雷达目标跟踪算法研究
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摘要
在众多领域,比如军事上的战场监视、防空系统,民用上的交通管制、机器智能、医疗器械,目标跟踪都是一个基本的或重要的问题。雷达跟踪系统中的关键就是目标跟踪算法的设计。随着应用的推广,各种新的技术被应用到雷达目标跟踪中来以适应更加复杂的环境。而目标跟踪中的一个核心部分就是滤波算法,本文重点研究了现阶段应用比较广泛的几种滤波算法,并讨论了这些跟踪算法目前所存在的问题。
本文首先概述了目标跟踪模型的建立,给出了几种常见的机动目标运动模型和量测模型坐标系的选择,在此基础上介绍了α-β滤波和α-β-γ滤波,改进型α-β滤波,重点分析了kalman滤波(包括扩展kalman滤波)跟踪技术,通过建立相应的模型仿真了解到,标准kalman滤波对于匀速直线运动跟踪效果较好,而基于EKF的跟踪方法对于线性或者弱机动性的目标有很精确的跟踪性能,但是,对于多维状态的跟踪系统,EKF中的雅克比矩阵计算会很复杂也很困难。其次,本文还详细介绍了基于kalman滤波的交互多模型(IMM:Interacting Multiple Model)目标跟踪技术,阐述了该算法的原理和滤波步骤,分析了其性能和优点,提出了一种优化的2模型IMM算法,并通过建立相同目标模型的matlab仿真,和其他算法的性能作了对比,结果表明改进的IMM算法具有良好的跟踪性能,是一种可行的算法。最后对其他几种常见滤波进行了扼要的介绍,结论部分对未来的研究方向、发展趋势以及滤波发散问题作了展望和建议。
In many fields, like in the field of the battlefield surveillance, antiaircraft system in a war, and the civil traffic control, machine intelligence, medical equipment, target tracking is a basic or an important problem. The key of radar tracking system is design of target tracking algorithm. As its application in more fields, many new techniques are introduced to the radar target tracking for more complicated situation. While, one core part in target tracking is filtering algorithm. This dissertation studies several usually ways in filter arithmetic and advances some problems.
Firstly, this dissertation summarizes the establishment of the target tracking model, and gives some of familiar maneuvering models and introduces the choice of coordinate. And then,α-βfilter arithmetic,α-β-γfilter arithmetic and improvedα-βfilter arithmetic are introduced. The principle analyzes the classical target tracking method based on kalman filter. Through a simulation, it is known that traditional kalman method is the most useful in a linear system and target tracking method based EKF performs well when tracking a target in a linear system or with small maneuver. Also, the Jacobians matrix of EKF is very hard to calculate in tracking system with multidimensional state. Secondly, the algorithm of Interacting Multiple Model (IMM) basing on kalman for the maneuvering target and its merits are mostly studied. And a new method: 2-model IMM algorithm is proposed. Through making matlab experiment, we can draw the conclusion that this algorithm obtains a better performance in target tracking. At last, we introduce other filter algorithms and summary this paper and prospect the future research directions and development trend.
本文首先概述了目标跟踪模型的建立,给出了几种常见的机动目标运动模型和量测模型坐标系的选择,在此基础上介绍了α-β滤波和α-β-γ滤波,改进型α-β滤波,重点分析了kalman滤波(包括扩展kalman滤波)跟踪技术,通过建立相应的模型仿真了解到,标准kalman滤波对于匀速直线运动跟踪效果较好,而基于EKF的跟踪方法对于线性或者弱机动性的目标有很精确的跟踪性能,但是,对于多维状态的跟踪系统,EKF中的雅克比矩阵计算会很复杂也很困难。其次,本文还详细介绍了基于kalman滤波的交互多模型(IMM:Interacting Multiple Model)目标跟踪技术,阐述了该算法的原理和滤波步骤,分析了其性能和优点,提出了一种优化的2模型IMM算法,并通过建立相同目标模型的matlab仿真,和其他算法的性能作了对比,结果表明改进的IMM算法具有良好的跟踪性能,是一种可行的算法。最后对其他几种常见滤波进行了扼要的介绍,结论部分对未来的研究方向、发展趋势以及滤波发散问题作了展望和建议。
In many fields, like in the field of the battlefield surveillance, antiaircraft system in a war, and the civil traffic control, machine intelligence, medical equipment, target tracking is a basic or an important problem. The key of radar tracking system is design of target tracking algorithm. As its application in more fields, many new techniques are introduced to the radar target tracking for more complicated situation. While, one core part in target tracking is filtering algorithm. This dissertation studies several usually ways in filter arithmetic and advances some problems.
Firstly, this dissertation summarizes the establishment of the target tracking model, and gives some of familiar maneuvering models and introduces the choice of coordinate. And then,α-βfilter arithmetic,α-β-γfilter arithmetic and improvedα-βfilter arithmetic are introduced. The principle analyzes the classical target tracking method based on kalman filter. Through a simulation, it is known that traditional kalman method is the most useful in a linear system and target tracking method based EKF performs well when tracking a target in a linear system or with small maneuver. Also, the Jacobians matrix of EKF is very hard to calculate in tracking system with multidimensional state. Secondly, the algorithm of Interacting Multiple Model (IMM) basing on kalman for the maneuvering target and its merits are mostly studied. And a new method: 2-model IMM algorithm is proposed. Through making matlab experiment, we can draw the conclusion that this algorithm obtains a better performance in target tracking. At last, we introduce other filter algorithms and summary this paper and prospect the future research directions and development trend.
引文
[1]丁鹭飞,耿富录.雷达原理.第三版.西安:西安电子科技大学出版社,2005
[2]A.费利那,F.A.斯塔德.雷达数据处理第一卷.第一版.北京:国防工业出版社,1988
[3]孙仲康.雷达数据数字处理.第一版.北京:国防工业出版社,1983
[4]王红军,徐敬.舰载无源被动定位与卡尔曼滤波.火力与指挥控制,2002,24(2)
[5]周宏仁,敬忠良,王培德.机动目标跟踪.北京:北京国防工业出版社,1991
[6]陶冶,孙富春,孙继河,袁小虎.一类新型机动目标跟踪算法.海军航空工程学院学报,2005,20(1):107-110
[7]Kalman R E.A new approach to linear filtering and prediction problems.Journal of Basic Engineering Trans.On ASME,1960,82D(1):35-45
[8]Tenney R,Hebbert R,Sandell N Jr.A tracking filter for maneuvering sources.IEEE Trans.On Automation Control,1977,22(2):246-251
[9]Johnson G W.Choice of coordinates and computational difficulty.IEEE Trans On Automatic Control,1974,19(2):77-80
[10]Friedland B.Optimum steady-state position and velocity estimation using noisy sampled position data[J].IEEE Trans.On Aerospace and Electronic Systems,1973,9(6):906-111
[11]Singer R A.Estimating optimal tracking filter performance for manned maneuvering target[J].IEEE Trans.On Aerospace and Electronic Systems,1970,6(4):473-483
[12]陆光华,彭学愚,张林让等.随机信号处理。西安:西安电子科技大学出版社,2002
[13]Howard R A.System analysis of semi-Markov processor[J].IEEE Trans.On Military Electronics,1964,8(2):114-124
[14]Moose R L.An adaptive state estimation solution to the maneuvering target problem [J].IEEE Trans.On Automatic Control,1975,20(6):359-362
[15]王建新,钱冬宁,周俊羽.数字滤波技术在弹道外推中的应用.火控雷达技术.1996(6):47-51
[16]王红亮,李枫,赵亦工.一种机动目标跟踪的自适应α-β滤波算法.雷达科学与技术,2007(4):278-283
[17]潘显俊,吴彦鸿,贾鑫.α-β滤波器在相控阵雷达机动目标跟踪中的应用.装备指挥技术学院学报,2005,16(2):96-100
[18]金宏斌,徐毓,钱琼芬.机动目标跟踪的改进α-β算法.空军雷达学院学报,2003,17(2):27-29
[19]许录平。跟踪机动目标的自适应α-β滤波算法.西安电子科技大学学报,1998,25(3):314-317
[20]王立辉,申卯兴,赵海洲,吴文洲.Kalman滤波在雷达系统中的应用.弹箭与制导学报,2006,26(1):584-586
[21]苏林,尚朝轩.基于卡尔曼滤波器的雷达跟踪.微计算机信息,2006,22(9):20-22
[22]王海军,刘进忙.基于卡尔曼滤波的无源雷达目标跟踪分析.战术导弹技术,2005(6):43-45
[23]程赛先.三维雷达跟踪改进的卡尔曼滤波设计.情报指挥控制系统与仿真技术,2002(7):33-44
[24]李燕,郭立,朱嘉.一种精确跟踪目标的非线性滤波算法[J].中国科学技术大学学报,2001(4):488-494
[25]王宏强,黎湘,刘丹,郭桂蓉.非线性系统中的机动目标跟踪算法.国防科技大学学报,2002,24(4):57-60
[26]杨春玲,倪晋麟,刘国岁等.转换坐标卡尔曼滤波器的雷达目标跟踪.电子学报,1999(3):121-123
[27]宋志勇.非线性随机离散系统推广卡尔曼滤波方法收敛性分析[J].控制理论与应用,2000(2):264-269
[28]唐涛,黄永梅.改进的EKF算法在目标跟踪中的运用.光电工程,2005,32(9):16-18
[29]方青,梅晓春,张育平.用于机动目标跟踪的Kalman滤波器的设计.雷达科学与技术,2006(1):50-55
[30]高勤,李志强,都学新.一种新型自适应卡尔曼滤波算法.现代雷达,2001(6):29-34
[31]汪颖进,张桂林.新的基于Kalman滤波的跟踪方法。红外与激光工程,2004,33(5):505-509
[32]王银坤,肖明清.一种基于改进型Kalman滤波器的目标定位算法.空军工程大学学报,2002,3(5):17-20
[33]Boers Y,Driessen J N.Interacting multiple model particle filter.IEEE Proc.Radar Sonar Navig,2003,150(5):344-349
[34]Mazor E,Averbuch A,Bar-shalom Y,etal.Interacting multiple model methods in target tracking.IEEE Trans On Aerospace and Electronic Systems,1998,34(1):103-122
[35]Blom H A P,Bar-shalom Y.The interacting multiple model algorithm for systems with Markovian switching coefficients.IEEE Trans.On Automatic Control,1988,33(8):780-783
[36]Bar-Shalom Y,Chang K C,Blom H A P.Tracking a maneuvering target using input estimation versus the interacting multiple model algorithm.IEEE Transactions on Aerospace and Electronic System,1989,AES-25(2):296-300
[37]张孝令.贝叶斯动态模型及其预测.济南:山东科学技术出版社,1992
[38]Deng X L,Xie J Y,Guo W H.Bayesian Target Tracking Based on Particle Filter.Journal of Systems Engineering and Electronics,2005,16(3):545-549
[39]王志敏,熊纯.IMM滤波算法在目标跟踪中的建模和仿真。长沙航空职业技术学院学报,2003,3(4):33-36
[40]王志敏,肖卫初.机动目标跟踪中IMM算法的性能分析.湖南城市学院学报,2003,24(6):109-111
[41]朱志宇,戴晓强.基于改进自适应IMM算法的机动目标跟踪.弹箭与制导学报,2006,27(4):43-46
[42]杨飞,巴宏欣,奚和平,赵宗贵.一种机动目标跟踪的IMM模型优化设计方法.解放军理工大学学报,2005,6(5):428-431
[43]严超.目标跟踪下的Kalman算法与IMM算法性能比较。科技情报开发与经济,2007,17(15):229-231
[44]刘士建,郭立,李士民.变结构多模型估计单Kalman滤波跟踪机动目标算法.电路与系统学报,2003,8(5):28-31
[45]戴晓强,刘维亭,朱志宇.基于模糊自适应IMM算法的机动目标跟踪方法.船舶工程,2007,29(3):11-14
[46]Bar-Shalom Y,Huimin C.IMM Estimator with Out-of Sequence Measurement.IEEE Trans On Aerospace and Electronic Systems,2005,41(1):90-98
[2]A.费利那,F.A.斯塔德.雷达数据处理第一卷.第一版.北京:国防工业出版社,1988
[3]孙仲康.雷达数据数字处理.第一版.北京:国防工业出版社,1983
[4]王红军,徐敬.舰载无源被动定位与卡尔曼滤波.火力与指挥控制,2002,24(2)
[5]周宏仁,敬忠良,王培德.机动目标跟踪.北京:北京国防工业出版社,1991
[6]陶冶,孙富春,孙继河,袁小虎.一类新型机动目标跟踪算法.海军航空工程学院学报,2005,20(1):107-110
[7]Kalman R E.A new approach to linear filtering and prediction problems.Journal of Basic Engineering Trans.On ASME,1960,82D(1):35-45
[8]Tenney R,Hebbert R,Sandell N Jr.A tracking filter for maneuvering sources.IEEE Trans.On Automation Control,1977,22(2):246-251
[9]Johnson G W.Choice of coordinates and computational difficulty.IEEE Trans On Automatic Control,1974,19(2):77-80
[10]Friedland B.Optimum steady-state position and velocity estimation using noisy sampled position data[J].IEEE Trans.On Aerospace and Electronic Systems,1973,9(6):906-111
[11]Singer R A.Estimating optimal tracking filter performance for manned maneuvering target[J].IEEE Trans.On Aerospace and Electronic Systems,1970,6(4):473-483
[12]陆光华,彭学愚,张林让等.随机信号处理。西安:西安电子科技大学出版社,2002
[13]Howard R A.System analysis of semi-Markov processor[J].IEEE Trans.On Military Electronics,1964,8(2):114-124
[14]Moose R L.An adaptive state estimation solution to the maneuvering target problem [J].IEEE Trans.On Automatic Control,1975,20(6):359-362
[15]王建新,钱冬宁,周俊羽.数字滤波技术在弹道外推中的应用.火控雷达技术.1996(6):47-51
[16]王红亮,李枫,赵亦工.一种机动目标跟踪的自适应α-β滤波算法.雷达科学与技术,2007(4):278-283
[17]潘显俊,吴彦鸿,贾鑫.α-β滤波器在相控阵雷达机动目标跟踪中的应用.装备指挥技术学院学报,2005,16(2):96-100
[18]金宏斌,徐毓,钱琼芬.机动目标跟踪的改进α-β算法.空军雷达学院学报,2003,17(2):27-29
[19]许录平。跟踪机动目标的自适应α-β滤波算法.西安电子科技大学学报,1998,25(3):314-317
[20]王立辉,申卯兴,赵海洲,吴文洲.Kalman滤波在雷达系统中的应用.弹箭与制导学报,2006,26(1):584-586
[21]苏林,尚朝轩.基于卡尔曼滤波器的雷达跟踪.微计算机信息,2006,22(9):20-22
[22]王海军,刘进忙.基于卡尔曼滤波的无源雷达目标跟踪分析.战术导弹技术,2005(6):43-45
[23]程赛先.三维雷达跟踪改进的卡尔曼滤波设计.情报指挥控制系统与仿真技术,2002(7):33-44
[24]李燕,郭立,朱嘉.一种精确跟踪目标的非线性滤波算法[J].中国科学技术大学学报,2001(4):488-494
[25]王宏强,黎湘,刘丹,郭桂蓉.非线性系统中的机动目标跟踪算法.国防科技大学学报,2002,24(4):57-60
[26]杨春玲,倪晋麟,刘国岁等.转换坐标卡尔曼滤波器的雷达目标跟踪.电子学报,1999(3):121-123
[27]宋志勇.非线性随机离散系统推广卡尔曼滤波方法收敛性分析[J].控制理论与应用,2000(2):264-269
[28]唐涛,黄永梅.改进的EKF算法在目标跟踪中的运用.光电工程,2005,32(9):16-18
[29]方青,梅晓春,张育平.用于机动目标跟踪的Kalman滤波器的设计.雷达科学与技术,2006(1):50-55
[30]高勤,李志强,都学新.一种新型自适应卡尔曼滤波算法.现代雷达,2001(6):29-34
[31]汪颖进,张桂林.新的基于Kalman滤波的跟踪方法。红外与激光工程,2004,33(5):505-509
[32]王银坤,肖明清.一种基于改进型Kalman滤波器的目标定位算法.空军工程大学学报,2002,3(5):17-20
[33]Boers Y,Driessen J N.Interacting multiple model particle filter.IEEE Proc.Radar Sonar Navig,2003,150(5):344-349
[34]Mazor E,Averbuch A,Bar-shalom Y,etal.Interacting multiple model methods in target tracking.IEEE Trans On Aerospace and Electronic Systems,1998,34(1):103-122
[35]Blom H A P,Bar-shalom Y.The interacting multiple model algorithm for systems with Markovian switching coefficients.IEEE Trans.On Automatic Control,1988,33(8):780-783
[36]Bar-Shalom Y,Chang K C,Blom H A P.Tracking a maneuvering target using input estimation versus the interacting multiple model algorithm.IEEE Transactions on Aerospace and Electronic System,1989,AES-25(2):296-300
[37]张孝令.贝叶斯动态模型及其预测.济南:山东科学技术出版社,1992
[38]Deng X L,Xie J Y,Guo W H.Bayesian Target Tracking Based on Particle Filter.Journal of Systems Engineering and Electronics,2005,16(3):545-549
[39]王志敏,熊纯.IMM滤波算法在目标跟踪中的建模和仿真。长沙航空职业技术学院学报,2003,3(4):33-36
[40]王志敏,肖卫初.机动目标跟踪中IMM算法的性能分析.湖南城市学院学报,2003,24(6):109-111
[41]朱志宇,戴晓强.基于改进自适应IMM算法的机动目标跟踪.弹箭与制导学报,2006,27(4):43-46
[42]杨飞,巴宏欣,奚和平,赵宗贵.一种机动目标跟踪的IMM模型优化设计方法.解放军理工大学学报,2005,6(5):428-431
[43]严超.目标跟踪下的Kalman算法与IMM算法性能比较。科技情报开发与经济,2007,17(15):229-231
[44]刘士建,郭立,李士民.变结构多模型估计单Kalman滤波跟踪机动目标算法.电路与系统学报,2003,8(5):28-31
[45]戴晓强,刘维亭,朱志宇.基于模糊自适应IMM算法的机动目标跟踪方法.船舶工程,2007,29(3):11-14
[46]Bar-Shalom Y,Huimin C.IMM Estimator with Out-of Sequence Measurement.IEEE Trans On Aerospace and Electronic Systems,2005,41(1):90-98