基于特征值分解的小天体着陆自主导航系统可观度分析
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摘要
针对非线性导航系统中状态估计可观性与导航精度之间的关系,采用基于误差方差阵特征值分解的可观度分析方法,结合扩展卡尔曼滤波(EKF)算法对非线性预测滤波(NPF)算法进行改进,推导改进预测滤波的误差协方差矩阵,并对其进行特征值分解.分析特征值和特征向量与导航精度的关系,以小天体探测器着陆自主导航系统为例进行仿真验证,与EKF导航精度比较的基础上验证改进的NPF算法的有效性和精确性,并分析不同误差因素(模型误差,陀螺噪声,陆标误差)对可观度的影响,为航天器实际过程中自主导航系统的滤波器设计提供参考.
In order to solve the problem of the relationship between navigationobservability and accuracy in nonlinear navigation system, the observability analysis method based on the error covariance matrix is adopted. The nonlinear predictive filter( NPF) is improved combined with extended Kalman filter( EKF),and the error covariance of improved predictive filter is deduced. Then the eigenvalue decomposition is carried out to analyze the relationship between the eigenvalue and navigation accuracy. Taking the autonomous navigation system of the small celestial probe landing as an example, the simulation validation is carried out and the validity and accuracy of the improved NPF algorithm are verified comparin with the EKF. The influence of different error factors on observability is analyzed, which provide a reference for the filter design of autonomous navigation system in the actual spacecraft process.
In order to solve the problem of the relationship between navigationobservability and accuracy in nonlinear navigation system, the observability analysis method based on the error covariance matrix is adopted. The nonlinear predictive filter( NPF) is improved combined with extended Kalman filter( EKF),and the error covariance of improved predictive filter is deduced. Then the eigenvalue decomposition is carried out to analyze the relationship between the eigenvalue and navigation accuracy. Taking the autonomous navigation system of the small celestial probe landing as an example, the simulation validation is carried out and the validity and accuracy of the improved NPF algorithm are verified comparin with the EKF. The influence of different error factors on observability is analyzed, which provide a reference for the filter design of autonomous navigation system in the actual spacecraft process.
引文
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[9]杨静,冀红霞,魏明坤.一种非线性滤波器的误差分析及应用[J].航空学报,2011,32(8):1469-1477.YANG J, JI H X, WEI M K. Error analysis and application of a nonlinear filter[J]. Chinese Journal of Aeronautics, 2011,32(8),1469-1477.
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[2]QIAO G,WANG D,LI T. Observability analysis of autonomous navigation system for earth-lunar transfer orbit phase[C]//Proceeding. 2007 IEEE International Conference on Robotics and Biomimetics,2007:946-951.
[3] HAM F M, BROWN R G. Observability, eigenvalues,and kalman filtering[J]. IEEE Transactions on Aerospace and Electronic Systems, 1983, AES-19(2):269-273.
[4]宁晓琳,房建成.一种深空探测器自主天文导航新方法及其可观测性分析[J].空间科学学报,2005,25(4):286-292.NING X L,FANG J C. A new autonomous celestial navigation method for deep space probe and its observability analysis[J]. Chinese Journal of Space Science,2005,25(4):286-292.
[5]黄翔宇,崔平远,崔祜涛.深空自主导航系统的可观性分析.宇航学报,2006,27(3):332-337.HUANG X Y,CUI P Y,CUI H T. Observability analysis of deep space autonomous navigation system[J]. Journal of Astronautics,2006,27(3):332-337.
[6]LEFFERTS E J. Kalman Filtering for Spacecraft Attitude Estimation[D]. AIAA-82-0070R.
[7]MOOK D J,JUNKINS J L. Minimum model error estimation for poorly modeled dynamic systems[J]. Journal of Guidance, Control, and Dynamics, 1988, 11(3):256-261.
[8]秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理[M].西安:西北工业大学出版社,1998.
[9]杨静,冀红霞,魏明坤.一种非线性滤波器的误差分析及应用[J].航空学报,2011,32(8):1469-1477.YANG J, JI H X, WEI M K. Error analysis and application of a nonlinear filter[J]. Chinese Journal of Aeronautics, 2011,32(8),1469-1477.
[10]邢光谦.量测系统的能观度和状态估计精度[J].控制工程. 1982,(4):1-7.