捷联惯导系统传递对准技术及误差补偿方法研究
|
摘要
传递对准技术是为运动中的载体提供准确的初始基准。在瞬息万变的现代战争中，传递对准技术已成功应用于舰载、机载战术制导武器。而在舰载机传递对准中，由于载机指向不定，此时极有可能出现方位失准角为大角的情况；同时，海浪冲击、载舰机动将引起船体的挠曲变形；而机载惯导与舰载惯导之间的距离较远，挠曲变形和杆臂效应的耦合将使误差补偿问题变得更加复杂。针对上述情况，本文在比较和分析各类误差模型、匹配方法、滤波算法及误差补偿方法的基础上，对大方位失准角传递对准和误差补偿技术展开研究。主要研究内容如下：
首先针对传递对准的三个主要误差源：惯性测量元件误差、挠曲变形误差和杆臂误差建立相应的误差模型，在此基础上分别推导了经典传递对准误差模型和快速传递对准误差模型。从速度误差和姿态失准角的定义出发，分析了两种误差模型中参考坐标系之间的相互关系，通过深入研究，给出了经典传递对准误差模型和快速传递对准误差模型的一致性条件与适用范围，为后面的匹配方法研究和四元数传递对准算法打下基础。
匹配方法是传递对准技术的重要组成部分，本文深入研究速度匹配和姿态匹配。速度匹配不受到惯导类型的影响，且具备较为突出的综合性能。针对速度匹配的可观测性问题，在分析研究速度匹配量测与状态变量之间关系的基础上，提出一种更为直观的可观测性解析方法，并通过推导匀速直线运动下各状态与量测多阶微分的关系式验证了该方法的有效性。当主、子惯导都为捷联惯导时，姿态匹配成为一个重要的选择。针对姿态匹配量测与速度误差耦合较弱的问题，从量测量的获取和算法复杂度出发，深入研究了姿态角匹配、姿态矩阵匹配和量测失准角匹配。在不同机动条件下对速度匹配和速度+姿态匹配进行了仿真验证。
深入研究大失准角传递对准中的非线性滤波算法。针对系统状态维数较高的问题，在比较分析两种单形采样策略的基础上选取超球体采样策略，降低了sigma点数量，提高算法实时性。同时为提高非线性滤波算法的计算稳定性，结合平方根UKF滤波算法，提出了超球体采样SRUKF对大失准角传递对准下的非线性系统进行估计。并通过舰载机大方位失准角传递对准仿真分析验证所提算法的有效性。
针对欧拉角法在大失准角传递对准问题中存在的奇异性、运算繁琐等问题，引入非奇异、精度高和计算简单的姿态四元数法。在定义姿态误差四元数的基础上，首先推导得到四元数经典传递对准误差模型和四元数快速传递对准误差模型。与“速度+姿态”匹配相对应，深入研究四元数量测失准角匹配并给出量测方程。在该匹配方法中，量测量由主、子惯导的即时修正四元数相乘得到。得到四元数非线性误差模型的基础上，对四元数传递对准UKF算法进行研究。其中，针对四元数UKF中的四元数协方差阵奇异问题，利用误差四元数中非冗余的状态误差矢量作协方差阵运算，并根据UT变换作适当改进。同时，针对四元数加权均值的规范性问题，利用姿态参数切换和特征值向量求解的方法进行解决。后者在构造四元数代价函数的基础上，通过特征向量求解获得MMSE下的四元数加权均值，避免了姿态参数切换引起的实时性和数值稳定性下降问题。最后针对扩维滤波中采样点数量增加和高阶误差方差阵的平方根运算问题，引入超球体采样和平方根滤波思想，提出了四元数SSRUKF滤波。大方位失准角下的仿真实验证明了四元数传递对准算法的有效性。
针对挠曲变形噪声补偿法中噪声方差难以确定的问题，深入研究描述挠曲变形的Markov过程的统计特性，并给出计算方法。在此基础上对挠曲变形角与杆臂效应的耦合问题进行定量分析，并将其统一等价为噪声补偿问题。针对噪声补偿法无法实时跟踪外界变化的问题，引入极大似然法及强跟踪滤波算法。其中，Sage-Husa自适应滤波对初值较为敏感，且滤波不稳定。对此，融入强跟踪滤波在线调整协方差阵和增益矩阵的思想，并在强跟踪滤波中增加量测噪声协方差阵的权重，重新定义渐消因子，从而使其更好发挥当前量测的作用。最后结合极大似然法，给出改进Sage-Husa自适应滤波算法。通过仿真实验验证在补偿噪声方差初值小于真实值的情况下改进Sage-Husa自适应滤波的有效性。
Transfer alignment technology provides accurate initial reference for vehicles in motion.In rapidly changing modern war，transfer alignment technology has been applied to shipborneand airborne tactical guided weapons successfully. But in the transfer alignment ofcarrier-based aircrafts, the situation of carrier aircraft’s direction cannot be determined willlead to the large azimuth misalignment. Meanwhile, the shock of waves and maneuvering ofcarrier ship will cause flexural deformation, and high distance between shipborne inertialnavigation system(INS) and airborne INS give rise to the coupling of flexural deformationand lever arm effect, which make the error compensation problem more complicated. Aimingat above problems, the transfer alignment technology under large misalignments and errorcompensation methods will be studied in this paper through comparing and analysising ofdifferent error models, matching methods, filtering algorithms and error compensationmethods.
The main error sources of transfer alignment like errors of inertial measurementunit(imu), errors of flexural deformation and lever arm errors are modeled firstly, then classictransfer alignment error models and rapid transfer alignment error models are deducedrespectively. According to the definition of velocity and attitude errors, the relations ofreference coordinate systems of two error models are analyzed. On the basis of above job, theconsistency and scope of the application of two error models are deeply studied, which laysthe foundations for the following matching methods and quaternion transfer alignmentalgorithm.
Matching methods are important parts of transfer alignment technology, and the velocitymatching and attitude matching are mainly studied. Velocity matching is not subjected to theINS type, and have good comprehensive performance. Aiming at the observability problem ofvelocity matching, a more intuitive analytical method is proposed based on the analysis of therelation between measurements in velocity matching and states. The effectiveness is verifiedby deriving the relationship between states and measurement of multi-order differential underthe situation of uniform linear motion. When main INS and slave INS are both strapdowninertial navigation system(SDINS), attitude matching method becomes an important option.Because of the weak coupling relationship between measurements in attitude matching andvelocity errors, the attitude angle matching、 attitude matrix matching and measuredmisalignment matching are studied and compared according to the measurement obtainingand the complexity of the measurement equations, which resultes in the “velocity+attitude” matching, whose state and measurement equations are given finally. The velocity matchingand“velocity+attitude” matching are simulated under different maneuvering.
Aiming at transfer alignment of large misalignment, the nonlinear filtering algorithm ismainly studied. To deal with the problem of high state dimension, the spherical sampling ischosen by comparing two simplex sampling strategy, so that the number of sigma point canbe reduced and real-time of algorithm can be achieved. Meanwhile, the square rootUKF(SRUKF) is used to improve the computational stability of nonlinear filtering algorithm.Finally the spherical sampling SRUKF(SSRUKF) is proposed. The effeteness of the methodis verified by the simulation experiment of transfer alignment of carrier-based aircraft underlarge azimuth misalignment.
Aiming at the problems of singularity and high computational burden of euler anglemethod in transfer alignment under large misalignment, the nonsingular，precise and easyattitude quaternion is introduced. On the basis of defining error attitude quaternion, thequaternion classic transfer alignment error models and rapid transfer alignment error modelsare derived firstly. Corresponding to “velocity+attitude” matching, the quaternion measuredmisalignment matching method is studied deeply and the measurement equations are given,where the measurements are obtained by multiplying the immediate correction quaternion ofMINS and SINS. On the basis of above job, the quaternion UKF is studied. Thenon-redundant vectors of error quaternion are used to compute the covariance, so that thesingularity of quaternion covariance can be avoid. The covariance equation is adjustedappropriately by UT transformation. The method based on solving eigenvalue vector is usedto calculate the weighted mean of normal quaternion which is based on the construction of thecost function. Finally, the augmented UKF is given as a result of the multiplicative noise. Theeffeteness of proposed method is verified by the simulation experiment of transfer alignmentof carrier-based aircraft under large azimuth misalignment.
The statistical properties of markov process which describe the flexural deformation arestudied and the equations are given to determine the noise variance for flexural deformation.On the basis of above job, the coupling of flexural deformation and lever arm effect isquantitatively analyzed, and equaled to the problem of noise compensation. In order to solvethe problem that the compensated noise cannot follow the external changes in real time,maximum likelihood method and strong tracking filtering are introduced. The idea ofadjusting covariance and gain matrix online is integrated to solve the problem that theSage-Husa adaptive filtering is unstable and sensitive to the initial value of filtering. To takefull advantage of current measurements, the weight of measurement noise covariance is increased, and the fading factors are redefined in strong tracking filtering. By combiningmaximum likelihood method, an improved Sage-Husa adaptive filtering is given finally. Theeffectiveness of Sage-Husa adaptive filtering is verified by the simulation experiment, wherethe variance of compensated noise is set smaller than the true value.
首先针对传递对准的三个主要误差源：惯性测量元件误差、挠曲变形误差和杆臂误差建立相应的误差模型，在此基础上分别推导了经典传递对准误差模型和快速传递对准误差模型。从速度误差和姿态失准角的定义出发，分析了两种误差模型中参考坐标系之间的相互关系，通过深入研究，给出了经典传递对准误差模型和快速传递对准误差模型的一致性条件与适用范围，为后面的匹配方法研究和四元数传递对准算法打下基础。
匹配方法是传递对准技术的重要组成部分，本文深入研究速度匹配和姿态匹配。速度匹配不受到惯导类型的影响，且具备较为突出的综合性能。针对速度匹配的可观测性问题，在分析研究速度匹配量测与状态变量之间关系的基础上，提出一种更为直观的可观测性解析方法，并通过推导匀速直线运动下各状态与量测多阶微分的关系式验证了该方法的有效性。当主、子惯导都为捷联惯导时，姿态匹配成为一个重要的选择。针对姿态匹配量测与速度误差耦合较弱的问题，从量测量的获取和算法复杂度出发，深入研究了姿态角匹配、姿态矩阵匹配和量测失准角匹配。在不同机动条件下对速度匹配和速度+姿态匹配进行了仿真验证。
深入研究大失准角传递对准中的非线性滤波算法。针对系统状态维数较高的问题，在比较分析两种单形采样策略的基础上选取超球体采样策略，降低了sigma点数量，提高算法实时性。同时为提高非线性滤波算法的计算稳定性，结合平方根UKF滤波算法，提出了超球体采样SRUKF对大失准角传递对准下的非线性系统进行估计。并通过舰载机大方位失准角传递对准仿真分析验证所提算法的有效性。
针对欧拉角法在大失准角传递对准问题中存在的奇异性、运算繁琐等问题，引入非奇异、精度高和计算简单的姿态四元数法。在定义姿态误差四元数的基础上，首先推导得到四元数经典传递对准误差模型和四元数快速传递对准误差模型。与“速度+姿态”匹配相对应，深入研究四元数量测失准角匹配并给出量测方程。在该匹配方法中，量测量由主、子惯导的即时修正四元数相乘得到。得到四元数非线性误差模型的基础上，对四元数传递对准UKF算法进行研究。其中，针对四元数UKF中的四元数协方差阵奇异问题，利用误差四元数中非冗余的状态误差矢量作协方差阵运算，并根据UT变换作适当改进。同时，针对四元数加权均值的规范性问题，利用姿态参数切换和特征值向量求解的方法进行解决。后者在构造四元数代价函数的基础上，通过特征向量求解获得MMSE下的四元数加权均值，避免了姿态参数切换引起的实时性和数值稳定性下降问题。最后针对扩维滤波中采样点数量增加和高阶误差方差阵的平方根运算问题，引入超球体采样和平方根滤波思想，提出了四元数SSRUKF滤波。大方位失准角下的仿真实验证明了四元数传递对准算法的有效性。
针对挠曲变形噪声补偿法中噪声方差难以确定的问题，深入研究描述挠曲变形的Markov过程的统计特性，并给出计算方法。在此基础上对挠曲变形角与杆臂效应的耦合问题进行定量分析，并将其统一等价为噪声补偿问题。针对噪声补偿法无法实时跟踪外界变化的问题，引入极大似然法及强跟踪滤波算法。其中，Sage-Husa自适应滤波对初值较为敏感，且滤波不稳定。对此，融入强跟踪滤波在线调整协方差阵和增益矩阵的思想，并在强跟踪滤波中增加量测噪声协方差阵的权重，重新定义渐消因子，从而使其更好发挥当前量测的作用。最后结合极大似然法，给出改进Sage-Husa自适应滤波算法。通过仿真实验验证在补偿噪声方差初值小于真实值的情况下改进Sage-Husa自适应滤波的有效性。
Transfer alignment technology provides accurate initial reference for vehicles in motion.In rapidly changing modern war，transfer alignment technology has been applied to shipborneand airborne tactical guided weapons successfully. But in the transfer alignment ofcarrier-based aircrafts, the situation of carrier aircraft’s direction cannot be determined willlead to the large azimuth misalignment. Meanwhile, the shock of waves and maneuvering ofcarrier ship will cause flexural deformation, and high distance between shipborne inertialnavigation system(INS) and airborne INS give rise to the coupling of flexural deformationand lever arm effect, which make the error compensation problem more complicated. Aimingat above problems, the transfer alignment technology under large misalignments and errorcompensation methods will be studied in this paper through comparing and analysising ofdifferent error models, matching methods, filtering algorithms and error compensationmethods.
The main error sources of transfer alignment like errors of inertial measurementunit(imu), errors of flexural deformation and lever arm errors are modeled firstly, then classictransfer alignment error models and rapid transfer alignment error models are deducedrespectively. According to the definition of velocity and attitude errors, the relations ofreference coordinate systems of two error models are analyzed. On the basis of above job, theconsistency and scope of the application of two error models are deeply studied, which laysthe foundations for the following matching methods and quaternion transfer alignmentalgorithm.
Matching methods are important parts of transfer alignment technology, and the velocitymatching and attitude matching are mainly studied. Velocity matching is not subjected to theINS type, and have good comprehensive performance. Aiming at the observability problem ofvelocity matching, a more intuitive analytical method is proposed based on the analysis of therelation between measurements in velocity matching and states. The effectiveness is verifiedby deriving the relationship between states and measurement of multi-order differential underthe situation of uniform linear motion. When main INS and slave INS are both strapdowninertial navigation system(SDINS), attitude matching method becomes an important option.Because of the weak coupling relationship between measurements in attitude matching andvelocity errors, the attitude angle matching、 attitude matrix matching and measuredmisalignment matching are studied and compared according to the measurement obtainingand the complexity of the measurement equations, which resultes in the “velocity+attitude” matching, whose state and measurement equations are given finally. The velocity matchingand“velocity+attitude” matching are simulated under different maneuvering.
Aiming at transfer alignment of large misalignment, the nonlinear filtering algorithm ismainly studied. To deal with the problem of high state dimension, the spherical sampling ischosen by comparing two simplex sampling strategy, so that the number of sigma point canbe reduced and real-time of algorithm can be achieved. Meanwhile, the square rootUKF(SRUKF) is used to improve the computational stability of nonlinear filtering algorithm.Finally the spherical sampling SRUKF(SSRUKF) is proposed. The effeteness of the methodis verified by the simulation experiment of transfer alignment of carrier-based aircraft underlarge azimuth misalignment.
Aiming at the problems of singularity and high computational burden of euler anglemethod in transfer alignment under large misalignment, the nonsingular，precise and easyattitude quaternion is introduced. On the basis of defining error attitude quaternion, thequaternion classic transfer alignment error models and rapid transfer alignment error modelsare derived firstly. Corresponding to “velocity+attitude” matching, the quaternion measuredmisalignment matching method is studied deeply and the measurement equations are given,where the measurements are obtained by multiplying the immediate correction quaternion ofMINS and SINS. On the basis of above job, the quaternion UKF is studied. Thenon-redundant vectors of error quaternion are used to compute the covariance, so that thesingularity of quaternion covariance can be avoid. The covariance equation is adjustedappropriately by UT transformation. The method based on solving eigenvalue vector is usedto calculate the weighted mean of normal quaternion which is based on the construction of thecost function. Finally, the augmented UKF is given as a result of the multiplicative noise. Theeffeteness of proposed method is verified by the simulation experiment of transfer alignmentof carrier-based aircraft under large azimuth misalignment.
The statistical properties of markov process which describe the flexural deformation arestudied and the equations are given to determine the noise variance for flexural deformation.On the basis of above job, the coupling of flexural deformation and lever arm effect isquantitatively analyzed, and equaled to the problem of noise compensation. In order to solvethe problem that the compensated noise cannot follow the external changes in real time,maximum likelihood method and strong tracking filtering are introduced. The idea ofadjusting covariance and gain matrix online is integrated to solve the problem that theSage-Husa adaptive filtering is unstable and sensitive to the initial value of filtering. To takefull advantage of current measurements, the weight of measurement noise covariance is increased, and the fading factors are redefined in strong tracking filtering. By combiningmaximum likelihood method, an improved Sage-Husa adaptive filtering is given finally. Theeffectiveness of Sage-Husa adaptive filtering is verified by the simulation experiment, wherethe variance of compensated noise is set smaller than the true value.
引文
[1] Benson D. O. A comparison of two approaches to pure-inertial and doppler-inertialerror analysis. IEEE Tran on AES.1975,11(4):447-455P.
[2] Goshen-Meskin D, Bar-itzhack I Y. Unified approach to inertial navigation systemerror modeling. Journal of GCD.1992,15(3):648-653P.
[3]秦永元.惯性导航.北京:科学出版社,2006.
[4] Bar-itzhack I Y, Goshen-Meskin D. Identity between INS Position and velocity errormodels. Journal of GCD.1981,4(5):569-570P.
[5] KAIN J E, CLOUTIER J R. Rapid transfer alignment for tactical weapon application.Proceedings of the AIAA Guidance, Navigation and Control Conference. Boston,1989:1290-1300P.
[6]郝曙光,张洪钺.几种传递对准方程的比较研究.中国惯性技术学报,2003,11(6):53-58,63页.
[7]陈凯,鲁浩,闫杰.快速传递对准方程与传统传递对准方程的一致性研究.西北工业大学学报,2008,26(3):326-329页.
[8] Friedlan B. Analysis strapdown navigation using quaternions. IEEE Tran on AES.1978,4(5):764-768P.
[9] Minoru Shibata. Error analysis strapdown inertial navigation using Quaternions.Journal of GCD.1986,9(3):379-381P.
[10] Doh Young Chung, Jang Gyu Lee, Chan Gook Park, Heung Won Park. Strapdown INSerror model for multiposition aignment. IEEE Tran on AES.1996,32(4):1362-1366P.
[11] M-Jong Y, Jang G L, H-Won P. Comparison of SDINS in-flight alignment usingequivalent error models. IEEE Transactions on Aerospace and Electronic Systems.1993,35(3):1046-1053P.
[12] M-Jong Y, Heng W P and Jean, C B. Equivalent nonlinear error model of strapdowninertial navigation system. Proeeedings of AIAA1997GNC conference.1997:97-3563P.
[13] Hao Y L, Xiong Z L,Wang W. Rapid transfer alignment based on uncented Kalmanfilter. Proceedings of the2006American Control Conference, Minneapolis USA,2006:2215-2220P.
[14]熊芝兰,郝燕玲,孙枫.基于四元数的惯导系统快速匹配对准算法.哈尔滨工程大学学报,2008,29(1):28-34P.
[15]戴邵武,李娟,戴洪德等.一种快速传递对准方法的误差模型研究.宇航学报,2009,30(3):942-946P.
[16]付梦印,邓志红,闫莉萍. Kalman滤波理论及其在导航系统中的应用(第二版).北京:科学出版社,2010.
[17] Vepa, N. M. A dynamic alignment system for applications on flexible plotforms suchas ship. Gyro technology.1989:16.10-16.13P.
[18] Titterton, D. H., Weston, J. L., Rae, F. The alignment of ship launched missile INsystems. IEEE Colloquium on Inertial Navigation Sensor Development.1990:1/1-116P.
[19] Ross, C. C., Elbert, T. F. A transfer alignment algorithm study based on actual flighttest data from a tactical air-to-ground weapon launch. Proc. of the1994IEEE PositionLocation and Navigation Symposium. Las Vegas, NV, USA.1994:431-438P.
[20] Bar-Itzhack, I. Y. Minimal order time sharing filters for INS in-flight alignment.Journal of Guidance, Control, and Dynamics.1982,5(4):396-402P.
[21] Bar-Itzhack, I. Y., Vitek, Y. The enigma of false bias detection in a strapdown systemduring transfer alignment. Journal of Guidance, Control, and Dynamics.1985,8(2):175-180P.
[22] Farrell, J. L. Airborne transfer alignment simulation results. IEEE PLANS Orlando,FL, USA.1988:269-270P.
[23] Spalding, K. An efficient rapid transfer alignment filter. AIAA Guidance, Navigationand Control Conference. Hilton Head Island, SC.1992:1276-1286P.
[24] D. Tarrant, C. Roberts, D. Jones et al. Rapid and robust transfer alignment. IEEEProceedings of Aerospace Control Systems.1993:758-762P.
[25] Shortelle, K., Graham, W. Advanced alignment concepts for precision-guidedweapons. Proc. of the Institute of Navigation Technical Meeting. Anaheim, CA.1995:131-142P.
[26] Graham, W., Shortelle, K. Advanced Transfer Alignment for Inertial Navigators(A-TRAIN). Proc. of the Institute of Navigation Technical Meeting. Anaheim, CA.1995:113-124P.
[27] Shortelle, K. J., Graham, W. R., Rabourn, C.. F-16flight tests of a rapid transferalignment procedure. IEEE1998Position Location and Navigation Symposium. PalmSprings, CA, USA.1998:379-386P.
[28]孙昌跃,邓正隆.舰载导弹INS在低机动条件下传递对准研究.哈尔滨工业大学学报.2007,39(12):1916-1919P.
[29]陈凯,鲁浩,闫杰.传递对准姿态匹配的优化算法.航空学报.2008,29(4):981-987页.
[30] Reiner, J. In-flight transfer-alignment using aircraft-to-wing stiff-angle estimation.36th Israel Annual Conference on Aerospace Sciences Tel Aviv and Haifa, Israel.1996:237-245P.
[31] Reiner, J., Method for airbourne transfer alignment of an inertial measurement unit.US Patent, Patent No.:5,948,045,1999.
[32] Titterton, D. H., Weston, J. L. Dynamic shipboard alignment techniques. Proceedingsof DGON Symposium on Gyro technology. Germany.1987:9.0-9.27P.
[33] Lim, Y. C., Lyou, J. An error compensation method for transfer alignment.Proceedings of IEEE Region10International Conference on Electrical and ElectronicTechnology. Singapore.2001:850-855P.
[34] Lim, Y. C., Lyou, J. Transfer alignment error compensator design using H∞filter.Proceedings of the American Control Conference. Anchorage AK.2002:1460-1465P.
[35] Goshen-Meskin, D., Bar-Itzhack, I. Y., Ind, M. I. A., et al. Observability analysis ofpiece-wise constant systems. I. Theory. IEEE Transactions on Aerospace andElectronic Systems.1992,28(4):1056-1067P.
[36] Goshen-Meskin, D., Bar-Itzhack, I. Y., Ind, M. I. A., et al. Observability analysis ofpiece-wise constant systems. II. Application to inertial navigation in-flight alignment
[military applications]. IEEE Transactions on Aerospace and Electronic Systems.1992,28(4):1068-1075P.
[37] Ham, F. M., Brown, R. G. Observability, Eigenvalues, and Kalman Filtering. IEEETransactions on Aerospace and Electronic Systems.1983:269-273P.
[38]程向红,万德钧,仲巡.捷联惯导系统的可观测性和可观测度研究.东南大学学报.1997,37(6):6-10页.
[39]万德钧,房建成.惯性导航初始对准.南京:东南大学出版社,1998.
[40] Bar-Itzhack, I. Y., Porat, B. Azimuth observability enhancement during inertialnavigation system in-flight alignment. Journal of Guidance, Control, and Dynamics.1980,3(2):337-344P.
[41] Titterton, D. H., Weston, J. L. Strapdown Inertial Navigation Technology. IEEE Radar,Sonar, Navigation and Avionics Series,1997.
[42]韩军海,陈家斌.舰船在风浪干扰下的快速传递对准技术研究.北京理工大学学报,2004,24(10):894-896,909P.
[43] Gao W, Ben Y Y etal. Rapid fine strapdown INS alignment method under marinemooring condition. IEEE Transactions on Aerospace and Electronic Systems.2011,47(4):2887-1896P
[44] Meyers, B. C., Weiderman, N. H., Performance Specification for a Shipboard InertialNavigation System Simulator, www.sei. cmu. edu/pub/documents/88. reports/pdf/tr24.88. pdf(1988).
[45]陈哲.捷联惯导系统原理.北京:宇航出版社,1986.
[46] M. J. Grimble. H∞Design of Optimal Linear Filters. Proc.1987MTNS, Phoenix,Arizona, June1987.
[47] KM. Nagpal, P. P. Khargonekar. Filtering and Smoothing in an H∞Setting. IEEETrans. Automatic Control,1991,36(2):152-166P.
[48] Peng Shi. Robust Filtering for Uncertain Sampled-data Systems. International Journalof Systems Science, Dec,1996,27(12):1403-1415P.
[49]刘锡祥,徐晓苏.杆臂效应补偿中H∞滤波器的应用与设计.东南大学学报(自然科学版),2009.11,39(6):1142-1145页.
[50]顾冬晴,秦永元.姿态匹配传递对准的H∞滤波器设计.空军工程大学学报,2005,6(2):32-35页.
[51] Halil E S. Chingiz H. Pico satellite attitude estimation via Robust Unscented KalmanFilter in the presence of measurement faults. ISA Transactions,2010,49(5):249-256.
[52]王司,邓正隆.机载导弹空中二次快速传递对准方法研究.航空学报.2005,26(4):486-489页.
[53] Mehra R K. Approaches to adaptive filtering. IEEE Transactions on AutomaticControl,1972,17(5):903-908P.
[54] Averbuch A, Itzikowitz S. Radar target tracking-viterbi versus IMM. IEEEtransactions on aerospace and electronic systems.1991,27(3):550-563P.
[55] A. H. Mohamed, K. P. Schwarz. Adaptive Kalman Filtering for INS/GPS. Journal ofGeodesy.1999,73:193-203P.
[56]岳晓奎,袁建平.一种基于极大似然准则的自适应卡尔曼滤波算法.西北工业大学学报.2005,23(4):469-474页.
[57] Mehra R K. On the identification of variances and adaptive Kalman filtering. IEEETransactions on Automatic Control,1970,15(12):175-184P.
[58] Sage A P, Husa G W. Adaptive filtering with prior statistics. Joint automatic controlconf. Boulder, CO.1969:760-769P.
[59]张常云.自适应滤波方法研究.航空学报.1998,19(7):96-99页.
[60]李振营,沈毅,胡恒章.带未知时变噪声系统的卡尔曼滤波算法研究.系统工程与电子技术,26(2):160-162页.
[61]赵琳,王小旭,薛红香,夏全喜.带噪声统计估计器的Unscented卡尔曼滤波器设计.控制与决策,2009,24(10):1483-1488页.
[62] Vinay A. Bavdekar, Anjali P. Deshpande, Sachin C. Patwardhan. Identification ofprocess and measurement noise covariance for state and parameter estimation usingextended Kalman filter. Journal of Process Control.2011,21(4):585-601P.
[63]王璐,李光春,乔相伟等.基于极大似然准则和最大期望算法的自适应UKF算法.自动化学报.2012,38(7):1200-1210页.
[64]周东华,叶银忠.现代故障诊断与容错控制.北京:清华大学出版社,2000.
[65]鲍其莲,孙朔冬,刘英.动基座传递对准非线性滤波器的设计及应用.中国惯性技术学报.2010,18(1):33-37.
[66]胡健,马大为,周百令.快速传递对准用联合强跟踪Kalman滤波器设计与仿真.中国惯性技术学报.2010,18(1):48-51,57页.
[67]高青伟,赵国荣,吴芳,王希彬.衰减记忆自适应滤波在惯性导航传递对准中的应用.系统工程与电子技术,2010.12,32(12):2648-2651页.
[68] Naeem K, Khattak I M. Robust state estimation and its application to spacecraftcontrol. Automatica.2012,(42)7:3142-3150P
[69]周峰,孟秀云.基于自适应UKF算法的机载INS/GPS空中对准研究.系统工程与电子技术.2010,32(2):367-371页.
[70] Fang J C, Yang Sh. Study on innovation adaptive EKF for In-flight alignment ofairborne POS. IEEE Transactions on Instrumentation and Measurement.2011,60(4):1378-1388P
[71]解春明,赵剡,邓俊云.一种改进的自适应平方根传递对准滤波算法.系统工程与电子技术.2011,33(3):622-626页.
[72] Sunahara Y. An approximate method of state estimation for nonlinear dynaxnicalsystems. Joint Automatic Control Conf, Univ. of Colorado,1969.
[73] Bucy R S, Renne K D. Digital synthesis of nonlinear filter. Automatica.1971,7(3):287-289P.
[74]张金槐,蔡洪.飞行器试验统计学.国防科技大学出版社,1995.
[75] Maybeck P S. Stochastic models estimation and control. New York: Academic,1970.
[76] Caballero-Gil P, Fuster-Sabater A. A wide family of nonlinear filter functions with alarge linear span. Information Science.2003,164(1-4):197-207P.
[77] Jazwinski A H. Stochastic processes and filtering theory. New York: Academic,1970.
[78] Julier S J, Uhlmann J K. A new approach for filtering nonlinear system. Proceedingsof the1995American Control Conference.1995:1628-1632P.
[79] Julier S J, Uhlmann J K. A new method for the nonlinear transformation of means andcovariances in filters and estimators. IEEE Transactions on Automatic Control.2000,45(3):477-482P.
[80] Chen Z. Bayesian filtering: From Kalman filters to particle filters, andbeyond[EB/OL].[2003-09-19]. http://www.dsi.unifi.it/users/chisci/idfric/Nonlinear_filtering_Chen.pdf,(2003).
[81]谭红力,黄新生,岳冬雪.捷联惯导大失准角误差模型在快速传递对准中的应用.国防科技大学学报,2008,30(6):19-23页.
[82]孙昌跃,邓正隆.大方位失准角的舰载武器INS对准.中国惯性技术学报.2008,16(5):534-537,542页.
[83] E. A. Wan, R. van der Merwe. The Unseented kalman filter for nonlinear estimation.Proc. of IEEE Symposium2000, Lake Louise, Alberta, Canada, Oct.2000.
[84] R. van der Merwe, E. A.. Wan, The Square-Root unscented kalman filter for state andparameter estimation. IEEE International Conference on Acoustics, Speech, andSignal Processing.2001,6:3461-3464P.
[85] Julier S J, Uhlmann J K. Reduced sigma point filters for the propagation of means andconvariances through nonlinear transformation. proc of American control Conf.Jefferson City,2002:887-892P.
[86] Julier S J. The spherical simplex unscented transformation. Proceedings of theAmerican Control Conference. Piscataway, NJ, USA. IEEE.2003:2430-2434P.
[87] Wang Y F, Sun F C etal. Central difference particle filter applied to transfer alignmentfor SINS on missiles. IEEE Transactions on Aerospace and Electronic Systems.2012,48(1):375-387P
[88] M. D. Shuster. Constraint in Attitude Estimation Part I: Constrained Estimation.Journal of the Astronautical Sciences.2003,51(1):51-74P.
[89] M. D. Shuster. Constraint in Attitude Estimation Part I: Constrained Estimation.Journal of the Astronautical Sciences,2003,51(1):75-101P.
[90] J. L. Crassidis, F. L.Markley. Attitude Estimation Using Modified RodriguesParameters. Proceedings of the Flight Mechanics/Estimation Theory Symposium,(NASA/CP-1996-3333) NASA-Goddard Space Flight Center, Greenbelt, MD,1996:71-83P.
[91]陈记争,袁建平,方群.基于Rodrigues参数的姿态估计算法.航空学报,2008,29(4):960-965页.
[92] Y. Oshman, F. L. Markley. Sequential Attitude and Attitude-Rate Estimation UsingIntegrated-Rate Parameters. Journal of Guidance, Control, and Dynamics.1999,22(3):385-394P.
[93] M. E. Pittelkau, Rotation Vector Attitude Estimation. Journal of Guidance, Control,and Dynamics.2003,26(6):855–860P.
[94] F. L. Markley, Y. Cheng, J. L. Crassidis, Y. Oshman. Averaging quaternions. Journal ofGuidance, Control, and Dynamics.2007,30(4):1193-1197P.
[95] Y. Oshman, A. Carmi. Attitude estimation from vector observations Usinggenetic-algorithm-embedded quaternion particle filter. Journal of Guidance, Control,and Dynamics.2006,29(4):879-891P.
[96] Henzeh L., Yoonhyuk C, Belgacem A J. Uncorrelated unscented filtering forspacecraft attitude determination. Acta Astronautica.2010,67(2):135-144
[97] E. J. Lefferts, F. L. Markley, M D Shuster. Kalman filtering for spacecraft attitudeestimation. Journal of Guidance, Control, and Dynamics.1982,5(5):417-429P.
[98] S. VATHSAL. Spacecraft attitude determination using a second–order nonlinear filter.Journal of Guidance, Control and Dynamics,1987,10(5):559-566P.
[99] M L PSIAKI. The super-iterated Extended Kalman Filter. Proceedings of the AIAAGuidance, Navigation, and Control Conference.2004,8, AIAA–04-5418.
[100] M. E. Pittelkau, Rotation Vector Attitude Estimation. Journal of Guidance, Control,and Dynamics,2003,26(6):855–860P.
[101] Tang X. J., Liu Z. B., Zhang J. S.. Square-root quaternion cubature Kalman filteringfor spacecraft attitude estimation. Acta Astronautica.2012,76(2):84-94
[102] Groves, P. D. Transfer alignment using an integrated INS/GPS as the reference.Institute of Navigation,55th Annual Meeting Cambridge, MA, USA.1999:731-737P.
[103] Groves, P. D., Haddock, J. C. An all-purpose rapid transfer alignment algorithm set.Proc. of the Institute of Navigation, National Technical Meeting2001.Long Beach,CA.2001:160-171P.
[104] Groves, P. D.,Wilson, G. G., Mather, C. J. Robust rapid transfer alignment with anINS/GPS reference. Proc. of the2002ION National Technical Meeting. California,USA.2002:301-311P.
[105] Klotz, K., Graham, W. Advanced alignment concepts for precision-guided weapons.Proc of the Institute of Navigation Technical Meeting. Anaheim, CA.1995:131-142P.
[106]徐晓苏,万德钧.杆臂效应对捷联惯导系统初始对准精度的影响及其在线补偿方法研究.中国惯性技术学报,1994,2(2):22-27页.
[107]李良君.传递对准误差补偿及精度评估方法研究.哈尔滨工程大学硕士学位论文,2008.
[108]高青伟,赵国荣,吴芳.大方位失准角传递对准非线性模型研究.控制与决策,2011,26(3):402-406页.
[109] Noureldin, A., Shin, E., El-Sheimy, N. Improving the performance of alignmentprocesses of inertial measurement units utilizing adaptive pre-filtering methodology.Proceedings of the58th Annual Meeting of the Institute of Navigation and CIGTF21st Guidance Test Symposium.2002:63-69P.
[110] El-Sheimy, N., Nassar, S., Noureldin, A. Wavelet de-noising for IMU alignment. IEEEAerospace and Electronic Systems Magazine.2004,19(10):32-39P.
[111]肖艳霞,张洪钺.考虑机翼弹性变形时的传递对准方法研究.航天控制,2001,(2):27-35页.
[112]孙昌跃.捷联惯导系统传递对准研究.哈尔滨工业大学博士学位论文,2009.
[113]解春明,赵剡,杨传春.传递对准滤波中机翼变形噪声的在线补偿算法.系统工程与电子技术.2011,33(2):370-375页.
[114] Schneider, A. M. Kalman filter formulations for transfer alignment of strapdowninertial units. Navigation.1983,30(1):72-89.
[115]王小旭.非线性SPKF滤波算法研究及其在组合导航中的应用.哈尔滨工程大学博士学位论文,2010.
[116] Dan Simon. Optimal State Estimation. Hoboken, New Jersey: A John Wiley&Sons,2006.
[117] Wendel J., Metzger J., Trommer G.F. Rapid Transfer Alignment in the Presence ofTime Correlated Measurement and System Noise//AIAA Guidance, Navigation, andControl Conference and Exhibit. Providence, Rhode Island.2004:1-12P.
[118] D. Jones, C. Roberts, D. Tarrant. Transfer Alignment Design and EvaluationEnvironment//IEEE Proceedings of Aerospace Control Systems.1993:753-757P.
[119] Chueh, V. K., Huddle, J. R., Transfer alignment of navigation systems.USA. Patent.2007.
[120] Grewal, M. S., Weill, L. R., Andrews, A. P. Global Positioning Systems, InertialNavigation, and Integration. John Wiley&Sons, Inc.,2007.
[121] Titterton, D. H., Weston, J. L. Strapdown Inertial Navigation Technology （2nd）.Institution of Engineering and Technology,2004.
[122]王司,邓正隆.惯导系统动基座传递对准技术综述.中国惯性技术学报.2003,11(2):61-67页.
[123]秦永元,严恭敏,顾冬晴等.摇摆基座上基于信息的捷联惯导粗对准研究.西北工业大学学报,2005,23:681页.
[124] Maybeck, P. S. Stochastic models, estimation and control. Vol.1. Academic PressLondon,1982.
[125] Maybeck, P. S. Stochastic models, estimation and control: Vol.2. Academic PressLondon,1982.
[126] P. J. Nordlundand F. Gustafsson. Sequential monte carlo Filtering techniques appliedto integrated navigation systems. In Proc. of the American Control Conferenee,Arlington, Virginia, U.S.A, June2001.
[127]方开泰,王元,吴启宏.数论方法在统计中的应用.科学出版社,1996.
[128]秦永元,张士邀.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):17-21页.
[129]王丹力.几种可观性分析方法及其在惯导中的应用.北京航空航天大学学报,1999,25(3):342-346页.
[130]程国采.四元数法及其应用.国防科技大学出版社.1991.
[131] Johnson, C., Ohlmeyer, E.J., Pepitone, T.R. Attitude dilution of precision-a new metricfor observability of inflight alignment errors. AIAA Guidance, Navigation, andControl Conference and Exhibit. Denver, Co: AIAA-2000-4277.
[132] Hyo-SungAhn, Chang-HeeWon. Fast Alignment using Rotation Vector and AdaptiveKalman Filter. IEEE Transaetions on Aerospace and Electronic Systems,2006,42(l).
[2] Goshen-Meskin D, Bar-itzhack I Y. Unified approach to inertial navigation systemerror modeling. Journal of GCD.1992,15(3):648-653P.
[3]秦永元.惯性导航.北京:科学出版社,2006.
[4] Bar-itzhack I Y, Goshen-Meskin D. Identity between INS Position and velocity errormodels. Journal of GCD.1981,4(5):569-570P.
[5] KAIN J E, CLOUTIER J R. Rapid transfer alignment for tactical weapon application.Proceedings of the AIAA Guidance, Navigation and Control Conference. Boston,1989:1290-1300P.
[6]郝曙光,张洪钺.几种传递对准方程的比较研究.中国惯性技术学报,2003,11(6):53-58,63页.
[7]陈凯,鲁浩,闫杰.快速传递对准方程与传统传递对准方程的一致性研究.西北工业大学学报,2008,26(3):326-329页.
[8] Friedlan B. Analysis strapdown navigation using quaternions. IEEE Tran on AES.1978,4(5):764-768P.
[9] Minoru Shibata. Error analysis strapdown inertial navigation using Quaternions.Journal of GCD.1986,9(3):379-381P.
[10] Doh Young Chung, Jang Gyu Lee, Chan Gook Park, Heung Won Park. Strapdown INSerror model for multiposition aignment. IEEE Tran on AES.1996,32(4):1362-1366P.
[11] M-Jong Y, Jang G L, H-Won P. Comparison of SDINS in-flight alignment usingequivalent error models. IEEE Transactions on Aerospace and Electronic Systems.1993,35(3):1046-1053P.
[12] M-Jong Y, Heng W P and Jean, C B. Equivalent nonlinear error model of strapdowninertial navigation system. Proeeedings of AIAA1997GNC conference.1997:97-3563P.
[13] Hao Y L, Xiong Z L,Wang W. Rapid transfer alignment based on uncented Kalmanfilter. Proceedings of the2006American Control Conference, Minneapolis USA,2006:2215-2220P.
[14]熊芝兰,郝燕玲,孙枫.基于四元数的惯导系统快速匹配对准算法.哈尔滨工程大学学报,2008,29(1):28-34P.
[15]戴邵武,李娟,戴洪德等.一种快速传递对准方法的误差模型研究.宇航学报,2009,30(3):942-946P.
[16]付梦印,邓志红,闫莉萍. Kalman滤波理论及其在导航系统中的应用(第二版).北京:科学出版社,2010.
[17] Vepa, N. M. A dynamic alignment system for applications on flexible plotforms suchas ship. Gyro technology.1989:16.10-16.13P.
[18] Titterton, D. H., Weston, J. L., Rae, F. The alignment of ship launched missile INsystems. IEEE Colloquium on Inertial Navigation Sensor Development.1990:1/1-116P.
[19] Ross, C. C., Elbert, T. F. A transfer alignment algorithm study based on actual flighttest data from a tactical air-to-ground weapon launch. Proc. of the1994IEEE PositionLocation and Navigation Symposium. Las Vegas, NV, USA.1994:431-438P.
[20] Bar-Itzhack, I. Y. Minimal order time sharing filters for INS in-flight alignment.Journal of Guidance, Control, and Dynamics.1982,5(4):396-402P.
[21] Bar-Itzhack, I. Y., Vitek, Y. The enigma of false bias detection in a strapdown systemduring transfer alignment. Journal of Guidance, Control, and Dynamics.1985,8(2):175-180P.
[22] Farrell, J. L. Airborne transfer alignment simulation results. IEEE PLANS Orlando,FL, USA.1988:269-270P.
[23] Spalding, K. An efficient rapid transfer alignment filter. AIAA Guidance, Navigationand Control Conference. Hilton Head Island, SC.1992:1276-1286P.
[24] D. Tarrant, C. Roberts, D. Jones et al. Rapid and robust transfer alignment. IEEEProceedings of Aerospace Control Systems.1993:758-762P.
[25] Shortelle, K., Graham, W. Advanced alignment concepts for precision-guidedweapons. Proc. of the Institute of Navigation Technical Meeting. Anaheim, CA.1995:131-142P.
[26] Graham, W., Shortelle, K. Advanced Transfer Alignment for Inertial Navigators(A-TRAIN). Proc. of the Institute of Navigation Technical Meeting. Anaheim, CA.1995:113-124P.
[27] Shortelle, K. J., Graham, W. R., Rabourn, C.. F-16flight tests of a rapid transferalignment procedure. IEEE1998Position Location and Navigation Symposium. PalmSprings, CA, USA.1998:379-386P.
[28]孙昌跃,邓正隆.舰载导弹INS在低机动条件下传递对准研究.哈尔滨工业大学学报.2007,39(12):1916-1919P.
[29]陈凯,鲁浩,闫杰.传递对准姿态匹配的优化算法.航空学报.2008,29(4):981-987页.
[30] Reiner, J. In-flight transfer-alignment using aircraft-to-wing stiff-angle estimation.36th Israel Annual Conference on Aerospace Sciences Tel Aviv and Haifa, Israel.1996:237-245P.
[31] Reiner, J., Method for airbourne transfer alignment of an inertial measurement unit.US Patent, Patent No.:5,948,045,1999.
[32] Titterton, D. H., Weston, J. L. Dynamic shipboard alignment techniques. Proceedingsof DGON Symposium on Gyro technology. Germany.1987:9.0-9.27P.
[33] Lim, Y. C., Lyou, J. An error compensation method for transfer alignment.Proceedings of IEEE Region10International Conference on Electrical and ElectronicTechnology. Singapore.2001:850-855P.
[34] Lim, Y. C., Lyou, J. Transfer alignment error compensator design using H∞filter.Proceedings of the American Control Conference. Anchorage AK.2002:1460-1465P.
[35] Goshen-Meskin, D., Bar-Itzhack, I. Y., Ind, M. I. A., et al. Observability analysis ofpiece-wise constant systems. I. Theory. IEEE Transactions on Aerospace andElectronic Systems.1992,28(4):1056-1067P.
[36] Goshen-Meskin, D., Bar-Itzhack, I. Y., Ind, M. I. A., et al. Observability analysis ofpiece-wise constant systems. II. Application to inertial navigation in-flight alignment
[military applications]. IEEE Transactions on Aerospace and Electronic Systems.1992,28(4):1068-1075P.
[37] Ham, F. M., Brown, R. G. Observability, Eigenvalues, and Kalman Filtering. IEEETransactions on Aerospace and Electronic Systems.1983:269-273P.
[38]程向红,万德钧,仲巡.捷联惯导系统的可观测性和可观测度研究.东南大学学报.1997,37(6):6-10页.
[39]万德钧,房建成.惯性导航初始对准.南京:东南大学出版社,1998.
[40] Bar-Itzhack, I. Y., Porat, B. Azimuth observability enhancement during inertialnavigation system in-flight alignment. Journal of Guidance, Control, and Dynamics.1980,3(2):337-344P.
[41] Titterton, D. H., Weston, J. L. Strapdown Inertial Navigation Technology. IEEE Radar,Sonar, Navigation and Avionics Series,1997.
[42]韩军海,陈家斌.舰船在风浪干扰下的快速传递对准技术研究.北京理工大学学报,2004,24(10):894-896,909P.
[43] Gao W, Ben Y Y etal. Rapid fine strapdown INS alignment method under marinemooring condition. IEEE Transactions on Aerospace and Electronic Systems.2011,47(4):2887-1896P
[44] Meyers, B. C., Weiderman, N. H., Performance Specification for a Shipboard InertialNavigation System Simulator, www.sei. cmu. edu/pub/documents/88. reports/pdf/tr24.88. pdf(1988).
[45]陈哲.捷联惯导系统原理.北京:宇航出版社,1986.
[46] M. J. Grimble. H∞Design of Optimal Linear Filters. Proc.1987MTNS, Phoenix,Arizona, June1987.
[47] KM. Nagpal, P. P. Khargonekar. Filtering and Smoothing in an H∞Setting. IEEETrans. Automatic Control,1991,36(2):152-166P.
[48] Peng Shi. Robust Filtering for Uncertain Sampled-data Systems. International Journalof Systems Science, Dec,1996,27(12):1403-1415P.
[49]刘锡祥,徐晓苏.杆臂效应补偿中H∞滤波器的应用与设计.东南大学学报(自然科学版),2009.11,39(6):1142-1145页.
[50]顾冬晴,秦永元.姿态匹配传递对准的H∞滤波器设计.空军工程大学学报,2005,6(2):32-35页.
[51] Halil E S. Chingiz H. Pico satellite attitude estimation via Robust Unscented KalmanFilter in the presence of measurement faults. ISA Transactions,2010,49(5):249-256.
[52]王司,邓正隆.机载导弹空中二次快速传递对准方法研究.航空学报.2005,26(4):486-489页.
[53] Mehra R K. Approaches to adaptive filtering. IEEE Transactions on AutomaticControl,1972,17(5):903-908P.
[54] Averbuch A, Itzikowitz S. Radar target tracking-viterbi versus IMM. IEEEtransactions on aerospace and electronic systems.1991,27(3):550-563P.
[55] A. H. Mohamed, K. P. Schwarz. Adaptive Kalman Filtering for INS/GPS. Journal ofGeodesy.1999,73:193-203P.
[56]岳晓奎,袁建平.一种基于极大似然准则的自适应卡尔曼滤波算法.西北工业大学学报.2005,23(4):469-474页.
[57] Mehra R K. On the identification of variances and adaptive Kalman filtering. IEEETransactions on Automatic Control,1970,15(12):175-184P.
[58] Sage A P, Husa G W. Adaptive filtering with prior statistics. Joint automatic controlconf. Boulder, CO.1969:760-769P.
[59]张常云.自适应滤波方法研究.航空学报.1998,19(7):96-99页.
[60]李振营,沈毅,胡恒章.带未知时变噪声系统的卡尔曼滤波算法研究.系统工程与电子技术,26(2):160-162页.
[61]赵琳,王小旭,薛红香,夏全喜.带噪声统计估计器的Unscented卡尔曼滤波器设计.控制与决策,2009,24(10):1483-1488页.
[62] Vinay A. Bavdekar, Anjali P. Deshpande, Sachin C. Patwardhan. Identification ofprocess and measurement noise covariance for state and parameter estimation usingextended Kalman filter. Journal of Process Control.2011,21(4):585-601P.
[63]王璐,李光春,乔相伟等.基于极大似然准则和最大期望算法的自适应UKF算法.自动化学报.2012,38(7):1200-1210页.
[64]周东华,叶银忠.现代故障诊断与容错控制.北京:清华大学出版社,2000.
[65]鲍其莲,孙朔冬,刘英.动基座传递对准非线性滤波器的设计及应用.中国惯性技术学报.2010,18(1):33-37.
[66]胡健,马大为,周百令.快速传递对准用联合强跟踪Kalman滤波器设计与仿真.中国惯性技术学报.2010,18(1):48-51,57页.
[67]高青伟,赵国荣,吴芳,王希彬.衰减记忆自适应滤波在惯性导航传递对准中的应用.系统工程与电子技术,2010.12,32(12):2648-2651页.
[68] Naeem K, Khattak I M. Robust state estimation and its application to spacecraftcontrol. Automatica.2012,(42)7:3142-3150P
[69]周峰,孟秀云.基于自适应UKF算法的机载INS/GPS空中对准研究.系统工程与电子技术.2010,32(2):367-371页.
[70] Fang J C, Yang Sh. Study on innovation adaptive EKF for In-flight alignment ofairborne POS. IEEE Transactions on Instrumentation and Measurement.2011,60(4):1378-1388P
[71]解春明,赵剡,邓俊云.一种改进的自适应平方根传递对准滤波算法.系统工程与电子技术.2011,33(3):622-626页.
[72] Sunahara Y. An approximate method of state estimation for nonlinear dynaxnicalsystems. Joint Automatic Control Conf, Univ. of Colorado,1969.
[73] Bucy R S, Renne K D. Digital synthesis of nonlinear filter. Automatica.1971,7(3):287-289P.
[74]张金槐,蔡洪.飞行器试验统计学.国防科技大学出版社,1995.
[75] Maybeck P S. Stochastic models estimation and control. New York: Academic,1970.
[76] Caballero-Gil P, Fuster-Sabater A. A wide family of nonlinear filter functions with alarge linear span. Information Science.2003,164(1-4):197-207P.
[77] Jazwinski A H. Stochastic processes and filtering theory. New York: Academic,1970.
[78] Julier S J, Uhlmann J K. A new approach for filtering nonlinear system. Proceedingsof the1995American Control Conference.1995:1628-1632P.
[79] Julier S J, Uhlmann J K. A new method for the nonlinear transformation of means andcovariances in filters and estimators. IEEE Transactions on Automatic Control.2000,45(3):477-482P.
[80] Chen Z. Bayesian filtering: From Kalman filters to particle filters, andbeyond[EB/OL].[2003-09-19]. http://www.dsi.unifi.it/users/chisci/idfric/Nonlinear_filtering_Chen.pdf,(2003).
[81]谭红力,黄新生,岳冬雪.捷联惯导大失准角误差模型在快速传递对准中的应用.国防科技大学学报,2008,30(6):19-23页.
[82]孙昌跃,邓正隆.大方位失准角的舰载武器INS对准.中国惯性技术学报.2008,16(5):534-537,542页.
[83] E. A. Wan, R. van der Merwe. The Unseented kalman filter for nonlinear estimation.Proc. of IEEE Symposium2000, Lake Louise, Alberta, Canada, Oct.2000.
[84] R. van der Merwe, E. A.. Wan, The Square-Root unscented kalman filter for state andparameter estimation. IEEE International Conference on Acoustics, Speech, andSignal Processing.2001,6:3461-3464P.
[85] Julier S J, Uhlmann J K. Reduced sigma point filters for the propagation of means andconvariances through nonlinear transformation. proc of American control Conf.Jefferson City,2002:887-892P.
[86] Julier S J. The spherical simplex unscented transformation. Proceedings of theAmerican Control Conference. Piscataway, NJ, USA. IEEE.2003:2430-2434P.
[87] Wang Y F, Sun F C etal. Central difference particle filter applied to transfer alignmentfor SINS on missiles. IEEE Transactions on Aerospace and Electronic Systems.2012,48(1):375-387P
[88] M. D. Shuster. Constraint in Attitude Estimation Part I: Constrained Estimation.Journal of the Astronautical Sciences.2003,51(1):51-74P.
[89] M. D. Shuster. Constraint in Attitude Estimation Part I: Constrained Estimation.Journal of the Astronautical Sciences,2003,51(1):75-101P.
[90] J. L. Crassidis, F. L.Markley. Attitude Estimation Using Modified RodriguesParameters. Proceedings of the Flight Mechanics/Estimation Theory Symposium,(NASA/CP-1996-3333) NASA-Goddard Space Flight Center, Greenbelt, MD,1996:71-83P.
[91]陈记争,袁建平,方群.基于Rodrigues参数的姿态估计算法.航空学报,2008,29(4):960-965页.
[92] Y. Oshman, F. L. Markley. Sequential Attitude and Attitude-Rate Estimation UsingIntegrated-Rate Parameters. Journal of Guidance, Control, and Dynamics.1999,22(3):385-394P.
[93] M. E. Pittelkau, Rotation Vector Attitude Estimation. Journal of Guidance, Control,and Dynamics.2003,26(6):855–860P.
[94] F. L. Markley, Y. Cheng, J. L. Crassidis, Y. Oshman. Averaging quaternions. Journal ofGuidance, Control, and Dynamics.2007,30(4):1193-1197P.
[95] Y. Oshman, A. Carmi. Attitude estimation from vector observations Usinggenetic-algorithm-embedded quaternion particle filter. Journal of Guidance, Control,and Dynamics.2006,29(4):879-891P.
[96] Henzeh L., Yoonhyuk C, Belgacem A J. Uncorrelated unscented filtering forspacecraft attitude determination. Acta Astronautica.2010,67(2):135-144
[97] E. J. Lefferts, F. L. Markley, M D Shuster. Kalman filtering for spacecraft attitudeestimation. Journal of Guidance, Control, and Dynamics.1982,5(5):417-429P.
[98] S. VATHSAL. Spacecraft attitude determination using a second–order nonlinear filter.Journal of Guidance, Control and Dynamics,1987,10(5):559-566P.
[99] M L PSIAKI. The super-iterated Extended Kalman Filter. Proceedings of the AIAAGuidance, Navigation, and Control Conference.2004,8, AIAA–04-5418.
[100] M. E. Pittelkau, Rotation Vector Attitude Estimation. Journal of Guidance, Control,and Dynamics,2003,26(6):855–860P.
[101] Tang X. J., Liu Z. B., Zhang J. S.. Square-root quaternion cubature Kalman filteringfor spacecraft attitude estimation. Acta Astronautica.2012,76(2):84-94
[102] Groves, P. D. Transfer alignment using an integrated INS/GPS as the reference.Institute of Navigation,55th Annual Meeting Cambridge, MA, USA.1999:731-737P.
[103] Groves, P. D., Haddock, J. C. An all-purpose rapid transfer alignment algorithm set.Proc. of the Institute of Navigation, National Technical Meeting2001.Long Beach,CA.2001:160-171P.
[104] Groves, P. D.,Wilson, G. G., Mather, C. J. Robust rapid transfer alignment with anINS/GPS reference. Proc. of the2002ION National Technical Meeting. California,USA.2002:301-311P.
[105] Klotz, K., Graham, W. Advanced alignment concepts for precision-guided weapons.Proc of the Institute of Navigation Technical Meeting. Anaheim, CA.1995:131-142P.
[106]徐晓苏,万德钧.杆臂效应对捷联惯导系统初始对准精度的影响及其在线补偿方法研究.中国惯性技术学报,1994,2(2):22-27页.
[107]李良君.传递对准误差补偿及精度评估方法研究.哈尔滨工程大学硕士学位论文,2008.
[108]高青伟,赵国荣,吴芳.大方位失准角传递对准非线性模型研究.控制与决策,2011,26(3):402-406页.
[109] Noureldin, A., Shin, E., El-Sheimy, N. Improving the performance of alignmentprocesses of inertial measurement units utilizing adaptive pre-filtering methodology.Proceedings of the58th Annual Meeting of the Institute of Navigation and CIGTF21st Guidance Test Symposium.2002:63-69P.
[110] El-Sheimy, N., Nassar, S., Noureldin, A. Wavelet de-noising for IMU alignment. IEEEAerospace and Electronic Systems Magazine.2004,19(10):32-39P.
[111]肖艳霞,张洪钺.考虑机翼弹性变形时的传递对准方法研究.航天控制,2001,(2):27-35页.
[112]孙昌跃.捷联惯导系统传递对准研究.哈尔滨工业大学博士学位论文,2009.
[113]解春明,赵剡,杨传春.传递对准滤波中机翼变形噪声的在线补偿算法.系统工程与电子技术.2011,33(2):370-375页.
[114] Schneider, A. M. Kalman filter formulations for transfer alignment of strapdowninertial units. Navigation.1983,30(1):72-89.
[115]王小旭.非线性SPKF滤波算法研究及其在组合导航中的应用.哈尔滨工程大学博士学位论文,2010.
[116] Dan Simon. Optimal State Estimation. Hoboken, New Jersey: A John Wiley&Sons,2006.
[117] Wendel J., Metzger J., Trommer G.F. Rapid Transfer Alignment in the Presence ofTime Correlated Measurement and System Noise//AIAA Guidance, Navigation, andControl Conference and Exhibit. Providence, Rhode Island.2004:1-12P.
[118] D. Jones, C. Roberts, D. Tarrant. Transfer Alignment Design and EvaluationEnvironment//IEEE Proceedings of Aerospace Control Systems.1993:753-757P.
[119] Chueh, V. K., Huddle, J. R., Transfer alignment of navigation systems.USA. Patent.2007.
[120] Grewal, M. S., Weill, L. R., Andrews, A. P. Global Positioning Systems, InertialNavigation, and Integration. John Wiley&Sons, Inc.,2007.
[121] Titterton, D. H., Weston, J. L. Strapdown Inertial Navigation Technology （2nd）.Institution of Engineering and Technology,2004.
[122]王司,邓正隆.惯导系统动基座传递对准技术综述.中国惯性技术学报.2003,11(2):61-67页.
[123]秦永元,严恭敏,顾冬晴等.摇摆基座上基于信息的捷联惯导粗对准研究.西北工业大学学报,2005,23:681页.
[124] Maybeck, P. S. Stochastic models, estimation and control. Vol.1. Academic PressLondon,1982.
[125] Maybeck, P. S. Stochastic models, estimation and control: Vol.2. Academic PressLondon,1982.
[126] P. J. Nordlundand F. Gustafsson. Sequential monte carlo Filtering techniques appliedto integrated navigation systems. In Proc. of the American Control Conferenee,Arlington, Virginia, U.S.A, June2001.
[127]方开泰,王元,吴启宏.数论方法在统计中的应用.科学出版社,1996.
[128]秦永元,张士邀.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):17-21页.
[129]王丹力.几种可观性分析方法及其在惯导中的应用.北京航空航天大学学报,1999,25(3):342-346页.
[130]程国采.四元数法及其应用.国防科技大学出版社.1991.
[131] Johnson, C., Ohlmeyer, E.J., Pepitone, T.R. Attitude dilution of precision-a new metricfor observability of inflight alignment errors. AIAA Guidance, Navigation, andControl Conference and Exhibit. Denver, Co: AIAA-2000-4277.
[132] Hyo-SungAhn, Chang-HeeWon. Fast Alignment using Rotation Vector and AdaptiveKalman Filter. IEEE Transaetions on Aerospace and Electronic Systems,2006,42(l).