基于几何距离准则的弹道外推方法

Trajectory Extrapolation Method Based on Criterion of Geometric Distance

为提高雷达软件系统弹道导弹弹道外推的精度,提出一种基于三维空间几何距离准则的弹道外推方法。该方法基于在地球惯性坐标系中标准弹道为位于过地球质心的一个二维平面内的椭圆这一事实,首先由拉格朗日数乘法确定椭圆所在的平面,使所有量测点到该平面的几何距离平方和最小,然后用各量测点在平面内的投影点代替原始点迹,在平面内用最小二乘法作平滑,确定椭圆方程,最后取中点进行弹道外推。应用STK软件进行弹道仿真,结果表明这一方法可以明显提高弹道外推的精度。

A new method based on the criterion of geometric distance is proposed to improve the accuracy of the ballistic missile trajectory extrapolation of the software systems of radars.The base of the method is that the standard orbit of a ballistic missile is a 2-dimensional ellipse crossing the core of the earth.First,the method of Lagrange multipliers is used to find the 2D plane,which is the global minima of the sum of the square of the geometric distances between the measuring points and the plane.Then the projective points,instead of the origin measuring points,are calculated to determine the elliptic equation,smoothed by using the least squares method.At last,the middle point is selected as the initial point to do the trajectory extrapolation.The STK simulation experiments indicate that the accuracy of trajectory extrapolation is obviously improved.