改进四元数无味卡尔曼滤波算法

针对四元数无味卡尔曼滤波计算量较大等问题,提出一种改进的四元数无味卡尔曼滤波算法,通过四元数与修正罗德里格斯参数的线性变换,避免了四元数无味卡尔曼滤波中,四元数与误差罗德里格斯参数频繁切换所带来的计算量增大的问题,从而降低了算法的计算量。推导了修正罗德里格斯参数出现奇异值时,改进四元数无味卡尔曼滤波的奇异值避免的转换公式。在捷联惯性导航系统/全球卫星定位系统(strapdown inertial navigation system / global positioning system,SINS/GPS)直接式位置松组合仿真试验中,对比了乘性扩展卡尔曼滤波、四元数无味卡尔曼滤波和改进四元数无味卡尔曼滤波的估计性能,证明了所提出算法的有效性。

Modified quaternion unscented Kalman filter

Aiming at the problem of larger calculation burden of the quaternion unscented Kalman filter (USQUE), a modified USQUE (MUSQUE) is proposed. Based on the transformation between the quaternion and the modified rodriguez parameter (MRP), the novel method can reduce calculation amount by avoiding frequent transformation between the quaternion and the error-MRP for the USQUE. Meanwhile, the singularity avoidance method is also derived in case when the MRP is singularity. By simulating strapdown inertial navigation system/global positioning system (SINS/GPS) direct integrated navigation, the results prove the validation of the novel method comparing with the multiplicative extended Kalman filter and USQUE.