基于样条拟合和双向滤波的助推段弹道估计

三次B样条拟合在助推段弹道估计中应用广泛,但存在弹道两端点邻域估计误差过大的问题.通过对B样条基函数矩阵的特性进行分析,发现其原因为端点邻域估计时能利用的有效观测数据最少.因此,提出一种基于样条拟合和双向滤波相结合的弹道估计策略：首先将双星观测数据利用无迹变换转换为等效位置观测;然后利用三次B样条拟合弹道;最后基于一种自适应卡尔曼滤波器,采用双向滤波策略改善样条拟合的端点估计精度.仿真结果表明：组合方法使样条拟合的端点估计误差减少40％,同时使估计弹道更平滑.此结果满足实时性要求.

Trajectory Estimation in Boost Phase Based on Spline Fitting and Bidirectional Filtering

Cubic B-spline fitting is widely used for trajectory estimation in boost phase, but its error is outstanding in the neighboring regions of endpoints during trajectory estimation. Analysis of the characteristics of the B-spline basis function matrix finds the reason is that the amount of valid observation data used for endpoint neighborhood estimate is the least. This paper proposes a trajectory estimation strategy featuring combination of spline fitting and bidirectional filtering. First, the dual-satellite observation is transformed into equivalent position observation by using unscented transform. Then, cubic B-spline is used to fit the trajectory. Finally, based on an adaptive Kalman filter, a bidirectional filtering strategy is adopted to improve the endpoint estimation accuracy of the spline fitting method. Simulation results show that the combination method reduces 40% of endpoint estimation errors of spline fitting, producing smoother estimated trajectory. Moreover, it meets realtime operation requirements.