基于插值短时分数阶傅里叶变换-变权拟合的线性调频信号参数估计

doi:10.3969/j.issn.1000-1093.2020.01.010

兵工学报 ›› 2020, Vol. 41 ›› Issue (1): 86-94.doi: 10.3969/j.issn.1000-1093.2020.01.010

基于插值短时分数阶傅里叶变换-变权拟合的线性调频信号参数估计

曹伟浩¹，姚直象¹，夏文杰²，闫肃³

(1.海军工程大学电子工程学院, 湖北武汉 430033;2.国家海洋技术中心漳州基地筹建办公室，福建厦门 361000; 3.91388部队，广东湛江 524000)

收稿日期:2019-03-04 修回日期:2019-03-04 上线日期:2020-02-22
通讯作者: 夏文杰（1994—），男，助理工程师 E-mail:15972196703@163.com
作者简介:曹伟浩（1994—），男，硕士研究生。E-mail:15972196703@163.com；
姚直象(1976—)，男，副教授，硕士生导师，博士。E-mail: whyaozx@163.com
基金资助:
国家自然科学基金项目（51679247）

Parameter Estimation of Linear Frequency Modulation Signal Based on Interpolated Short-time Fractional Fourier Transformand Variable Weight Least Square Fitting

CAO Weihao¹， YAO Zhixiang¹， XIA Wenjie²， YAN Su³

(1.School of Electronic Engineering, Naval University of Engineering, Wuhan 430033, Hubei, China;2.Zhangzhou Base Preparation Office of National Ocean Technology Center, Xiamen 361000, Fujian, China;3.Unit 91388 of PLA, Zhanjiang 524000, Guangdong, China)

Received:2019-03-04 Revised:2019-03-04 Online:2020-02-22

摘要/Abstract

摘要： 针对低信噪比下线性调频（LFM）信号参数估计精度不高的问题，提出一种基于Rife插值短时分数阶傅里叶变换（STFRFT）-变权拟合（VWSF）方法。该方法利用STFRFT提高LFM信号的聚集性，实现对LFM信号瞬时频率的高精度估计，并通过VWSF进一步提高信号初始频率和调频率的估计精度。推导得到了初始频率和调频率估计的克拉美-罗限（CRLB），分析了信号时长、滑窗次数等因素对CRLB的影响。仿真实验及海试结果表明，相比于传统基于短时傅里叶变换的估计方法，Rife插值STFRFT-VWSF方法具有更高的LFM信号参数估计精度。

关键词: 线性调频信号, 参数估计, 短时分数阶傅里叶变换, 变权拟合, Rife插值, 克拉美-罗限

Abstract: A Rife interpolation short-time fractional Fourier transform (STFRFT) -variable weight least square fitting (VWSF) algorithm is proposed for solving the problem of low parameter estimation accuracy of linear frequency modulation (LFM) signal under low signal-to-noise ratio (SNR). STFRFT is used to improve the aggregation of LFM signals, and the estimation accuracy of instantaneous frequency of signal is improved by VWSF, thus estimating the instantaneous frequency, initial frequency and modulation frequency of LFM signal. The Cramer-Rao lower bound (CRLB) of the signal parameters estimation is derived, and the factors affecting the estimated parameter CRLB and the variation of CRLB with it are analyzed. The simulated results show that the Rife interpolation STFRFT-VWSF algorithm has better estimation accuracy of LFM signal parameters, the parameter estimation and CRLB theoretical analysis are rational, and the feasibility of the algorithm is proven through sea test. Key

Key words: linearfrequencymodulationsignal, parameterestimation, short-timefractionalFouriertransform, variableweightleastsquarefitting, Rifeinterpolation, Cramer-Raolowerbound

中图分类号:

TN911.72

曹伟浩，姚直象，夏文杰，闫肃. 基于插值短时分数阶傅里叶变换-变权拟合的线性调频信号参数估计[J]. 兵工学报, 2020, 41(1): 86-94.

CAO Weihao， YAO Zhixiang， XIA Wenjie， YAN Su. Parameter Estimation of Linear Frequency Modulation Signal Based on Interpolated Short-time Fractional Fourier Transformand Variable Weight Least Square Fitting[J]. Acta Armamentarii, 2020, 41(1): 86-94.

参考文献

［1］ KWOK H K, JONES D L. Improved instantaneous frequency estimation using an adaptive short-time Fourier transform［C］∥Proceedings of Asilomar Conference on Signals. Pacific Grove, CA, US：IEEE, 2000.
［2］王娟娟,王瑞,李珂,等.基于Rife算法的LFM信号性能分析［J］.舰船电子对抗,2018,41(4):36-39，48.
WANG J J, WANG R, LI K, et al. Performance research of LFM signal based on Rife algorithm［J］. Shipboard Electronic Countermeasure, 2018, 41(4):36-39，48. (in Chinese)
［3］段宇. 低信噪比下的线性调频信号检测与参数估计方法研究［D］.长沙：国防科学技术大学,2013.
DUAN Y. Research on LFM signal detection and parameter estimation method under low SNR［D］.Changsha：National University of Defense Technology,2013. (in Chinese)
［4］尉宇.线性调频和非线性调频信号的检测与参数估计［D］.武汉：华中科技大学, 2005.
WEI Y. The detection and parameter estimation of the linear frequency modulated signals and nonlinear frequency modulated signal in low SNR［D］.Wuhan：Huazhong University of Science and Technology, 2005. (in Chinese)
［5］ TIAN L. Adaptive short-time fractional Fourier transform used in time-frequency analysis［C］∥Proceedings of the 7th International Conference on Computer Engineering and Networks. Shanghai, China：PoS-Proceedings of Science,2017:078.
［6］黄响,唐世阳,张林让,等.一种基于高效FRFT的LFM信号检测与参数估计快速算法［J］.电子与信息学报,2017,39(12):2905-2911.
HUANG X, TANG S Y, ZHANG L R, et al. A fast algorithm of LFM signal detection and parameter estimation based on efficient FRFT［J］. Journal of Electronics and Information Technology,2017,39(12):2905-2911.(in Chinese)
［7］徐舟,张浩,程水英. 未知包络多分量线性调频脉冲信号参数估计［J］.兵工学报,2016,37(3):462-470.
XU Z, ZHANG H, CHENG S Y. Parameter estimation of unknown envelope multicomponent LFM signal［J］. Acta Armamentarii, 2016, 37(3):462-470. (in Chinese)
［8］ TAO R, LI Y L, WANG Y. Short-time fractional Fourier transform and its applications［J］.IEEE Transactions on Signal Processing, 2010, 58(5):2568-2580.
［9］王瑞, 马艳. 基于分数阶傅里叶变换的线性调频脉冲信号波达方向估计［J］.兵工学报,2014,35(3):421-427.
WANG R, MA Y. DOA estimation of wideband linear frequency modulated pulse signals based on fractional Fourier transform［J］. Acta Armamentarii, 2014, 35(3):421-427. (in Chinese)

［10］陶然, 邓兵, 王越. 分数阶傅里叶变换及其应用［M］.北京：清华大学出版社, 2009.
TAO R, DENG B, WANG Y. Fractional Fourier transform and its applications［M］.Beijing：Tsinghua University Press,2009. (in Chinese)
［11］姚帅, 方世良, 王晓燕. 一种IQuinn-Rife综合CW脉冲信号频率精确估计方法［C］∥2016年全国声学学术会议论文集.武汉：中国声学学会，2016.
YAO S, FANG S L, WANG X Y. Frequency estimation of CW
signal based on combined IQuinn-Rife interpolation method［C］∥
Proceedings of the National Acoustic Conference. Wuhan：Acoustical Society of China，2016. (in Chinese)
［12］姚帅, 方世良, 王晓燕. 联合STFT-迭代变权拟合的LFM信号参数估计方法［J］.信号处理, 2012, 28(10):1408-1415.
YAO S, FANG S L, WANG X Y. Parameter-estimation of LFM signal based on combined short time Fourier transform and iteratively reweighted fit［J］. Journal of Signal Processing, 2012, 28(10): 1408-1415. (in Chinese)
［13］ PELEG S, PORAT B. The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase［J］.IEEE Transactions on Signal Processing, 1991, 39(3):749-752.
［14］齐国清，贾欣乐.插值FFT估计正弦信号频率的精度分析［J］. 电子学报, 2004, 32(4):625-629.
QI G Q, JIA X L. Accuracy analysis of frequency estimation of sinusoid based on interpolated FFT［J］. Acta Electronica Sinica, 2004, 32(4):625-629. (in Chinese)
［15］朱埜.主动声呐检测信息原理（下册）：主动声呐信道特性和系统优化原理［M］. 北京：科学出版社，2014:575-580.
ZHU Y. Active sonar detection information principles(volume 2): active sonar channel characteristics and system optimization principles［M］.Beijing: Science Press, 2014:575-580. (in Chinese)

第41卷第1期
2020 年1月兵工学报ACTA
ARMAMENTARIIVol.41No.1Jan.2020

[1]	闫晓鹏, 王珂, 刘强, 郝新红, 于洪海. 基于Duffing振子参数估计的伪码调相引信干扰信号设计[J]. 兵工学报, 2022, 43(4): 729-736.
[2]	马剑飞，颜冰，林春生. 基于正交基函数的矢量磁梯度异常探测[J]. 兵工学报, 2021, 42(11): 2433-2443.
[3]	何耀民，何华锋，徐永壮，王依繁，苏敬. 基于多特征量的海杂波参数估计[J]. 兵工学报, 2020, 41(3): 517-525.
[4]	柯肇捷，周文雅. 基于灰自助和未确知有理数的小样本试验数据估计[J]. 兵工学报, 2019, 40(4): 874-879.
[5]	何耀民，何华锋，徐永壮，苏敬，王依繁. 基于反向传播神经网络的海杂波参数估计[J]. 兵工学报, 2019, 40(12): 2473-2481.
[6]	李文军，王潇楠，郑永军. 热电偶分数阶传递函数阶次和参数估计[J]. 兵工学报, 2018, 39(9): 1820-1828.
[7]	李海洋，谢里阳，李铭，李强，钟海. 一种新的无失效数据可靠性评估方法研究[J]. 兵工学报, 2018, 39(8): 1622-1631.
[8]	熊光明，鲁浩，郭孔辉，陈慧岩. 基于滑动参数实时估计的履带车辆运行轨迹预测方法研究[J]. 兵工学报, 2017, 38(3): 600-607.
[9]	王谦，侯宏，尹韶平，陈志菲. 水下高速直线运动目标的双参考源航迹估计方法研究[J]. 兵工学报, 2016, 37(4): 677-683.
[10]	赵建忠，欧阳中辉，张磊，赵建印. 基于多智能体遗传算法优化的航空电子设备状态组合预测[J]. 兵工学报, 2016, 37(4): 727-734.
[11]	徐舟，张浩，程水英. 未知包络多分量线性调频脉冲信号参数估计[J]. 兵工学报, 2016, 37(3): 462-470.
[12]	肖泽龙，张恒，董浩，倪碧雪，许建中. 多普勒对空引信回波分析及碰炸优先判决准则研究[J]. 兵工学报, 2016, 37(10): 1820-1827.
[13]	邓兵，栾俊宝. 分数傅里叶域宽带信道化侦察接收算法研究[J]. 兵工学报, 2015, 36(6): 1040-1045.
[14]	邓兵，栾俊宝，唐光胜. 基于短时分数阶傅里叶变换的瞬时频率估计误差分析[J]. 兵工学报, 2015, 36(11): 2104-2110.
[15]	朱航，张淑宁，赵惠昌. 单通道多分量伪码复合线性调频信号分离及参数估计[J]. 兵工学报, 2014, 35(9): 1363-1374.

基于插值短时分数阶傅里叶变换-变权拟合的线性调频信号参数估计

Parameter Estimation of Linear Frequency Modulation Signal Based on Interpolated Short-time Fractional Fourier Transformand Variable Weight Least Square Fitting

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价