基于矩阵化原子范数的高频雷达距离-多普勒二维估计方法

doi:10.12263/DZXB.20210479

电子学报 ›› 2022, Vol. 50 ›› Issue (5): 1150-1158.DOI: 10.12263/DZXB.20210479

基于矩阵化原子范数的高频雷达距离-多普勒二维估计方法

吕明久¹, 马建朝¹, 韦旭², 陈文峰³, 杨军³, 马晓岩³

^1.空军预警学院雷达士官学校, 湖北武汉 430019
^2.空军预警学院研究生队, 湖北武汉 430019
^3.空军预警学院预警技术系, 湖北武汉 430019

收稿日期:2021-04-14 修回日期:2021-05-21 出版日期:2022-05-25
- 作者简介:
- 吕明久男，1985年出生于安徽庐江，现为空军预警学院雷达士官学校讲师，主要从事压缩感知在雷达成像中的应用研究. E‑mail:lv_mingjiu@163.com
  马建朝男，1973年出生于河北邢台，现为空军预警学院雷达士官学校副教授，主要从事雷达系统设计、情报分析等研究.E‑mail: shuilianfeng.com@163.com
  韦旭男，1994年出生于江苏宜兴.现为空军预警学院研究生队学员，博士研究生，主要从事压缩感知理论、雷达成像、深度学习技术等研究.E‑mail: weixu_1003@163.com
  陈文峰男，1989年出生于新疆，空军预警学院预警技术系讲师，博士，研究方向为双基地雷达成像.E‑mail: chenwf925@163.com
- 基金资助:
- 国家自然科学基金 (61671469)

Two-Dimensional Range-Doppler Estimation Method for High Frequency Radar Based on Matrix Atomic Norm

LÜ Ming-jiu¹, MA Jian-chao¹, WEI Xu², CHEN Wen-feng³, YANG Jun³, MA Xiao-yan³

^1.Radar NCO School, Air Force Early Warning Academy, Wuhan, Hubei 430019, China
^2.Graduate team, Air Force Early Warning Academy, Wuhan, Hubei 430019, China
^3.Early Warning Technology, Air Force Early Warning Academy, Wuhan, Hubei 430019, China

Received:2021-04-14 Revised:2021-05-21 Online:2022-05-25 Published:2022-06-18
- Supported by:
- National Natural Science Foundation of China (61671469)

摘要/Abstract

摘要：

针对传统合成带宽高频雷达存在相参时间长，传统处理算法二维分辨能力弱等问题，提出一种基于矩阵化原子范数的多周期脉冲内随机稀疏步进频率信号距离-多普勒二维估计方法. 通过在每个脉冲重复时间内连续发射一串由多个载频步进子脉冲组成的脉冲序列来减少相参处理周期. 构造矩阵形式的连续原子集合，将距离-多普勒二维估计转化为矩阵形式的原子范数最小化模型，并基于半正定规划问题进行快速求解. 所提方法有效降低了运算量且实现了网格失配目标的二维高分辨. 理论分析与仿真实验验证了所提方法的有效性.

关键词: 高频雷达, 连续压缩感知, 矩阵化原子范数, 网格失配, Vandermonde分解, 稀疏重构

Abstract:

In order to solve the problems of long coherent time and weak two-dimensional resolution in traditional synthetic bandwidth high frequency radar, a two-dimensional range-Doppler estimation method based on matrix atomic norm for multi-cycle intra-pulse random sparse stepped frequency signal is proposed. Firstly, a series of pulse, which is composed of sequences multiple carriers stepped sub-pulses, has been continuously transmitted in each pulse repetition time to reduce the coherent processing period. Secondly, a continuous set of atoms in matrix form is constructed, and the two-dimensional range-Doppler estimation is transformed into a matrix form of atomic norm minimization problem. The above optimization problem is transformed into a positive semi-definite programming problem, and can be solved. The proposed method can not only effectively reduce the amount of computation, but also achieve the high resolution under the condition of off grid. Theoretical analysis and simulation experiments verify the effectiveness of the proposed method.

Key words: high frequency radar, compressed sensing, matrix atomic norm minimization, off grid, Vandermonde decomposition, sparse reconstruction

中图分类号:

TN957.52

吕明久, 马建朝, 韦旭, 陈文峰, 杨军, 马晓岩. 基于矩阵化原子范数的高频雷达距离-多普勒二维估计方法[J]. 电子学报, 2022, 50(5): 1150-1158.

LÜ Ming-jiu, MA Jian-chao, WEI Xu, CHEN Wen-feng, YANG Jun, MA Xiao-yan. Two-Dimensional Range-Doppler Estimation Method for High Frequency Radar Based on Matrix Atomic Norm[J]. Acta Electronica Sinica, 2022, 50(5): 1150-1158.

图/表 5

图1 MIRSSF发射信号示意图

图2 不同算法距离多普勒二维重构结果对比(a)网格匹配 (b)网格失配

图3 不同算法计算复杂度对比(a)内存需求对比 (b)运算时间对比

图4 不同条件下重构误差对比曲线(a)不同信噪比 (b)不同采样率

图5 不同条件下重构误差对比曲线

参考文献 26

1	QUANY H, WUY J, et al. Range-Doppler reconstruction for frequency agile and PRF-jittering radar[J]. IET Radar, Sonar & Navigation, 2018, 12(3): 348‑352.
2	ZHAOJ R, TIANY W, et al. Unambiguous wind direction field extraction using a compact shipborne high-frequency radar[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(10): 7448‑7458.
3	CHENQ S, YANGQ, ZHANGX, et al. High resolution target range estimation in discontinuous spectra high frequency radar[J]. Remote Sensing Letters, 2018, 9(7): 676 ‑685.
4	ZHUJiang, GUOHonghui, ZHANGNing, et al. Newtonalized orthogonal matching pursuit for linear frequency modulated pulse frequency agile radar[EB/OL]. [2021-04-01]. .
5	ZHAOD H, WEIY S. Adaptive gradient search for optimal sidelobe design of hopped-frequency waveform[J]. IET Radar, Sonar & Navigation, 2014, 8(4): 282‑289.
6	毛二可, 范花玉. 合成宽带脉冲多普勒雷达[J]. 系统工程与技术, 2016, 38(12): 2718‑2724.
	MAOEr-ke, FANHua-yu. Synthetic wideband pulse Doppler radar[J]. Systems Engineering and Electronics, 2016, 38(12): 2718‑2724. (in Chinese)
7	翟文帅, 张云华. 运用Super-SVA方法处理频谱不连续调频步进信号[J]. 电子与信息学报, 2009, 31(12): 2848‑ 2852.
	ZHAIWen-shuai, ZANGYun-hua. Apply super-SVA to processing stepped frequency chirp signal with bandwidth gaps[J]. Journal of Electronics & Information Technology, 2009, 31(12): 2848‑2852. (in Chinese)
8	黄大荣, 张磊, 郭新荣, 等. 全极化频谱外推的合成孔径雷达成像分辨率增强方法[J]. 电波科学学报, 2014, 29(5): 799‑805, 814.
	HUANGDa-rong, ZHANGLei, GUOXin-rong, et al. Enhanced resolution in fully polarimetric synthetic aperture radar imaging using bandwidth extrapolation[J]. Chinese Journal of Radio Science, 2014, 29(5): 79‑805, 814. (in Chinese)
9	位寅生. 非连续谱高频雷达信号的综合研究[D]. 哈尔滨: 哈尔滨工业大学, 2002.
10	DONOHOD L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289‑1306.
11	WEIS P, ZANGL, MAH, et al. Sparse frequency waveform optimization for high-resolution ISAR imaging[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(1): 546‑566.
12	SHAHS, YAOY, PETROPULUA. Step-frequency radar with compressive sampling(SFR-CS)[C]//SCOTT D. 2010 IEEE International Conference on Acoustics Speech and Signal Processing(ICASSP). Dallas: IEEE Press, 2010: 1686‑1689.
13	CHIY, SCHARFL L, PEZESHKIA, et al. Sensitivity to basis mismatch in compressed sensing[J]. IEEE Transactions on Signal Processing, 2011, 59(5): 2182‑2195.
14	HUL, SHIZ G, ZHOUJ X, et al. Compressed sensing of complex sinusoids: an approach based on dictionary refinement[J]. IEEE Transactions on Signal Processing, 2012, 60(7): 3809‑3822.
15	DUANK Q, LIUW J, DUANG Q, et al. Off-grid effects mitigation exploiting knowledge of the clutter ridge for sparse recovery STAP[J]. IET Radar Sonar & Navigation, 2018, 12(5): 557‑564.
16	王伟, 胡子英, 龚琳舒. MIMO雷达三维成像自适应Off-grid校正方法[J]. 电子与信息学报, 2019, 41(6): 1294‑ 1301.
	WANGWei, HUZi-ying, GONGLin-shu. Adaptive off-grid calibration method for MIMO radar 3D imaging[J]. Journal of Electronics & Information Technology, 2019, 41(6): 1294‑1301. (in Chinese)
17	CHAITANYAE, DANIELT, et al. Recovery of sparse translation-invariant signals with continuous basis pursuit[J]. IEEE Transactions on Signal Processing, 2011, 59(10): 4735‑4744.
18	BHASKARB N, TANGG, RECHTB. Atomic norm denoising with applications to line spectral estimation[J]. IEEE Transactions on Signal Processing, 2013, 61(23): 5987‑5999.
19	HUX W, TONGN N, DINGS S, et al. ISAR imaging with sparse stepped frequency waveforms via matrix completion[J]. Remote Sensing Letters, 2016, 7(9): 847‑854.
20	陈秋实, 杨强, 董英凝, 等. 基于矩阵填充的合成宽带高频雷达非网格目标分辨技术研究[J]. 电子与信息学报, 2017, 39(12): 2874‑2880.
	CHENQiu-shi, YANGQiang, DONGYing-ning, et al. Off-the-grid targets resolution of synthetic bandwidth high frequency radar based on matrix completion[J]. Journal of Electronics & Information Technology, 2017, 39(12): 2874‑2880. (in Chinese)
21	CHIY J, CHENY X. Compressive two-dimensional harmonic retrieval via atomic norm minimization[J]. IEEE Transactions on Signal Processing, 2015, 63(4): 1030‑ 1042.
22	CHANDRAEKARANV, RECHTB, PARRILOP A, et al. The convex algebraic geometry of linear inverse problems[C]//IEEE 2010 48th Annual Allerton Conference on Communication, Control, and Computing(Allerton). Monticello, USA: IEEE, 2010: 699‑703.
23	YANGZ, XIEL, STOICAP. Vandermonde decomposition of multilevel Toeplitz matrices with application to multidimensional super-resolution[J]. IEEE Transactions on Information Theory, 2016, 62(6): 3685‑3701.
24	ZHANGZ, WANGY, TIANZ. Eﬃcient two-dimensional line spectrum estimation based on decoupled atomic norm minimization[J].Signal Processing, 2019, 163: 95 ‑ 106.
25	KRISHNANK, TERLAKYT. Graph Theory and Combinatorial Optimization[M]. Switzerland: Springer, 2005: 101‑157.
26	MOHIMANIH, BABAIE-ZADEHM, GORODNITSKYI, et al. Sparse recovery using smoothed L0(SL0): Convergence analysis[DB/OL]. [2021‑04‑01]. .

[1]	位寅生, 周希波, 刘佳俊. 稳健的基于参数化协方差矩阵估计的空时自适应处理方法[J]. 电子学报, 2019, 47(9): 1943-1950.
[2]	位寅生, 张国成, 朱永鹏, 许荣庆. 天发舰收高频雷达一阶海杂波电磁散射特性分析[J]. 电子学报, 2019, 47(3): 513-520.
[3]	张素玲, 陈胜垚, 席峰, 刘中. 亚奈奎斯特采样雷达的运动目标回波信号的快速重构[J]. 电子学报, 2019, 47(10): 2098-2107.
[4]	李少东, 陈文峰, 杨军, 马晓岩. 任意稀疏结构的多量测向量快速稀疏重构算法研究[J]. 电子学报, 2015, 43(4): 708-715.
[5]	沈明威, 王杰, 吴迪, 朱岱寅. 基于降维稀疏重构的高效数据域STAP算法研究[J]. 电子学报, 2014, 42(11): 2286-2290.
[6]	王军华, 黄知涛, 周一宇, 王丰华. 基于近似l₀范数的稳健稀疏重构算法[J]. 电子学报, 2012, 40(6): 1185-1189.
[7]	毛兴鹏;刘爱军;邓维波;曹斌;张钦宇. 斜投影极化滤波器[J]. 电子学报, 2010, 38(9): 2003-2008.
[8]	毛兴鹏１，刘永坦２，邓维波２. 频域零相移多凹口极化滤波器 [J]. 电子学报, 2008, 36(3): 537-542.
[9]	李雷, 许荣庆, 李高鹏, 刘源. 高频雷达电台干扰抑制的稳健最小二乘方法[J]. 电子学报, 2006, 34(12): 2288-2292.
[10]	李高鹏, 李雷, 许荣庆. 高频地波雷达干扰抑制方法研究[J]. 电子学报, 2005, 33(3): 514-516.
[11]	周浩, 文必洋, 吴世才, 马志刚. 基于时频分析的高频雷达目标检测与定向[J]. 电子学报, 2005, 33(12): 2265-2268.
[12]	毛兴鹏;刘永坦;邓维波;于长军;马子龙. 零相移瞬时极化滤波器[J]. 电子学报, 2004, 32(9): 1495-1498.
[13]	周浩;文必洋;吴世才;刘晓峰. 应用时频分析进行高频雷达射频干扰抑制[J]. 电子学报, 2004, 32(9): 1546-1548.
[14]	陈志群;权太范;赵淑清. 高频雷达射频干扰自适应对消[J]. 电子学报, 2001, 29(10): 1439-1440.

基于矩阵化原子范数的高频雷达距离-多普勒二维估计方法

Two-Dimensional Range-Doppler Estimation Method for High Frequency Radar Based on Matrix Atomic Norm

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 5

参考文献 26

相关文章 14

编辑推荐

Metrics