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基于有限新息率的非瞬时扩散点源参数估计方法

付宁 沈孟垚 尉志良 乔立岩

付宁, 沈孟垚, 尉志良, 乔立岩. 基于有限新息率的非瞬时扩散点源参数估计方法[J]. 电子与信息学报, 2022, 44(8): 2739-2748. doi: 10.11999/JEIT210540
引用本文: 付宁, 沈孟垚, 尉志良, 乔立岩. 基于有限新息率的非瞬时扩散点源参数估计方法[J]. 电子与信息学报, 2022, 44(8): 2739-2748. doi: 10.11999/JEIT210540
FU Ning, SHEN Mengyao, WEI Zhiliang, QIAO Liyan. A Parameter Estimation Method of Non-instantaneous Diffusion Point Source Based on Finite Rate of Innovation[J]. Journal of Electronics & Information Technology, 2022, 44(8): 2739-2748. doi: 10.11999/JEIT210540
Citation: FU Ning, SHEN Mengyao, WEI Zhiliang, QIAO Liyan. A Parameter Estimation Method of Non-instantaneous Diffusion Point Source Based on Finite Rate of Innovation[J]. Journal of Electronics & Information Technology, 2022, 44(8): 2739-2748. doi: 10.11999/JEIT210540

基于有限新息率的非瞬时扩散点源参数估计方法

doi: 10.11999/JEIT210540
基金项目: 国家自然科学基金(62071149, 61671177)
详细信息
    作者简介:

    付宁:男,1979年生,教授,博士生导师,研究方向为信息域采样理论及技术、稀疏信号处理及压缩感知、智能信号处理、虚拟仪器技术、自动测试技术等

    沈孟垚:女,1997年生,硕士,研究方向为有限新息率采样理论、扩散源参数估计

    尉志良:男,1994年生,博士生,研究方向为欠奈奎斯特采样、有限新息率采样理论

    乔立岩:男,1973年生,教授,博士生导师,研究方向为数据采集技术、大容量数据记录技术和测试信息处理等

    通讯作者:

    付宁 funinghit@163.com

  • 中图分类号: TN911.7

A Parameter Estimation Method of Non-instantaneous Diffusion Point Source Based on Finite Rate of Innovation

Funds: The National Natural Science Foundation of China (62071149, 61671177)
  • 摘要: 扩散现象在农业真菌传播、大气污染等现实场景广泛存在,扩散源参数估计也因此在农业、工业等实际应用中具有重要意义。目前针对扩散源参数估计提出的方法大多针对理想的瞬时点源信号,对于非瞬时的实际扩散过程存在模型失配问题,极大地限制了算法的实际应用场景。为了解决模型不匹配的问题,同时有效估计扩散源持续时间参数,该文将扩散源信号模型拓展为脉宽可变信号,并提出相应的非瞬时点源模型的参数估计算法。该算法中,利用无线传感网络采样得到实际测量值,找到一个组合系数将实际测量值线性组合为指数函数,再根据有限新息率(FRI)采样理论对组合后的数据用零化滤波器方法求解扩散源参数。仿真结果表明,在信噪比20 dB,位置参数重构MAE能够达到0.008左右,脉宽参数能够达到0.1左右,持续时间参数能够达到0.05左右,这验证了非瞬时点源参数估计的准确性。同时我们分析了传感器个数等因素对参数恢复性能的影响。
  • 图  1  VPW脉冲时域波形

    图  2  位置恢复结果

    图  3  MAE与SNR的变化关系

    图  4  传感器密度与参数恢复误差

    图  5  非瞬时时间函数

    图  6  瞬时点源模型与本文点源模型恢复误差对比

    表  1  非理想时间脉冲扩散点源参数估计过程

     输入:传感器位置${{\boldsymbol{x}}_n}$,采样时刻${t_l}$,传感器采样值$ {\varphi _n}({t_l}) $,扩散
        系数$\mu $,脉冲个数K,采样时长T
     输出:位置参数${\boldsymbol{\xi}}$,时延参数,脉宽参数,幅度参数。
     (1) 根据式(40)计算当$ r = 0 $时的组合加权系数
       $\{ {w_{{\boldsymbol{n}},l} }({\boldsymbol{k} },0)\} _{ {\boldsymbol{k} } = (0,0)}^{({K_1},{K_2})}$。
     (2) 根据式(28)对采样值进行组合,得到$\hat Q({\boldsymbol{k}},0)$。
     (3) 利用2维谱估计算法得到($ {\xi _1},{\xi _2} $)。
     (4) 根据式(40)计算当$ {k_1} = 0 $, $ {k_2} = 1 $时的加权系数
       $\{ {w_{{\boldsymbol{n}},l} }(k,r)\} _{r = 0}^{2K + 1}$。
     (5) 根据式(28)对采样值进行组合,得到$\hat Q({\boldsymbol{k}},r)$。
     (6) 根据式(26)与式(27)获取傅里叶系数$ H(r) $。
     (7) 利用改进的零化滤波器恢复时延,脉宽和幅度参数。
    下载: 导出CSV

    表  2  参数设置及恢复结果

    实验组参数真实值估计均值估计值方差
    脉宽$ {r_k} $(1.0000, 1.0000)(0.9171, 1.0102)(0.0018, 0.0028)
    第1组时延$ {t_k} $(3.0000, 7.0000)(2.9996, 7.1626)(5.9602$ \times $10–4, 9.7505$ \times $10–4)
    幅度$ {c_k} $(5.0000, 5.0000)(6.4175, 4.6885)(0.7995, 0.8620)
    脉宽$ {r_k} $(0.8000, 0.8000)(0.7122, 0.7689)(7.4302$ \times $10–4, 7.1916$ \times $10–4)
    第2组时延$ {t_k} $(4.0000, 7.0000)(4.0159, 7.0212)(2.8550$ \times $10–4, 3.3058$ \times $10–4)
    幅度$ {c_k} $(4.0000, 4.0000)(4.6386, 4.0244)(0.1670, 0.1475)
    脉宽$ {r_k} $(0.9000, 0.9000)(0.7965, 0.8395)(8.3376$ \times $10–4, 0.0011)
    第3组时延$ {t_k} $(2.0000, 7.0000)(1.9525, 7.1132)(8.0755$ \times $10–4, 5.3718$ \times $10–4)
    幅度$ {c_k} $(5.0000, 5.0000)(5.2004, 4.7983)(0.0901, 0.1080)
    下载: 导出CSV

    表  3  参数估计结果

    实验组参数真实值瞬时点源模型估计值瞬时点源估计方差本文点源模型估计值本文点源估计方差
    第1组时延2.00001.54976.5657$ \times $10–72.00552.6604$ \times $10–5
    幅值398.8178560.829384.2846405.411331.8795
    第2组时延7.00006.54751.7676$ \times $10–66.99881.5820$ \times $10–5
    幅值159.5271222.794411.8788158.62286.1016
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-08
  • 修回日期:  2022-03-10
  • 录用日期:  2022-03-31
  • 网络出版日期:  2022-04-08
  • 刊出日期:  2022-08-17

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