四元数约束的容积卡尔曼滤波及其应用

针对一些非线性系统状态变量中存在四元数约束的情况,提出了一种四元数约束下的容积卡尔曼滤波(quaternion constrained cubature kalman filter,QCCKF)算法．基于最小约束代价函数,采用三阶球面-相径容积规则近似计算系统状态的后验均值和协方差,给出了QCCKF滤波递推公式．设计的QCCKF算法可以有效地对状态进行估计,扩展了CKF的应用范围．最后对飞行器姿态估计系统进行仿真,仿真结果表明,该算法估计精度优于常规CKF和无迹四元数估计法(unscented quaternion estimator, USQUE),并满足四元数约束条件,较好地解决了非线性系统存在四元数约束的问题,验证了算法的有效性．

Cubature Kalman filter with quaternion constraint and its application

Aiming at the case of the state vector with quaternion constraint in some nonlinear systems, a quaternion constrained cubature Kalman filter algorithm is presented. Based on a minimum constrained cost function, this algorithm uses three-degree spherical-radial cubature rule to approximate the posterior mean and covariance, and gives the QCCKF recursive formula. It can estimate the state effectively, and extends the applications of the cubature Kalman filter (CKF). By simulating for the spacecraft attitude estimation system, simulation results show that the proposed algorithm is superior to CKF and unscented quaternion estimator(USQUE) in precision, satisfies the quaternion constraint, and solves the problem that the nonlinear system has quaternion constraint, which show the validation of the proposed method.