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Probability model for early warning aircraft radar flight test based on probability of detection curve
WANG Han, MA Xiaobing , ZHAO Yu
School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:A novel probability model was proposed to ensure the coverage rate and the accuracy of probability of detection (POD) curve in early warning aircraft radar flight test, which can also provide the distance sampling intervals and boundary conditions of flight routes. Firstly, we derived the optimal number of sampling points used for curve-fitting after the test based on the requirements of the coverage rate and the accuracy of POD curve. Then, an algorithm was proposed based on the empirical distribution function of POD curve, which could calculate the minimum and maximum detection distance of early warning aircraft radar flight test. Simultaneously, the length of distance sampling intervals was obtained on the basis of the algorithm. Finally, we calculated the number of sampling points in distance sampling intervals and the number of flights according to the statistical properties of the detection probability. The proposed model provides a quantitative basis for the design of radar flight test and the performance evaluation of early warning.
Key words: radar flight test     probability of detection curve     distance sampling interval     sampling points     number of flights
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1 预警机雷达检飞场景

 图 1 预警机雷达检飞场景图 Fig. 1 Scenegraph of early warning aircraft radar flight test

 图 2 距离取样间隔示意图 Fig. 2 Schematic of distance sampling interval

2 POD曲线试验数据点的确定

 置信度/% 子样容量 p0=80% p0=85% p0=90% p0=95% p0=99% 90 17 24 37 76 387 95 21 29 45 93 472

3 POD曲线的覆盖范围

1) 确定两个探测距离r1r2.根据经验,r1发现概率的点估计设计在0.4~0.6区间,r2的发现概率的点估计设计在0.8~0.95区间.

2) 在规定的试验条件下,分别对这两个探测点进行检测,检测次数按照经验确定,得到对应的发现概率点估计pd1pd2:

3) 根据式(2),并考虑到距离r1r2对应的发现概率分别为pd1pd2,则参数μσ的估计值为

4 距离取样间隔的确定

 图 3 预警机雷达检飞航线示意图 Fig. 3 Flight route schematic graph of early warning aircraft radar flight test

5 采样点数的确定

n为距离取样间隔Δr内的采样点数,根据滑窗发现概率统计法[11],可得

n取正解,得到

 图 4 不同置信度时采样点数分布图 Fig. 4 Distribution graph of sampling points at different confidence levels

6 检飞架次数

7 模型结果及其分析

 图 5 对角线航路示意图 Fig. 5 Schematic graph of diagonal flight route

r0=440km,检飞试验中预警机速度VA=180 m/s,目标机速度VT=270m/s,预警机相对目标机的视线角φ=60°,雷达相邻两次采样间隔T=10s,由等φ飞行条件可得

VΤ=310km/s

 覆盖率/% 数据点数 距离取样间隔/km 飞行架次数 80 17 28.3 5 85 24 20.4 6 90 31 15.9 8 95 76 6.6 19

8 结 论

1) 基于POD曲线的覆盖率和精确性要求,给出了预警机雷达检飞试验最优数据点数及最小、最大探测距离等边界条件的计算方法,为检飞航线设计提供了理论依据.

2) 结合检飞试验中典型的对角线航路,给出不同置信度及不同精确性要求下距离取样间隔长度的计算方法.通过划分检飞航线解决了距离取样间隔的设定问题.

3) 根据滑窗发现概率统计法确定了距离取样间隔内的采样点数,进而得到航次数、飞行架次数等试验参数.基于POD曲线建立的检飞概率模型,有助于指导雷达检飞试验的开展.

#### 文章信息

WANG Han, MA Xiaobing, ZHAO Yu

Probability model for early warning aircraft radar flight test based on probability of detection curve

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(7): 1307-1312.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0536