Abstract

We consider the problem of planning the optimal route of an object moving at a constant speed on a plane trying to evade detection by a single sensor with the aim to minimize the integral level of useful signal arriving at the observer. It is shown that various mechanisms for detecting a moving object can be reduced to a general mathematical formalization, namely, to the study of the detection problem for different types of signal and a small signal-to-noise ratio. As a result of the study, the solution of the two-point variational problem with an integral constraint is reduced to the solution of three types of systems of algebraic integral equations, which include the normal elliptic Legendre integrals of the first and second kind, with the type of the system determined by various initial conditions and the values of the integral constraint. A numerical procedure for its solution is implemented for each of the systems described in the paper.

中文翻译：

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通过以给定速度移动的物体避开单个检测器

摘要

我们考虑规划物体在平面上以恒定速度移动的最佳路线的问题，试图逃避单个传感器的检测，目的是最小化到达观察者的有用信号的积分水平。结果表明，检测运动物体的各种机制可以简化为一般的数学形式化，即研究不同类型信号和小信噪比的检测问题。作为研究的结果，具有积分约束的两点变分问题的解被简化为三种类型的代数积分方程组的解，其中包括第一类和第二类正规椭圆Legendre积分，其中由各种初始条件和积分约束值确定的系统类型。