基于Legendre多项式的一种高精度捷联惯导姿态更新算法

A high-accuracy SINS attitude update algorithm based on Legendre polynomial

高超声速飞行器(hypersonic flight vehicle,HFV)大加速度运动、旋转导弹的高速转动和战斗机的大机动飞行等对捷联惯导系统(strapdown inertial navigation system,SINS)提出了更高的要求,只有在减小IMU(inertial measurement unit)测量误差的同时改进捷联惯导算法,才能在高动态大机动条件下实现高精度定位。传统的捷联惯导算法,在忽略Bortz方程高阶项后,通过构建圆锥误差补偿项完成高精度姿态解算。在大机动条件下补偿后的残差已不再是可以忽略的小量,激励出的算法误差已严重影响导航解算精度。为了提升大机动条件下的捷联惯导算法精度,用Legendre多项式作基完成角速度函数逼近,以四元数微分方程数值求解为核心,设计一种高精度SINS姿态解算。由于在推导过程中没有近似,在精确数值计算中实现了高阶圆锥误差补偿。在圆锥运动和大机动环境下进行姿态解算仿真,与目前精度最高的四次叉乘圆锥误差算法相比,新算法在圆锥运动下的误差不到其算法误差的1/3,在大机动条件下算法精度可以提升一个量级。基于Legendre多项式的高精度捷联惯导算法对未来高超音速飞行器精确定位、原子陀螺惯导系统研究以及捷联惯导算法设计都有一定的参考意义。

The large-acceleration motion of HFV(hypersonic flight vehicle), the high-speed rolling of spinning missile, and the large-maneuver flight of fighter aircraft has put forward higher performance demand for SINS(strapdown inertial navigation system). The high-accuracy positing will be realized under the high-dynamic maneuver environment after decreasing measurement error of IMU(inertial measurement unit), meanwhile the algorithm of SINS must be improved. The conventional algorithm calculates the flight attitude with determining the compensation term of coning error, after ignoring the high-order term of the Bortz equation. To improve the algorithm accuracy of SINS under high-dynamic maneuver environment, a high-accuracy algorithm, which uses Legendre polynomial to complete angular velocity function approximation and takes the numerical method of quaternion differential equation as core, is proposed herein. The high-order coning error is compensated in the numerical solving period in the proposed novel algorithm, because no approximation exists in deducing process. The attitude calculating simulations are finished in coning motion condition and high-dynamic maneuver condition respectively. Compared with the quadruple-cross-product compensation algorithm which has the highest accuracy at present, the attitude error of proposed algorithm is less than its 1/3 in coning motion condition. And algorithm accuracy is raised an order of magnitude under the high-dynamic maneuver environment. The high-accuracy algorithm based on Legendre polynomial has reference significance for accurate positing of future HFV, atomic gyroscope INS research and high-accuracy algorithm design of SINS.