平方根Spherical Simplex UKF在飞船姿态估计中的应用

Spacecraft Attitude Estimation using Square-Root Spherical Simplex Unscented Kalman Filter

提出了一种用矢量观测来估计飞船姿态的平方根spherical simplex unscented卡尔曼滤波算法。该算法将spherical simplex unscented变换与unscented卡尔曼滤波结合起来,与采用scaled unscented变换的unscented卡尔曼滤波相比,具有更低的计算量。其平方根形式由于协方差阵的半正定性,拥有更好的数值稳定性。飞船的姿态运动学描述采用了四元数,而用广义罗德里格斯参数来克服卡尔曼滤波过程中的四元数归一化误差。仿真结果表明,该算法比标准扩展卡尔曼滤波具有更低的姿态估计误差及更快的收敛率。

A square-root spherical simplex unscented Kalman filter is proposed to estimate the spacecraft attitude from the vector measurements. The algorithm combines a better-behaved spherical simplex unscented transformation, which can simplify the computational complexity in comparison with the scaled unscented transformation, with the unscented Kalman filter. The square-root forms have a consistently increased numerical stability as all resulting covariance matrices are guaranteed to stay semipositive definite. The quaternion is used to describe the spacecraft attitude kinematics, while a threedimensional generalized Rodrigues parameter is used to maintain the quaternion normalization constraint in the filter formulation. Simulation results indicate that the proposed filter can provide lower attitude estimate errors with faster convergence rate than the standard extended Kalman filter.