鲁棒EKF在脉冲星导航系统中的应用

针对脉冲星导航系统的滤波问题,传统的扩展卡尔曼滤波(EKF)算法存在不能克服系统模型存在不确定性参数以及乘性噪声等缺陷,提出一种鲁棒EKF算法。首先,分析了状态预测误差方程和估计误差方程,利用统计学原理,得到了状态预测方差矩阵和状态估计方差矩阵计算等式。由于系统模型存在不确定性参数,状态预测协方差矩阵和状态估计协方差矩阵无法计算;因此,利用4个重要矩阵不等式,分析并找到预测方差矩阵和状态估计方差矩阵的上界。最后,利用状态估计误差协方差矩阵上界设计状态增益矩阵,使得状态估计协方差矩阵的迹最小。将该算法对脉冲星导航系统进行仿真,仿真结果验证了所提算法的有效性。

A robust extended Kalman filter algorithm for X-ray pulsar navigation system

Considering that the traditional extended Kalman filter (EKF) algorithm has low accuracy and poor robustness in the application of the X-ray pulsar navigation system with uncertainty of model parameters, multiplicative noises and additive noises, a robust EKF algorithm is proposed in this paper. The equations for state prediction errors and state estimation errors are established. Then, state prediction error covariance and state estimation error covariance are obtained. However, as there are uncertainties in model parameters, the accurate value of state prediction error covariance and state estimation error covariance cannot be calculated. Hence, the upper bound of the state prediction error covariance and the upper bound of the state estimation error covariance are identified by using four matrix inequalities. The gain matrix is designed by minimizing the upper bound of the state estimation error covariance for all admissible uncertainties. The method is applied to X-ray pulsar navigation system, and simulation results show the effectiveness of the algorithm.