随机恒速运动目标的搜索方程及持续探测概率

根据目标位置的初始分布和速度分布,给出了随机恒速运动目标在任意时刻位置和速度分布密度函数。定义了探测函数、目标存在和探测不成功的联合概率密度函数和目标存活概率函数,建立了基于目标速度分布的搜索方程并给出了其特征迹线解。在目标初始分布和速度分布均为圆正态分布条件下,分析了搜索方程特征迹线的基本特征和持续探测发现概率积分域的形态。给出了一个以直升机吊放声纳探测潜艇为背景的持续探测发现概率的算例,算例表明,对随机恒速运动目标持续探测的发现概率,与对静止目标进行持续探测的发现概率相似,服从时间的指数规律。

Search Equation of Moving Target with Random Constant Velocityand the Probability of Persistence Detecting

According to the target distribution density functions of initial location and velocity, the distribution density function of moving target with a random constant velocity at any time was given. Defined the detection function, the joint probability density function of target existence and unsuccessful detection, and the survival probability function, the search equation based on the velocity distribution density function was established, then its trace solution was obtained. Under the condition of target distribution of initial location and velocity were both circular normal distribution, the basic characteristics of the trace of search equation and the integral domains of the probability with persistence detecting was analysed. A computing example of persistence detecting probability based on detect a submarine with helicopter dipping sonar was given. The simulation results showed that the discovery probability detecting a random moving target, similarly with a stationary target, was an index function of time.