基于改进的CKF低轨卫星多普勒定位解算

Doppler positioning solution for low earth orbit satellites based on improved CKF

针对低轨卫星多普勒定位中最小二乘法(the least squar method,LSM)和扩展卡尔曼滤波(extended Kalman filter,EKF)带来的解算误差,采用容积卡尔曼滤波(cubature Kalman filter,CKF)算法的思想来进行定位解算。首先设计了一种基于GeoSOT剖分网格的初值搜索方法进行粗定位,避免迭代发散;在解算过程中,对CKF进行改进,用QR分解代替其中的Cholesky分解,防止误差协方差矩阵非正定导致计算终止;最后以铱星星座对地面站的静态定位为例,通过STK进行仿真验证算法的有效性。结果表明,改进的CKF(improved CKF,ICKF)算法对于目标的定位误差在百米以内;且相较于LSM和EKF,定位精度大约可以提高17%。

Because of the calculation errors caused by the least square method(LSM)and ex-tended Kalman filter(EKF)in the Doppler positioning of low earth orbit satellites,the cuba-ture Kalman filter(CKF)algorithm was used to solve the location problem.Firstly,an initial value search method based on the GeoSOT grid was designed to avoid iterative divergence.Then,in the process of solving,CKF was improved and the Cholesky decomposition was re-placed by QR decomposition to prevent the error covariance matrix from being positive defi-nite and resulting in calculation termination.Finally,the static location of the ground station by the IRIDIUM constellation was taken as an example,and the validity of the algorithm was verified by STK simulation.The results show that the localization error of the improved CKF(ICKF)algorithm is less than 100 m.Compared with least square and EKF,the positioning accuracy can be improved by about 17%.