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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。
Fitting the projectile trajectory of a missile and estimating its ballistic parameters is one of the important tasks of the spaceborne infrared system (SBIRS). Firstly, the cubic spline function is used to describe the trajectory of the missile active stage, and the motion model and the measurement model of the active stage trajectory are established. Secondly, the maximum likelihood estimation method is used to convert the missile trajectory estimation problem into the spline under the nonlinear least square criterion Coefficients and spline nodes. Finally, the spline coefficient estimation is separated from the spline node estimation using projection theorem, and the method to determine the optimal spline number is given by iterative approximation. The simulation results show that the proposed method not only has high fitting accuracy for the trajectory of the active stage, but also reduces the number of parameters to be estimated, simplifies the solving process, and can better solve the missile trajectory under the condition of no prior information The estimation problem.