基于机抖激光陀螺信号频域特性的SINS动态误差分析与补偿算法研究
|
摘要
随着国内激光陀螺水平的不断提高,机抖激光陀螺捷联惯导系统在国内惯性技术应用领域正日益受到重视,发挥越来越重要的作用。机抖陀螺特有的机械抖动特性,在消除陀螺锁区的同时,也使捷联系统具有一系列新的更为复杂的动态误差特性,系统的优化设计与误差补偿研究具有尤其重要的理论和现实意义。论文以机抖激光陀螺捷联惯导系统为研究对象,提出了捷联系统的算法设计必须与系统的信号特性和应用环境相适应的思想,基于机抖激光陀螺在不同条件下的信号频域特性,开展了捷联惯导系统动态误差与补偿算法研究。论文主要完成了以下研究工作：
1.研究了激光陀螺的数字控制特性,设计了新的数字控制方法,为陀螺信号频域特性研究奠定了基础。根据陀螺的抖动偏频机理,研究了陀螺静态和动态锁区的误差特性,探讨了抖动参数与陀螺精度的关系,得到了陀螺抖动参数的选取原则；设计了一种新的不同于模拟抖动的非线性抖幅控制方法、随机注入方法和一种新的适于数字实现的直流稳频控制算法,建立了机抖激光陀螺数字控制系统。新算法大大简化了陀螺控制系统的硬件实现,提高了系统可靠性和可扩展性,改善了控制精度。
2.研究了机抖激光捷联系统的动态误差特性,建立了系统动态误差的优化处理原则。首先比较研究了整周期同步和数字滤波两种抖动解调方法,指出数字滤波法为提高捷联系统精度提供了更多更灵活的手段和可能性,已逐步取代前者得到了广泛应用；之后分类研究了捷联系统的动态特性,根据运动来源和运动性质的不同,对系统可能存在的圆锥和划摇运动进行了分类,建立了以减振器滤除干扰运动、以滤波器滤除干扰噪声的系统动态误差优化处理原则；最后把上述结论应用于机抖激光捷联系统,结合实际信号的频谱特点,研究了静态环境中陀螺抖动偏频和抖动耦合引入的各种动态误差及处理方法,振动环境中高频谐波振动引入的动态误差及处理方法,指出主振动的高频谐波是振动环境下影响系统精度的主要因素。
3.基于陀螺数字滤波的信号处理方式,提出应把陀螺信号滤波后的幅频和相频畸变作为影响捷联系统姿态解算精度的重要误差因素进行研究,指出通常的滤波器通带指标一般不能满足姿态解算的信号稳定性要求,可能严重影响捷联系统姿态解算精度。设计了一种新的能与信号频域特性相匹配的圆锥优化算法,推导了经典圆锥运动下的圆锥优化算法公式,研究了算法的误差特性,证明了该算法在任意运动形式下的普适性,并扩展了其在消除伪圆锥误差和补偿陀螺自身频率特性时的应用。优化算法不增加任何算法实现难度和计算量,优化效果与滤波器性能相关。仿真和实验研究表明：优化算法能有效补偿信号滤波引入的圆锥误差,随信号滤波条件的不同能提高数倍到数个量级的姿态解算精度。
4.圆锥算法受陀螺信号滤波影响,划摇算法同时受陀螺和加速度计两者的信号滤波影响。提出把陀螺和加速度计两者信号的滤波畸变作为影响捷联系统导航解算精度的重要误差因素进行研究,设计了一种新的能与信号频域特性相匹配的划摇优化算法,推导了经典划摇运动下的划摇优化算法公式,揭示了在相同的信号滤波条件下的划摇优化算法和圆锥优化算法依然满足算法的“对偶”关系,并证明了优化算法在任意运动形式下的普适性。仿真和实验表明,划摇优化算法具有与圆锥优化算法相似的误差特性,能有效补偿信号滤波引入的划摇误差,显著改善捷联系统导航精度。
5.针对角振动环境,设计了一种新的基于固定频率运动优化的圆锥算法。不同于标准算法误差随圆锥频率单调变化的特性,新算法在设定频点处具有误差极小点,因而能有效改善系统在特定频带上的姿态解算精度。当系统运动环境已知且运动频带较窄时,优化算法具有良好的应用效果。
最后,把基于信号频域特性的圆锥和划摇优化算法组成一套完整的优化导航算法,通过Matlab捷联系统仿真平台和某型机抖激光捷联系统在转台晃动、环形车载和远距离车载等动态环境中的实验,研究了信号频域特性对捷联系统导航精度的影响,验证了优化算法在不同运动环境和不同信号滤波条件下的补偿性能。
With the improvement of ring laser gyro (RLG) in China, the dither RLG strapdown inertial navigation system (SINS) is playing a more and more important role in domestic inertial area. The gyros'unique mechanic dither property which is used to alleviate the gyro lock-in brings a lot of new and complicated dynamic error characteristics to the SINS, so system optimization and error compensation have important theoretic and practical meaning. Focusing on dither RLG-based SINS, the dissertation proposes that SINS algorithms must be designed to match the system signals and application environments, and researches on the dynamic error and compensation algorithms of dither RLG SINS based on the frequency domain characteristics of the RLG signals in various conditions. The main contents of this dissertation are:
1. New digital control methods of RLG are designed through studying the gyro digital control characteristics, which sets a sound foundation for the ensuing research on the gyro signal frequency domain characteristics. According to the dither biasing mechanism, error characteristics of gyro static and dynamic lock-in are investigated. The relation between the dither parameters and the gyro precision is argued to obtain the design principles of dither parameters. Different from the analog methods, the new control methods of nonlinear dither magnitude and random dither are designed, and DC frequency-stabilization algorithm is implemented digitally. We then set up the whole digital control system of dither RLG. The new algorithms simplify the hardware and increase the reliability, expandability and precision of the control system.
2. The dynamic errors of the dither RLG SINS are investigated and its optimization process principles are constituted. Firstly, it is underlined through peer comparison that the digital filter method, which gives more flexible ways and possibilities to increase the SINS accuracy, has been used widely instead of the whole period-synchronization method. Then, the SINS dynamic characteristics are investigated. The coning and sculling motions which might exist in SINS are assorted according to the source and property of motions. Optimization principles of system dynamic errors that the shock absorbers alleviate the disturbed motions and the filters eliminate the noise signals are set up. Finally, these conclusions are applied to the dither RLG SINS. The SINS dynamic errors introduced by the gyro dither bias, dither coupling in the static environment and the high frequency resonance in the vibration environment are studied, along with their process methods. It is pointed out that the high frequency harmonic vibrations are the major dynamic error source of SINS in the vibration environment.
3. Based on the gyro signals process way of digital filter, it is proposed that the magnitude-frequency and phase-frequency distortion of gyro filtered signals should be studied as the important error factors of attitude computation for the SINS. The passband standard of the normal filters can not generally meet the requirement of signals stabilization for the attitude calculation, which may seriously decay the attitude precision. New optimal coning algorithms are thus designed to match the signals' frequency domain characteristics. Algorithm formulas are derived for the classical coning motions and its error characteristics are studied. It is proved that the optimal algorithms can also be used in general environments. Additionally, the optimization algorithms are extended to eliminate the pseudo coning errors and compensate the gyro frequency characteristics itself. The new algorithms do not complicate the algorithm realization and computation burden. The optimization effect depends on the filter performance. Simulations and experiments show that the optimized coning algorithms can compensate significantly coning errors introduced by signal filter and increase the attitude algorithm accuracy from times to orders depending on various filtering conditions.
4. Sculling algorithms are influenced by both gyro and accelerometer signals, in contrast to coning algorithms that is affected only by gyro signals. Regarding the distortion of gyro and accelerometer filtered signals as the important error factors of navigation computation, new optimization sculling algorithms are designed to match the signals'frequency domain characteristics. Algorithm formulas are derived in the classical sculling motions. It is revealed that the optimal coning and sculling algorithms still keep the duality in common filtering conditions and can be also used in the general environments. Simulations and experiments show that the optimal sculling algorithms have similar error characteristics with the optimal coning algorithms and can improve remarkably SINS navigation accuracy by compensating the filter-dependence sculling errors.
5. For angle vibration environments, a new coning algorithm is designed which is optimized to the fixed frequency motion. Different from the monotonic error characteristics of the standard algorithm with the coning frequency, the optimal coning algorithm has a minimization point at the specified frequency and can improve the attitude accuracy remarkably for those motions with the specified frequency band. The optimal algorithm has good effect for the motions with the known narrow frequency band.
Finally, the optimal coning and sculling algorithms are integrated to form the whole navigation algorithms. SINS Matlab models and experiments (turn-table swinging, land runs in circles and in a long way) are carried out to investigate the effect of signals frequency domain characteristics on the SINS navigation accuracy. The performance of the optimization algorithms are verified favorably for various environments and signal filters.
1.研究了激光陀螺的数字控制特性,设计了新的数字控制方法,为陀螺信号频域特性研究奠定了基础。根据陀螺的抖动偏频机理,研究了陀螺静态和动态锁区的误差特性,探讨了抖动参数与陀螺精度的关系,得到了陀螺抖动参数的选取原则；设计了一种新的不同于模拟抖动的非线性抖幅控制方法、随机注入方法和一种新的适于数字实现的直流稳频控制算法,建立了机抖激光陀螺数字控制系统。新算法大大简化了陀螺控制系统的硬件实现,提高了系统可靠性和可扩展性,改善了控制精度。
2.研究了机抖激光捷联系统的动态误差特性,建立了系统动态误差的优化处理原则。首先比较研究了整周期同步和数字滤波两种抖动解调方法,指出数字滤波法为提高捷联系统精度提供了更多更灵活的手段和可能性,已逐步取代前者得到了广泛应用；之后分类研究了捷联系统的动态特性,根据运动来源和运动性质的不同,对系统可能存在的圆锥和划摇运动进行了分类,建立了以减振器滤除干扰运动、以滤波器滤除干扰噪声的系统动态误差优化处理原则；最后把上述结论应用于机抖激光捷联系统,结合实际信号的频谱特点,研究了静态环境中陀螺抖动偏频和抖动耦合引入的各种动态误差及处理方法,振动环境中高频谐波振动引入的动态误差及处理方法,指出主振动的高频谐波是振动环境下影响系统精度的主要因素。
3.基于陀螺数字滤波的信号处理方式,提出应把陀螺信号滤波后的幅频和相频畸变作为影响捷联系统姿态解算精度的重要误差因素进行研究,指出通常的滤波器通带指标一般不能满足姿态解算的信号稳定性要求,可能严重影响捷联系统姿态解算精度。设计了一种新的能与信号频域特性相匹配的圆锥优化算法,推导了经典圆锥运动下的圆锥优化算法公式,研究了算法的误差特性,证明了该算法在任意运动形式下的普适性,并扩展了其在消除伪圆锥误差和补偿陀螺自身频率特性时的应用。优化算法不增加任何算法实现难度和计算量,优化效果与滤波器性能相关。仿真和实验研究表明：优化算法能有效补偿信号滤波引入的圆锥误差,随信号滤波条件的不同能提高数倍到数个量级的姿态解算精度。
4.圆锥算法受陀螺信号滤波影响,划摇算法同时受陀螺和加速度计两者的信号滤波影响。提出把陀螺和加速度计两者信号的滤波畸变作为影响捷联系统导航解算精度的重要误差因素进行研究,设计了一种新的能与信号频域特性相匹配的划摇优化算法,推导了经典划摇运动下的划摇优化算法公式,揭示了在相同的信号滤波条件下的划摇优化算法和圆锥优化算法依然满足算法的“对偶”关系,并证明了优化算法在任意运动形式下的普适性。仿真和实验表明,划摇优化算法具有与圆锥优化算法相似的误差特性,能有效补偿信号滤波引入的划摇误差,显著改善捷联系统导航精度。
5.针对角振动环境,设计了一种新的基于固定频率运动优化的圆锥算法。不同于标准算法误差随圆锥频率单调变化的特性,新算法在设定频点处具有误差极小点,因而能有效改善系统在特定频带上的姿态解算精度。当系统运动环境已知且运动频带较窄时,优化算法具有良好的应用效果。
最后,把基于信号频域特性的圆锥和划摇优化算法组成一套完整的优化导航算法,通过Matlab捷联系统仿真平台和某型机抖激光捷联系统在转台晃动、环形车载和远距离车载等动态环境中的实验,研究了信号频域特性对捷联系统导航精度的影响,验证了优化算法在不同运动环境和不同信号滤波条件下的补偿性能。
With the improvement of ring laser gyro (RLG) in China, the dither RLG strapdown inertial navigation system (SINS) is playing a more and more important role in domestic inertial area. The gyros'unique mechanic dither property which is used to alleviate the gyro lock-in brings a lot of new and complicated dynamic error characteristics to the SINS, so system optimization and error compensation have important theoretic and practical meaning. Focusing on dither RLG-based SINS, the dissertation proposes that SINS algorithms must be designed to match the system signals and application environments, and researches on the dynamic error and compensation algorithms of dither RLG SINS based on the frequency domain characteristics of the RLG signals in various conditions. The main contents of this dissertation are:
1. New digital control methods of RLG are designed through studying the gyro digital control characteristics, which sets a sound foundation for the ensuing research on the gyro signal frequency domain characteristics. According to the dither biasing mechanism, error characteristics of gyro static and dynamic lock-in are investigated. The relation between the dither parameters and the gyro precision is argued to obtain the design principles of dither parameters. Different from the analog methods, the new control methods of nonlinear dither magnitude and random dither are designed, and DC frequency-stabilization algorithm is implemented digitally. We then set up the whole digital control system of dither RLG. The new algorithms simplify the hardware and increase the reliability, expandability and precision of the control system.
2. The dynamic errors of the dither RLG SINS are investigated and its optimization process principles are constituted. Firstly, it is underlined through peer comparison that the digital filter method, which gives more flexible ways and possibilities to increase the SINS accuracy, has been used widely instead of the whole period-synchronization method. Then, the SINS dynamic characteristics are investigated. The coning and sculling motions which might exist in SINS are assorted according to the source and property of motions. Optimization principles of system dynamic errors that the shock absorbers alleviate the disturbed motions and the filters eliminate the noise signals are set up. Finally, these conclusions are applied to the dither RLG SINS. The SINS dynamic errors introduced by the gyro dither bias, dither coupling in the static environment and the high frequency resonance in the vibration environment are studied, along with their process methods. It is pointed out that the high frequency harmonic vibrations are the major dynamic error source of SINS in the vibration environment.
3. Based on the gyro signals process way of digital filter, it is proposed that the magnitude-frequency and phase-frequency distortion of gyro filtered signals should be studied as the important error factors of attitude computation for the SINS. The passband standard of the normal filters can not generally meet the requirement of signals stabilization for the attitude calculation, which may seriously decay the attitude precision. New optimal coning algorithms are thus designed to match the signals' frequency domain characteristics. Algorithm formulas are derived for the classical coning motions and its error characteristics are studied. It is proved that the optimal algorithms can also be used in general environments. Additionally, the optimization algorithms are extended to eliminate the pseudo coning errors and compensate the gyro frequency characteristics itself. The new algorithms do not complicate the algorithm realization and computation burden. The optimization effect depends on the filter performance. Simulations and experiments show that the optimized coning algorithms can compensate significantly coning errors introduced by signal filter and increase the attitude algorithm accuracy from times to orders depending on various filtering conditions.
4. Sculling algorithms are influenced by both gyro and accelerometer signals, in contrast to coning algorithms that is affected only by gyro signals. Regarding the distortion of gyro and accelerometer filtered signals as the important error factors of navigation computation, new optimization sculling algorithms are designed to match the signals'frequency domain characteristics. Algorithm formulas are derived in the classical sculling motions. It is revealed that the optimal coning and sculling algorithms still keep the duality in common filtering conditions and can be also used in the general environments. Simulations and experiments show that the optimal sculling algorithms have similar error characteristics with the optimal coning algorithms and can improve remarkably SINS navigation accuracy by compensating the filter-dependence sculling errors.
5. For angle vibration environments, a new coning algorithm is designed which is optimized to the fixed frequency motion. Different from the monotonic error characteristics of the standard algorithm with the coning frequency, the optimal coning algorithm has a minimization point at the specified frequency and can improve the attitude accuracy remarkably for those motions with the specified frequency band. The optimal algorithm has good effect for the motions with the known narrow frequency band.
Finally, the optimal coning and sculling algorithms are integrated to form the whole navigation algorithms. SINS Matlab models and experiments (turn-table swinging, land runs in circles and in a long way) are carried out to investigate the effect of signals frequency domain characteristics on the SINS navigation accuracy. The performance of the optimization algorithms are verified favorably for various environments and signal filters.
引文
[1]Titterton, D.H., Weston, J.L. Strapdown Inertial Navigation Technology:Peter Peregrinus Ltd. on behalf of the Institute of Electrical Engineers, London, United Kingdom,2nd Ed,2004.
[2]张树侠,孙静.捷联式惯性导航系统.北京：国防工业出版社,1992.
[3]袁信,俞济祥,陈哲.导航系统.北京：航空工业出版社,1993.
[4]陈哲.捷联惯导系统原理.北京：宇航出版社,1986.
[5]W.W.Chow, J.Gea-Banacloche, L.M.Pedrotti. The ring laser gyro. Review of Modern Physics 1985.57(1):61-104.
[6]杨培根,龚智炳.光电惯性技术.北京：兵器工业出版社,1999.
[7]Hadfield, M.J., Leiser, K.E. Ring laser gyros come down to Earth:Field test results on the RLG modular azimuth position system. IEEE PLANS, Position Location and Navigation Symposium,1998:61-72.
[8]Majure, R.G. Demonstration of a ring laser gyro system for pointing and stabilization applications. IEEE PLANS, Position Location and Navigation Symposium,1990:219-225.
[9]Nelson, K.D. Flight results of the ring laser gyro based inertial navigation system for Atlas/cetaur.1992:440-445.
[10]Oelschlaeger, J.M., Thielman, L.O. GG1308 Ring Laser Gyro Inertial Measurement Systems-Honeywell's Low Cost Solution For Tactical Applications. IEEE PLANS, Position Location and Navigation Symposium, 1990:528-536.
[11]Stamenkovich, M., Carvil, J. Application of the digital nautical chart (DNC) database to help identify areas of vertical deflection in the ring laser gyro inertial navigator. IEEE PLANS, Position Location and Navigation Symposium,2000: 299-303.
[12]Curran, G.L., Engelken, D.J. Ring laser gyro applications for tactical missiles. IEEE PLANS, Position Location and Navigation Symposium,1990:543-548.
[13]Wright, R.J., Sponnick, J.V. A ring laser gyro based navigator for space launch vehicle guidance. IEEE PLANS, Position Location and Navigation Symposium, 1988:271-279.
[14]Gilster, G. High accuracy performance capabilities of the military standard ring laser gyro inertial navigation unit. IEEE PLANS, Position Location and Navigation Symposium,1994:464-473.
[15]王宇.机抖激光陀螺捷联惯导系统的初步探索.博士学位论文.长沙：国防科技大学,2005.
[16]Savage, P.G. Strapdown inertial navigation integration algorithm design part 1: attitude algorithms. Journal of Guidance, Control, and Dynamics,1998.21(1): 19-28.
[17]Savage, P.G. Strapdown inertial navigation integration algorithm design part 2: velocity and position algorithm. Journal of Guidance, Control, and Dynamics, 1998.21(2):208-221.
[18]秦永元.惯性导航.北京：科学出版社,2006.
[19]Post, E.J. Sagnac Effect. Review of Modern Physics,1967.39(2):475-493.
[20]Aronowitz, F. The Laser Gyro. Laser Application,1971(1):134-199.
[21]Cresser, J.D., Louisell, W.H., Meystre, P., Schleich, W., et al. Quantum noise in ring laser gyros. I. Theoretical formulation of problem. Physical Review A,1982. 25(4):2214-2225.
[22]Cresser, J.D., Hammonds, D., Louisell, W.H., Meystre, P., et al. Quantum noise in ring laser gyros. Ⅱ. Numerical results. Physical Review A,1982.25(4): 2226-2234.
[23]Cresser, J.D. Quantum noise in ring laser gyros. Ⅲ. Approximate analytic results in unlocked region. Physical Review A,1982.26(1):398-409.
[24]Andrews, D.A., Roden, S. A model for lock-in growth in ring laser gyroscopes. IEEE Journal of Quantum Electronics 1995.31(9):1709-1715.
[25]Wu, G., Gu, Q. Thermal characteristics and thermal compensation of four frequency ring laser gyro. IEEE PLANS, Position Location and Navigation Symposium,2002:271-276.
[26]曾庆化,刘建业,赖际舟,熊智.环形激光陀螺的最新发展.传感器技术,2004.23(11)：1-4.
[27]J.R.Wilkinson. ring lasers. Prog.Quant.Electr,1987.11:1-103.
[28]Bo.H.G.Ljung. Ring Laser Gyroscope Dither Drive Circuit. United States Patent, 4277173,1981.
[29]Daniel A.Tazartes, W.H., John G.Mark, P., Robert E. Ebner, T., all of Calif;. Ring laser gyroscope dither drive system and method United States Patent, 4,981,359,1991.
[30]Fritze, K.R. Laser gyro dither drive. United States Patent,5225889,1993.
[31]Joseph.E. Dither control system for a ring laser gyro. United States Patent, 6,476,918 Bl,2002.
[32]J.Murphy, H. Digital path length control for ring laser gyros. United States Patent,5,108,182,1992.
[33]John G.Mark, P. Multioscilator ring laser gyroscope adaptive digitally controlled cavity length control system. United States Patent,5,208,653,1993.
[34]姜亚南.环形激光陀螺.北京：清华大学出版社,1985.
[35]杜建邦.三角形激光陀螺谐振腔的精度分析.航天控制,1998(3)：53-61.
[36]张惟叙,邓兆炯.激光陀螺抖动偏频研究.北京航空航天大学学报,1990(3)：15-20.
[37]章燕申,汤全安,潘珍吾.激光陀螺及其误差补偿.航空学报,1990.11(3)：120-126.
[38]罗晖,张广发.激光陀路信号检测系统的理论与实验研究.激光技术,1997.21(3)：132-137.
[39]付文羽.四频差动激光陀螺稳频系统研究.激光与光电子学进展(增刊)第八届全国光电技术与系统学术会议论文专辑,1999(9)：77.
[40]刘巧光,许辅义,滕云鹤,章燕申.环形激光陀螺仪随机误差模型的研究.清华大学学报(自然科学版),1999(2).
[41]谢元平,曾淳,汤建勋.机械抖动激光陀螺过锁区分析与处理.光电子·激光,2000.11(1)：45-48.
[42]韩宗虎,陈林峰,陈勇,吉翠萍.激光陀螺锁区特性的研究.光子学报,2006.35(6)：807-809.
[43]杨海军,郭美凤,章燕申.激光陀螺的闭锁阀值及抖动偏频.惯导与仪表,1999(3)：43-48.
[44]王京献.激光陀螺抖动偏频技术研究.硕士学位论文.西安：西北工业大学,1999.
[45]汤建勋.机械抖动激光陀螺抖动偏频系统的研究与设计.博士学位论文.长沙：国防科技大学,2000.
[46]谢元平.机械抖动激光陀螺鉴相解调与稳频技术研究.博士学位论文.长沙：国防科技大学,2000.
[47]刘放.环形激光陀螺的稳频计算机控制系统及其FUZZY-PID算法.硕士学位论文.西安：西北工业大学,2000.
[48]杨卓.机械抖动激光陀螺稳频和鉴相技术研究.硕士学位论文.北京：北京理工大学,2003.
[49]汤建勋,罗晖,李革.机抖激光陀螺抖动控制环路频率特性的校正.中国惯性技术学报,2003.11(4)：36-39.
[50]杨恒,蒋东方,范东远.环形激光陀螺频率稳定性的研究.西北工业大学学报,1999.17(3)：414-418.
[51]杨恒,刘放.微机控制环形激光陀螺自动扫模的研究与实现.西北工业大学学报,2000.18(2)：203-206.
[52]刘放,张士邈,陈明.模糊PID控制算法及其在激光陀螺稳频控制中的应用.测控技术,2001.20(7)：21-23.第143页
[53]Bo.H.G.Ljung. Ring laser gyro dither pulse eliminator. United States Patent, 4344706,1982.
[54]Daniel A.Tazartes, W.H. Apparatus and method for correcting ring laser gyroscope phase error at turnround. United States Patent,5,004,344,1991.
[55]Elbert, H.F. Apparatus and method for the elimination of angular vibration induced errors in ring laser gyroscopes. United States Patent,4248534,1981.
[56]Fritze, K.R. Ring laser gyro dither stripper. United States Patent,5249031,1993.
[57]Geston, D.R. Dither signal remover for a dithered ring laser angular rate sensor utilizing an adaptive digital filter. United States Patent,5331402,1994.
[58]Ignagni, M.B. Dither signal remover for a dithered ring laser gyro. United States Patent,5048963,1991.
[59]P.Callahan, S., E.Killpatrick, J. Dither signal remover for a dithered ring gyro angular rate sensor. United States Patent,4,826,320,1989.
[60]陈楸,陈明,李岁劳.陀螺输出信号的超高速处理.航空计测技术,2003.23(2)：6-9.
[61]刘宗玉,陈明,王玮,倪家琳.抖动偏频激光陀螺中的解调及实现技术.测控技术,2004.23(9)：67-75.
[62]Johnson, D.P. Frequency Domain Analysis for RLG System Design. Journal of the Insititute of Navigation,1987.34(3):179-189.
[63]Lahham, J.I., Wigent, D.J., L.Coleman, A. Tuned support structure for structure-borne noise reduction of inertial navigator with dithered ring laser gyros (RLG). IEEE PLANS, Position Location and Navigation Symposium, 2000:419-428.
[64]王可东,顾启泰,钟德贵,田海峰.机抖式激光陀螺基础抖动消除研究.中国惯性技术学报,2002.10(6)：62-67.
[65]王可东,顾启泰,钟德贵.配重式激光陀螺机械抖动系统的实验研究.激光杂志,2003.24(2)：44-46.
[66]吴文启,庹洲慧,江明明.激光陀螺机械抖动偏频对等效转动矢量姿态计算的影响.航空学报,2006.27(1)：71-76.
[67]李俊峰,刘进江,唐献林.激光陀螺捷联惯性组合的系统结构抗振控制.中国惯性技术学报,2006.14(1)：21-26.
[68]Britting, K.R. Inertial Navigation Systems Analysis:John Wiley & Sons, Inc., 1971.
[69]Savage, P.G. A new second-order solution for strapped-down attitude computation. AIAA/JACC Guidance and Control Conference.1966.
[70]Bortz, J.E. A New Mathematical Formulation for Strapdown Inertial Navigation. IEEE Transactions on Aerospace and Electronics System,1971.7(AES-1): 61-66.
[71]Miller, R.B. A New Strapdown Attitude Algorithms. Journal of Guidance, Control, and Dynamics,1983.6(4):287-291.
[72]Lee, J.G., Yoon, Y.J. Extension of Strapdown Attitude Algorithm for High-Frequency Base Motion. Journal of Guidance, Control, and Dynamics, 1990.13(4):738-743.
[73]Ignagni, M.B. Efficient Class of Optimized Coning Compensation Algorithms Journal of Guidance, Control, and Dynamics,1996.19(2):424-429.
[74]Ignagni, M.B. Optimal Strapdown Attitude Integration Algorithms. Journal of Guidance, Control, and Dynamics,1990.13(2):363-369.
[75]Jiang, Y.F., Lin, Y.P. Improved Strapdown Coning Algrithms. IEEE Transactions on Aerospace and Electronics System,1992.28(2):484-490.
[76]Musoff, H., Murphy, J.H. Study of Strapdown Navigation Attitude Algorithms. Journal of Guidance, Control, and Dynamics,1995.18(2):287-290.
[77]Park, C.G., Kim, K.J. Formalized Approach to Obtaining Optimal Coefficients for Coning Algorithms. Journal of Guidance, Control, and Dynamics,1999. 22(1):165-168.
[78]Jordon, J.W. An Accurate Strapdown Direction Cosine Algorithm. NASA TND-5384,1969.
[79]JIANG, Y.F., LIN, Y.P. On The Rotation Vector Differential Equation. IEEE Transactions on Aerospace and Electronic Systems,1991.27(1):181-183.
[80]Litmanovich, Y.A., Mark, J.G. Process In strapdown Algorithm Design at the West and East as Appeared at Saint Petersburg Conferences:Decade Overview. Proceeding of the 10rd Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,2003.369-377.
[81]Savage, P.G., Strapdown system algorithms, systems, A.i.s.i., Editor.1984.
[82]Mortensen, R.E. Strapdown guidance error analysis. IEEE Transactions on Aerospace and Electronic Systems,1974.10(4):451-457.
[83]Ignagni, M.B. On the Orientation Vector Differential Equation in Strapdown Inertial System. IEEE Transactions on Aerospace and Electronics System,1994. 30(4):1076-1081.
[84]Gusinsky, V.Z., Lesyuchevsky, V.M., Litmanovich, Y.A. New Procedure for Deriving Optimized Strapdown Attitude Algorithms. Journal of Guidance, Control, and Dynamics,1997.20 (4):673-680.
[85]Gusinsky, V.Z., Lesyuchevsky, V.M., Litmanovich, Y.A. Optimization of a Strapdown Attitude Algorithm for a Stochastic Motion. Navigation:Journal of The Institute of Navigation,1997.44(2):163-170.
[86]Savage, P.G. Analytical modeling of sensor quantization in strapdown inertial navigation error equation. Journal of Guidance, Control, and Dynamics,2002.
25(No.5):833-842.
[87]Savage, P.G. A unified Mathematical Framework for strapdown algorithm design. Journal of Guidance, Control, and Dynamics,2006.29(3):237-249.
[88]Harasty, G.A., G., U.F. Computational requirements for a digital analytic inertial platform system. the 12th East Coast Conf. on Aerospace and Navigational Electronics. Baltimore, Md.,1965.
[89]Bar-Itzhack, I.Y. Navigation computation in terrestrial strapdown inertial navigation systems. IEEE Transactions on Aerospace and Electronic Systems, 1977. AES-13(6):679-689.
[90]Ignagni, M.B. Duality of Optimal Strapdown Sculling and Coning Compensition Algorithms. Journal of the Insititute of Navigation,1998.45(2):85～95.
[91]Roscoe, K.M. Equivalency Between Strapdown Inertial Navigation Coning and Sculling Integrals/Algorithms. Journal of Guidance, Control, and Dynamics, 2001.24(2):201-205.
[92]Mark, J.G., Tazartes, D.A. On sculling Algorithms. Proceeding of the 3rd Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,1996.22-26.
[93]赵健,以光衢.捷联惯导中的等效旋转矢量算法及其仿真研究.中国惯性技术学报,1996.4(4)：1-6.
[94]王养柱,崔中兴.捷联惯导系统圆锥补偿算法优化设计.惯性技术学报,2000.8(1)：7-10.
[95]王养柱,崔中兴.捷联式惯性导航系统算法研究.中国惯性技术学报,2000.8(2)：31-35.
[96]薛祖瑞.关于捷联惯导系统圆锥误差的诠释.中国惯性技术学报,2000.8(4)：46-50.
[97]周江华,苗育红,肖刚.扩展旋转矢量捷联姿态算法.宇航学报,2003.24(4)：414-417.
[98]余杨,张洪钺.捷联惯导系统中的圆锥和伪圆锥运动研究.中国惯性技术学报,2006.14(5)：1-4.
[99]曾庆化,刘建业,熊智,赵伟.一种角速率激光陀螺惯导系统高精度姿态算法.上海交通大学学报,2006.40(12)：2159-2163.
[100]孙丽,秦永元.捷联惯导系统姿态算法比较.中国惯性技术学报,2006.14(3)：6-10.
[101]练军想,胡德文,胡小平,吴文启.捷联惯导姿态算法中的圆锥误差与量化误差.航空学报,2006.27(1)：98-103.
[102]周顺林,以光衢.抑制动态环境误差的算法研究.中国惯性技术学报,1996.4(1)：22-27.
[103]刘巧光,杨海军,郭美凤.捷联惯性导航系统的姿态算法优化设计.中国惯性技术学报,1999.7(2)：1-5.
[104]王养柱,崔中兴.捷联惯导系统圆锥补偿算法研究.北京航空航天大学学报,2001.27：264—267.
[105]秦永元,张士邈.捷联惯导姿态更新的四子样旋转矢量优化算法研究.中国惯性技术学报,2001.9(4)：1-7.
[106]刘危,解旭辉,李圣怡.捷联惯性导航系统的姿态算法.北京航空航天大学学报,2005.31(1)：45-50.
[107]耿延睿,王养柱,崔中兴.捷联惯导系统划船效应补偿算法研究.北京航空航天大学学报,2001.27(6)：694-696.
[108]陈小刚,赵琳,高伟.捷联惯导中的划船效应及其补偿算法.中国惯性技术学报,2002.10(2)：12-17.
[109]刘危,解旭辉,李圣怡.微导航系统的划船算法优化设计.弹箭与制导学报,2003.23(4)：44-48.
[110]张玲霞,陈明,曹晓青.基于对偶性原理捷联惯导划船误差补偿优化算法.中国惯性技术学报,2003.11(5)：33-38.
[111]蒲广平,裴听国,万彦辉.圆锥积分算法在划船效应补偿算法中的应用.中国惯性技术学报,2003.11(5)：39-47.
[112]Litmanovich, Y.A. Use of angular rate multiple integrals as input signals for strapdown attitude algorithms. Proceedings of Symposium Gyro Technology Stuttgart, Germany,1997.20.0-20.9.
[113]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. New procedure for deriving optimized strapdown attitude algorithms. Journal of Guidance, Control, and Dynamics,1997.20(4):673-680.
[114]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. Optimization of a strapdown attitude algorithm for a stochastic motion. Navigation:Journal of The Institute of Navigation,1998.44(2):163-170.
[115]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. Signal processing using the increments of signal multiple integrals:from strapdown INS to other real-time systems. Proceedings of 6th International Conference on Integrated Navigation Systems. St. Petersburg 1999.8.1-8.7.
[116]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. Two New Classes of Strapdown Navigation Algorithms. Journal of Guidance, Control, and Dynamics, 2000.23(1):34-44.
[117]Soloviev, A. Investigation into performance enhancement of integrated global positioning/inertial navigation systems by frequency domain implementation of inertial computational procedures. PhD thesis, Ohio University,2002.
[118]Wu, Y., Hu, X., Wu, M., Hu, D. Error analysis of inertial navigation system using dual quaternions. IEEE PLANS. Monterey, California,2004.
[119]Wu, Y., Hu, X., Hu, D., Li, T., et al. Strapdown inertial navigation system algorithms based on dual quaternions. IEEE Transactions on Aerospace and Electronic Systems,2005.41(1):110-132.
[120]武元新.对偶四元数导航算法与非线性高斯滤波.博士学位论文.长沙：国防科技大学,2005.
[121]Wu, Y., Wu, M., Hu, D., Hu, X. Strapdown inertial navigation system using dual quaternions:error analysis. IEEE Transactions on Aerospace and Electronic Systems,2006.1(1):259-266.
[122]Wu, Y. On'A unified mathematical framework for strapdown algorithm design'. Journal of Guidance, Control, and Dynamics,2006.29(6):1482-1484.
[123]Mark, J.G., Tazartes, D.A. Resolution Enhancement Technique for Laser Gyroscopes. Proceedings of 4th International Conference on Integrated Navigation Systems. St.Petersburg,1997.378-387.
[124]Mark, J.G., Tazartes, D.A. Tuning of Coning Algorithms to Gyro Data Frequency Response Characteristics. Journal of Guidance, Control, and Dynamics,2001.24(4):641-647.
[125]Mark, J.G., Tazartes, D.A. Application of Coning Algorithms to Frequency Shaped Gyro Data. Proceeding of the 6th Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,1999. 2.1-2.11.
[126]Slyusar, V. Attitude Integration Algorithms Design for Strapdown DTG Inertial Systems. Proceedings of Symposium Gyro Technology Stuttgart, Germany, 2003.15.0-15.13.
[127]Slyusar, V. Extension of Navigation Sculling Algorithms Design for Frequency Shaped IMU Data. Proceedings of 11th International Conference on Integrated Navigation Systems. St. Petersburg 2004.294-297.
[128]Slyusar, V.M. On Effect of Instrumental Factors On Strapdown Attitude Drift Rate. Proceeding of the 13th Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,2006.311-314.
[129]曾庆化,刘建业,赵伟,赖际舟.一种滤波角速率输入的圆锥误差补偿算法研究. 中国航空学会控制与应用第十二届学术年会.西安,2006.554-558.
[130]曾庆化,刘建业,赵伟.激光捷联惯导系统角增量输入姿态算法.南京航空航天大学学报,2007.39(2)：143-148.
[131]曾庆化,刘建业,赵伟,熊智.激光陀螺惯导系统硬件增强角速率输入圆锥算法.东南大学学报,2006.36(5)：746-750.
[132]王可东,顾启泰.环形激光陀螺仪机械抖动参数的选定.光学技术,2000.26(4)：354-360.
[133]王可东,顾启泰.随机噪声对激光陀螺输出特性的影响.光学学报,2003.23(12)：1479-1483.
[134]汤建勋,谢元平,付文羽.抖动偏频激光陀螺的抖动控制器.应用激光,2000.20(1)：24-26.
[135]Priddy, L.W. RLG dither noise injection by means of reference modulation. United States Patent,5,774,216,1998.
[136]M.Kay, R. Sinusoidal noise injection into the dither of a ring laser gyroscope. United States Patent,5,416,584,1995.
[137]谭新洪,杜建邦.激光陀螺数字式稳频方法的研究.计量学报,2002.23(3)：216-218.
[138]刘宗玉,陈明,王玮.抖动偏频激光陀螺中的解调及实现技术.测控技术,2004.23(9)：67—75.
[139]Mitra, S.K. Digital Signal Processing:A Computer-Based Approach:The McGraw-Hill Companies,2001.
[140]Kim, K., Lee, T.G. Analysis of the Two-frequency Coning Motion with SDINS. AIAA Guidance, Navigation, and Control Conference and Exhibit. Montreal, Canada,2001.6-9
[141]Zarchan, P. Strapdown Inertial Navigation Technology. Second Edition ed. Lexington, Massachusetts:American Institute of Aeronautics and Astronautics, Inc,2004.
[142]王岩.机抖激光陀螺捷联惯导系统的标定方法研究.硕士.长沙：国防科技大学,2004.
[143]胡广书.数字信号处理—理论、算法与实现.北京：清华大学出版社,2003.
[2]张树侠,孙静.捷联式惯性导航系统.北京：国防工业出版社,1992.
[3]袁信,俞济祥,陈哲.导航系统.北京：航空工业出版社,1993.
[4]陈哲.捷联惯导系统原理.北京：宇航出版社,1986.
[5]W.W.Chow, J.Gea-Banacloche, L.M.Pedrotti. The ring laser gyro. Review of Modern Physics 1985.57(1):61-104.
[6]杨培根,龚智炳.光电惯性技术.北京：兵器工业出版社,1999.
[7]Hadfield, M.J., Leiser, K.E. Ring laser gyros come down to Earth:Field test results on the RLG modular azimuth position system. IEEE PLANS, Position Location and Navigation Symposium,1998:61-72.
[8]Majure, R.G. Demonstration of a ring laser gyro system for pointing and stabilization applications. IEEE PLANS, Position Location and Navigation Symposium,1990:219-225.
[9]Nelson, K.D. Flight results of the ring laser gyro based inertial navigation system for Atlas/cetaur.1992:440-445.
[10]Oelschlaeger, J.M., Thielman, L.O. GG1308 Ring Laser Gyro Inertial Measurement Systems-Honeywell's Low Cost Solution For Tactical Applications. IEEE PLANS, Position Location and Navigation Symposium, 1990:528-536.
[11]Stamenkovich, M., Carvil, J. Application of the digital nautical chart (DNC) database to help identify areas of vertical deflection in the ring laser gyro inertial navigator. IEEE PLANS, Position Location and Navigation Symposium,2000: 299-303.
[12]Curran, G.L., Engelken, D.J. Ring laser gyro applications for tactical missiles. IEEE PLANS, Position Location and Navigation Symposium,1990:543-548.
[13]Wright, R.J., Sponnick, J.V. A ring laser gyro based navigator for space launch vehicle guidance. IEEE PLANS, Position Location and Navigation Symposium, 1988:271-279.
[14]Gilster, G. High accuracy performance capabilities of the military standard ring laser gyro inertial navigation unit. IEEE PLANS, Position Location and Navigation Symposium,1994:464-473.
[15]王宇.机抖激光陀螺捷联惯导系统的初步探索.博士学位论文.长沙：国防科技大学,2005.
[16]Savage, P.G. Strapdown inertial navigation integration algorithm design part 1: attitude algorithms. Journal of Guidance, Control, and Dynamics,1998.21(1): 19-28.
[17]Savage, P.G. Strapdown inertial navigation integration algorithm design part 2: velocity and position algorithm. Journal of Guidance, Control, and Dynamics, 1998.21(2):208-221.
[18]秦永元.惯性导航.北京：科学出版社,2006.
[19]Post, E.J. Sagnac Effect. Review of Modern Physics,1967.39(2):475-493.
[20]Aronowitz, F. The Laser Gyro. Laser Application,1971(1):134-199.
[21]Cresser, J.D., Louisell, W.H., Meystre, P., Schleich, W., et al. Quantum noise in ring laser gyros. I. Theoretical formulation of problem. Physical Review A,1982. 25(4):2214-2225.
[22]Cresser, J.D., Hammonds, D., Louisell, W.H., Meystre, P., et al. Quantum noise in ring laser gyros. Ⅱ. Numerical results. Physical Review A,1982.25(4): 2226-2234.
[23]Cresser, J.D. Quantum noise in ring laser gyros. Ⅲ. Approximate analytic results in unlocked region. Physical Review A,1982.26(1):398-409.
[24]Andrews, D.A., Roden, S. A model for lock-in growth in ring laser gyroscopes. IEEE Journal of Quantum Electronics 1995.31(9):1709-1715.
[25]Wu, G., Gu, Q. Thermal characteristics and thermal compensation of four frequency ring laser gyro. IEEE PLANS, Position Location and Navigation Symposium,2002:271-276.
[26]曾庆化,刘建业,赖际舟,熊智.环形激光陀螺的最新发展.传感器技术,2004.23(11)：1-4.
[27]J.R.Wilkinson. ring lasers. Prog.Quant.Electr,1987.11:1-103.
[28]Bo.H.G.Ljung. Ring Laser Gyroscope Dither Drive Circuit. United States Patent, 4277173,1981.
[29]Daniel A.Tazartes, W.H., John G.Mark, P., Robert E. Ebner, T., all of Calif;. Ring laser gyroscope dither drive system and method United States Patent, 4,981,359,1991.
[30]Fritze, K.R. Laser gyro dither drive. United States Patent,5225889,1993.
[31]Joseph.E. Dither control system for a ring laser gyro. United States Patent, 6,476,918 Bl,2002.
[32]J.Murphy, H. Digital path length control for ring laser gyros. United States Patent,5,108,182,1992.
[33]John G.Mark, P. Multioscilator ring laser gyroscope adaptive digitally controlled cavity length control system. United States Patent,5,208,653,1993.
[34]姜亚南.环形激光陀螺.北京：清华大学出版社,1985.
[35]杜建邦.三角形激光陀螺谐振腔的精度分析.航天控制,1998(3)：53-61.
[36]张惟叙,邓兆炯.激光陀螺抖动偏频研究.北京航空航天大学学报,1990(3)：15-20.
[37]章燕申,汤全安,潘珍吾.激光陀螺及其误差补偿.航空学报,1990.11(3)：120-126.
[38]罗晖,张广发.激光陀路信号检测系统的理论与实验研究.激光技术,1997.21(3)：132-137.
[39]付文羽.四频差动激光陀螺稳频系统研究.激光与光电子学进展(增刊)第八届全国光电技术与系统学术会议论文专辑,1999(9)：77.
[40]刘巧光,许辅义,滕云鹤,章燕申.环形激光陀螺仪随机误差模型的研究.清华大学学报(自然科学版),1999(2).
[41]谢元平,曾淳,汤建勋.机械抖动激光陀螺过锁区分析与处理.光电子·激光,2000.11(1)：45-48.
[42]韩宗虎,陈林峰,陈勇,吉翠萍.激光陀螺锁区特性的研究.光子学报,2006.35(6)：807-809.
[43]杨海军,郭美凤,章燕申.激光陀螺的闭锁阀值及抖动偏频.惯导与仪表,1999(3)：43-48.
[44]王京献.激光陀螺抖动偏频技术研究.硕士学位论文.西安：西北工业大学,1999.
[45]汤建勋.机械抖动激光陀螺抖动偏频系统的研究与设计.博士学位论文.长沙：国防科技大学,2000.
[46]谢元平.机械抖动激光陀螺鉴相解调与稳频技术研究.博士学位论文.长沙：国防科技大学,2000.
[47]刘放.环形激光陀螺的稳频计算机控制系统及其FUZZY-PID算法.硕士学位论文.西安：西北工业大学,2000.
[48]杨卓.机械抖动激光陀螺稳频和鉴相技术研究.硕士学位论文.北京：北京理工大学,2003.
[49]汤建勋,罗晖,李革.机抖激光陀螺抖动控制环路频率特性的校正.中国惯性技术学报,2003.11(4)：36-39.
[50]杨恒,蒋东方,范东远.环形激光陀螺频率稳定性的研究.西北工业大学学报,1999.17(3)：414-418.
[51]杨恒,刘放.微机控制环形激光陀螺自动扫模的研究与实现.西北工业大学学报,2000.18(2)：203-206.
[52]刘放,张士邈,陈明.模糊PID控制算法及其在激光陀螺稳频控制中的应用.测控技术,2001.20(7)：21-23.第143页
[53]Bo.H.G.Ljung. Ring laser gyro dither pulse eliminator. United States Patent, 4344706,1982.
[54]Daniel A.Tazartes, W.H. Apparatus and method for correcting ring laser gyroscope phase error at turnround. United States Patent,5,004,344,1991.
[55]Elbert, H.F. Apparatus and method for the elimination of angular vibration induced errors in ring laser gyroscopes. United States Patent,4248534,1981.
[56]Fritze, K.R. Ring laser gyro dither stripper. United States Patent,5249031,1993.
[57]Geston, D.R. Dither signal remover for a dithered ring laser angular rate sensor utilizing an adaptive digital filter. United States Patent,5331402,1994.
[58]Ignagni, M.B. Dither signal remover for a dithered ring laser gyro. United States Patent,5048963,1991.
[59]P.Callahan, S., E.Killpatrick, J. Dither signal remover for a dithered ring gyro angular rate sensor. United States Patent,4,826,320,1989.
[60]陈楸,陈明,李岁劳.陀螺输出信号的超高速处理.航空计测技术,2003.23(2)：6-9.
[61]刘宗玉,陈明,王玮,倪家琳.抖动偏频激光陀螺中的解调及实现技术.测控技术,2004.23(9)：67-75.
[62]Johnson, D.P. Frequency Domain Analysis for RLG System Design. Journal of the Insititute of Navigation,1987.34(3):179-189.
[63]Lahham, J.I., Wigent, D.J., L.Coleman, A. Tuned support structure for structure-borne noise reduction of inertial navigator with dithered ring laser gyros (RLG). IEEE PLANS, Position Location and Navigation Symposium, 2000:419-428.
[64]王可东,顾启泰,钟德贵,田海峰.机抖式激光陀螺基础抖动消除研究.中国惯性技术学报,2002.10(6)：62-67.
[65]王可东,顾启泰,钟德贵.配重式激光陀螺机械抖动系统的实验研究.激光杂志,2003.24(2)：44-46.
[66]吴文启,庹洲慧,江明明.激光陀螺机械抖动偏频对等效转动矢量姿态计算的影响.航空学报,2006.27(1)：71-76.
[67]李俊峰,刘进江,唐献林.激光陀螺捷联惯性组合的系统结构抗振控制.中国惯性技术学报,2006.14(1)：21-26.
[68]Britting, K.R. Inertial Navigation Systems Analysis:John Wiley & Sons, Inc., 1971.
[69]Savage, P.G. A new second-order solution for strapped-down attitude computation. AIAA/JACC Guidance and Control Conference.1966.
[70]Bortz, J.E. A New Mathematical Formulation for Strapdown Inertial Navigation. IEEE Transactions on Aerospace and Electronics System,1971.7(AES-1): 61-66.
[71]Miller, R.B. A New Strapdown Attitude Algorithms. Journal of Guidance, Control, and Dynamics,1983.6(4):287-291.
[72]Lee, J.G., Yoon, Y.J. Extension of Strapdown Attitude Algorithm for High-Frequency Base Motion. Journal of Guidance, Control, and Dynamics, 1990.13(4):738-743.
[73]Ignagni, M.B. Efficient Class of Optimized Coning Compensation Algorithms Journal of Guidance, Control, and Dynamics,1996.19(2):424-429.
[74]Ignagni, M.B. Optimal Strapdown Attitude Integration Algorithms. Journal of Guidance, Control, and Dynamics,1990.13(2):363-369.
[75]Jiang, Y.F., Lin, Y.P. Improved Strapdown Coning Algrithms. IEEE Transactions on Aerospace and Electronics System,1992.28(2):484-490.
[76]Musoff, H., Murphy, J.H. Study of Strapdown Navigation Attitude Algorithms. Journal of Guidance, Control, and Dynamics,1995.18(2):287-290.
[77]Park, C.G., Kim, K.J. Formalized Approach to Obtaining Optimal Coefficients for Coning Algorithms. Journal of Guidance, Control, and Dynamics,1999. 22(1):165-168.
[78]Jordon, J.W. An Accurate Strapdown Direction Cosine Algorithm. NASA TND-5384,1969.
[79]JIANG, Y.F., LIN, Y.P. On The Rotation Vector Differential Equation. IEEE Transactions on Aerospace and Electronic Systems,1991.27(1):181-183.
[80]Litmanovich, Y.A., Mark, J.G. Process In strapdown Algorithm Design at the West and East as Appeared at Saint Petersburg Conferences:Decade Overview. Proceeding of the 10rd Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,2003.369-377.
[81]Savage, P.G., Strapdown system algorithms, systems, A.i.s.i., Editor.1984.
[82]Mortensen, R.E. Strapdown guidance error analysis. IEEE Transactions on Aerospace and Electronic Systems,1974.10(4):451-457.
[83]Ignagni, M.B. On the Orientation Vector Differential Equation in Strapdown Inertial System. IEEE Transactions on Aerospace and Electronics System,1994. 30(4):1076-1081.
[84]Gusinsky, V.Z., Lesyuchevsky, V.M., Litmanovich, Y.A. New Procedure for Deriving Optimized Strapdown Attitude Algorithms. Journal of Guidance, Control, and Dynamics,1997.20 (4):673-680.
[85]Gusinsky, V.Z., Lesyuchevsky, V.M., Litmanovich, Y.A. Optimization of a Strapdown Attitude Algorithm for a Stochastic Motion. Navigation:Journal of The Institute of Navigation,1997.44(2):163-170.
[86]Savage, P.G. Analytical modeling of sensor quantization in strapdown inertial navigation error equation. Journal of Guidance, Control, and Dynamics,2002.
25(No.5):833-842.
[87]Savage, P.G. A unified Mathematical Framework for strapdown algorithm design. Journal of Guidance, Control, and Dynamics,2006.29(3):237-249.
[88]Harasty, G.A., G., U.F. Computational requirements for a digital analytic inertial platform system. the 12th East Coast Conf. on Aerospace and Navigational Electronics. Baltimore, Md.,1965.
[89]Bar-Itzhack, I.Y. Navigation computation in terrestrial strapdown inertial navigation systems. IEEE Transactions on Aerospace and Electronic Systems, 1977. AES-13(6):679-689.
[90]Ignagni, M.B. Duality of Optimal Strapdown Sculling and Coning Compensition Algorithms. Journal of the Insititute of Navigation,1998.45(2):85～95.
[91]Roscoe, K.M. Equivalency Between Strapdown Inertial Navigation Coning and Sculling Integrals/Algorithms. Journal of Guidance, Control, and Dynamics, 2001.24(2):201-205.
[92]Mark, J.G., Tazartes, D.A. On sculling Algorithms. Proceeding of the 3rd Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,1996.22-26.
[93]赵健,以光衢.捷联惯导中的等效旋转矢量算法及其仿真研究.中国惯性技术学报,1996.4(4)：1-6.
[94]王养柱,崔中兴.捷联惯导系统圆锥补偿算法优化设计.惯性技术学报,2000.8(1)：7-10.
[95]王养柱,崔中兴.捷联式惯性导航系统算法研究.中国惯性技术学报,2000.8(2)：31-35.
[96]薛祖瑞.关于捷联惯导系统圆锥误差的诠释.中国惯性技术学报,2000.8(4)：46-50.
[97]周江华,苗育红,肖刚.扩展旋转矢量捷联姿态算法.宇航学报,2003.24(4)：414-417.
[98]余杨,张洪钺.捷联惯导系统中的圆锥和伪圆锥运动研究.中国惯性技术学报,2006.14(5)：1-4.
[99]曾庆化,刘建业,熊智,赵伟.一种角速率激光陀螺惯导系统高精度姿态算法.上海交通大学学报,2006.40(12)：2159-2163.
[100]孙丽,秦永元.捷联惯导系统姿态算法比较.中国惯性技术学报,2006.14(3)：6-10.
[101]练军想,胡德文,胡小平,吴文启.捷联惯导姿态算法中的圆锥误差与量化误差.航空学报,2006.27(1)：98-103.
[102]周顺林,以光衢.抑制动态环境误差的算法研究.中国惯性技术学报,1996.4(1)：22-27.
[103]刘巧光,杨海军,郭美凤.捷联惯性导航系统的姿态算法优化设计.中国惯性技术学报,1999.7(2)：1-5.
[104]王养柱,崔中兴.捷联惯导系统圆锥补偿算法研究.北京航空航天大学学报,2001.27：264—267.
[105]秦永元,张士邈.捷联惯导姿态更新的四子样旋转矢量优化算法研究.中国惯性技术学报,2001.9(4)：1-7.
[106]刘危,解旭辉,李圣怡.捷联惯性导航系统的姿态算法.北京航空航天大学学报,2005.31(1)：45-50.
[107]耿延睿,王养柱,崔中兴.捷联惯导系统划船效应补偿算法研究.北京航空航天大学学报,2001.27(6)：694-696.
[108]陈小刚,赵琳,高伟.捷联惯导中的划船效应及其补偿算法.中国惯性技术学报,2002.10(2)：12-17.
[109]刘危,解旭辉,李圣怡.微导航系统的划船算法优化设计.弹箭与制导学报,2003.23(4)：44-48.
[110]张玲霞,陈明,曹晓青.基于对偶性原理捷联惯导划船误差补偿优化算法.中国惯性技术学报,2003.11(5)：33-38.
[111]蒲广平,裴听国,万彦辉.圆锥积分算法在划船效应补偿算法中的应用.中国惯性技术学报,2003.11(5)：39-47.
[112]Litmanovich, Y.A. Use of angular rate multiple integrals as input signals for strapdown attitude algorithms. Proceedings of Symposium Gyro Technology Stuttgart, Germany,1997.20.0-20.9.
[113]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. New procedure for deriving optimized strapdown attitude algorithms. Journal of Guidance, Control, and Dynamics,1997.20(4):673-680.
[114]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. Optimization of a strapdown attitude algorithm for a stochastic motion. Navigation:Journal of The Institute of Navigation,1998.44(2):163-170.
[115]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. Signal processing using the increments of signal multiple integrals:from strapdown INS to other real-time systems. Proceedings of 6th International Conference on Integrated Navigation Systems. St. Petersburg 1999.8.1-8.7.
[116]Litmanovich, Y.A., Lesyuchevsky, V.M., Gusinsky, V.Z. Two New Classes of Strapdown Navigation Algorithms. Journal of Guidance, Control, and Dynamics, 2000.23(1):34-44.
[117]Soloviev, A. Investigation into performance enhancement of integrated global positioning/inertial navigation systems by frequency domain implementation of inertial computational procedures. PhD thesis, Ohio University,2002.
[118]Wu, Y., Hu, X., Wu, M., Hu, D. Error analysis of inertial navigation system using dual quaternions. IEEE PLANS. Monterey, California,2004.
[119]Wu, Y., Hu, X., Hu, D., Li, T., et al. Strapdown inertial navigation system algorithms based on dual quaternions. IEEE Transactions on Aerospace and Electronic Systems,2005.41(1):110-132.
[120]武元新.对偶四元数导航算法与非线性高斯滤波.博士学位论文.长沙：国防科技大学,2005.
[121]Wu, Y., Wu, M., Hu, D., Hu, X. Strapdown inertial navigation system using dual quaternions:error analysis. IEEE Transactions on Aerospace and Electronic Systems,2006.1(1):259-266.
[122]Wu, Y. On'A unified mathematical framework for strapdown algorithm design'. Journal of Guidance, Control, and Dynamics,2006.29(6):1482-1484.
[123]Mark, J.G., Tazartes, D.A. Resolution Enhancement Technique for Laser Gyroscopes. Proceedings of 4th International Conference on Integrated Navigation Systems. St.Petersburg,1997.378-387.
[124]Mark, J.G., Tazartes, D.A. Tuning of Coning Algorithms to Gyro Data Frequency Response Characteristics. Journal of Guidance, Control, and Dynamics,2001.24(4):641-647.
[125]Mark, J.G., Tazartes, D.A. Application of Coning Algorithms to Frequency Shaped Gyro Data. Proceeding of the 6th Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,1999. 2.1-2.11.
[126]Slyusar, V. Attitude Integration Algorithms Design for Strapdown DTG Inertial Systems. Proceedings of Symposium Gyro Technology Stuttgart, Germany, 2003.15.0-15.13.
[127]Slyusar, V. Extension of Navigation Sculling Algorithms Design for Frequency Shaped IMU Data. Proceedings of 11th International Conference on Integrated Navigation Systems. St. Petersburg 2004.294-297.
[128]Slyusar, V.M. On Effect of Instrumental Factors On Strapdown Attitude Drift Rate. Proceeding of the 13th Saint Petersburg International Conference on Integrated Navigation Systems. St. Petersburg. Russia,2006.311-314.
[129]曾庆化,刘建业,赵伟,赖际舟.一种滤波角速率输入的圆锥误差补偿算法研究. 中国航空学会控制与应用第十二届学术年会.西安,2006.554-558.
[130]曾庆化,刘建业,赵伟.激光捷联惯导系统角增量输入姿态算法.南京航空航天大学学报,2007.39(2)：143-148.
[131]曾庆化,刘建业,赵伟,熊智.激光陀螺惯导系统硬件增强角速率输入圆锥算法.东南大学学报,2006.36(5)：746-750.
[132]王可东,顾启泰.环形激光陀螺仪机械抖动参数的选定.光学技术,2000.26(4)：354-360.
[133]王可东,顾启泰.随机噪声对激光陀螺输出特性的影响.光学学报,2003.23(12)：1479-1483.
[134]汤建勋,谢元平,付文羽.抖动偏频激光陀螺的抖动控制器.应用激光,2000.20(1)：24-26.
[135]Priddy, L.W. RLG dither noise injection by means of reference modulation. United States Patent,5,774,216,1998.
[136]M.Kay, R. Sinusoidal noise injection into the dither of a ring laser gyroscope. United States Patent,5,416,584,1995.
[137]谭新洪,杜建邦.激光陀螺数字式稳频方法的研究.计量学报,2002.23(3)：216-218.
[138]刘宗玉,陈明,王玮.抖动偏频激光陀螺中的解调及实现技术.测控技术,2004.23(9)：67—75.
[139]Mitra, S.K. Digital Signal Processing:A Computer-Based Approach:The McGraw-Hill Companies,2001.
[140]Kim, K., Lee, T.G. Analysis of the Two-frequency Coning Motion with SDINS. AIAA Guidance, Navigation, and Control Conference and Exhibit. Montreal, Canada,2001.6-9
[141]Zarchan, P. Strapdown Inertial Navigation Technology. Second Edition ed. Lexington, Massachusetts:American Institute of Aeronautics and Astronautics, Inc,2004.
[142]王岩.机抖激光陀螺捷联惯导系统的标定方法研究.硕士.长沙：国防科技大学,2004.
[143]胡广书.数字信号处理—理论、算法与实现.北京：清华大学出版社,2003.