基于最优样条节点的导弹主动段弹道估计方法

拟合导弹主动段弹道并估计其弹道参数是天基红外系统(SBIRS)的重要任务之一。首先采用三次样条函数对导弹主动段弹道进行描述,并建立主动段弹道的运动模型和测量模型;其次采用最大似然估计方法将导弹弹道估计问题转化为非线性最小二乘准则下的样条系数和样条节点分布最优估计问题;最后利用投影定理将样条系数估计和样条节点分布估计分离开来,并通过迭代逼近给出了最优样条节点数的确定方法。仿真实验结果表明,所提方法不仅对主动段弹道的拟合精度高,而且还减少了待估参数的数目,简化了求解过程,可在无先验信息条件下较好地解决导弹主动段弹道的估计问题。

Trajectory estimation method of missile in boost phase using optimal knots spline

Fitting the missile trajectory in boost phase and estimate its ballistic parameters is an important task of the space-based infrared system (SBIRS). Firstly, the cubic spline function is applied to describing the missile trajectory in boost phase, and the motion model and measurement model of the missile trajectory in boost phase are established. Secondly, by using the method of maximum likelihood, the estimation problem of missile trajectory is transformed into the optimal estimation problems of spline coefficients and the distribution of spline nodes under the criterion of nonlinear least squares. Finally, the above-memtioned estimation problems are separated by projection theorem, and the method for optimally determining the number of spline nodes is proposed by iterative approximation. The simulation and experimental results show that the proposed method not only has high fitting precision for missile trajectory in boost phase, but also reduces the number of parameters to be estimated, and simplifies the solving process. The proposed method can better solve the estimation problem of missile trajectory in boost phase without prior information.