基于四元数平方根容积卡尔曼滤波的姿态估计

针对飞行器姿态确定中乘性扩展卡尔曼滤波(MEKF, Multiplicative Extended Kalman Filter)在较大初始姿态误差角情况下存在估计精度低及收敛速度慢的问题,提出了一种四元数平方根容积卡尔曼滤波(QSCKF,Quaternion Square-root Cubature Kalman Filter)算法.在推导姿态确定系统四元数非线性误差模型的基础上,采用容积数值积分理论来计算非线性函数的均值与方差,同时使用平方根的形式来提高数值稳定性;针对四元数规范化问题,采用拉格朗日代价函数法求解四元数加权均值.仿真结果表明:在初始姿态误差较大的情况下,该算法相比较于MEKF以及无迹四元数估计法(USQUE, Unscented Quaternion Estimator),估计精度高且收敛速度快,滤波稳定性好,同时估计时间比USQUE缩短了1/3.

Attitude estimation based on quaternion square-root cubature Kalman filter

Considering that a multiplicative extended Kalman filter (MEKF) existed lower estimation accuracy and slower convergence rate for large initialization errors, a quaternion square-root cubature Kalman filter (QSCKF) was proposed. A quaternion nonlinear error model was derived for attitude determination system, and then the cubature numerical integration theory was used to calculate the mean and variance of the nonlinear function. The square-root forms were used to improve numerical stability. To avoid the quaternion normalization problem, a Lagrange loss function was derived to compute the average quaternion. The simulation results indicate that the proposed algorithm provides higher estimation precision with faster convergence rate and better filter's stability than MEKF and unscented quaternion estimator (USQUE) for large initialization errors. And, the estimated time of this algorithm is shortened by 1/3 compared to USQUE.