为准确估算远程预警雷达对弹道导弹探测的时间窗口,需要联立导弹轨迹与雷达探测范围的数学模型,求解非线性二次方程组.提出了一种非线性二次方程组的求解方法,首先将核问题转化为二次等式的优化问题,引入误差范数约束非凸优化问题,将二次等式进行一阶和二阶泰勒展开,将原问题在局部近似为一个最优化问题并利用迭代凸优化求解,得到雷达探测范围与导弹弹道的交汇点坐标的解析解,实现对雷达探测时间窗口的准确估算.通过场景模拟与求解分析证明了该方法的正确性,并表明该方法具有精度高、通用性强的特点.%To accurately estimate the time-window of long-range early-warning radar dectecting ballistic missile,the simultaneous mathematical model of missile trajectory and radar detection-range was built,and a method of solving the nonlinear quadratic equations was proposed. The core problem was transformed into an optimization problem, and the error norm was introduced to constrain the non-convex optimal problem. The first and second order Taylor expansion of the quadratic equation was carried out,and the original problem was approximated to an optimization problem locally, and the iterative convex optimization was used to solve the problem. The analytical solution of radar detection-range and trajectory joint-point were obtained to realize the accurate estimation of radar detection time-window. Scene simulation and solution analysis prove that the method is correct,and this method has the characteristics of high precision and versatility.
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