大角速率机动下捷联惯性姿态误差评估与补偿算法研究

发布时间：2018-02-16 07:04

本文关键词： 频率级数算法显式频率整形算法大角速率转动规范化四元数不可交换性误差陀螺器件误差数据量化　出处：《国防科学技术大学》2014年硕士论文　论文类型：学位论文

【摘要】：在捷联惯性导航姿态更新算法研究中,Musoff用Jacobian椭圆函数和Richardson外推法评估了Miller优化圆锥算法的性能。他证明了,当载体的角速度是由Jacobian椭圆函数描述的广义圆锥运动时,Miller的优化圆锥算法不再是最优的。虽然Musoff证明了Miller的优化圆锥算法不再是最优的,但是却没给出如何求取最优系数的方法。本文基于一种广义定义的圆锥运动环境即圆锥运动和大角速率转动并存的环境,对于传统的圆锥算法进行了精度分析和评价,并设计了更高精度的姿态更新算法。本文做了如下的工作:(1)基于大角速率转动和圆锥运动并存环境下的规范化四元数,对频率级数圆锥算法和显式频率整形圆锥算法进行了算法精度的理论分析,并给出了两种算法在此环境下的理论误差。在大角速率转动和圆锥运动并存环境下,本文采取了等效旋转矢量二阶近似的方法,提高了其理论值的精度。仿真发现,在大角速率转动和圆锥运动并存的环境下,当载体在低频率圆锥运动下时,显式频率整形算法比频率级数算法精度更高。(2)通过理论分析,推导出了在圆锥运动和大角速率转动并存环境下,传统姿态更新算法中忽略掉的不可交换性误差高阶项的理论值,证明了其不可忽略性。设计了高阶不可交换性误差补偿算法,并对三子样算法的系数进行求解。基于大角速率转动和圆锥运动并存环境下的规范化四元数和Savage的恶劣角速率环境对设计的高阶算法进行了仿真验证,从仿真结果可以看出,新的高阶姿态更新算法可以很好的提高姿态更新的精度。(3)考虑陀螺器件误差因素(陀螺标度因数,非正交误差和陀螺常值漂移),全面地分析了不可交换性误差,推导了其补偿前后的算法漂移方程。分析了一般的捷联惯导系统中常用的脉冲数据量化的方法对姿态更新算法精度的影响,并设计了FIR滤波器降低量化误差。
[Abstract]:In the research of attitude updating algorithm for strapdown inertial navigation, Musoff evaluates the performance of Miller optimization cone algorithm by using Jacobian elliptic function and Richardson extrapolation. When the angular velocity of the carrier is the generalized cone motion described by the Jacobian elliptic function, the optimal cone algorithm is no longer optimal, although Musoff proves that Miller's optimized cone algorithm is no longer optimal. However, the method of finding the optimal coefficient is not given. Based on a generalized definition of conical motion environment, that is, the conical motion and the rotation of large angular velocity, the accuracy of the traditional cone algorithm is analyzed and evaluated in this paper. A more accurate attitude updating algorithm is designed. In this paper, the following work is done: 1) based on the normalized quaternion in the environment of large angular velocity rotation and conical motion, The theoretical analysis of the accuracy of the frequency series cone algorithm and the explicit frequency shaping cone algorithm is made, and the theoretical errors of the two algorithms in this environment are given. In this paper, the method of equivalent rotation vector second order approximation is adopted to improve the accuracy of the theoretical value. The simulation results show that under the condition that the rotation of large angular velocity and the conical motion coexist, when the carrier is in low frequency conical motion, The explicit frequency shaping algorithm is more accurate than the frequency series algorithm. Based on the theoretical analysis, the theoretical value of the higher order term of non-commutative error neglected in the traditional attitude updating algorithm is derived under the environment of conical motion and large angular rate rotation. It is proved that it can not be ignored. A high order noncommutative error compensation algorithm is designed. Based on the normalized quaternion in the environment of large angular rotation and conical motion and the bad angular rate environment of Savage, the high order algorithm is simulated and verified. The new high-order attitude updating algorithm can improve the precision of attitude updating. It takes into account the factors of gyroscope error (gyroscope scale factor, non-orthogonal error and gyro constant drift), and analyzes the non-commutative error comprehensively. The drift equation of the algorithm before and after compensation is derived, the influence of the usual pulse data quantization methods in sins on the precision of attitude updating algorithm is analyzed, and the FIR filter is designed to reduce the quantization error.
【学位授予单位】：国防科学技术大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN96

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