考虑状态约束的容积卡尔曼滤波估计算法

Cubature Kalman Filter Estimation Algorithm with State Constraints

针对传统非线性滤波未考虑状态约束的局限,提出一种考虑状态约束的容积卡尔曼滤波算法。将状态约束转化为增益约束,结合最小方差估计给出最小约束代价函数;同时,采用相径容积规则近似计算系统状态的后验均值和协方差,给出等式状态约束下的容积卡尔曼滤波递推公式。最后,对路径约束条件下的导航定位系统进行仿真,结果表明算法定位精度优于常规容积卡尔曼滤波算法,较好地解决了非线性系统存在等式状态约束时、常规容积卡尔曼滤波算法不满足约束条件且估计精度差的问题,验证了算法的有效性。

To overcome the limitations of traditional nonlinear filtering taking no consideration of state constraints, a cubature Kalman filter （CKF） algorithm with state constraints was presented. Combined with minimum mean square error estimation, this algorithm gained the minimum constraint cost function by converting the state constraint into the gain constraint. Meanwhile,the CKF recursive formula with state constraints was deduced by using radial cubature rule for the approximate estimation of the system＇s posterior mean and covariance. The path-constrained navigation positioning system was then simulated. The simulation results indicate that the proposed algorithm is superior to CKF in positioning precision and solves constraint dissatisfaction and poor estimation accuracy of conventional CKF algorithm for the nonlinear system with the equality state constraint,verifying the validity of the proposed method.