基于离差差分滤波算法的再入目标状态估计

再入弹道目标的状态估计是个复杂的非线性滤波问题，使用扩展卡尔曼滤波算法（Extended Kalman Filter，EKF），会引入较大的误差，甚至发散．为了提高估计精度，提出使用离差差分滤波算法（Divided Difference Filter，DDF）对再入弹道目标的状态进行估计．DDF算法使用二阶多维Stirling内插多项式近似非线性状态和测量方程获得状态和方差的估计．该算法只需要计算函数值，避免了求导运算，降低了计算复杂度．Monte Carlo数值仿真表明，离差差分滤波方法降低了再入目标的状态估计误差，提高了估计精度，且运行速度比无迹卡尔曼滤波方法（Unscendted Kalman Filter，UKF）要快的多．

State Estimation of Reentry Target Based on Divided Difference Filter

State estimation of reentry ballistic target is a complex nonlinear problem. The large error of state estimation of reentry ballistic target,even divergence in the EKF is introduced. In order to improve the estimation accuracy, the divided difference filter （DDF） is used to estimate the state of reentry target with unknown ballistic coefficient. In the DDF algorithm, the state estimation and covariance are obtained by using the second-order multidimensional stirling interpolation polynomial to approximate the nonlinear state and measurement equation. The DDF algorithm is simple, free-derivative, decreasing the computational complexity. Monte Carlo simulation results indicate that the DDF algorithm can decrease the estimation error of the state estimation and improve the state accuracy. Moreover, the running time of the DDF is much less than that of the UKF.