal of Beijing institute of technology,2002, 11(1)
36王新龙,陈涛,杜宇.基于ARMA模型的光纤陀螺漂移数据建模方法研究.弹箭与制导学报, 2006, 20(1): 5-7
37侯青剑,缪栋,彭云辉.激光陀螺随机漂移数据建模与滤波.中国惯性技术学报, 2005, 13(4): 39-42
38 Simon D, Chizeck H J. Kalman Filtering with Statistica l State Constraints.Control and Intelligent Systems (S1480-1752), 2006, 34(1): 73-79
39 Hornby G S, Pollack J B. Creating high-level homponents with a generativerepresentation for body-brain evolution. Artificia l Life, 2002, 8(3), 26-29
40王海,陈家斌. FOG随机漂移测试及分析.光学技术. 2004, 30(5): 623-625
41 Hao Wang, TIAN Weifeng. Modeling the random drift of micro-machinedgyroscope with neura l network. Neural Processing Letters, 2005, 22(3): 234-238
42缪玲娟.小波分析在光纤陀螺信号滤波中的应用.宇航学报. 2006. 21(1): 42-46
43 Sweldend W. The lifting scheme: A custom-design construction of biorthogoa nlwavelets. Applied and Computaion Harmonic Analysis, 2006, 3(2): 186-200
44秦前清,杨宗凯.实用小波分析.西安电子科技大学出版社. 1995: 112-134
45 Cohen A, Daubechies I. Orthonormal bases of compactly supported wavelets.Bette frequency resolution. SIAM J. Math. Anal. 2004, 24(2): 517-529
46刘镇平,张春熹,王妍.小波分析在捷联惯导陀螺信号中的应用.中国惯性技术学报. 2005, 2(1): 74-86
47袁瑞铭,韦锡华,李自怡,袁瑞雪.基于小波阈值滤波的光纤陀螺信号消噪算法.中国惯性技术学报. 2003, 12(5): 43-47
48 Daubechiesi. orthonorma l bases of compactly supported wavelets. variations on atheme. SIAM J. Math. Anal. 2005, 24(2): 490-524
49黄文梅,熊桂林,杨勇.信号分析与处理MATLAB语言及应用.国防科技大学出版社. 2007: 99-107
50屠善澄.卫星姿态动力学与控制.北京:宇航出版社, 1998, 4-8
51黄圳奎.航天器姿态动力学.长沙:国防科技大学出版社,1997, 3-9