基于平方根Unscented卡尔曼滤波的无陀螺卫星的姿态估计

针对无陀螺卫星的姿态和速度估计问题，提出基于平方根UKF滤波（square Root Unscented Kalman Filter）的估计算法。为了避免欧拉角带来的奇异问题，采用四元数描述卫星的姿态参数。考虑卫星的非线性模型，采用Cholesky和QR分解，从而平方根UKF滤波方法不仅能保证协方差矩阵的正定性，并且还可以提高算法的计算精度。利用测量矢量的信息，该算法能估计三轴稳定卫星的姿态，且计算简单，无需计算Jacobian矩阵。数值仿真结果表明，所给出的方法是可行而有效的。

Gyroless Satellite Attitude Estimation for Square Root Unscented Kalman Filter

The algorithm based on the square root Unscented Kalman filter (UKF) is presented to solve the attitude and rate estimation problem for gyroless satellite. To avoid the singular problem from Euler angle, quaternion parameterization is implemented to describe the attitude. Considering the satellite nonlinear model, the orthogonalization and Cholesky decomposition are used as computational tools in square root UKF, rendering the state covariance with positive semi-definiteness and exceptional estimation accuracy. The attitude estimation algorithm is simple in computation, and no Jacobian matrix is required to be calculated in the proposed algorithm. The efficiency of the square root UKF estimator is tested through numerical simulation of a fully actuated rigid body with only three-axis-magnetometers (TAM). The simulation results show that the algorithm is feasible and efficient.