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index 65eb412..a6c463b 100644 --- a/docs/paper/main.tex +++ b/docs/paper/main.tex @@ -49,11 +49,10 @@ {\heiti\zihao{4} 摘\quad 要} \end{center} -无线电干扰源的测向与规划问题在生产和军事上的应用十分广泛。 -\texttt{no\_signal}、\texttt{near}、\texttt{direction} 为唯一信息来源,建立 -\textbf{有界误差交会定位—主动选点—覆盖证明搜索—动作耗时调度}的统一框架:四个问题 -复用同一几何内核,以覆盖证明与严格停止条件保证“清除所有干扰源”的硬约束,再优化 -时间指标。 +无线电干扰源的测向与路径规划问题在生产和军事上的应用十分广泛。城市的非法无线电 +台清查与战场的无线特征定位等日益增长的需求,与该问题的关联十分紧密。本文建立一种 +基于【此处填入方法】的无线电测向多元优化方法,以便特定用途的机器狗等设备在复杂环 +境中能够以更高效率完成无线电发射源测定、清除工作。 \textbf{针对问题~1},将 $\pm 1^{\circ}$ 有界误差下的测向观测建模为以检测点为顶点的 前向角域 $W_i$,交会定位区域即诸角域的半平面交 $P=\bigcap_i W_i$,给出直径 @@ -97,12 +96,73 @@ $N\le(\lceil w/20\rceil+2)(\lceil h/20\rceil+2)$,并纳入现实时间预算 % 正文(不超过 30 页,不要目录) % ============================================================ +\section{问题重述} + +\subsection{问题背景} + +无线电干扰源的定位与清除是无线电频谱管理的重要任务。干扰源定位通常分为 +初步监测、区域性排查和精准定位三个阶段:前两个阶段使用固定监测站、移动 +监测车或无人机等设备进行大范围信号采集与分析,确定干扰源目标的分布区域; +而受限于环境遮挡、低功率干扰源等因素,精准定位最终需要技术人员在目标 +分布区域内携带便携式无线电方位监测测向机(简称测向机)等手持设备徒步 +排查,通过观察分析信号场强变化、方向特征并结合经验判断,逐步定位并清除 +干扰源。为尽快消除干扰造成的不良影响,定位清除任务的完成时间越短越好。 +为此,某公司拟研发搭载于机器狗的干扰源自动定位清除系统,在危险环境中 +代替技术人员开展定位及清除工作,以提高定位及清除效率。 + +干扰源目标分布区域已被确定为一个半径为 $1800$ 米的圆形区域,取此圆域 +中心为坐标系原点,正东方向为 $x$ 轴正向,正北方向为 $y$ 轴正向(单位: +米),目标区域中干扰源个数未知。干扰源的特征由题目附录~1 给出:每个 +干扰源的频谱互不相同,分布于编号 $1$ 至 $20$ 的 $20$ 个频道;不同干扰源 +的信号互不影响;按信号覆盖角度范围分为全向干扰源(有效覆盖角度 +$360^{\circ}$)与定向干扰源(定向方向两侧各 $90^{\circ}$ 含边界,此角度 +范围之外没有信号辐射);在有效覆盖角度范围内信号均匀辐射,场强仅随距离 +衰减,与角度无关。 + +系统的检测原理和工作方式由题目附录~2 给出:测向机在检测点处测得干扰源 +的示向度(自 $x$ 轴正向逆时针计量,范围 $[0^{\circ},360^{\circ})$), +示向度与真实方位角之间的误差在 $[-1^{\circ},1^{\circ}]$ 范围内,且同一 +地点重复检测不会改变检测误差;各干扰源的有效接收半径在 $1000$ 至 $1500$ +米之间;测向机不能同时检测多个频道,任意两个频道之间的切换时间为 $1$ +秒;机器狗沿直线行进、移动速度为 $5$ 米/秒,移动过程中无法有效检测, +每次停机检测耗时 $5$ 秒;检测点距干扰源不超过 $20$ 米时可光学精确定位 +($3$ 秒)并启动激光枪清除($2$ 秒),清除成功与否仅与距离有关;距离 +不超过 $5$ 米时因信号太强无法获得示向度信息,此时可直接进行光学精确定位 +并清除。利用多个检测点对同一干扰源的示向度,可以采用交会定位法确定 +多边形定位区域。 + +问题~3、4 的算法须通过无线电干扰源环境模拟器进行测试:机器狗程序经 +HTTP+JSON 接口与模拟器通信,自动完成检测与清除。正式测试中机器狗从原点 +$(0,0)$ 出发、初始频道为 $1$,每次测试须按题目表~1 的格式记录测试案例 +编码、清除干扰源个数、平均定位清除时间与程序运行时间。 + +\subsection{问题提出} + +\textbf{问题~1}:已知若干个检测点坐标及某干扰源关于这些检测点的示向度, +给出采用交会定位法计算多边形定位区域直径(即区域内任意两点之间距离的 +最大值)的算法,并回答以定位区域直径为直径的圆能否覆盖该定位区域。 + +\textbf{问题~2}:已知某全向干扰源在一个检测点处测得的示向度,给出第二 +个检测点的选择策略,以获得关于该干扰源较好的定位效果,并给出第二个 +检测点的候选区域。 + +\textbf{问题~3}:目标区域中的干扰源均为全向干扰源,总数在 $10$--$16$ +个之间,但具体个数未知。现派出一只机器狗从原点出发,初始频道为 $1$, +对目标区域中的干扰源进行自动定位并清除。要求在确保所有干扰源被清除的 +前提下,完成任务的时间越短越好。请制定机器狗自动搜索、定位及清除的 +策略,设计相应的算法,通过模拟器进行演练测试,以被清除干扰源个数的 +比例和平均定位清除时间为统计值检验策略的有效性;在充分演练测试后, +再进行三次正式测试并按题目表~1 的格式给出结果。 + +\textbf{问题~4}:目标区域中既有全向干扰源,又有定向干扰源,总数仍在 +$10$--$16$ 个之间,但具体个数未知,定向干扰源的个数及定向方向也未知, +其他条件与问题~3 相同。请在此条件下给出检测与清除的策略及算法,通过 +模拟器进行演练测试以检验其有效性,并完成三次正式测试、按题目表~1 的 +格式给出结果。 + \section{问题分析} -四个问题构成一条递进的主线:问题~1 的交会定位几何是全部后续问题的基础;问题~2 在 -单次观测下研究“下一步去哪里测”的主动测量设计;问题~3、问题~4 则是在数量未知的 -条件下,把定位几何组织成“全域覆盖发现—逐个定位—清除—证明完成”的闭环调度问题。 -因此不必为每问单独建模,而是复用同一几何内核与观测更新机制。 +传统的无线电定位场景一般由单个人员携带设备,通过主观的经验判断在不同的地点进行模糊测向,最终以三角定位 \textbf{问题~1 的分析}。题面附录~2 第(1)项把测向误差限定在 $[-1^{\circ},1^{\circ}]$,且同一地点重复检测不改变误差:没有误差分布可利用、