船用MEMS航姿测量系统算法研究与实现
|
摘要
基于MEMS惯性器件的低成本航姿测量系统在军事领域和民用领域的都具有广泛的应用前景。本文依托实验室有关低成本船用卫星天线姿态测量系统的在研项目,开展基于MEMS惯性器件、磁强计及GPS的组合航姿系统相关算法研究,并通过仿真验证了算法的可行性及有效性,为MEMS航姿测量系统在船载卫星天线稳定系统中的实际应用奠定了一定的基础。
(1)MEMS陀螺随机漂移是影响姿态解算精度的主要因素,针对其误差模型的未知性,本文利用时间序列分析法通过静态测试数据建立了陀螺随机漂移的ARMA模型,并将其应用于后续姿态估计算法比较中。
(2)在不使用GPS的情况下,根据船舶运动特点与系统工作要求,通过对多种姿态更新算法的理论分析与仿真比较,得出修正的Rodrigues参数法计算量明显比四元数法和旋转矢量法要小,计算精度与四元数相近,同时克服了四元数描述姿态时存在冗余带来的不足,为姿态更新算法选择提供依据。
(3)在前述研究的基础上,推导了以陀螺零偏和修正的Rodrigues参数为状态向量,以加速度计、磁强计输出为观测向量的EKF姿态估计模型,利用与其影子参数相互切换的方法解决了修正的Rodrigues参数在描述姿态时存在奇异的问题。通过全姿态以及摇摆运动条件下的仿真验证了算法的可行性及优越性。
(4)为检验ARMA模型的适用性,通过静止及摇摆运动条件的仿真得出,采用ARMA模型对姿态角和陀螺零偏的估计及补偿精度在静态条件下较随机游走模型高,但在摇摆运动条件下精度和计算量均不理想,而基于后者的MRP EKF估计算法更具普适性。在调整观测噪声方差阵的前提下,为进一步减小重力和地磁向量在受到干扰时的系统输出误差,引入GPS信息,开展了MEMS AHRS/GPS组合系统松耦合Kalman滤波算法的研究,仿真实验证实了方案的有效性。
Low-cost Attitude and Heading Reference Systems based on MEMS inertial sensors have broad application prospects both in the field of national defense and civilian areas. The paper relies on the going project of the laboratory which is low-cost shipborne satellite antenna micro attitude measurement system, makes a study of correlation algorithms of an integrated attitude measurement system based on MEMS inertial sensors, magnetometers and GPS, and the approach is verified to be feasible and effectiveness by simulations.The work makes a foundation for the practical application of the MEMS Attitude and Heading Reference System on the shipborne satellite antenna stable system.
(1) The large random drift of MEMS gyro is the great factor on impacting the accuracy of attitude algorithm. Aiming at the unknown nature of its error model, the paper establishes a gyro random drift of ARMA models using the time series analysis through the static test data, and applied it to the compare of the following attitude estimation algorithm.
(2) On the condition of without GPS, taking the characteristic of the shipborne movement and the AHRS working application requirements into account, through the theoretical analysis and the comparison of simulation results about the various attitude updating algorithms, the paper finds that the calculational complexity of the modified Rodrigues parameter algorithm is significantly smaller than the quaternion algorithm and the rotation vector algorithm, the calculational accuracy is similar to the quaternion algorithm, while overcoming redundant when using quaternion to descript the attitude. It supplies the gist for choosing the attitude updating algorithm.
(3) According to the above analysis, the extended Kalman filter for attitude estimation algorithm is derived with gyro bias and the modified Rodrigues parameters for the state vector and output of accelerometers, and magnetometer for the observation vector, and used the switch between the modified Rodrigues parameters and its shadow parameters to solve the singularity problem.. The validity and superiority of the algorithm are verified by the simulation under the conditions of the whole attitude and the swing movement.
(4) To checkout the applicability of the ARMA model, through the simulation of the conditions of the static and swing motions, the paper obtained the conclusion that in static condition the estimation algorithm based on the ARMA model for gyro bias has higher precision both of the attitude estimation and the gyro bias compensation than the random walk model. However, under the conditions of swing movement the accuracy is less than the estimation algorithm with the random walk model for gyro bias, while the calculating amount is larger. Therefore, the MRP EKF estimation algorithm used random walk model for gyro bias has more universality. In the precondition of adjusting the observation noise variance matrix, to minish the output error ulteriorly in the condition of the gravity and magnetic vectors are disturbed, the GPS information is introduced, and carries out a study of loosely coupled Kalman filter algorithm for MEMS AHRS/GPS integrated system, and the simulation verified the feasibility of the algorithm.
(1)MEMS陀螺随机漂移是影响姿态解算精度的主要因素,针对其误差模型的未知性,本文利用时间序列分析法通过静态测试数据建立了陀螺随机漂移的ARMA模型,并将其应用于后续姿态估计算法比较中。
(2)在不使用GPS的情况下,根据船舶运动特点与系统工作要求,通过对多种姿态更新算法的理论分析与仿真比较,得出修正的Rodrigues参数法计算量明显比四元数法和旋转矢量法要小,计算精度与四元数相近,同时克服了四元数描述姿态时存在冗余带来的不足,为姿态更新算法选择提供依据。
(3)在前述研究的基础上,推导了以陀螺零偏和修正的Rodrigues参数为状态向量,以加速度计、磁强计输出为观测向量的EKF姿态估计模型,利用与其影子参数相互切换的方法解决了修正的Rodrigues参数在描述姿态时存在奇异的问题。通过全姿态以及摇摆运动条件下的仿真验证了算法的可行性及优越性。
(4)为检验ARMA模型的适用性,通过静止及摇摆运动条件的仿真得出,采用ARMA模型对姿态角和陀螺零偏的估计及补偿精度在静态条件下较随机游走模型高,但在摇摆运动条件下精度和计算量均不理想,而基于后者的MRP EKF估计算法更具普适性。在调整观测噪声方差阵的前提下,为进一步减小重力和地磁向量在受到干扰时的系统输出误差,引入GPS信息,开展了MEMS AHRS/GPS组合系统松耦合Kalman滤波算法的研究,仿真实验证实了方案的有效性。
Low-cost Attitude and Heading Reference Systems based on MEMS inertial sensors have broad application prospects both in the field of national defense and civilian areas. The paper relies on the going project of the laboratory which is low-cost shipborne satellite antenna micro attitude measurement system, makes a study of correlation algorithms of an integrated attitude measurement system based on MEMS inertial sensors, magnetometers and GPS, and the approach is verified to be feasible and effectiveness by simulations.The work makes a foundation for the practical application of the MEMS Attitude and Heading Reference System on the shipborne satellite antenna stable system.
(1) The large random drift of MEMS gyro is the great factor on impacting the accuracy of attitude algorithm. Aiming at the unknown nature of its error model, the paper establishes a gyro random drift of ARMA models using the time series analysis through the static test data, and applied it to the compare of the following attitude estimation algorithm.
(2) On the condition of without GPS, taking the characteristic of the shipborne movement and the AHRS working application requirements into account, through the theoretical analysis and the comparison of simulation results about the various attitude updating algorithms, the paper finds that the calculational complexity of the modified Rodrigues parameter algorithm is significantly smaller than the quaternion algorithm and the rotation vector algorithm, the calculational accuracy is similar to the quaternion algorithm, while overcoming redundant when using quaternion to descript the attitude. It supplies the gist for choosing the attitude updating algorithm.
(3) According to the above analysis, the extended Kalman filter for attitude estimation algorithm is derived with gyro bias and the modified Rodrigues parameters for the state vector and output of accelerometers, and magnetometer for the observation vector, and used the switch between the modified Rodrigues parameters and its shadow parameters to solve the singularity problem.. The validity and superiority of the algorithm are verified by the simulation under the conditions of the whole attitude and the swing movement.
(4) To checkout the applicability of the ARMA model, through the simulation of the conditions of the static and swing motions, the paper obtained the conclusion that in static condition the estimation algorithm based on the ARMA model for gyro bias has higher precision both of the attitude estimation and the gyro bias compensation than the random walk model. However, under the conditions of swing movement the accuracy is less than the estimation algorithm with the random walk model for gyro bias, while the calculating amount is larger. Therefore, the MRP EKF estimation algorithm used random walk model for gyro bias has more universality. In the precondition of adjusting the observation noise variance matrix, to minish the output error ulteriorly in the condition of the gravity and magnetic vectors are disturbed, the GPS information is introduced, and carries out a study of loosely coupled Kalman filter algorithm for MEMS AHRS/GPS integrated system, and the simulation verified the feasibility of the algorithm.
引文
[1]文炜.基于MEMS技术的惯性测量器件及系统的发展现状和应用.控制与制导.2006(9):56-59页
[2]李新刚,袁建平.微机械陀螺的发展现状.力学进展.2003(33):289-301页
[3]谷庆红.微机械陀螺仪的研制现状.中国惯性技术学报.2003(11):67-72页
[4]蒋庆仙.关于MEMS惯性传感器的发展及在组合导航中的应用前景.测绘通报.2006(9):5-8页
[5]陈伟平.MEMS在军事领域中的应用前景.遥测遥控.2003(19):14-19页
[6] Navid Yazd, Farrokh Ayazi.Micromachined Inertial Sensors. Proceedings of the IEEE.1998(86):1640-1659P
[7]李志信,罗小兵,过增元.MEMS在惯性测量中的应用.传感器技术.2001(7):58-60页
[8] Andrew Gripton MSc M.Inst.P. C.Phys.The Application and Future Development Of a MEMS SiVSG? For Commercial and Military Inertial Products. BAE SYSTEMS.2002
[9]王巍,何胜.MEMS惯性仪表技术发展趋势.导弹与航天运载技术.2009(301):23-28页
[10]秦永元.国际惯性器件发展现状和趋势.航空机载设备与技术.2008(9):68-69页
[11]何昆鹏.MEMS惯性器件参数辨识及系统误差补偿技术.哈尔滨工工程大学博士学位论文.2009
[12]赵民智、纪丽敏、万承军.我国惯性仪器仪表的技术特点及发展综述.传感器世界.2009(7):17-23页
[13]蔡春龙,刘翼,刘一薇.MEMS仪表惯性组合导航系统发展现状与趋势.中国惯性技术学报.2009(5):563-567页
[14]刘危.基于MEMS的低成本MIMU的应用研究.长沙:国防科学技术大学.2004
[15]李荣冰,刘建业.基于MEMS技术的微型惯性导航系统的发展现.中国惯性技术学报.2004(12):88-94页
[16]刘瑞华.微机电惯性测量元件在导航系统的应用研究.中国民航学院学报.2003(6):30-34页
[17] D.W.Allan.Statistics of atomic frequency standards. Proceedings of IEEE.1966(54):221-230P
[18] IEEE STD 952-1997.IEEE standard specification format guide and test procedure for single-axis interferometric fiber optic gyros. IEEE Sandard Board.1997
[19]李迪,孙尧,李绪友等.船用光纤陀螺随机漂移分析与研究.中国航海. 2005(1):35-37页
[20]李晓莹,胡敏,张鹏等.交叠式Allan方差在微机械陀螺随机误差辨识中的应用.西北工业大学学报.2007(2):225-229页
[21]顾颖玲,许江宁,卞鸿威.陀螺随机漂移误差模型建模方法研究.海军工程大学学报.2000(1):80-82页
[22]吉训生,王寿荣.MEMS陀螺仪随机漂移误差研究.宇航学报.2006(27): 640-642页
[23]赵世峰,张海,沈晓蓉.MEMS陀螺随机噪声的多尺度时间序列建模.中国惯性技术学报.2006(14):78-80页
[24]李杰,张文栋,刘俊.基于时间序列分析的Kalman滤波方法在MEMS陀螺仪随机漂移误差补偿中的应用研究.传感技术学报.2006(19):2215-2219页
[25]李杰,张文栋,刘俊.基于时间序列分析的Kalman滤波方法在MEMS陀螺仪随机漂移误差补偿中的应用研究.传感技术学报.2006(19):2215-2219页
[26]赵伟臣,付梦印,张启鸿,邓志红.微机械IMU数据建模与滤波方法研究.中国惯性技术学报.2005(12):13-17页
[27]张智永,范大鹏,李凯.微机电陀螺零点漂移数据滤波方法的研究.中国惯性技术学报.2006(14):67-69页
[28]张克志,田蔚风,金志华.基于UKF的动力调谐陀螺随机漂移建模研究.传感技术学报.2007(20):1555-1557页
[29]关秋菊,刘桂雄,金军.基于递推并行Kalman时序模型的随机误差的分离方法.现代制造工程.2008(2):116-118页
[30] Chen Xiyuan.Modeling Random Gyro Drift by Time Series neural networks and by traditional method.IEEE Int.Conf.Neural Networks & Signal Processing Nanjing, China.2003(12):14-17P
[31]朱利平.基于神经网络的微硅陀螺输出补偿系统研究.南京:南京航空航天大学.2005
[32]王昊,王俊璞,田蔚风,金志华.梯度RBF神经网络在MEMS陀螺仪随机漂移建模中的应用.中国惯性技术学报.2006(8):44-48页
[33]傅建国,王孝通,李博,金良安,马野.MEMS陀螺随机误差模型研究.传感器技术.2005(24):75-77页
[34] Fuqiang Liu, Fanming Liu, Wenjing Wang and Bo Xu.MEMS Gyro’s Output Signal De-noising Based on Wavelet Analysis.Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation.2007(8):5-8P
[35]夏敦柱,周白令,王寿荣.实时小波滤波方法在硅微陀螺仪中的应用研究.中国惯性技术学报.2007(1):92-95页
[36]黄旭.微机械惯性器件/GPS/磁强计组合航向姿态确定研究.哈尔滨工业大学博士学位论文.2005
[37]黄雪樵.克服欧拉方程奇异性的双欧方法.飞行力学.1994(4):28-38页
[38]熊志斌,刘喜斌.克服欧拉方程奇异性的方法研究.岳阳师范学院学报自然科学版.2000(4):60-63页
[39]王海峰,王成良.解决欧拉方程奇异性的方法探讨.飞行力学.2006(3):94-96页
[40]黄卫权,程建华.提高捷联惯导系统精度的系统研究现状与发展趋势.惯性技术发展动态发展方向研讨文集.2003:27-36页
[41]秦永元.惯性导航.北京:科学出版社.2006
[42]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(3):6-10页
[43]曹小平.光纤陀螺姿态系统的旋转矢量算法研究.电光与控制.2006(3):81-84页
[44]宋桂华,赵伟,刘建业.光纤陀螺捷联惯导系统改进航姿算法应用.应用科学学报.2008(6):645-649页
[45]李辉,孟秀云,刘藻珍.角速率输入下的捷联惯导系统改进航姿算法.弹道学报.2006(2):20-22页
[46]黄昊,邓正隆.角速率输入下的航姿算法研究.中国惯性技术学报.2000(2):21-26页
[47]黄昊,邓正隆.旋转矢量航姿算法的一种新的表达式.宇航学报.2001(3):38-44页
[48] Hanspeter S, Junk ins J L.Steregraphic Orientation Parameters for Attitude Dynamics:A Generalization of the Rodrigues Parameters.The Journal of the Astronautical Sciences. 1996(44):1-19P
[49]周江华,苗育红,王明海.姿态运动的Rodrigues参数描述.宇航学报.2004(9):514-519页
[50]王勇军,秦永元,舒东亮.Rodrigues参数与四元数间的关系分析.火力与指挥控制.2008(3):71-73页
[51]程杨,杨涤,崔祜涛.利用修正罗德里格参数进行飞行器姿态估计.飞行力学.2002(4):18-21页
[52]杨亚非,李建国.基于UPF和修正Rodrigues参数的无陀螺姿态确定算法.中国惯性技术学报.2009(17):148-152页
[53]方群,陈记争,马卫华.广义Rodrigues参数姿态描述方法.自然科学进展.2007(5):672-677页
[54]陈记争,袁建平,方群双.双Rodrigues参数方法及其在姿态确定中的应用宇航学报.2008(3):534-538页
[55] Bar-Itzhack, I. Y., and Oshman, Y.Attitude determination from vector observations:Quaternion estimation.IEEE Transactions on Aerospace and Electronic Systems.1985(21):128—136P
[56] Lefferts E J, Markly F L, Shuster M D.Kalman filter for spacecraft attitude estimation.Journal of Guidance Control and Dynamics.1982(5):417-429P
[57]刘海颖.微小卫星姿态控制系统关键技术研究.南京航空航天大学博士学位论文.2008
[58] J. L. Marins, X. Yun, E. R. Bachmann, R. B. McGhee, and M. J. Zyda, An extended Kalman filter for quaternion-based orientation estimation using MARG sensors in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems.2001(29):2003–2011P
[59]黄旭,王常虹,伊国兴等.利用磁强计及微机械加速度计和陀螺的姿态估计扩展卡尔曼滤波器.中国惯性技术学报.2005(2):27-30页
[60] Paul G.Savage.Strapdown Inertial Navigation Integration Algorithm Design Part 1: Attitude Algorithms.Journal of guidance, control, and dynamics.1998(21):19-28P
[61] D.Choukroun, I.Y.Bar-Itzhack, Y.Oshman. Novel quaternion kalman filter.IEEE Trans. on Aerospace and electronic system.2006(1):174-190P
[62] Bar-Itzhack, I.Y., Deutschmann, J., and Markley, F. L.Quaternion normalization in additive EKF for spacecraft attitude determination.Presented at the Guidance, Navigation, and Control Conference. New Orleans.1991:2691-2706P
[63] BERNARD I RIF.DLAND.Analysis Strapdown Navigation Using Quaternions.IEEE TRANSAC TIONS ON AEROSPACE AND ELECTRONIC SYSTEMS.1978(3):764-768P
[64]王亚锋,刘华平,孙富春,张友安.基于误差四元数的捷联惯导全姿态导航与控制.中国惯性技术学报.2007(8):390-393页
[65]周江华,苗育红,李宏.四元数在刚体姿态仿真中的应用研究.飞行力学.2000(4):28-32页
[66] Angelo M. Sabatini.Quaternion-Based Extended Kalman Filter forDetermining Orientation by Inertial and Magnetic Sensing.IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. 2006(53): 1346-1356P
[67] Joseph J. LaViola Jr.A Comparison of Unscented and Extended Kalrnan Filtering for Estimating Quaternion Motion.Proceedings of the American Control Conference Denver.2003:4-6P
[68] Wan, E. A., and R. van der Menve. The Unscented Kalman Filter for Nonlinear Estimation. In Proceedings of Symposium 2000 on Adaptive Systems for Signal Processing.Communication and Control(AS-SP CC),IEEE Press, 2000.
[69] Yee-Jin Cheon.Unscented Filtering in a Unit Quaternion Space for Spacecraft Attitude Estimation.2007
[70] Shuster M D. A survey of attitude representations.Journal of the Astronautical Sciences,1993, 41(4):437-517P
[71]刘付强.船用卫星天线微型姿态测量系统关键技术研究.哈尔滨工程大学博士学位论文.2008
[72]牛小骥.微机械姿态测量单元及其用于卫星电视天线稳定的研究.清华大学博士学位论文.2002
[73]牛小骥,高钟毓,张嵘,陈志勇.基于微机械惯性传感器的卫星电视天线稳定系统.中国惯性技术学报.2002(10):11-15页
[74]许丽佳,陈阳舟,崔平远.GPS/INS组合导航系统中的信息融合算法研究.计算机仿真.2004(3):21-25页
[75]夏琳琳.低成本AHRS/GPS紧耦合融合滤波技术研究.哈尔滨工程大学博士学位论文.2008
[76]王昊.面向车辆导航的MIMU及其与GPS组合的研究.上海交通大学博士学位论文.2007
[77]苑海静.微机械惯性测量单元的测试与标定技术研究.哈尔滨工程大学学士学位论文.2007
[78]彭秀艳,赵希人.工程随机过程.哈尔滨工程大学出版社.2000
[79]王燕.应用时间序列分析.中国人民大学出版社.2005
[80]张树京,齐立心.时间序列分析简明教程.清华大学出版社.2003
[81]陈国强,赵俊伟,黄俊杰,刘万里.基于Matlab的AR模型参数估计.工具技术.2005(39):39-40页
[82]谭琪林.微机械加速度计发展简述.学术探讨与研究.2007(1):15-21页
[83]李海涛.加速度计_磁强计捷联惯导系统姿态解算方法研究.中北大学硕士论文.2007
[84]晏登洋,任建新,牛尔卓.惯性与地磁组合导航系统自适应卡尔曼滤波算法研究.电光与控制.2004(6):74-78页
[85] Thomas Bak.Spacecraft Attitude Determination-a Magnetometer Approach.Department of Control Engineering Aalborg University. 1999:153-156P
[86]马建军,郑志强.数字罗盘辅助实现MIMU静基座初始对准.系统仿真学报.2007(19):2260-2263页
[87]陈哲.捷联惯导系统原理.宇航出版社.1986
[88]黄德鸣,程禄.惯性导航系统.国防工业出版社.1986
[89]夏琳琳,赵琳,刘繁明,胡晓形.基于对偶四元数的航姿系统姿态更新算法研究.系统仿真学报.2008(2):276-281页
[90]武元新.对偶四元数导航算法与非线性高斯滤波研究.国防科技大学博士学位论文.2005
[91]杨金显.微惯性测量系统关键技术研究.哈尔滨工程大学博士学位论文.2008
[92]陈新龙,杨涤,翟坤.AEKF在姿态确定中的应用研究.航天控制.2008(26):47-50页
[93]秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西北工业大学出版社.1998:175-188页
[94]赵琳.卫星导航系统.哈尔滨工程大学出版社.2000
[95] CHEN Ji-zheng, YUAN Jian-ping, FANG Qun.Flight Vehicle Attitude Determination Using the Modified Rodrigues Parameters.Chinese Journal of Aeronautics.2008(5):1622-1626P
[96]赵琳,苑海静,刘付强,刘凤鸣.基于修正的Rodrigues参数的EKF算法在姿态估计中的应用.中国惯性技术学报.2009(5):557-561页
[97]周星伶.GPS/INS组合导航系统松、紧耦合性能比较.航空电子技术.2007(129):1-6页
[98]安亮,王可东.GPS与MEMS/IMU组合导航技术发展现状.全球定位系统.2008(3):49-54页
[2]李新刚,袁建平.微机械陀螺的发展现状.力学进展.2003(33):289-301页
[3]谷庆红.微机械陀螺仪的研制现状.中国惯性技术学报.2003(11):67-72页
[4]蒋庆仙.关于MEMS惯性传感器的发展及在组合导航中的应用前景.测绘通报.2006(9):5-8页
[5]陈伟平.MEMS在军事领域中的应用前景.遥测遥控.2003(19):14-19页
[6] Navid Yazd, Farrokh Ayazi.Micromachined Inertial Sensors. Proceedings of the IEEE.1998(86):1640-1659P
[7]李志信,罗小兵,过增元.MEMS在惯性测量中的应用.传感器技术.2001(7):58-60页
[8] Andrew Gripton MSc M.Inst.P. C.Phys.The Application and Future Development Of a MEMS SiVSG? For Commercial and Military Inertial Products. BAE SYSTEMS.2002
[9]王巍,何胜.MEMS惯性仪表技术发展趋势.导弹与航天运载技术.2009(301):23-28页
[10]秦永元.国际惯性器件发展现状和趋势.航空机载设备与技术.2008(9):68-69页
[11]何昆鹏.MEMS惯性器件参数辨识及系统误差补偿技术.哈尔滨工工程大学博士学位论文.2009
[12]赵民智、纪丽敏、万承军.我国惯性仪器仪表的技术特点及发展综述.传感器世界.2009(7):17-23页
[13]蔡春龙,刘翼,刘一薇.MEMS仪表惯性组合导航系统发展现状与趋势.中国惯性技术学报.2009(5):563-567页
[14]刘危.基于MEMS的低成本MIMU的应用研究.长沙:国防科学技术大学.2004
[15]李荣冰,刘建业.基于MEMS技术的微型惯性导航系统的发展现.中国惯性技术学报.2004(12):88-94页
[16]刘瑞华.微机电惯性测量元件在导航系统的应用研究.中国民航学院学报.2003(6):30-34页
[17] D.W.Allan.Statistics of atomic frequency standards. Proceedings of IEEE.1966(54):221-230P
[18] IEEE STD 952-1997.IEEE standard specification format guide and test procedure for single-axis interferometric fiber optic gyros. IEEE Sandard Board.1997
[19]李迪,孙尧,李绪友等.船用光纤陀螺随机漂移分析与研究.中国航海. 2005(1):35-37页
[20]李晓莹,胡敏,张鹏等.交叠式Allan方差在微机械陀螺随机误差辨识中的应用.西北工业大学学报.2007(2):225-229页
[21]顾颖玲,许江宁,卞鸿威.陀螺随机漂移误差模型建模方法研究.海军工程大学学报.2000(1):80-82页
[22]吉训生,王寿荣.MEMS陀螺仪随机漂移误差研究.宇航学报.2006(27): 640-642页
[23]赵世峰,张海,沈晓蓉.MEMS陀螺随机噪声的多尺度时间序列建模.中国惯性技术学报.2006(14):78-80页
[24]李杰,张文栋,刘俊.基于时间序列分析的Kalman滤波方法在MEMS陀螺仪随机漂移误差补偿中的应用研究.传感技术学报.2006(19):2215-2219页
[25]李杰,张文栋,刘俊.基于时间序列分析的Kalman滤波方法在MEMS陀螺仪随机漂移误差补偿中的应用研究.传感技术学报.2006(19):2215-2219页
[26]赵伟臣,付梦印,张启鸿,邓志红.微机械IMU数据建模与滤波方法研究.中国惯性技术学报.2005(12):13-17页
[27]张智永,范大鹏,李凯.微机电陀螺零点漂移数据滤波方法的研究.中国惯性技术学报.2006(14):67-69页
[28]张克志,田蔚风,金志华.基于UKF的动力调谐陀螺随机漂移建模研究.传感技术学报.2007(20):1555-1557页
[29]关秋菊,刘桂雄,金军.基于递推并行Kalman时序模型的随机误差的分离方法.现代制造工程.2008(2):116-118页
[30] Chen Xiyuan.Modeling Random Gyro Drift by Time Series neural networks and by traditional method.IEEE Int.Conf.Neural Networks & Signal Processing Nanjing, China.2003(12):14-17P
[31]朱利平.基于神经网络的微硅陀螺输出补偿系统研究.南京:南京航空航天大学.2005
[32]王昊,王俊璞,田蔚风,金志华.梯度RBF神经网络在MEMS陀螺仪随机漂移建模中的应用.中国惯性技术学报.2006(8):44-48页
[33]傅建国,王孝通,李博,金良安,马野.MEMS陀螺随机误差模型研究.传感器技术.2005(24):75-77页
[34] Fuqiang Liu, Fanming Liu, Wenjing Wang and Bo Xu.MEMS Gyro’s Output Signal De-noising Based on Wavelet Analysis.Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation.2007(8):5-8P
[35]夏敦柱,周白令,王寿荣.实时小波滤波方法在硅微陀螺仪中的应用研究.中国惯性技术学报.2007(1):92-95页
[36]黄旭.微机械惯性器件/GPS/磁强计组合航向姿态确定研究.哈尔滨工业大学博士学位论文.2005
[37]黄雪樵.克服欧拉方程奇异性的双欧方法.飞行力学.1994(4):28-38页
[38]熊志斌,刘喜斌.克服欧拉方程奇异性的方法研究.岳阳师范学院学报自然科学版.2000(4):60-63页
[39]王海峰,王成良.解决欧拉方程奇异性的方法探讨.飞行力学.2006(3):94-96页
[40]黄卫权,程建华.提高捷联惯导系统精度的系统研究现状与发展趋势.惯性技术发展动态发展方向研讨文集.2003:27-36页
[41]秦永元.惯性导航.北京:科学出版社.2006
[42]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(3):6-10页
[43]曹小平.光纤陀螺姿态系统的旋转矢量算法研究.电光与控制.2006(3):81-84页
[44]宋桂华,赵伟,刘建业.光纤陀螺捷联惯导系统改进航姿算法应用.应用科学学报.2008(6):645-649页
[45]李辉,孟秀云,刘藻珍.角速率输入下的捷联惯导系统改进航姿算法.弹道学报.2006(2):20-22页
[46]黄昊,邓正隆.角速率输入下的航姿算法研究.中国惯性技术学报.2000(2):21-26页
[47]黄昊,邓正隆.旋转矢量航姿算法的一种新的表达式.宇航学报.2001(3):38-44页
[48] Hanspeter S, Junk ins J L.Steregraphic Orientation Parameters for Attitude Dynamics:A Generalization of the Rodrigues Parameters.The Journal of the Astronautical Sciences. 1996(44):1-19P
[49]周江华,苗育红,王明海.姿态运动的Rodrigues参数描述.宇航学报.2004(9):514-519页
[50]王勇军,秦永元,舒东亮.Rodrigues参数与四元数间的关系分析.火力与指挥控制.2008(3):71-73页
[51]程杨,杨涤,崔祜涛.利用修正罗德里格参数进行飞行器姿态估计.飞行力学.2002(4):18-21页
[52]杨亚非,李建国.基于UPF和修正Rodrigues参数的无陀螺姿态确定算法.中国惯性技术学报.2009(17):148-152页
[53]方群,陈记争,马卫华.广义Rodrigues参数姿态描述方法.自然科学进展.2007(5):672-677页
[54]陈记争,袁建平,方群双.双Rodrigues参数方法及其在姿态确定中的应用宇航学报.2008(3):534-538页
[55] Bar-Itzhack, I. Y., and Oshman, Y.Attitude determination from vector observations:Quaternion estimation.IEEE Transactions on Aerospace and Electronic Systems.1985(21):128—136P
[56] Lefferts E J, Markly F L, Shuster M D.Kalman filter for spacecraft attitude estimation.Journal of Guidance Control and Dynamics.1982(5):417-429P
[57]刘海颖.微小卫星姿态控制系统关键技术研究.南京航空航天大学博士学位论文.2008
[58] J. L. Marins, X. Yun, E. R. Bachmann, R. B. McGhee, and M. J. Zyda, An extended Kalman filter for quaternion-based orientation estimation using MARG sensors in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems.2001(29):2003–2011P
[59]黄旭,王常虹,伊国兴等.利用磁强计及微机械加速度计和陀螺的姿态估计扩展卡尔曼滤波器.中国惯性技术学报.2005(2):27-30页
[60] Paul G.Savage.Strapdown Inertial Navigation Integration Algorithm Design Part 1: Attitude Algorithms.Journal of guidance, control, and dynamics.1998(21):19-28P
[61] D.Choukroun, I.Y.Bar-Itzhack, Y.Oshman. Novel quaternion kalman filter.IEEE Trans. on Aerospace and electronic system.2006(1):174-190P
[62] Bar-Itzhack, I.Y., Deutschmann, J., and Markley, F. L.Quaternion normalization in additive EKF for spacecraft attitude determination.Presented at the Guidance, Navigation, and Control Conference. New Orleans.1991:2691-2706P
[63] BERNARD I RIF.DLAND.Analysis Strapdown Navigation Using Quaternions.IEEE TRANSAC TIONS ON AEROSPACE AND ELECTRONIC SYSTEMS.1978(3):764-768P
[64]王亚锋,刘华平,孙富春,张友安.基于误差四元数的捷联惯导全姿态导航与控制.中国惯性技术学报.2007(8):390-393页
[65]周江华,苗育红,李宏.四元数在刚体姿态仿真中的应用研究.飞行力学.2000(4):28-32页
[66] Angelo M. Sabatini.Quaternion-Based Extended Kalman Filter forDetermining Orientation by Inertial and Magnetic Sensing.IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. 2006(53): 1346-1356P
[67] Joseph J. LaViola Jr.A Comparison of Unscented and Extended Kalrnan Filtering for Estimating Quaternion Motion.Proceedings of the American Control Conference Denver.2003:4-6P
[68] Wan, E. A., and R. van der Menve. The Unscented Kalman Filter for Nonlinear Estimation. In Proceedings of Symposium 2000 on Adaptive Systems for Signal Processing.Communication and Control(AS-SP CC),IEEE Press, 2000.
[69] Yee-Jin Cheon.Unscented Filtering in a Unit Quaternion Space for Spacecraft Attitude Estimation.2007
[70] Shuster M D. A survey of attitude representations.Journal of the Astronautical Sciences,1993, 41(4):437-517P
[71]刘付强.船用卫星天线微型姿态测量系统关键技术研究.哈尔滨工程大学博士学位论文.2008
[72]牛小骥.微机械姿态测量单元及其用于卫星电视天线稳定的研究.清华大学博士学位论文.2002
[73]牛小骥,高钟毓,张嵘,陈志勇.基于微机械惯性传感器的卫星电视天线稳定系统.中国惯性技术学报.2002(10):11-15页
[74]许丽佳,陈阳舟,崔平远.GPS/INS组合导航系统中的信息融合算法研究.计算机仿真.2004(3):21-25页
[75]夏琳琳.低成本AHRS/GPS紧耦合融合滤波技术研究.哈尔滨工程大学博士学位论文.2008
[76]王昊.面向车辆导航的MIMU及其与GPS组合的研究.上海交通大学博士学位论文.2007
[77]苑海静.微机械惯性测量单元的测试与标定技术研究.哈尔滨工程大学学士学位论文.2007
[78]彭秀艳,赵希人.工程随机过程.哈尔滨工程大学出版社.2000
[79]王燕.应用时间序列分析.中国人民大学出版社.2005
[80]张树京,齐立心.时间序列分析简明教程.清华大学出版社.2003
[81]陈国强,赵俊伟,黄俊杰,刘万里.基于Matlab的AR模型参数估计.工具技术.2005(39):39-40页
[82]谭琪林.微机械加速度计发展简述.学术探讨与研究.2007(1):15-21页
[83]李海涛.加速度计_磁强计捷联惯导系统姿态解算方法研究.中北大学硕士论文.2007
[84]晏登洋,任建新,牛尔卓.惯性与地磁组合导航系统自适应卡尔曼滤波算法研究.电光与控制.2004(6):74-78页
[85] Thomas Bak.Spacecraft Attitude Determination-a Magnetometer Approach.Department of Control Engineering Aalborg University. 1999:153-156P
[86]马建军,郑志强.数字罗盘辅助实现MIMU静基座初始对准.系统仿真学报.2007(19):2260-2263页
[87]陈哲.捷联惯导系统原理.宇航出版社.1986
[88]黄德鸣,程禄.惯性导航系统.国防工业出版社.1986
[89]夏琳琳,赵琳,刘繁明,胡晓形.基于对偶四元数的航姿系统姿态更新算法研究.系统仿真学报.2008(2):276-281页
[90]武元新.对偶四元数导航算法与非线性高斯滤波研究.国防科技大学博士学位论文.2005
[91]杨金显.微惯性测量系统关键技术研究.哈尔滨工程大学博士学位论文.2008
[92]陈新龙,杨涤,翟坤.AEKF在姿态确定中的应用研究.航天控制.2008(26):47-50页
[93]秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西北工业大学出版社.1998:175-188页
[94]赵琳.卫星导航系统.哈尔滨工程大学出版社.2000
[95] CHEN Ji-zheng, YUAN Jian-ping, FANG Qun.Flight Vehicle Attitude Determination Using the Modified Rodrigues Parameters.Chinese Journal of Aeronautics.2008(5):1622-1626P
[96]赵琳,苑海静,刘付强,刘凤鸣.基于修正的Rodrigues参数的EKF算法在姿态估计中的应用.中国惯性技术学报.2009(5):557-561页
[97]周星伶.GPS/INS组合导航系统松、紧耦合性能比较.航空电子技术.2007(129):1-6页
[98]安亮,王可东.GPS与MEMS/IMU组合导航技术发展现状.全球定位系统.2008(3):49-54页