This article considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2-D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This article shows that the 3-D trajectory in the reentry phase can be obtained by estimating the target’s state at the end of the observation interval. The 7-d motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed, and 3-D position) is estimated by the maximum likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher information matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer–Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method.

中文翻译：

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移动无源传感器在再入阶段的弹道物体轨迹和撞击点估计


本文考虑使用移动无源传感器的二维测量（方位角和仰角）来估计弹道目标在再入阶段的轨迹的问题。以前的工作研究了单个固定无源传感器对物体在推力和初始弹道阶段的估计问题。本文表明，再入阶段的 3D 轨迹可以通过估计观测间隔结束时目标的状态来获得。 7 维运动参数矢量（速度方位角、速度仰角、阻力系数、目标速度和 3 维位置）由最大似然 (ML) 估计器通过数值搜索进行估计。然后我们可以预测任意时间的未来位置以及目标的弹着点。匀速移动或机动的快速飞机上的传感器系统的可观测性通过 Fisher 信息矩阵的可逆性进行验证。这是对静止无源传感器观测引力场中目标的最新可观测性证明的适用性的主要扩展。评估了估计参数的 Cramer-Rao 下限，结果表明估计在统计上是有效的。 ML 估计器的角度估计性能也与多项式拟合方法进行了比较。仿真结果说明了该方法的有效性。