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To address spectrum scarcity, complex airspace, and moving obstacles in large-scale low-altitude operations, a UAV decision framework that couples communication, control, surveillance, and trajectory are proposed. Two performance maps, Information Performance Map (IPM) and Surveillance Performance Map (SPM), are built to quantify control-link availability and radar reliability. A cumulative outage constraint ensures both flyability and controllability while three-dimensional point-cloud data are exploited to maximize the air-to-ground rate. A DQN (Deep Q-Network)-based algorithm is then introduced: point-cloud and CNN(Convolutional Neural Network) features are jointly processed to select the next waypoint and vehicle access in a discrete action space, with experience replay and a target network stabilizing training. After 8 000 training episodes, the UAV cruises efficiently through areas of robust control and radar coverage while avoiding blind spots, as rewards converge and losses stabilize. The proposed method offers a scalable solution that balances spectrum efficiency, safety, and regulation.

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面向低空经济规模化运行中频谱稀缺、空域复杂与动态障碍并存的安全挑战,本文提出了一种“通感—信控—监视—航迹”四元耦合的无人机(Unmanned Aerial Vehicle,UAV)自主决策框架。首先,构建城市低空基站的地空信控性能地图与雷达监视性能地图,分别量化控制链路的可用性与雷达探测的可靠性;通过引入累计中断约束,实现“可飞”与“可控”的双重安全闭环,并以UAV感知地面车辆三维点云数据作为实时先验信息,最大化空地数据传输速率。针对传统凸优化难以应对的不确定性动态场景,本文设计了基于深度Q网络的强化学习算法:利用点云深度网络与卷积网络并行提取环境特征,联合离散动作空间实时决策下一航迹点与车辆接入向量,并借助经验回放、固定目标网络与惩罚奖励机制,保障训练稳定性。仿真结果表明:所提方法在8 000轮训练后奖励收敛、损失稳定,UAV可在信控与监视强区内高效巡航,显著规避了信号盲区与雷达失捕区域。

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张智博 1994年生,博士,博士后。

常青 1962年生,博士,教授,博士生导师。

陈乐言 1994年生,博士。

邢进 1994年生,博士,讲师。

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journalId=1238841944844054536, articleId=1239165055275692135, language=CN, label=图4, caption=UAV轨迹和通信关联结果, figureFileSmall=rueA+wS+Vi9A7KB1HiT94g==, figureFileBig=NVVz7bGUADuNf9P6/nJUpA==, tableContent=null), ArticleFig(id=1239265688477552658, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165055275692135, language=EN, label=Table 1, caption=

Results comparison on community quantity

, figureFileSmall=null, figureFileBig=null, tableContent=
对比算法通信量(Kbit)
本文方法16.92
仅UAV轨迹优化11.58
仅车辆接入优化8.88
深度Q学习方法14.89
), ArticleFig(id=1239265688548855830, tenantId=1146029695717560320, journalId=1238841944844054536, articleId=1239165055275692135, language=CN, label=表1, caption=

通信量结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
对比算法通信量(Kbit)
本文方法16.92
仅UAV轨迹优化11.58
仅车辆接入优化8.88
深度Q学习方法14.89
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低空信控与监视下的无人机自主通感与航迹规划方法
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张智博 1, 2 , 常青 1 , 陈乐言 1 , 邢进 3
遥测遥控 | 导航技术专栏 2025,46(5): 20-27
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遥测遥控 | 导航技术专栏 2025, 46(5): 20-27
低空信控与监视下的无人机自主通感与航迹规划方法
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张智博1, 2, 常青1, 陈乐言1, 邢进3
作者信息
  • 1北京航空航天大学电子信息工程学院 北京 100191
  • 2空地一体新航行系统技术全国重点实验室 北京 100191
  • 3中国地质大学(北京)人工智能学院 北京 100083
  • 张智博 1994年生,博士,博士后。

    常青 1962年生,博士,教授,博士生导师。

    陈乐言 1994年生,博士。

    邢进 1994年生,博士,讲师。

Autonomous Communication-Sensing and Trajectory Planning Methods for UAV under Low-Altitude Information Control and Surveillance
Zhibo ZHANG1, 2, Qing CHANG1, Leyan CHEN1, Jin XING3
Affiliations
  • 1.School of Electronics and Information Engineering, Beihang University, Beijing 100191, China
  • 2.State Key Laboratory of CNS/ATM, Beijing 100191, China
  • 3.School of Artificial Intelligence, China University of Geosciences, Beijing 100083, China
出版时间: 2025-09-15 doi: 10.12347/j.ycyk.20250729001
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面向低空经济规模化运行中频谱稀缺、空域复杂与动态障碍并存的安全挑战,本文提出了一种“通感—信控—监视—航迹”四元耦合的无人机(Unmanned Aerial Vehicle,UAV)自主决策框架。首先,构建城市低空基站的地空信控性能地图与雷达监视性能地图,分别量化控制链路的可用性与雷达探测的可靠性;通过引入累计中断约束,实现“可飞”与“可控”的双重安全闭环,并以UAV感知地面车辆三维点云数据作为实时先验信息,最大化空地数据传输速率。针对传统凸优化难以应对的不确定性动态场景,本文设计了基于深度Q网络的强化学习算法:利用点云深度网络与卷积网络并行提取环境特征,联合离散动作空间实时决策下一航迹点与车辆接入向量,并借助经验回放、固定目标网络与惩罚奖励机制,保障训练稳定性。仿真结果表明:所提方法在8 000轮训练后奖励收敛、损失稳定,UAV可在信控与监视强区内高效巡航,显著规避了信号盲区与雷达失捕区域。

无人机  /  航迹规划  /  通感一体化  /  三维点云  /  强化学习  /  低空经济  /  频谱稀缺  /  深度Q网络

To address spectrum scarcity, complex airspace, and moving obstacles in large-scale low-altitude operations, a UAV decision framework that couples communication, control, surveillance, and trajectory are proposed. Two performance maps, Information Performance Map (IPM) and Surveillance Performance Map (SPM), are built to quantify control-link availability and radar reliability. A cumulative outage constraint ensures both flyability and controllability while three-dimensional point-cloud data are exploited to maximize the air-to-ground rate. A DQN (Deep Q-Network)-based algorithm is then introduced: point-cloud and CNN(Convolutional Neural Network) features are jointly processed to select the next waypoint and vehicle access in a discrete action space, with experience replay and a target network stabilizing training. After 8 000 training episodes, the UAV cruises efficiently through areas of robust control and radar coverage while avoiding blind spots, as rewards converge and losses stabilize. The proposed method offers a scalable solution that balances spectrum efficiency, safety, and regulation.

UAV  /  Trajectory planning  /  Integrated sensing and communication  /  Three-dimensional point-cloud  /  Reinforcement learning  /  Low-altitude economy  /  Spectrum scarcity  /  Deep Q-Network
张智博, 常青, 陈乐言, 邢进. 低空信控与监视下的无人机自主通感与航迹规划方法. 遥测遥控, 2025 , 46 (5) : 20 -27 . DOI: 10.12347/j.ycyk.20250729001
Zhibo ZHANG, Qing CHANG, Leyan CHEN, Jin XING. Autonomous Communication-Sensing and Trajectory Planning Methods for UAV under Low-Altitude Information Control and Surveillance[J]. Journal of Telemetry, Tracking and Command, 2025 , 46 (5) : 20 -27 . DOI: 10.12347/j.ycyk.20250729001
党的二十届三中全会指出“发展通用航空和低空经济”,在政策引导和技术创新的双重推动下,低空经济正快速崛起成为万亿级的产业新赛道,成为新质生产力的典型代表之一[1]。深圳-珠海跨海物流航线[2]、广州“空中出租车”示范航线[3]的常态化运营,标志着低空交通与物流已从实验走向商业闭环。然而,频谱稀缺、空域复杂、动态障碍三大瓶颈同步凸显,成为低空经济安全有序运行的重要威胁:一方面,海量低空飞行器对6 GHz以下频段提出近乎“无限”的带宽需求[48];另一方面,城市峡谷、临时起降点、突发风切变使传统“先感知后通信”的割裂模式难以满足毫秒级避障与高效通信的双重目标要求[912]
在这一背景下,通信感知一体化(Integrated Sensing and Communication,ISAC)成为潜在的重要技术之一[1315],其核心思想是在同一平台上深度融合通信与感知,利用无线信号的探测能力,在传递业务数据的同时主动获取信道、障碍物及目标信息,实现资源、能量与信息的三维共享。当ISAC技术下沉到无人机(Unmanned Aerial Vehicle,UAV)平台,便形成了空地协同UAV-ISAC系统。UAV凭借其三维机动性优势,更好地赋予了通信信号在传播过程的探测能力,其信号回波同时被实时用于信道估计与航迹修正,形成“发-收-算-控”毫秒闭环,为低空经济提供了可扩展的频谱与感知供给。
围绕该系统的资源优化与航迹规划,国内外已展开深入研究。北京邮电大学陈文韵研究了UAV系统的ISAC方法,构建了UAV系统的位置感知性能理论分析框架,提出可达性能界的位置感知算法,证明了基于UAV的轨迹规划提升了对目标位置感知的性能[16];北京邮电大学吴韵怡等面向6G智能协作感知,提出多UAV组网架构与性能评估方法,指出“感知-通信-计算”资源联合优化与可信协同决策是下一阶段关键,通过波束跟踪算法能显著提升波束跟踪精度与通信性能[17];哈尔滨工业大学时统志等针对应急场景,设计自适应多UAV覆盖机制,改进的人工蜂群聚类算法与传统聚类部署方法对比,显著提升了用户传输速率并验证通感需求[18]。在国际前沿,文献[19]构建UAV支撑的ISAC下行链路,协同设计UAV航迹与用户关联,在克拉美罗界约束下,利用逐次凸近似迭代算法灵活满足“感知优先”或“通信优先”需求,实现了系统性能的高效调配;文献[20]探讨了UAV-ISAC框架,将UAV同时配置为通信基站与雷达节点,通过同一波形完成信息传输与目标定位,仿真证实:相比仅具单一功能的UAV系统,该一体化方案在通信-感知折中效率与能耗控制上均取得了更优表现;文献[21]将UAV视为移动ISAC空中平台,针对对地感知与通信并存场景,联合优化用户接入、轨迹及功率以最大化最小加权频谱效率,作者提出集中式与分布式深度强化学习算法,并辅以随机/自适应数据增强机制,实验显示两种方案在训练收敛速度与频谱效率上均显著领先。
随着应用场景日益复杂,传统凸优化与启发式算法在动态环境、高维决策空间面前渐显乏力。北京科技大学张燕霞等提出联邦Q学习框架,联合优化发射功率与飞行轨迹,在能耗约束下最大化雷达感知与通信互信息[22];桑万超等[23]提出感知信息驱动的通感融合波形选择机制,先验辅助Q-Learning(Q学习)显著降低信令开销;文献[24]将三维部署与漫游用户场景建模为马尔科夫决策过程,强化学习在数据速率与波束增益间取得帕累托前沿;文献[25]针对非正交多址接入下行提出深度确定性策略梯度算法,解决非凸速率最大化问题;文献[26]综合考虑吞吐量、感知精度与速率,以深度强化学习实现轨迹控制与任务调度的自适应协同。
由于低空域开放高度有限、障碍物密集且电磁环境复杂,为平衡低空运行的效率和安全,UAV必须在“可飞”与“可控”之间取得平衡:一方面,信息管控系统需对UAV身份、遥控链路、任务载荷及实时位置进行可信注册与动态鉴权[27],防止恶意入侵与数据泄露;另一方面,地面监视网络(雷达、广播式自动相关监视、光学/红外复合传感器等)需提供高精度、低延迟的航迹监视数据,以支持冲突探测与避障决策[28]。因此,在航迹规划阶段就融合信息管控的安全约束和地面监视的感知能力,已成为保障低空UAV规模化运行的核心需求。无线电地图通过刻画城市无线信道的空间分布,为UAV提供“信号盲区”的实时感知能力,使其能动态重规划航迹,维持最优的覆盖与链路质量[29];文献[30]提出一种环境驱动的混合波束赋形框架,以无线电地图为轻量训练先验,在提升传输速率的同时显著压缩计算负担,优化了UAV网络的性能。此外,针对城市低空的动态监视覆盖[31],如基于雷达信号的回波信噪比,也可以构成监视性能地图,实时表征对低空空域的可靠感知能力。综上,本文提出一种将信息管控策略与地面监视数据内嵌于航迹规划框架的方法,通过构建“通感-信控-监视-航迹”四元耦合模型,实现UAV任务效率、空域安全与监管合规性的协同优化。
低空基础设施主要包括地面通信基站和地面低空监视雷达两类:地面第五代移动通信(Fifth Generation,5G)基站通过对低空空域的无线通信信号覆盖,完成与装备了如5G无线通信模块UAV的控制信令传输,实现地空信控;地面低空监视雷达通过发射如X波段感知信号并通过雷达接收机接收低空UAV的目标反射回波信号,完成对低空UAV的位置、速度探测,实现地空监视。因此,城市低空UAV运行面临两大相互独立的失效风险:与地面通信基站之间的控制链路中断,以及地面低空监视雷达对其回波的失检。为在同一空域内同时克服这两类风险,本文提出一套双层地图体系,分别对通信能力与雷达探测能力进行量化,刻画低空基础设施对UAV的信控和监视性能,并据此建立航迹约束。
信控性能地图(Information Performance Map, IPM)以三维位置u为索引,预测该点的下行控制信道容量
其中Bc为控制信道带宽,PB为地面基站发射功率,h(u)为综合路径损耗、阴影与小尺度衰落的信道增益,Pn为UAV端噪声功率。为保证链路连续性,定义第n时刻的通信中断指示
并施加累计约束
以确保在任意长度为Nc的帧窗内最多出现Nc-1次控制链路丢失。
监视性能地图(Surveillance Performance Map, SPM)用于刻画雷达对UAV的感知探测能力。考虑单基地脉冲雷达,位置u处的回波信噪比记为
其中Pt为发射功率,G为天线增益,λ为波长,σ为UAV在特定姿态与频率下的雷达截面积,R(u)为雷达到UAV的斜距,kBT0B为雷达接收机噪声功率,F为雷达接收机噪声系数,L为系统损耗。定义对UAV的雷达监视中断指示
并施加累计约束
以保证在任意长度为Ns的帧窗内至多出现Ns-1次雷达失捕。
针对低空UAV的航迹规划需要同时满足上述累计通信与监视中断约束式(3)和式(6),实现城市低空运行的信控与监视双重安全闭环。
本文面向低空无人机(UAV)为地面车辆提供空地数据卸载的典型场景,旨在通过提升机载感知能力来优化航迹规划与通信效率。受大疆Matrice 400搭载高精度毫米波雷达以及美团第四代UAV集成四维毫米波雷达的启发,本文在UAV端同步部署毫米波雷达,以实现对地面车辆的高精度定位与三维点云实时获取,该先验信息进一步用于UAV航迹的在线优化。空地链路方面,UAV与地面车辆均配备2.4 GHz无线通信模块,保障业务数据的低时延、高可靠传输。
在机载毫米波雷达信号处理流程中,回波首先经过匹配滤波、恒虚警检测与监测点聚类,最终每帧仅保留散射强度最大的Np[n]≤Nmax个散射中心。在每个离散时刻n,记全部地面车辆中的第j个散射点的三维坐标为
而UAV保持固定高度h悬停或匀速巡航,记其三维坐标为
两者间的瞬时欧氏距离为
相对位置向量表示为
从而,可以计算出空地感知的俯仰角和方位角
为降低存储与计算开销,仅保留点云(Point Cloud,PC)的空间几何信息,第n帧UAV对地感知的点云集合可表示为
完成空地感知后,UAV立即进入空地数据卸载阶段。为刻画城市中由于随机遮挡出现的视距(Line of Sight,LoS)传输与非视距(Non-LoS,NLoS)传输情况,引入二元状态变量
其发生概率由UAV和车辆的俯仰角θk[n]决定
从而可以将空地通信路径损耗表示为
其中,ς0为固定路径损耗,ΔNLoS为额外的穿透损耗,αLoSαNLoS为超参数。接收端的平均信噪比即为
其中,P0为UAV通信信号发射功率,Bk为第k辆车的接收机带宽。
进而得到第k辆车的期望容量
该表达式将UAV与车辆距离、俯仰角以及LoS、NLoS概率统一纳入平均吞吐量的闭合形式,为后续轨迹-带宽联合优化提供了解析化的优化目标。
考虑在低空信控与监视下,共N个时刻内的UAV自主通感与航迹规划问题,时刻间隔为Δt。采用二元变量ak[n]∈{0,1}表示在每个时刻UAV与地面车辆的通信连接情况,则基于UAV在每个时刻对地感知得到的车辆三维点云集合,可以得到最大化全部N辆车总的期望空地通信容量的优化问题
其中,u0代表UAV的起始位置,Vmax代表UAV的最大飞行速度,[xmin,xmax,ymin,ymax]代表UAV的运行区域。因此,优化问题中的前两个约束条件表示UAV的有效运行区域,第三个约束条件表示UAV的最大运行速度,第四个约束条件表示UAV的起始位置,第五个约束条件表示UAV的空地信道选择约束,最后两个约束条件分别表示UAV位置满足基站地空信控和基站地空监视约束。
上述优化问题结合基站地空信控模型、基站地空监视模型两张性能地图,并实时利用UAV的空地感知信息,针对全部时刻的UAV飞行航迹和通信用户选择进行优化。由于实际场景中基站地空信控和监视地图可能发生变化,同时UAV空地感知点云集合也具有时变特性,优化问题(式(19))难以基于传统的凸优化方法求解。
为解决低空信控和监视下UAV自主通感与航迹联合优化问题(式(19)),本文提出了一种基于深度强化学习技术的方法。深度Q网络(Deep Q-Network,DQN)是在高维状态空间与离散动作空间场景下实现稳定收敛的深度强化学习算法之一,其在不依赖精确环境模型的情况下,使得智能体学习到近似最优的马尔可夫决策策略。具体而言,智能体采用基于神经网络参数化逼近的方法,能够直接将原始传感器观测映射到各离散UAV机动和通信接入选择等动作的长期回报估值,如图1所示。为保证训练过程的数值稳定性和样本效率,DQN方法引入了三大关键技术:其一,经验回放机制(experience replay),将智能体与环境交互产生的转移样本缓存至回放缓冲区,并在每次参数更新时随机抽取小批量数据,有效打破时间相关性并提高样本复用率;其二,固定目标网络(target network),通过周期性复制主网络参数生成目标Q网络,以缓解自举误差与策略漂移导致的非平稳问题;其三,探索策略(ε-greedy),在训练早期以较高概率随机探索动作空间,随后逐步衰减ε值以平衡探索与利用过程。
在每个决策时隙将UAV实时采集的三维点云与基站下发的信控性能地图C(u)、监视性能地图S(u)统一编码为环境状态,并采用离散的动作空间联合优化UAV的下一航迹点与车辆接入向量。针对每一个输入的状态量的特点,即是点云形式、C(u)和S(u)是矩阵形式,分别利用点云深度网络和卷积深度网络将输入状态处理为特征向量gPC[n]和gPM[n]。其中,点云深度网络对无序三维点集执行共享多层感知机(MLP,Multi-Layer Perceptron)的点态变换,随后通过最大池化实现置换不变的全局聚合
卷积深度网络则在规则二维格点上采用滑动卷积核,逐层提取局部空间特征并生成层级化的特征图,其权值共享机制有效保留平移等变性并显著降低参数量。网络将C(u)与S(u)沿通道维堆叠为张量,通过两层二维卷积后展平:
随后,采用特征拼接的方法,将点云深度网络和卷积深度网络输出的特征向量拼接在一起,形成当前时刻感知的深度特征向量
动作a[n]完全离散,定义为
其中表示UAV在最大速度范围内可行点的集合,{0,1}K表示全部车辆形成的通信连接情况集合。
离散动作值函数由三层全连接Q网络给出:
奖励函数依据最大化通信容量设计,并以惩罚项的形式考虑通信与监视中断约束(式(3)和式(6))
式中,为示性函数,分别表示长度为NcNs的帧窗内通信与监视约束满足的可行域,λIλS分别表示基站地空信控和基站地空监视的惩罚权重。
智能体的训练采用优先级经验回放,损失函数为Bellman(贝尔曼)误差:
目标网络参数θ-通过软更新θ-τθ+(1-τ)θ-保持稳定性。经过迭代式最小化时序差分误差,网络参数逐渐收敛至近似最优的Q函数,进而支持在低空信控与监视下的UAV的自主通感与航迹规划。
本节通过仿真实验对所提出的UAV自主通感与航迹规划算法进行了全面评估。假定在城市路口车辆交汇的场景下,无人机在地面5G通信基站和地面X波段低空监视雷达的保障下,基于2.4 GHz通信链路完成空地数据卸载,设定UAV在边长为100 m的区域中运行,高度为30 m,地面两辆速度不同的车辆交叉而行,速度分别为10 m/s和7 m/s,同时设定IPM和SPM具有不同的信号较强区域。
仿真实验中相关的超参数设置如下:回放缓冲区的容量为8 000,探索概率ε从初始值0.95线性递减至0.1,折扣因子设置为0.9,神经网络学习率设置为0.95,目标网络每1 000步更新一次,采用的批训练维度为16。
在训练过程中,设置每轮包含100个时隙,共训练8 000轮。图2图3分别展示了归一化的训练奖励曲线和归一化的网络损失值曲线。随着训练次数的增加,训练奖励和评估奖励曲线均呈现上升趋势并最终收敛,表明智能体通过学习和经验回放,逐步形成了自主运行和控制的能力。同时,网络的平均损失值逐渐下降并趋于稳定,证明了智能体网络的收敛性和稳定性。
UAV和地面车辆的轨迹与通信关联的结果如图4所示,UAV的飞行轨迹主要集中在信控性能地图和监视性能地图中的较强性能区域内活动,以确保基站对UAV的可靠信息控制和监视,从而支撑通信任务完成。实验结果表明:所提出的深度强化学习算法能够根据实时环境信息动态调整UAV的飞行路径和车辆关联策略,从而在复杂场景下实现高效的任务执行。此外,UAV的轨迹避开了控制信号弱区和潜在监视盲区,在确保低空运行安全的前提下提升了系统的通信效率。
最后,将所提出的算法与下面的基线算法进行对比,包括仅优化UAV轨迹、仅优化用户接入、基于深度Q学习的方法,所实现的通信量如表1所示。可以看出,相比于其他基线算法,本文提出的自主通感与航迹规划方法实现了最佳的性能,相比仅仅UAV轨迹优化提升约46%,相比仅车辆接入优化提升约91%,相比深度Q学习方法提升约14%。
本文针对面向低空经济规模化运行中频谱稀缺、空域复杂与动态障碍并存的安全瓶颈,构建了“通感-信控-监视-航迹”四元耦合框架:以信控/监视性能地图显式刻画控制链路与雷达探测可靠性,将机载毫米波点云与地面车辆信道状态联合建模,提出了基于深度Q网络的强化学习算法,在离散动作空间中同步优化UAV航迹与车辆接入以提升空地通信的效率。仿真结果表明:经过模型训练后,智能体收敛稳健,UAV始终航行于高信控、高监视区域且通信量较基线算法有显著提升,研究为低空规模化运行提供了兼顾效率、安全与合规的一体化技术路径。下一步研究将聚焦于低空信控与监视下,多多UAV协同运行场景中的UAV自主通感与航迹规划问题。
  • 国家自然科学基金(62401032)
  • 国家资助博士后研究人员计划(GZC20242161)
  • 北航基科费项目(501XYGG2025102009)
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2025年第46卷第5期
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doi: 10.12347/j.ycyk.20250729001
  • 接收时间:2025-07-29
  • 首发时间:2026-03-13
  • 出版时间:2025-09-15
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  • 收稿日期:2025-07-29
  • 修回日期:2025-08-07
基金
国家自然科学基金(62401032)
国家资助博士后研究人员计划(GZC20242161)
北航基科费项目(501XYGG2025102009)
作者信息
    1北京航空航天大学电子信息工程学院 北京 100191
    2空地一体新航行系统技术全国重点实验室 北京 100191
    3中国地质大学(北京)人工智能学院 北京 100083
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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