高精度捷联惯导姿态算法的性能分析
|
摘要
针对不可交换性误差一般采用多子样旋转矢量法对其进行补偿,但传统多子样旋转矢量法在大半锥角或者其他更为复杂的角运动条件下,性能会有所退化,新出现的多子样四元数算法和方向余弦算法没有显式地考虑不可交换性误差,直接求解姿态微分方程。为了综合比较这些算法的性能,在圆锥运动和大角度机动条件下对其进行仿真分析,采用理想和非理想采样两种数据条件,同时变换不同的采样频率,并比较了算法的计算负担。结果表明,在理想条件下,新算法的周期性误差小于旋转矢量法,且子样数的增加使新算法精度明显提高;对比理想与非理想采样两种情况,算法精度相差4～5个数量级。3种算法各有优缺点,需要对惯性器件数据进行充分补偿才能完全发挥算法的精度潜力。
The non-commutativity error is generally compensated by the multi-subsample rotation vector method, but the performance of the traditional multi-subsample rotation vector method is degraded under the condition of large half cone angle or other more complicated angular motion. The new multi-subsample quaternion algorithm and the direction cosine algorithm do not directly consider the non-commutativity error, and the two algorithms directly solve the attitude differential equation. In order to comprehensively compare the performance of these algorithms, a simulation analysis is carried out under conical motion and large angle maneuvering conditions. Two data conditions, ideal and non-ideal sampling, are used to transform different sampling frequencies, and comparison is made to the computational burden of the algorithms. The results show that under ideal conditions, the periodic error of the new algorithm is smaller than that of the rotation vector method, and the accuracy of the new algorithm is improved significantly with the increase of the number of subsamples. By comparing ideal sampling with non-ideal sampling, it can be seen that the accuracy of the algorithm differs by 4～5 orders of magnitude. Each of the three algorithms has its own advantages and disadvantages. Only by fully compensating the inertial device data can the accuracy potential of the algorithm be fully realized.
The non-commutativity error is generally compensated by the multi-subsample rotation vector method, but the performance of the traditional multi-subsample rotation vector method is degraded under the condition of large half cone angle or other more complicated angular motion. The new multi-subsample quaternion algorithm and the direction cosine algorithm do not directly consider the non-commutativity error, and the two algorithms directly solve the attitude differential equation. In order to comprehensively compare the performance of these algorithms, a simulation analysis is carried out under conical motion and large angle maneuvering conditions. Two data conditions, ideal and non-ideal sampling, are used to transform different sampling frequencies, and comparison is made to the computational burden of the algorithms. The results show that under ideal conditions, the periodic error of the new algorithm is smaller than that of the rotation vector method, and the accuracy of the new algorithm is improved significantly with the increase of the number of subsamples. By comparing ideal sampling with non-ideal sampling, it can be seen that the accuracy of the algorithm differs by 4～5 orders of magnitude. Each of the three algorithms has its own advantages and disadvantages. Only by fully compensating the inertial device data can the accuracy potential of the algorithm be fully realized.
引文
[1] 秦永元.惯性导航[M].北京:科学出版社,2006.
[2] WANG M S,WU W Q,WANG J L,et al.High-order attitude compensation in coning and rotation coexisting environment [J].IEEE Transactions on Aerospace and Electronic Systems,2015,51(2):1178-1190.
[3] SONG M,WU W Q,PAN X F.Approach to recovering maneuver accuracy in classical coning algorithms[J].Journal of Guidance,Control & Dynamics,2013,36(6):1872-1880.
[4] 严恭敏,严卫生,徐德民.经典圆锥误差补偿算法中剩余误差估计的局限性研究[J].中国惯性技术学报,2008,16(4):379-385.
[5] 严恭敏,翁浚,杨小康,等.基于毕卡迭代的捷联姿态更新精确数值解法[J].宇航学报,2017,38(12):1308-1313.
[6] 李荣柞,周召发,徐梓皓.基于前周期优化子样数的姿态算法[J].压电与声光,2016,38(2):333-336.
[7] 严恭敏,杨小康,翁俊,等.一种无误差的捷联惯导数值更新新算法[J].宇航定位学报,2018,6(2):20-22.
[8] 顾冬晴,秦永元.捷联惯导量化误差建模研究[J].中国惯性技术学报,2004,12(6):13-17.
[9] 王小峰,董正芳.捷联惯导系统航姿算法的比较及仿真分析[J].现代导航,2016,7(2):103-106.
[10] 周召发,胡文,张志利,等.一种新的捷联惯性导航系统姿态四元数方程求解方法[J].兵工学报,2018,39(3):511- 518.
[11] XU Z H,XIE J,ZHOU Z F,et al.Accurate direct strapdown direction cosine algorithm[J/OL].IEEE Transactions on Aerospace and Electronic Systems,2018.[2019- 03- 04].http://www.onacademic.com/detail//journal_1000041625345199.html.doi:10.1109/TAES.2018.2881353.
[12] SAVAGE P G.A unified mathematical framework for strapdown algorithm design[J].Journal of Guidance, Control & Dynamics,2006,29(2):237- 249.
[2] WANG M S,WU W Q,WANG J L,et al.High-order attitude compensation in coning and rotation coexisting environment [J].IEEE Transactions on Aerospace and Electronic Systems,2015,51(2):1178-1190.
[3] SONG M,WU W Q,PAN X F.Approach to recovering maneuver accuracy in classical coning algorithms[J].Journal of Guidance,Control & Dynamics,2013,36(6):1872-1880.
[4] 严恭敏,严卫生,徐德民.经典圆锥误差补偿算法中剩余误差估计的局限性研究[J].中国惯性技术学报,2008,16(4):379-385.
[5] 严恭敏,翁浚,杨小康,等.基于毕卡迭代的捷联姿态更新精确数值解法[J].宇航学报,2017,38(12):1308-1313.
[6] 李荣柞,周召发,徐梓皓.基于前周期优化子样数的姿态算法[J].压电与声光,2016,38(2):333-336.
[7] 严恭敏,杨小康,翁俊,等.一种无误差的捷联惯导数值更新新算法[J].宇航定位学报,2018,6(2):20-22.
[8] 顾冬晴,秦永元.捷联惯导量化误差建模研究[J].中国惯性技术学报,2004,12(6):13-17.
[9] 王小峰,董正芳.捷联惯导系统航姿算法的比较及仿真分析[J].现代导航,2016,7(2):103-106.
[10] 周召发,胡文,张志利,等.一种新的捷联惯性导航系统姿态四元数方程求解方法[J].兵工学报,2018,39(3):511- 518.
[11] XU Z H,XIE J,ZHOU Z F,et al.Accurate direct strapdown direction cosine algorithm[J/OL].IEEE Transactions on Aerospace and Electronic Systems,2018.[2019- 03- 04].http://www.onacademic.com/detail//journal_1000041625345199.html.doi:10.1109/TAES.2018.2881353.
[12] SAVAGE P G.A unified mathematical framework for strapdown algorithm design[J].Journal of Guidance, Control & Dynamics,2006,29(2):237- 249.