全姿态飞机捷联式系统姿态角的计算

 本文讨论了飞机做全姿态角运动时捷联式系统姿态角计算中存在的几个问题:（1）为保证单值地确定飞机在空间的角位置,应恰当地规定姿态角的定义域;（2）由方向余弦矩阵元素求姿态角时要进行反三角函数运算,当反三角函数的自变量的分母或分子趋于零时会引起较大的误差,甚至导致计算机溢出,这些都应设法避免;（3）当俯仰角趋于±90°附近的小锥形区域时,三个姿态角自由度退化为两个自由度,这时姿态角的定义与计算方法应做新的改变。本文分析与解决了上述问题,给出了计算姿态角的程序框图。数学模拟的结果证明了理论分析的正确性。

CALCULATION FOR ATTITUDE ANGLES OF AN ALL ATTITUDE AEROPLANE STRAPDOWN SYSTEM

Several problems in calculating attitude angles of an aeroplane are discussed and their solutions are provided.（1）In order to determine the single valued angle position of an aeroplane,definition regions for attitude angles are given,so that determining attitude angles is facilitated.（2）When denominator（or numerator）of the independent variable in an arctangent function approaches to zero,there are a lot of troubles such as appearance of large error,overflow,etc..The solution is proposed to determine values of attitude angles directly according to whether values of the numerator（or the denominator）are positive or negative when absolute value of the denominator（or the numerator）is less than a small value e,which depends on the demanded accuracy of the system.（3）As the pitch angle 6 tends to a small conic region of ±90°,three degrees of freedom of attitude angles will reduce to two degrees of freedom.Let roll angle γ=0,and choose the other two elements T21 and T11 of the direction cosine matrix,so that calculation of yaw angle ψcan be accomplished.Programme diagram for attitude angle calculation is given and results of mathematic simulation show correctness of the above theoretic analysis.