异常值个数未知下辅助数据自适应筛选方法

简涛 马颖亮 王海鹏 郭磊 魏广芬

简涛, 马颖亮, 王海鹏, 等. 异常值个数未知下辅助数据自适应筛选方法[J]. 雷达学报(中英文), 2024, 13(5): 1049–1060. doi: 10.12000/JR24135
引用本文: 简涛, 马颖亮, 王海鹏, 等. 异常值个数未知下辅助数据自适应筛选方法[J]. 雷达学报(中英文), 2024, 13(5): 1049–1060. doi: 10.12000/JR24135
JIAN Tao, MA Yingliang, WANG Haipeng, et al. Adaptive screening approach of training data with an unknown number of outliers[J]. Journal of Radars, 2024, 13(5): 1049–1060. doi: 10.12000/JR24135
Citation: JIAN Tao, MA Yingliang, WANG Haipeng, et al. Adaptive screening approach of training data with an unknown number of outliers[J]. Journal of Radars, 2024, 13(5): 1049–1060. doi: 10.12000/JR24135

异常值个数未知下辅助数据自适应筛选方法

DOI: 10.12000/JR24135 CSTR: 32380.14.JR24135
基金项目: 国家自然科学基金(62471483, 61971432),泰山学者工程专项经费资助(tsqn201909156),山东省高等学校青创科技支持计划( 2019KJN031)
详细信息
    作者简介:

    简 涛,博士,教授,主要研究方向为雷达目标自适应检测

    马颖亮,硕士生,主要研究方向为雷达目标自适应检测

    王海鹏,博士,教授,主要研究方向为智能感知与融合、大数据技术与应用

    郭 磊,硕士,工程师,主要研究方向为雷达目标自适应检测

    魏广芬,博士,教授,主要研究方向为智能信息与信息处理技术及应用

    通讯作者:

    简涛 work_jt@163.com

  • 责任主编:高永婵 Corresponding Editor: GAO Yongchan
  • 中图分类号: TN958

Adaptive Screening Approach of Training Data with an Unknown Number of Outliers

Funds: The National Natural Science Foundation of China (62471483, 61971432), Taishan Scholars Project Special Funding (tsqn201909156), Shandong Provincial Youth Innovation Science and Technology Support Program for Colleges and Universities (2019KJN031)
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  • 摘要: 在雷达目标多通道自适应检测场景下,诸多非均匀背景因素易导致异常值干扰,使得辅助数据独立同分布条件难以满足,已有辅助数据筛选方法往往假定异常值个数已知,在个数未知的情况下面临较大性能损失。为此,该文研究了异常值个数未知情况下辅助数据自适应筛选方法。首先,在杂噪协方差矩阵已知条件下,建立了异常数据集合的最大似然估计,基于广义内积对辅助数据进行初步排序,将异常数据集合的最大似然估计过程简化为异常值个数估计。其次,利用快速最大似然方法进行未知协方差矩阵估计,提出了未知异常值个数下辅助数据自适应筛选方法。进一步地,为降低异常值对初步排序性能的不利干扰,基于归一化采样协方差矩阵设计了归一化广义内积形式,并结合迭代估计方式,对前述辅助数据自适应筛选流程进行改进。仿真结果表明,与广义内积相比,采用归一化广义内积可获得更高的筛选精度,采用较小迭代次数即可获得稳定的归一化信干比改善;与已有辅助数据筛选方法相比,该文所提方法在异常值个数未知条件下具有更好的筛选性能。

     

  • 图  1  RAC-NGIP与RAC-GIP方法${P_{\mathrm{r}}}$和NSIR随t的变化曲线($N = 8,{\text{ }}R = 12,{\text{ }}m = 4,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  1.  ${P_{\mathrm{r}}}$ and NSIR versus t of the RAC-NGIP and RAC-GIP with $N = 8,{\text{ }}R = 12,{\text{ }}m = 4,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  2  不同自适应筛选方法${P_{\mathrm{r}}}$和NSIR随R的变化曲线($N = 8,{\text{ }}m = 4,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  2.  ${P_{\mathrm{r}}}$ and NSIR versus R of different methods with $N = 8,{\text{ }}m = 4,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  3  不同自适应筛选方法${P_{\mathrm{r}}}$和NSIR随N的变化曲线($R = 12,{\text{ }}m = 4,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  3.  ${P_{\mathrm{r}}}$ and NSIR versus N of different methods with $R = 12,{\text{ }}m = 4,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  4  不同自适应筛选方法${P_{\mathrm{r}}}$和NSIR随m的变化曲线($N = 8,{\text{ }}R = 14,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  4.  ${P_{\mathrm{r}}}$ and NSIR versus m of different methods with $N = 8,{\text{ }}R = 14,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  5  当${m_0} < m$时,不同筛选方法${P_{\mathrm{r}}}$和NSIR随R的变化曲线($N = 8,{\text{ }}m = 4,{\text{ }}{m_0} = 3,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  5.  ${P_{\mathrm{r}}}$ and NSIR versus R of different methods for ${m_0} < m$ with $N = 8,{\text{ }}m = 4,{\text{ }}{m_0} = 3,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  6  当${m_0} = m$时,不同筛选方法${P_{\mathrm{r}}}$和NSIR随R的变化曲线($N = 8,{\text{ }}m = 4,{\text{ }}{m_0} = 4,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  6.  ${P_{\mathrm{r}}}$ and NSIR versus R of different methods for ${m_0} = m$ with $N = 8,{\text{ }}m = 4,{\text{ }}{m_0} = 4,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  7  当${m_0} > m$时,不同筛选方法${P_{\mathrm{r}}}$和NSIR随R的变化曲线($N = 8,{\text{ }}m = 4,{\text{ }}{m_0} = 5,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  7.  ${P_{\mathrm{r}}}$ and NSIR versus R of different methods for ${m_0} > m$ with $N = 8,{\text{ }}m = 4,{\text{ }}{m_0} = 5,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    图  8  当${m_0} = m$时,不同筛选方法${P_{\mathrm{r}}}$和NSIR随m的变化曲线($N = 8,{\text{ }}R = 14,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$)

    Figure  8.  ${P_{\mathrm{r}}}$ and NSIR versus m of different methods for ${m_0} = m$ with $N = 8,{\text{ }}R = 14,{\text{ }}T = 2,{\text{ }}{\mathrm{CNR}} = 10\;{\mathrm{dB}},{\text{ }}{\mathrm{ONR}} = 20\;{\mathrm{dB}}$

    1  RAC-NGIP方法

    1.   RAC-NGIP method

     输入:$N \times R$维辅助数据Z,最大迭代次数T
     输出:异常数据集合$ {\hat \varOmega _0} $
     1: $t = 1$
     2: $ \hat {\boldsymbol{M}}_{{\mathrm{N}}0}^{(1)} \leftarrow $式(19)
     3: FOR $i = 1:R$
     4:   $ \omega _i^{(t)} \leftarrow $式(20)
     5: END
     6: 对$ \omega _i^{(t)} $从大到小排序,提取索引序列$\{ (1),(2), \cdots ,(R)\} $
     7: FOR ${m_p} = 1:R$
     8:  $ {\hat \varOmega _p} = \{ (1),(2), \cdots ,({m_p})\} $
     9:  $ \varOmega - {\hat \varOmega _p} = \{ ({m_p} + 1),({m_p} + 2), \cdots ,(R)\} $
     10: $ {\hat {\boldsymbol{S}}_{p1}} $, $ {\hat {\boldsymbol{S}}_{p2}} \leftarrow $式(8)
     11: $ {{\boldsymbol{M}}_{{\mathrm{S}}1}} $, $ {{\boldsymbol{M}}_{{\mathrm{S}}2}} \leftarrow $式(12)
     12: $ {\hat {\boldsymbol{M}}_{p1}} $, $ {\hat {\boldsymbol{M}}_{p2}} \leftarrow $式(14)
     13: $ f\left({\boldsymbol{Z}}\left| {{{\hat {\boldsymbol{M}}}_{p1}},{{\hat {\boldsymbol{M}}}_{p2}};{H_p}} \right.,{m_p}\right) \leftarrow $式(15)
     14: END
     15: $ {\hat m^{(t)}} \leftarrow $式(16)
     16: $ \hat \varOmega _0^{(t)} = \left\{ (1),(2), \cdots ,({\hat m^{(t)}})\right\} $
     17: $t \leftarrow t + 1$
     18: $ \hat {\boldsymbol{M}}_{{\mathrm{N}}0}^{(t)} \leftarrow $式(21)
     19: REPEAT 步骤3—步骤18 until $t > T$
     20: $ {\hat \varOmega _0} = \hat \varOmega _0^{(T)} $
    下载: 导出CSV

    表  1  本文所提的辅助数据自适应筛选方法简要总结

    Table  1.   Brief summary of methods proposed in this paper

    方法 简要说明 计算复杂度
    AC-GIP 异常值个数未知的非迭代估计方法,采用GIP筛选处理对辅助数据进行初步排序 $ {O}\left( {{N^2}{R^2} + 3{N^3}R - 4{N^4}} \right) $
    AC-NGIP 异常值个数未知的非迭代估计方法,采用NGIP筛选处理对辅助数据进行初步排序 $ {O}\left( {{N^2}{R^2} + 3{N^3}R - 4{N^4}} \right) $
    RAC-GIP 异常值个数未知条件下,以AC-GIP为基础,对异常值集合进行迭代估计 $ {O}\left( {T{N^2}{R^2} + 3T{N^3}R - 4T{N^4}} \right) $
    RAC-NGIP 异常值个数未知条件下,以AC-NGIP为基础,对异常值集合进行迭代估计 $ {O}\left( {T{N^2}{R^2} + 3T{N^3}R - 4T{N^4}} \right) $
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-07-04
  • 修回日期:  2024-08-17
  • 网络出版日期:  2024-09-19
  • 刊出日期:  2024-09-28

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