为提高静基座初始对准精度,缩短对准时间,采用了基于大方位失准角的对准模型,引入了高斯-厄米特滤波器(GHF)。针对GHF中均值和协方差阵的多元非线性高斯积分求解问题,利用初始对准误差方程的非线性是由大方位失准角导致的特点,通过状态的线性变换,求其线性状态解析解,将高维积分转化成一元数值积分,在不损失精度的前提下,解决了GHF在对准应用的"维数灾难"问题。将此算法用于实际系统,对比于扩展卡尔曼滤波器(EKF)、无迹卡尔曼滤波器(UKF),结果表明在大方位失准角条件下,GHF方法偏航角的对准精度提高了16%,对准时间缩短了75％。
In this paper investigate the alignment problem of a stationary based strapdown inertial navigation system . In order to improve the aligning accuracy and shorten the aligning time, a Gauss-Hermite filter (GHF) is adopted in the alignment model based on large azimuth misalignment angles. The nonlinear Gauss integration of multi-variables to the mean and covariance computation in the GHF is addressed. Since large azimuth misalignment angles will introduce the nonlinearity in the alignment error equations, this paper employs linear state transformation approach to obtain the analytic solution of the linear state vector in the underlying equations. The integration of multi-variables is thus converted to the integration of a single-variable. Hence the so called "dimension problem" in the application of GHF to alignment is solved without loss of accuracy. The proposed method is applied to a SINS, and it shows that the aligning accuracy of path angle is improved by 16% and the aligning time is reduced by 75% compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF).
[1] Yang Y F, Tan J B, Deng Z L. Review of technique for initial alignment of inertial navigation systems. Journal of Chinese Inertial Technology, 2002, 10(2): 68-72. (in Chinese) 杨亚非, 谭久彬, 邓正隆. 惯导系统初始对准技术综述. 中国惯性技术学报, 2002, 10(2): 68-72.
[2] Qv C S, Xu H L, Tan Y. A survey of nonlinear Bayesian filtering algorithms. Electronics Optics & Control, 2008, 15(8): 64-71. (in Chinese) 曲从善, 许化龙, 谭营. 非线性贝叶斯滤波算法综述. 电光与控制, 2008, 15(8): 64-71.
[3] Pan Q, Yang F, Ye L, et al. Survey of a kind of nonlinear filters—UKF. Control and Decision, 2005, 20(5): 481-489. (in Chinese) 潘泉, 杨峰, 叶亮, 等. 一类非线性滤波器——UKF综述. 控制与决策, 2005, 20(5): 481-489.
[4] Ding Y B, Shen G X. Study on unscented particle filter applied in initial alignment of large azimuth misalignment on static base of SINS. Acta Aeronautica et Astronautica Sinica, 2007, 28(2): 397-401. (in Chinese) 丁杨斌, 申功勋. Unscented粒子滤波在静基座捷联惯导系统大方位失准角初始对准中的应用研究. 航空学报, 2007,28(2): 397-401.
[5] Xiong K, Zhang H Y. Application of particle filter in INS non-linear alignment. Journal of Chinese Inertial Technology, 2003, 11(6): 20-26. (in Chinese) 熊凯, 张洪钺. 粒子滤波在惯导系统非线性对准中的应用.中国惯性技术学报, 2003, 11(6): 20-26.
[6] Julier S, Uhlmann J, Durrant-Whyte H F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482.
[7] Julier S J, Uhlmann J K. Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 2004, 92(3): 401-422.
[8] Anderson B D O, Moore J B. Optimal filtering. Englewood Cliffs: Prentice Hall, 1979: 193-211.
[9] Wu Y X. Research on dual-quaternion navigation algorithm and nonlinear Gaussian filtering. Changsha: College of Mechatronics and Automation, National University of Defense Technology, 2005. (in Chinese) 武元新. 对偶四元数导航算法与非线性高斯滤波研究. 长沙: 国防科学技术大学机电工程与自动化学院, 2005.
[10] Bar-Itzhack I Y, Goshen-Meskin D. Identity between INS position and velocity error models. Journal of Guidance, Control, and Dynamics, 1981, 4(5): 568-570.
[11] Bar-Itzhack I Y, Goshen-Meskin D. Identity between INS position and velocity error equations in the true frame. Journal of Guidance, Control, and Dynamics, 1988, 11(6): 590-592.
[12] Bar-Itzhack I Y, Goshen-Meskin D. Control theoretic approach to inertial navigation systems. Journal of Guidance, Control, and Dynamics, 1988, 11(3): 237-245.
[13] Ito K, Xiong K Q. Gaussian filters for nonlinear filtering problems. IEEE Transactions on Automatic Control, 2000, 45(5): 910-927.
[14] Yuan Z J, Zheng N N, Jia X C. The Gauss-Hermite particle filter. Acta Electronica Sinica, 2003, 31(7): 970-973. (in Chinese) 袁泽剑, 郑南宁, 贾新春. 高斯-厄米特粒子滤波器. 电子学报, 2003, 31(7): 970-973.
[15] Arasaratnam I, Haykin S, Elliott R J. Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proceedings of the IEEE, 2007, 95(5): 953-977.
[16] Qin Y Y, Zhang H Y, Wang S H. Kalman filter and theory of assembled navigation. Xi'an: Northwestern Polytechnical University Press, 1998: 33-34. (in Chinese) 秦永元, 张洪钺, 汪叔华. 卡尔曼滤波与组合导航原理. 西安: 西北工业大学出版社, 1998: 33-34.
CJA