基于動(dòng)態(tài)字典的卡車(chē)目標(biāo)微動(dòng)參數(shù)估計(jì)方法

李開(kāi)明,張 群,雷 磊,羅 迎,3

(1.空軍工程大學(xué)信息與導(dǎo)航學(xué)院,陜西西安 710077;2.空軍工程大學(xué)訓(xùn)練部,陜西西安 710051;3.西安電子科技大學(xué)雷達(dá)信號(hào)處理重點(diǎn)實(shí)驗(yàn)室,陜西西安 710071)

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基于動(dòng)態(tài)字典的卡車(chē)目標(biāo)微動(dòng)參數(shù)估計(jì)方法

李開(kāi)明1,張 群1,雷 磊2,羅 迎1,3

(1.空軍工程大學(xué)信息與導(dǎo)航學(xué)院,陜西西安 710077;2.空軍工程大學(xué)訓(xùn)練部,陜西西安 710051;3.西安電子科技大學(xué)雷達(dá)信號(hào)處理重點(diǎn)實(shí)驗(yàn)室,陜西西安 710071)

車(chē)輪旋轉(zhuǎn)產(chǎn)生的微多普勒是輪式車(chē)輛獨(dú)特的特征.卡車(chē)類(lèi)目標(biāo)微動(dòng)參數(shù)提取,可為地面車(chē)輛目標(biāo)的分類(lèi)識(shí)別提供重要依據(jù).(1)對(duì)窄帶雷達(dá)信號(hào)下的卡車(chē)目標(biāo)進(jìn)行回波建模,推導(dǎo)了車(chē)身非旋轉(zhuǎn)散射點(diǎn)多普勒和輪轂旋轉(zhuǎn)散射點(diǎn)微多普勒的數(shù)學(xué)表達(dá)式；(2)利用旋轉(zhuǎn)點(diǎn)的微動(dòng)參數(shù)構(gòu)造相應(yīng)的字典庫(kù)進(jìn)行匹配分解,建立了噪聲條件下微動(dòng)參數(shù)提取的凸優(yōu)化模型；(3)針對(duì)采用過(guò)完備字典方法進(jìn)行參數(shù)提取時(shí),維數(shù)過(guò)大帶來(lái)的計(jì)算和存儲(chǔ)負(fù)擔(dān)問(wèn)題,進(jìn)一步推導(dǎo)出關(guān)于微動(dòng)參數(shù)集的凸函數(shù),構(gòu)造出更小規(guī)模的動(dòng)態(tài)字典,通過(guò)對(duì)字典的動(dòng)態(tài)調(diào)整和最小二乘準(zhǔn)則下的迭代逼近,較快實(shí)現(xiàn)了卡車(chē)目標(biāo)微動(dòng)參數(shù)的準(zhǔn)確估計(jì)；(4)仿真驗(yàn)證了方法的有效性和穩(wěn)健性.

卡車(chē)目標(biāo); 微多普勒; 微動(dòng)參數(shù)估計(jì); 動(dòng)態(tài)字典

1 引言

卡車(chē)類(lèi)目標(biāo)的識(shí)別研究,對(duì)智能交通系統(tǒng)的發(fā)展和戰(zhàn)場(chǎng)監(jiān)測(cè)具有重要應(yīng)用價(jià)值[1,2].微波雷達(dá)對(duì)卡車(chē)類(lèi)目標(biāo)探測(cè)識(shí)別時(shí),車(chē)輪旋轉(zhuǎn)會(huì)對(duì)目標(biāo)回波產(chǎn)生主體多普勒以外的附加頻率調(diào)制,稱(chēng)為微多普勒效應(yīng)(Micro-Doppler effect)[3].微多普勒特征是雷達(dá)目標(biāo)獨(dú)特的特征[4～10],基于微多普勒特征的目標(biāo)識(shí)別技術(shù)已被公認(rèn)為是雷達(dá)目標(biāo)識(shí)別中最具發(fā)展?jié)摿Φ募夹g(shù)之一[1,3].相對(duì)于寬帶雷達(dá),窄帶雷達(dá)不具備利用目標(biāo)高分辨像進(jìn)行分類(lèi)識(shí)別的能力[5],但在最小可檢測(cè)信噪比恒定的條件下,窄帶雷達(dá)靈敏度更高,最大可探測(cè)距離更遠(yuǎn)且成本較低[6],更適合于探測(cè)地面車(chē)輛目標(biāo),同時(shí)窄帶雷達(dá)對(duì)卡車(chē)類(lèi)目標(biāo)微多普勒信息的提取,可獲得目標(biāo)精細(xì)的微動(dòng)特征,有助于提升窄帶雷達(dá)對(duì)地面車(chē)輛目標(biāo)的分類(lèi)識(shí)別能力[4].針對(duì)窄帶雷達(dá)目標(biāo)微動(dòng)參數(shù)提取,文獻(xiàn)[4]提出基于高階矩函數(shù)的微動(dòng)參數(shù)快速估計(jì)方法,計(jì)算量較小,但微動(dòng)點(diǎn)較多時(shí)干擾項(xiàng)對(duì)微動(dòng)參數(shù)的估計(jì)性能影響較大.文獻(xiàn)[7]提出基于經(jīng)驗(yàn)?zāi)B(tài)分解(Empirical Mode Decomposition,EMD)的振動(dòng)頻率提取方法,但該方法抗噪聲能力較弱[8],且對(duì)多分量信號(hào)分解效果欠佳.文獻(xiàn)[9]利用時(shí)頻分析-Hough變換方法完成對(duì)旋轉(zhuǎn)半徑和旋轉(zhuǎn)頻率的估計(jì),但該方法提取精度受限于時(shí)頻分析工具的分辨能力,且計(jì)算量較大.文獻(xiàn)[10]采用正交匹配追蹤(OMP,Orthogonal Matching Pursuit)方法提取目標(biāo)微動(dòng)參數(shù),在欠采樣條件下仍獲得較好的估計(jì)效果,但該算法需構(gòu)建多維度的原子集,計(jì)算量較大.凸優(yōu)化理論可避免求解優(yōu)化問(wèn)題陷入局部極值點(diǎn),同時(shí)能將原始優(yōu)化問(wèn)題轉(zhuǎn)化為對(duì)偶問(wèn)題求解,工程實(shí)現(xiàn)方便.目前,凸優(yōu)化已廣泛用于控制系統(tǒng)、信號(hào)和圖像處理、統(tǒng)計(jì)與金融等領(lǐng)域[11].本文在卡車(chē)目標(biāo)三維微動(dòng)建模基礎(chǔ)上,利用旋轉(zhuǎn)點(diǎn)微動(dòng)參數(shù)構(gòu)造字典庫(kù)進(jìn)行匹配分解,建立了噪聲條件下微動(dòng)參數(shù)提取的凸函數(shù)模型.針對(duì)過(guò)完備字典維數(shù)太大帶來(lái)的計(jì)算和存儲(chǔ)負(fù)擔(dān)問(wèn)題,借鑒文獻(xiàn)[12]的思想,推導(dǎo)出關(guān)于微動(dòng)參數(shù)集的凸函數(shù),提出基于動(dòng)態(tài)字典的卡車(chē)目標(biāo)微動(dòng)參數(shù)提取方法.仿真表明,該方法可有效解決過(guò)完備字典方法計(jì)算效能差的問(wèn)題,實(shí)現(xiàn)了卡車(chē)目標(biāo)微動(dòng)參數(shù)的準(zhǔn)確提取,在低信噪比條件下具有較高穩(wěn)健性.

2 卡車(chē)目標(biāo)微多普勒效應(yīng)分析

由于車(chē)輪外緣通常為橡膠材質(zhì),散射較弱,本文重點(diǎn)分析輪轂旋轉(zhuǎn)點(diǎn)的微多普勒效應(yīng).假設(shè)卡車(chē)位于雷達(dá)遠(yuǎn)場(chǎng),如圖1所示,以卡車(chē)運(yùn)動(dòng)方向?yàn)閄軸,建立全局坐標(biāo)系XYZ,卡車(chē)速度向量為v=[vX,0,0].雷達(dá)位于全局坐標(biāo)系的O′(0,0,Zr)處,以雷達(dá)為原點(diǎn),雷達(dá)視線(xiàn)方向(light of sight,LOS)為y軸建立雷達(dá)坐標(biāo)系xyz,設(shè)初始時(shí)刻雷達(dá)至卡車(chē)中心Q的距離向量為RLOS.以卡車(chē)中心Q(XQ,YQ,ZQ)為原點(diǎn),建立本地坐標(biāo)系x′y′z′.圖2為本地坐標(biāo)系示意圖,以卡車(chē)后輪為例,A為輪轂中心,r和r0分別表示車(chē)輪外緣半徑和輪轂半徑.

設(shè)卡車(chē)目標(biāo)包含兩類(lèi)散射點(diǎn):(1)M個(gè)非旋轉(zhuǎn)點(diǎn)Pm,包括車(chē)身主體散射點(diǎn)和輪轂中心,設(shè)其在本地坐標(biāo)系中的初始坐標(biāo)為(xm,ym,zm)；(2)N個(gè)旋轉(zhuǎn)點(diǎn)Pn,每個(gè)旋轉(zhuǎn)點(diǎn)以旋轉(zhuǎn)半徑r0、角速度ω=[0,ωY,0]及不同初相θn繞輪轂中心A旋轉(zhuǎn),點(diǎn)A在本地坐標(biāo)系的初始坐標(biāo)為(xA,yA,zA),雷達(dá)發(fā)射窄帶信號(hào)p(t)=exp(j(2πfct+φ)),φ為初相,記t時(shí)刻目標(biāo)回波信號(hào)為s(t),σm、σn分別為第m個(gè)非旋轉(zhuǎn)點(diǎn)和第n個(gè)旋轉(zhuǎn)點(diǎn)的反射系數(shù)(1≤m≤M,1≤n≤N),Rm(t)、Rn(t)分別為t時(shí)刻第m個(gè)非旋轉(zhuǎn)點(diǎn)和第n個(gè)旋轉(zhuǎn)點(diǎn)到雷達(dá)的距離.以卡車(chē)中心Q為參考點(diǎn),構(gòu)建參考信號(hào)sref(t),RQ(t)為t時(shí)刻卡車(chē)中心Q到雷達(dá)的距離.則將目標(biāo)回波與參考信號(hào)共軛相乘得:

(1)

其中ΔRm(t)=Rm(t)-RQ(t),表示t時(shí)刻雷達(dá)到非旋轉(zhuǎn)點(diǎn)的距離與雷達(dá)到卡車(chē)中心的距離差,ΔRn(t)=Rn(t)-RQ(t),表示t時(shí)刻雷達(dá)到旋轉(zhuǎn)點(diǎn)的距離和雷達(dá)到卡車(chē)中心的距離差.

由圖1和圖2的幾何關(guān)系得ΔRm(t)≈[PmQ(t)·PmO′(t)]/‖PmO′(t)‖,PmQ(t)和PmO′(t)分別表示t時(shí)刻非旋轉(zhuǎn)點(diǎn)Pm到卡車(chē)中心Q和雷達(dá)O′的距離向量.對(duì)于遠(yuǎn)場(chǎng)目標(biāo),O′Q與O′Pm近似一致,則ΔRm(t)≈-PmQ(t)·nLOS,nLOS為L(zhǎng)OS單位向量.由于PmQ(t)和PmO′(t)可表示為PmQ(t)=-[xmymzm],PmO′(t)=[0 0Zr]-[XQ+xm+vXtYQ+ymZQ+zm],則對(duì)ΔRm(t)進(jìn)行泰勒級(jí)數(shù)展開(kāi),并忽略高次項(xiàng)得:

(2)

·vXt-r0sinξcos(ωYt+θn)

(3)

將式(2)和式(3)代入式(1),對(duì)其相位除以2π并關(guān)于時(shí)間t求導(dǎo),可得主體散射點(diǎn)的多普勒為:

fm-Doppler=

(4)

(5)

3 基于字典學(xué)習(xí)的卡車(chē)目標(biāo)微動(dòng)參數(shù)估計(jì)方法

3.1 基于過(guò)完備字典的微動(dòng)參數(shù)估計(jì)方法

定義函數(shù)

(6)

由于x具有稀疏性,此時(shí)求解x的最優(yōu)化問(wèn)題可表述為:

(7)

或者

(8)

其中σ2為噪聲能量,β為常數(shù),T為x的稀疏度,也稱(chēng)作模型階數(shù)[13].

對(duì)式(7)和式(8)的求解是一個(gè)NP-hard問(wèn)題.進(jìn)一步將l0范數(shù)松弛為準(zhǔn)p范數(shù)(0

subject toxk≥0,k=1,2,…,K

(9)

3.2 基于動(dòng)態(tài)字典的微動(dòng)參數(shù)估計(jì)方法

(10)

(11)

(12)

式中,“?”表示Kronecker積(即直積),“13×1”表示3×1維全1向量,且

(13)

(14)

(15)

subject toxk≥0,k=1,2,…,K

(16)

(17)

4 仿真分析

設(shè)計(jì)動(dòng)態(tài)字典時(shí),輪轂半徑取值范圍為0.1m到0.5m,離散間隔為0.2m,旋轉(zhuǎn)頻率取值范圍為4Hz到10Hz,離散間隔為2Hz,初相取值范圍為0rad到2πrad,離散間隔為0.5πrad.此時(shí),動(dòng)態(tài)字典共有3×4×4=48列.仿真中βfinal=0.2,?=0.7.表1為SNR=0dB時(shí)目標(biāo)微動(dòng)參數(shù)和散射點(diǎn)反射系數(shù)的估計(jì)結(jié)果.

表1 SNR=0dB時(shí)采用動(dòng)態(tài)字典方法得到的微動(dòng)參數(shù)和散射點(diǎn)反射系數(shù)估計(jì)結(jié)果

表2 SNR=-15dB時(shí)采用動(dòng)態(tài)字典方法得到的微動(dòng)參數(shù)和散射點(diǎn)反射系數(shù)估計(jì)結(jié)果

圖9為SNR=-15dB時(shí)利用動(dòng)態(tài)字典方法估計(jì)的參數(shù)重構(gòu)的旋轉(zhuǎn)點(diǎn)回波時(shí)頻圖.可見(jiàn),重構(gòu)的微多普勒特征曲線(xiàn)能較為真實(shí)地反映目標(biāo)的微動(dòng)特征.

仿真實(shí)驗(yàn)表明,在低信噪比條件下Hough變換和EMD方法難以實(shí)現(xiàn)微動(dòng)參數(shù)的提取,而動(dòng)態(tài)字典方法在SNR=-15dB的條件下仍能準(zhǔn)確提取出輪轂旋轉(zhuǎn)點(diǎn)的微動(dòng)參數(shù).同時(shí),相對(duì)于過(guò)完備字典方法,動(dòng)態(tài)字典方法的字典規(guī)模更小,搜索速度相對(duì)更快,求解效率更高.實(shí)際中的雷達(dá)回波處理通常涉及到大量矩陣的計(jì)算,字典規(guī)模的減小對(duì)于計(jì)算機(jī)的矩陣分析與計(jì)算具有重要的價(jià)值,且隨著硬件水平的發(fā)展,動(dòng)態(tài)字典方法的計(jì)算效能會(huì)進(jìn)一步提升,更有利于工程實(shí)現(xiàn).

5 結(jié)論

車(chē)輛目標(biāo)微動(dòng)特征提取已成為當(dāng)前目標(biāo)分類(lèi)和識(shí)別領(lǐng)的研究熱點(diǎn)之一.在卡車(chē)目標(biāo)回波建模的基礎(chǔ)上,利用微動(dòng)參數(shù)構(gòu)造字典庫(kù)進(jìn)行匹配分解,建立了噪聲條件下微動(dòng)參數(shù)提取的凸函數(shù)模型.針對(duì)過(guò)完備字典方法帶來(lái)的計(jì)算和存儲(chǔ)負(fù)擔(dān)問(wèn)題,提出基于動(dòng)態(tài)字典的微動(dòng)參數(shù)估計(jì)方法,給出具體的實(shí)現(xiàn)步驟.最后通過(guò)仿真實(shí)驗(yàn),分別在SNR=0dB和SNR=-15dB的條件下,準(zhǔn)確提取了卡車(chē)輪轂旋轉(zhuǎn)點(diǎn)的微動(dòng)參數(shù),驗(yàn)證了方法的穩(wěn)健性和相對(duì)較高的計(jì)算效能,為地面車(chē)輛目標(biāo)的特征提取與分類(lèi)提供了借鑒.

[1]張群,等.雷達(dá)目標(biāo)微多普勒效應(yīng)研究概述[J].空軍工程大學(xué)學(xué)報(bào)(自然科學(xué)版),2011,12(2):22-26.

Zhang Qun,Luo Ying,He Jin.Review of the researches on micro-Doppler effect of radar targets [J].Journal of Air Force Engineering University (Natural Science Edition),2011,12(2):22-26.(in Chinese)

[2]李開(kāi)明,張 群,羅 迎,等.地面車(chē)輛目標(biāo)識(shí)別研究綜述[J].電子學(xué)報(bào),2014,42(3):538-546.

Li Kai-ming,Zhang Qun,Luo Ying,et al.Review of Ground Vehicles Recognition [J].Acta Electronica Sinica,2014,42(3):538-546.(in Chinese)

[3]Chen V C.Analysis of radar micro-Doppler signature with time-frequency transform [A].Proceedings of the 10thIEEE Workshop on Statistical Signal and Array Processing[C].Pocono Manor PA ,USA,2000,463-466.

[4]鄧冬虎,等.基于高階矩函數(shù)的雷達(dá)目標(biāo)微動(dòng)參數(shù)估計(jì)方法[J].電子學(xué)報(bào),2013,41(12):2339-2345.

Deng Dong-hu,Zhang Qun,Luo Ying,et al.Micro motion parameter estimation of radar target based on high order moment function [J].Acta Electronica Sinca,2013,41(12):2339-2345.(in Chinese)

[5]霍凱,李康樂(lè),姜衛(wèi)東,等.微動(dòng)目標(biāo)OFDM雷達(dá)回波調(diào)制機(jī)理分析[J].電子學(xué)報(bào),2011,39(3):685-689.

Huo Kai,Li Kang-le,Jiang Wei-dong,et al.Analysis of the modulation effects on OFDM radar echoes from targets with micro-motion [J].Acta Electronica Sinca,2011,39(3):685-689.(in Chinese)

[6]白雪茹,孫廣才,武其松,等.窄帶雷達(dá)自旋目標(biāo)成像[J].中國(guó)科學(xué):信息科學(xué),2010,40(11):1508-1518.

[7]Cai C,Liu W,Fu J S,et al.Empirical mode decomposition of micro-Doppler signature [A].Proceedings of International Conference on Radar [C].Washington,USA,2005.895-899.

[8]王宏,Narayanan R M,周正歐,等.基于改進(jìn)EEMD的穿墻雷達(dá)動(dòng)目標(biāo)微多普勒特性分析[J].電子與信息學(xué)報(bào),2010,32(6):1355-1360.

Wang Hong,Narayanan R M,Zhou Zheng-ou,et al.Micro-Doppler character analysis of moving objects using through-wall radar based on improved EEMD [J].Journal of Electronics & Information Technology,2010,32(6):1355-1360.(in Chinese)

[9]Liu Y X,Li X,Zhuang Z W.Estimation of micro-motion parameters based on micro-Doppler[J].IET Signal Processing,2010,4(3):213-217.

[10]Luo Y,Zhang Q,Qiu C W,et al.Three-dimensional micro-motion signature extraction of rotating targets in OFDM-LFM MIMO radar [J].Progress in Electromagnetics Research,2013,140:733-759.

[11]S Boyd，et al.Convex Optimization [M].Cambridge University Press,Cambridge,UK,2004.

[12]Austin C D,et al.Dynamic dictionary algorithms for model order and parameter estimation [J].IEEE Transactions on Signal Processing,2013,61(20):5117-5130.

[13]Mallat S G,Zhang Z.Matching pursuits with time-frequency dictionaries [J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.

[14]Pati Y,Rezaiifar R,Krishnaprasad P.Orthogonal matching pursuit:recursive function approximation with applications to wavelet decomposition [A].Proceedings of the 27thAsilomar Conference on Signals,System Computer Pacific Grove[C].CA,USA,1993.40-44.

李開(kāi)明 男,1982年12月生于山西應(yīng)縣.分別于2003年和2009年于空軍工程大學(xué)獲工學(xué)學(xué)士學(xué)位和工學(xué)碩士學(xué)位.現(xiàn)為空軍工程大學(xué)信息與導(dǎo)航學(xué)院講師,博士研究生.目前主要從事雷達(dá)成像及目標(biāo)識(shí)別領(lǐng)域的研究工作.

E-mail:likaiming1982@163.com

張 群 男,1964年11月生于陜西合陽(yáng).現(xiàn)為空軍工程大學(xué)信息與導(dǎo)航學(xué)院教授,博士生導(dǎo)師.發(fā)表學(xué)術(shù)論文200余篇,其中SCI、EI檢索120余篇,出版中英文專(zhuān)著各1部.研究方向:雷達(dá)信號(hào)處理、雷達(dá)成像及電子對(duì)抗.

E-mail:afeuzq@163.com

Micro-motion Parameters Estimation for Truck Target Based on Dynamic Dictionary

LI Kai-ming1,ZHANG Qun1,LEI Lei2,LUO Ying1,3

(1.SchoolofInformationandNavigation,AirForceEngineeringUniversity,Xi’an,Shaanxi710077,China; 2.TrainingDepartmentofAirForceEngineeringUniversity,Xi’an,Shaanxi710051,China; 3.KeyLab.forRadarSignalProcessing,XidianUniversity,Xi’an,Shaanxi710071,China)

Micro-Doppler generated by rotation of wheels is a unique characteristic of wheeled vehicles.Extraction of micro-motion parameters of truck,etc.will offer important proof for classification and recognition of ground vehicles.Firstly,the echoes model of truck was established under narrowband signal,the mathematic expressions of Doppler induced by non-rotation scatterers and micro-Doppler induced by rotation scatterers were deduced.Secondly,corresponding dictionary bank consists of micro-motion parameters was constructed for matching pursuit,and convex optimization model under noisy condition was established for extraction of micro-motion parameters.Thirdly,for avoiding the heavy computation and storage burden induced by parameters extraction based on overcomplete dictionary,the smaller dynamic dictionary was structured after deduction of the convex function about micro-motion parameters set,the accurate and faster parameters estimation was obtained by dynamic adaptation of the dictionary and iterative approach to optimal solution under Least Square criteria.The effectiveness and robustness of the method were proved by the simulation results.

truck target; micro-Doppler; micro-motion parameters estimation; dynamic dictionary

2015-09-29;

2016-03-11; 責(zé)任編輯:馬蘭英

國(guó)家自然科學(xué)基金(No.61471386); 陜西省統(tǒng)籌創(chuàng)新工程-特色產(chǎn)業(yè)創(chuàng)新鏈項(xiàng)目(No.S2015TDGY0045)

TN957

A

0372-2112 (2016)1-2618-07

??學(xué)報(bào)URL:http://www.ejournal.org.cn

10.3969/j.issn.0372-2112.2016.11.008