基于LPFT变换的雷达高分辨率距离像目标识别方法研究
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摘要
上世纪中后期随着雷达探测技术的发展，高分辨率雷达的应用对于目标回波的研究工作更加细致化、具体化。雷达的自动目标识别技术逐渐成为这一领域研究的热点。在这一领域中，对于高速机动目标的判别是非常重要的研究方向，根据目标的回波特性来判别目标是否存在的研究工作是非常重要的研究课题。
近些年来，众多学者对非平稳的雷达回波信号进行时频分析与研究，提出了很多的研究理论与方法，其中局部多项式傅里叶变换（LPFT）对非平稳信号的时频展开具有很好的时频聚特性集性，以及对多分量信号交叉项的抑制作用起到了很好的效果。本文所做的研究工作就是将这一时频分析的变换方法应用到高速机动目标回波的分析之中，并结合LPFT变换的时频分析处理，给出了目标判别存在与否的具体方法。
本文具体研究五个方面的问题：第一，研究了传统的魏格纳-威尔分布对于多分量的信号产生交叉项的原因；第二，研究了LPFT变换的基本理论，和对交叉项的抑制作用；第三，研究了距离像产生和信号模型；第四，提出了高斯白噪声背景下基于LPFT变换的高速机动目标的检测方案；第五，提出了高斯白噪声背景下基于目标相邻回波距离像的CLPP变换的目标判别方案。
In the middle of the last century, with the development of the radar detectiontechnology, high resolution radar was used more and more, specific. Radar automatictarget recognition technology has become a hot spot in the study of this field In thisfield, for high maneuvering target identification is a very important research direction,it is a very important research topic to determine the presence of the target of researchwork according to the target echo characteristics.
In recent years, many scholars have do some research about the non-stationaryradar echoes signal, puts forward a lot of methods, in which the local polynomialtransform (LPFT) for nonstationary time-frequency expansion has good timefrequency gathered characteristics, as well as played a very good effect onsuppressing the cross term of multi-component signal.The work done in this paper isusing the transformation method of this time-frequency analysis to analyse thehigh-speed maneuvering target echo, and combined with the LPFT transform, proposespecific methods of judging whether the target exists.
This paper studies five aspects: first, research the reason of producing a crossitem which using the tradition of Wegener-Will distribution to analyse the multicomponent signal; second, research the basic theory of the LPFT transformation, andthe ability of inhibiting the cross terms; third, research how to engender distanceimage generation and signal model; fourth, use LPFT transform to deal with highmaneuvering target detection scheme under the background of gaussian white noise;fifth, propose a solution of using CLPP transformation to judge adjacent target echodistance image under the background of gaussian white noise.
近些年来，众多学者对非平稳的雷达回波信号进行时频分析与研究，提出了很多的研究理论与方法，其中局部多项式傅里叶变换（LPFT）对非平稳信号的时频展开具有很好的时频聚特性集性，以及对多分量信号交叉项的抑制作用起到了很好的效果。本文所做的研究工作就是将这一时频分析的变换方法应用到高速机动目标回波的分析之中，并结合LPFT变换的时频分析处理，给出了目标判别存在与否的具体方法。
本文具体研究五个方面的问题：第一，研究了传统的魏格纳-威尔分布对于多分量的信号产生交叉项的原因；第二，研究了LPFT变换的基本理论，和对交叉项的抑制作用；第三，研究了距离像产生和信号模型；第四，提出了高斯白噪声背景下基于LPFT变换的高速机动目标的检测方案；第五，提出了高斯白噪声背景下基于目标相邻回波距离像的CLPP变换的目标判别方案。
In the middle of the last century, with the development of the radar detectiontechnology, high resolution radar was used more and more, specific. Radar automatictarget recognition technology has become a hot spot in the study of this field In thisfield, for high maneuvering target identification is a very important research direction,it is a very important research topic to determine the presence of the target of researchwork according to the target echo characteristics.
In recent years, many scholars have do some research about the non-stationaryradar echoes signal, puts forward a lot of methods, in which the local polynomialtransform (LPFT) for nonstationary time-frequency expansion has good timefrequency gathered characteristics, as well as played a very good effect onsuppressing the cross term of multi-component signal.The work done in this paper isusing the transformation method of this time-frequency analysis to analyse thehigh-speed maneuvering target echo, and combined with the LPFT transform, proposespecific methods of judging whether the target exists.
This paper studies five aspects: first, research the reason of producing a crossitem which using the tradition of Wegener-Will distribution to analyse the multicomponent signal; second, research the basic theory of the LPFT transformation, andthe ability of inhibiting the cross terms; third, research how to engender distanceimage generation and signal model; fourth, use LPFT transform to deal with highmaneuvering target detection scheme under the background of gaussian white noise;fifth, propose a solution of using CLPP transformation to judge adjacent target echodistance image under the background of gaussian white noise.
引文
[1]杜兰.雷达高分辨距离像目标识别方法研究[D].西安:西安电子科技大学雷达实验室，2007.
[2] Nebabin VG.Methods and techniques of radar recognition. Boston: ArtechHouse,1997.
[3] Barton D.K. Sputunik as observed by C band radar IRE National Conferenee.1959(5):67-73.
[4] Skolnik M. Radar Handbook.Second Edition.北京:电子工业出版社,2003.
[5] Lewis G N,Postol T. Future Challenges to Ballistic Missile Defense[J]. IEEESPeetrum.1997,(9):60-68.
[6] William P D，William W W. Radar Development at Lineoln Laboratoy:Anoverview of the First Fifty Years[J]. Lincoln Laboratoy Journal.2000，12(2):147-166.
[7]杜兰，保铮，邢孟道,直升机雷达回波的分析与检测[J].西安电子科技大学学报.2003,30(5)10:574-579.
[8]杜兰，刘宏伟，保铮,一种基于距离一多普勒二维联合的群目标分辨方法[J].电子学报.2004,30(5):881-885.
[9] Baum C E. On the singularity expansion method for the solution of electromagnet-tic inieraetion problem. Air Force Weapon Lab. Intemational Note88,1971.
[10] Mitehell R A，DewallR. Overview of high range resolution radar target idenifica-tion. In Proeeedings of Automatic Target Recognition Working Group,1994.
[11]裴炳南.高分辨雷达自动目标识别方法研究[D].西安：西安电子科技大学雷达实验室，2002.
[12]邢孟道.基于实测数据的雷达成像方法研究[D].西安:西安电子科技大学雷达实验室，2002.
[13]刘宏伟，杜兰，袁莉，保铮,雷达高分辨距离像目标识别研究进展[J].电子与信息学报.2005,27(8):1328-1334.
[14] An Overview of automatic target recognition[J]. The Lincoln Laboratory Journal.1993,6(l):33-56
[15] Xing M, Bao Z, Pei B,The propercies of high-resolution rang profiles[J].OpticalEngineering.2002,4(3):493-504
[16] Jacobs S P. Automatic target recognition using high-resolution radar range profil-es. Washington,Washington Universitiy,1999.
[17] Jacobs S P, Osollivan J A.Automatic target recognition using sequences of highresolution radar rang-profiles[J].IEEE Trans.on AES.2000,36(2):364-380
[18] Kim K T,Seo D K, Kim H T, Efficient radar target recognition using the MUSICalgorithm and invariant feature[J].IEEE Taans A P.2002:325-337
[19]杜兰,保铮,刘宏伟.高分辨距离像雷达自动目标识别的模板匹配问题[J]，第九届全国雷达学术年会论文集.2004,8:509-512.
[20] Bharadwaj P, Runkle P, Carin L.Multiaspact classification of airborne targetsviaphysics-based HMMs and matching pursuits[J].IEEE Trans.onA.E.S.2001:595-606
[21]张贤达，保铮.非平稳信号分析与处理[M].北京：国防工业出版社,1998.
[22] K. Abed-Meraim, A. Beghdadi, Multi-line fitting using polynomial phase transfo-rms and downsampling[C], Proceedings of IEEE International Conference onAcoustics, Speech, and Signal Processing,2001:1701-1704.
[23] S. Stankovi, I. Djurovi, Motion parameter estimation by using time-frequencyrepresentations[J], Electronics Letters,2001,37(24):1446-1448.
[24] S. Peleg, B. Porat, The Cramer-Rao lower bound for signals with constantamplitude and polynomial phase[J], IEEE Trans. Signal Process.,1991,39(3):749–752.
[25] P. O’Shea, A new technique for instantaneous frequency rate estimation[J], IEEESignal Processing Letters,2002,9(8):251–252.
[26] S. Peleg and B. Friedlander, The discrete polynomial phase transform[J], IEEETrans. Signal Process.,1995,43(8):1901-1914.
[27] S. Golden, B. Friedlander, A modification of the discrete polynomialtransform[J], IEEE Trans. Signal Process.,1998,46(5):1452-1455.
[28] T. J. Abatzoglou，Fast maximum likelihood joint estimation of frequency andfrequency rate[J], IEEE Trans. Aerosp. Electron. Syst.,1986,22:708-715.
[29] A. Scaglione, S. Barbarossa, Statistical analysis of the product high-orderambiguity function[J], IEEE Trans. Inf. Theory,1999,45(1):343-356.
[30] B. Porat, B. Friedlander, Asymptotic statistical analysis of the high-orderambiguity function for parameter estimation of polynomial-phase signals[J],IEEE Trans. Inf. Theory,1996,42(3):995-1001
[31] A. Scaglione, S. Barbarossa, On the spectral properties of polynomial-phasesignals[J], IEEE Signal Process. Lett.,1998,5(9):237-240.
[32] P. Tichavsky, P. Handel, Multicomponent polynomial phase signal analysis usinga tracking algorithm[J], IEEE Trans. Signal Process.,1999,47(5):1390-1395.
[33] B. Barkat, B. Boashash, Design of higher order polynomial Wigner-Villedistributions[J], IEEE Trans. Signal Process.,1999,47(9):2608-2611.
[34] M. Farquharson, P. O'Shea, G. Ledwich, A computationally efficient techniquefor estimating the parameters of polynomial-phase signals from noisyobservations[J], IEEE Trans. Signal Process.,2005,53(8):3337-3342.
[35] P. Wang, I. Djurovic, J. Yang, Generalized High-Order Phase Function forParameter Estimation of Polynomial Phase Signal[J], IEEE Trans. SignalProcess.,2008,56(7):3023-3028.
[36] J. ngeby, Aliasing of polynomial-phase signal parameters[J], IEEE Trans. Sig-nal Process.,2000,48(5):1488-1491.
[37] J. ngeby, Estimating signal parameters using the nonlinear instantaneous leastsquares approach[J], IEEE Trans. Signal Process.,2000,48(10):2721-2732.
[38] S. Barbarossa, V. Petrone, Analysis of polynomial-phase signals by the integratedgeneralised ambiguity function[J], IEEE Trans. Signal Process.,1997,45(2):316-327.
[39] J. M. Francos and B. J. Friedlander，Bounds for estimation of multicomponentsignals with random amplitude and deterministic phase[J], IEEE Trans. SignalProcess.,1995,43(5):1161-1172.
[40] B. Friedlander and J. M. Francos, Estimation of amplitudes and phase parametersof multicomponent signals[J], IEEE Trans. Signal Process.,1995,43(4):917-926.
[41] B. Boashash and P.J. O'Shea, Polynomial Wigner-Ville distributions and theirrelationship to time-varying higher order spectra[J], IEEE Trans. Signal Process.,1994，42(1):216-220.
[42] M. Benidir, A. Ouldali, Polynomial phase signal analysis based on the polyno-mial derivatives decompositions[J], IEEE Trans. Signal Process.,1999,47(7):1954-1965
[43] P. O'Shea, A fast algorithm for estimating the parameters of a quadratic FMsignal[J], IEEE Trans. Signal Process.,2004,52(2):385-393.
[44] K.K. Clarke, D.T. Hess, Communication Circuits: Analysis and Design[M],Addison-Wesley,1971.
[45] V. Katkovnik, Local polynomial periodagrams for signals with the time-varyingfrequency and amplitude[C], IEEE International Conference on Acoustics,Speech and Signal Processing,1996, pp.1399–1402.
[46] V. Katkovnik, A new form of the fourier transform for time-varying frequencyestimation[J], Signal Process. Int. J.,1995，47(2):187-200.
[47]许述文.窄带、宽带雷达机动目标检测技术研究[D].西安:西安电子科技大学雷达实验室，2011.
[48] Papoulis A,Pillai S.U.Probability,Random variables,and Stochastic Processes,(Fourth-edition).McGraw-Hill Higher Education,2002
[49] Barber C.B.,Dobkin D.P.,Huhdanpaa H.T.The Quick hull Algorithm for ConvexHulls[J].ACM Trans Mathematical Software,1996,22(4):496-483.
[50] Lim,Jae S.Two-Dimensional Signal and Image Processing,Englewood Cliffs[J].NJ,Prentice Hall,1990:469-476.
[51] M.Skolnik(Ed.),Radar Handbook(2nd ed.),New York:McGraw-Hill,1990,Ch.2.
[52] Xing M D, Bao Z, Pei B N. Properties of high-resolution range profiles[J].Optical Engineering,2002,41(2):493-504.
[53] Zyweck A, Bogner R E.Radar target classification of commercial aircraft[J].IEEE Transaction on Aerospace and Electronic Systems,1996,32(2):598-606.
[54] Du L, Liu H W, Bao Z.Radar HRRP target recognition based on higher orderspectra[J].IEEE Transaction on Signal Processing,2005,53(7):2359-2368.
[55] Du L, Liu H W,Bao Z.A two-distribution compounded statistical model forradar HRRP target recognition[J].IEEE Transaction on Signal Processing,2006,54(6):2226-2238.
[56] Du L, Liu H W, Bao Z. Radar HRRP statistical recognition:parament model andmodel selection [J]. IEEE Transaction on Singal Processing2008,56(5):1931-1944.
[57] Zyweck A, Boner R E. High-resolution radar imagery of the Mirage III aircr-aft[J].IEEE Transaction on Antenna Propagation,1994,42(9):1356-1360.
[58] Shui P L,Bao Z,Su H T.Nonparametric Detection of Frequency Modulated.Signals using Time-Frequency Ridge Energy[J].IEEE Transaction on signalProcessing,2008,56(5):1749-1760.
[59] Rousseeuw P J,Croux C.Alternative to the median absolute deviation[J].Jour.ofthe American Statistical Association,1993,88(424):1273-1283.
[60] Gerlach K,Steiner M.Detection of a spatially distributed target in white noise[J].IEEE Signal Processing Letters,1997,4(7):198-200.
[2] Nebabin VG.Methods and techniques of radar recognition. Boston: ArtechHouse,1997.
[3] Barton D.K. Sputunik as observed by C band radar IRE National Conferenee.1959(5):67-73.
[4] Skolnik M. Radar Handbook.Second Edition.北京:电子工业出版社,2003.
[5] Lewis G N,Postol T. Future Challenges to Ballistic Missile Defense[J]. IEEESPeetrum.1997,(9):60-68.
[6] William P D，William W W. Radar Development at Lineoln Laboratoy:Anoverview of the First Fifty Years[J]. Lincoln Laboratoy Journal.2000，12(2):147-166.
[7]杜兰，保铮，邢孟道,直升机雷达回波的分析与检测[J].西安电子科技大学学报.2003,30(5)10:574-579.
[8]杜兰，刘宏伟，保铮,一种基于距离一多普勒二维联合的群目标分辨方法[J].电子学报.2004,30(5):881-885.
[9] Baum C E. On the singularity expansion method for the solution of electromagnet-tic inieraetion problem. Air Force Weapon Lab. Intemational Note88,1971.
[10] Mitehell R A，DewallR. Overview of high range resolution radar target idenifica-tion. In Proeeedings of Automatic Target Recognition Working Group,1994.
[11]裴炳南.高分辨雷达自动目标识别方法研究[D].西安：西安电子科技大学雷达实验室，2002.
[12]邢孟道.基于实测数据的雷达成像方法研究[D].西安:西安电子科技大学雷达实验室，2002.
[13]刘宏伟，杜兰，袁莉，保铮,雷达高分辨距离像目标识别研究进展[J].电子与信息学报.2005,27(8):1328-1334.
[14] An Overview of automatic target recognition[J]. The Lincoln Laboratory Journal.1993,6(l):33-56
[15] Xing M, Bao Z, Pei B,The propercies of high-resolution rang profiles[J].OpticalEngineering.2002,4(3):493-504
[16] Jacobs S P. Automatic target recognition using high-resolution radar range profil-es. Washington,Washington Universitiy,1999.
[17] Jacobs S P, Osollivan J A.Automatic target recognition using sequences of highresolution radar rang-profiles[J].IEEE Trans.on AES.2000,36(2):364-380
[18] Kim K T,Seo D K, Kim H T, Efficient radar target recognition using the MUSICalgorithm and invariant feature[J].IEEE Taans A P.2002:325-337
[19]杜兰,保铮,刘宏伟.高分辨距离像雷达自动目标识别的模板匹配问题[J]，第九届全国雷达学术年会论文集.2004,8:509-512.
[20] Bharadwaj P, Runkle P, Carin L.Multiaspact classification of airborne targetsviaphysics-based HMMs and matching pursuits[J].IEEE Trans.onA.E.S.2001:595-606
[21]张贤达，保铮.非平稳信号分析与处理[M].北京：国防工业出版社,1998.
[22] K. Abed-Meraim, A. Beghdadi, Multi-line fitting using polynomial phase transfo-rms and downsampling[C], Proceedings of IEEE International Conference onAcoustics, Speech, and Signal Processing,2001:1701-1704.
[23] S. Stankovi, I. Djurovi, Motion parameter estimation by using time-frequencyrepresentations[J], Electronics Letters,2001,37(24):1446-1448.
[24] S. Peleg, B. Porat, The Cramer-Rao lower bound for signals with constantamplitude and polynomial phase[J], IEEE Trans. Signal Process.,1991,39(3):749–752.
[25] P. O’Shea, A new technique for instantaneous frequency rate estimation[J], IEEESignal Processing Letters,2002,9(8):251–252.
[26] S. Peleg and B. Friedlander, The discrete polynomial phase transform[J], IEEETrans. Signal Process.,1995,43(8):1901-1914.
[27] S. Golden, B. Friedlander, A modification of the discrete polynomialtransform[J], IEEE Trans. Signal Process.,1998,46(5):1452-1455.
[28] T. J. Abatzoglou，Fast maximum likelihood joint estimation of frequency andfrequency rate[J], IEEE Trans. Aerosp. Electron. Syst.,1986,22:708-715.
[29] A. Scaglione, S. Barbarossa, Statistical analysis of the product high-orderambiguity function[J], IEEE Trans. Inf. Theory,1999,45(1):343-356.
[30] B. Porat, B. Friedlander, Asymptotic statistical analysis of the high-orderambiguity function for parameter estimation of polynomial-phase signals[J],IEEE Trans. Inf. Theory,1996,42(3):995-1001
[31] A. Scaglione, S. Barbarossa, On the spectral properties of polynomial-phasesignals[J], IEEE Signal Process. Lett.,1998,5(9):237-240.
[32] P. Tichavsky, P. Handel, Multicomponent polynomial phase signal analysis usinga tracking algorithm[J], IEEE Trans. Signal Process.,1999,47(5):1390-1395.
[33] B. Barkat, B. Boashash, Design of higher order polynomial Wigner-Villedistributions[J], IEEE Trans. Signal Process.,1999,47(9):2608-2611.
[34] M. Farquharson, P. O'Shea, G. Ledwich, A computationally efficient techniquefor estimating the parameters of polynomial-phase signals from noisyobservations[J], IEEE Trans. Signal Process.,2005,53(8):3337-3342.
[35] P. Wang, I. Djurovic, J. Yang, Generalized High-Order Phase Function forParameter Estimation of Polynomial Phase Signal[J], IEEE Trans. SignalProcess.,2008,56(7):3023-3028.
[36] J. ngeby, Aliasing of polynomial-phase signal parameters[J], IEEE Trans. Sig-nal Process.,2000,48(5):1488-1491.
[37] J. ngeby, Estimating signal parameters using the nonlinear instantaneous leastsquares approach[J], IEEE Trans. Signal Process.,2000,48(10):2721-2732.
[38] S. Barbarossa, V. Petrone, Analysis of polynomial-phase signals by the integratedgeneralised ambiguity function[J], IEEE Trans. Signal Process.,1997,45(2):316-327.
[39] J. M. Francos and B. J. Friedlander，Bounds for estimation of multicomponentsignals with random amplitude and deterministic phase[J], IEEE Trans. SignalProcess.,1995,43(5):1161-1172.
[40] B. Friedlander and J. M. Francos, Estimation of amplitudes and phase parametersof multicomponent signals[J], IEEE Trans. Signal Process.,1995,43(4):917-926.
[41] B. Boashash and P.J. O'Shea, Polynomial Wigner-Ville distributions and theirrelationship to time-varying higher order spectra[J], IEEE Trans. Signal Process.,1994，42(1):216-220.
[42] M. Benidir, A. Ouldali, Polynomial phase signal analysis based on the polyno-mial derivatives decompositions[J], IEEE Trans. Signal Process.,1999,47(7):1954-1965
[43] P. O'Shea, A fast algorithm for estimating the parameters of a quadratic FMsignal[J], IEEE Trans. Signal Process.,2004,52(2):385-393.
[44] K.K. Clarke, D.T. Hess, Communication Circuits: Analysis and Design[M],Addison-Wesley,1971.
[45] V. Katkovnik, Local polynomial periodagrams for signals with the time-varyingfrequency and amplitude[C], IEEE International Conference on Acoustics,Speech and Signal Processing,1996, pp.1399–1402.
[46] V. Katkovnik, A new form of the fourier transform for time-varying frequencyestimation[J], Signal Process. Int. J.,1995，47(2):187-200.
[47]许述文.窄带、宽带雷达机动目标检测技术研究[D].西安:西安电子科技大学雷达实验室，2011.
[48] Papoulis A,Pillai S.U.Probability,Random variables,and Stochastic Processes,(Fourth-edition).McGraw-Hill Higher Education,2002
[49] Barber C.B.,Dobkin D.P.,Huhdanpaa H.T.The Quick hull Algorithm for ConvexHulls[J].ACM Trans Mathematical Software,1996,22(4):496-483.
[50] Lim,Jae S.Two-Dimensional Signal and Image Processing,Englewood Cliffs[J].NJ,Prentice Hall,1990:469-476.
[51] M.Skolnik(Ed.),Radar Handbook(2nd ed.),New York:McGraw-Hill,1990,Ch.2.
[52] Xing M D, Bao Z, Pei B N. Properties of high-resolution range profiles[J].Optical Engineering,2002,41(2):493-504.
[53] Zyweck A, Bogner R E.Radar target classification of commercial aircraft[J].IEEE Transaction on Aerospace and Electronic Systems,1996,32(2):598-606.
[54] Du L, Liu H W, Bao Z.Radar HRRP target recognition based on higher orderspectra[J].IEEE Transaction on Signal Processing,2005,53(7):2359-2368.
[55] Du L, Liu H W,Bao Z.A two-distribution compounded statistical model forradar HRRP target recognition[J].IEEE Transaction on Signal Processing,2006,54(6):2226-2238.
[56] Du L, Liu H W, Bao Z. Radar HRRP statistical recognition:parament model andmodel selection [J]. IEEE Transaction on Singal Processing2008,56(5):1931-1944.
[57] Zyweck A, Boner R E. High-resolution radar imagery of the Mirage III aircr-aft[J].IEEE Transaction on Antenna Propagation,1994,42(9):1356-1360.
[58] Shui P L,Bao Z,Su H T.Nonparametric Detection of Frequency Modulated.Signals using Time-Frequency Ridge Energy[J].IEEE Transaction on signalProcessing,2008,56(5):1749-1760.
[59] Rousseeuw P J,Croux C.Alternative to the median absolute deviation[J].Jour.ofthe American Statistical Association,1993,88(424):1273-1283.
[60] Gerlach K,Steiner M.Detection of a spatially distributed target in white noise[J].IEEE Signal Processing Letters,1997,4(7):198-200.