高频地波雷达舰船目标跟踪关键技术研究
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摘要
由于高频地波雷达具有探测距离远,探测范围大等优良特点,在一些领域有着重要的应用;然而其可能会随着目标自身特性或环境背景差异而出现探测概率低、角探测精度低等不足,给目标跟踪带来很大困难。本文面向高频地波雷达跟踪舰船目标要求,提出或改进了数据处理关键问题若干方法,复杂背景下远端舰船目标的航迹起始与跟踪与是本文研究的重点。
本文首先介绍了雷达目标跟踪中进行状态估计所需要的基本知识。介绍了目标跟踪中经典的卡尔曼滤波器原理、算法步骤;并分析了传统的非线性问题的滤波方法——扩展卡尔曼滤波,它将非线性问题线性化的近似性方法,从而使卡尔曼滤波应用于非线性领域中,本文指出了这种方法的优点与不足。目标机动时,交互多模型滤波方法是最常用的方法之一,本文介绍了这种方法的原理并提出了新的多模型间转移概率的选取方式,改进了算法性能。
地波超视距雷达数据处理过程中,由于远端目标角精度低所引起的切向距离误差更大,导致其航迹的形成往往比较困难。而且,针对远端目标相对较低的探测概率也使数据率变低,增加了航迹起始的不确定性。针对上述问题,基于信息论中的信息熵概念,利用目标探测角度误差与距离误差不相关的特性,本文提出了一种基于信息熵理论的远端航迹起始方法,通过考察目标点迹径向信息(距离、径向速度)与切向信息(角度),将远端航迹起始过程转化成一个从较大信息熵过渡到较小信息熵的过程。并基于贝叶斯估计的理论,引入了信息熵在航迹起始时的计算方法,讨论了信息熵理论框架下暂时航迹、确认航迹、假航迹的确认方法,最后分别通过仿真数据与实际数据验证了这种方法的有效性。
地波超视距雷达的量测方程是非线性的,而且其运动方式有时也存在非线性特征。传统的解决非线性滤波思路是对非线性方程进行线性化近似,但这种近似势必带来线性化误差,而误差的积累会使滤波器性能下降,甚至导致其发散;解决此问题的一种替代思想是根据当前状态值进行采样,采样出的“粒子”可以代替当前状态的分布状况,而采样方式可以分成两类:以无味滤波为代表的确定性采样方式和以粒子滤波为代表的随机采样方式。
无味滤波(UF)为解决非线性问题提供了一种新的思路;首先介绍了无味滤波的原理——无味变换思想,阐述了无味滤波算法步骤;通过与其与扩展卡尔曼滤波对比,证明与扩展卡尔曼滤波相比,无味滤波在计算量上变化不大,而在性能上有较大优势。
粒子滤波(PF)技术通过非参数化的蒙特卡罗模拟方法实现递推贝叶斯滤波,适用于非线性目标运动模型、非高斯噪声背景下的目标跟踪。它的本质是通过寻找一组在状态空间中传播的随机样本对概率密度函数进行近似,因此其初始化精度对滤波效果有较大影响。针对其在应用于雷达目标跟踪时的粒子初始化问题,本文提出了基于竞争机制的粒子初始化方法,根据初始阶段有效粒子数原理选择准确度高的粒子,从而改善其滤波效果。粒子滤波最大的困难是粒子退化,现有两种类型的方法以改善粒子退化问题:优化重要密度函数,重采样;然而它们在使用范围与计算量等方面还有待改善。针对这一情况,本文提出了一种新算法:一步采样粒子滤波方法,该方法与重采样方法出发点相同——即利用新的采样方法改善退化现象,不同点在于:这种方法完全摒弃了“一群粒子在空间中传播”的思维模式,通过滤波均值与方差产生粒子,本方法在计算量与滤波效果方面均优于重采样方法。
概率数据互联(PDA)算法是解决目标数据关联的最常用的方法之一,属于贝叶斯的滤波算法。最优的贝叶斯方法需要对当前时刻以前的所有确认量测集合进行研究,并给出每一个量测序列的概率;而PDA只对最新的确认量测集合进行研究,因此是次优的贝叶斯方法。实验证明:与次优的贝叶斯方法相比,最优贝叶斯方法性能更为优越,但计算量也大得多,很难工程化实现。为在计算量容许的情况下进一步提高PDA算法的性能,本文将历史统计得到的目标速度、航向信息引入PDA算法过程中,仿真实验证明新方法可有效提高数据关联精度和可靠性。
For its good detection performance in long distance and extensive areas, High Frequency Surface Wave Radar (HFSWR) has been in important application in some areas. However, some kinds of shortcomings, like low detection rate, low detection accuracy in angle, may happen with the different characters of targets or with the difference of surroundings, which makes the target tracking much more difficult.
Facing the request to ship target tracking of HFSWR, this paper brings up or improves methods for data processing. The main point is focused on the multi-ships tracking in complex backgrounds and track initiation of targets in long distance. Firstly the paper introduces the basic knowledge about the state estimation in radar target tracking. The classic filtering method in target tracking is Kalman Filter, the paper shows its basic theory and its algorithm process. The traditional filtering method of non-linear filtering is Extend Kalman Filtering (EKF), it extends the Kalman Filter into the non-linear areas through linearization, and the paper shows both the values and the limitations of EKF. When the target is maneuvering, the equation of motion is also non-linear, then the interacting multi-model (IMM) algorithm is one of the most valuable methods, this paper introduces the theory of IMM and brings up a new selection method of transfer probability matrix between multi-models, which improves the performance of the algorithm.
In data processing of HFSWR, a target that is further from the radar will lead to bigger tangential location error, which makes the track initiation difficult. What’s more, relatively low detection probability degreades the data rate, which further adds the indefinability. Aiming at this problem, based on the theory of information entropy, and taking advantage of the non-correlation between the angle error and the range error, this paper brings up a new track initiation method for the far targets, through research on the radial information (range and radial velocity) and tangential information (angle), the track initiation problem is transferred into a process of entropy decrese. The method also shows the calculation of entrapy and the determinant method of temporary tracks, affirmative tracks and false tracks. In the end, both the imitations and the real datas approve the validity of the method.
For the HFSWR, the measurement equation is non-linear and the motion is sometimes non-linear too. Traditional method to solve the non-linear filtering is to approcimate through linearization, while this approcimation will surely bring up the linearization error, and the error accumulation will reduce the performance of filtering and even make the filtering diverge. A substitution of the method is to sampling according to the current state, and the sampling“particles”can show the distribution of current state, there are two kinds of methods based on sampling methods: the confirmed sampling (as the unscented filtering) and the random sampling (as the particle filtering).
Unscented filtering (UF) provides a new way to solve the non-linear problem. The paper firstly introduces the basic principle of unscented filtering——unscented transform, and shows the basic algorithm process. Through compared with EKF, UKF costs a little more in calculation, while shows much better performance in precision for the maneuvering target.
Particle filtering (PF) achieves the recursive Bayes filtering through Monte-Carlo method, which is applicable to target tracking of non-linear and non-Gaussian background, the essence of PF is to seek random samples that spread in the state space, and the precision of initiation affects the filtering performance a lot. Aiming at the problem of initiation in target tracking, this paper brings up the particle filtering initiation method, which is based on the effective numbers of initial particles, in the new method, the filtering performance is improved for the more precise particles are selected. The most difficult problem of PF is particle degeneracy, two main kinds of methods to deal with degeneracy are: (1) optimize selection method of importance density function; (2) resampling. Although importance density function matters a lot to PF, there is still no perfect selection method in general circumstance. Resampling alleviates particle degeneracy, but it takes much calculation, and can hardly satisfy real-time operation. What’s more, resampling decreases diversity of particles hence make algorithm unrobust. Aiming at this problem, the paper brings up a new method: one-step particle filtering method, as well as the resampling method, the new method aims at solving the degeneracy through new sampling method; while the difference is that the new method sample particles not through the particles of prior time, but based on the mean and coviance of prior filtering results. This method shows better performance in both precision and calculation amount.
Probability data association (PDA) algorithm, which belongs to Bayes algorithm, is one of the most useful methods in target tracking. The optimal Bayes method need consider all affirmative measurements and calculate the probability of every measurement sequence, while the PDA algorithm only considers the current affirmative measurements, hence it is sub-optimal Bayes algorithm. It has been proved that at the cost of much more calculation, the optimal Bayes method shows better performance than the sub-optimal Bayes algorithm, while it is difficult in engineerring. To increase the performance of PDA at the condition of proper calculation, this paper leads into the velocity estimation and course estimation which is based on the history information, Simulations show that the new PDA algorithm combined with velocity and course information can improve the accuracy of association.
本文首先介绍了雷达目标跟踪中进行状态估计所需要的基本知识。介绍了目标跟踪中经典的卡尔曼滤波器原理、算法步骤;并分析了传统的非线性问题的滤波方法——扩展卡尔曼滤波,它将非线性问题线性化的近似性方法,从而使卡尔曼滤波应用于非线性领域中,本文指出了这种方法的优点与不足。目标机动时,交互多模型滤波方法是最常用的方法之一,本文介绍了这种方法的原理并提出了新的多模型间转移概率的选取方式,改进了算法性能。
地波超视距雷达数据处理过程中,由于远端目标角精度低所引起的切向距离误差更大,导致其航迹的形成往往比较困难。而且,针对远端目标相对较低的探测概率也使数据率变低,增加了航迹起始的不确定性。针对上述问题,基于信息论中的信息熵概念,利用目标探测角度误差与距离误差不相关的特性,本文提出了一种基于信息熵理论的远端航迹起始方法,通过考察目标点迹径向信息(距离、径向速度)与切向信息(角度),将远端航迹起始过程转化成一个从较大信息熵过渡到较小信息熵的过程。并基于贝叶斯估计的理论,引入了信息熵在航迹起始时的计算方法,讨论了信息熵理论框架下暂时航迹、确认航迹、假航迹的确认方法,最后分别通过仿真数据与实际数据验证了这种方法的有效性。
地波超视距雷达的量测方程是非线性的,而且其运动方式有时也存在非线性特征。传统的解决非线性滤波思路是对非线性方程进行线性化近似,但这种近似势必带来线性化误差,而误差的积累会使滤波器性能下降,甚至导致其发散;解决此问题的一种替代思想是根据当前状态值进行采样,采样出的“粒子”可以代替当前状态的分布状况,而采样方式可以分成两类:以无味滤波为代表的确定性采样方式和以粒子滤波为代表的随机采样方式。
无味滤波(UF)为解决非线性问题提供了一种新的思路;首先介绍了无味滤波的原理——无味变换思想,阐述了无味滤波算法步骤;通过与其与扩展卡尔曼滤波对比,证明与扩展卡尔曼滤波相比,无味滤波在计算量上变化不大,而在性能上有较大优势。
粒子滤波(PF)技术通过非参数化的蒙特卡罗模拟方法实现递推贝叶斯滤波,适用于非线性目标运动模型、非高斯噪声背景下的目标跟踪。它的本质是通过寻找一组在状态空间中传播的随机样本对概率密度函数进行近似,因此其初始化精度对滤波效果有较大影响。针对其在应用于雷达目标跟踪时的粒子初始化问题,本文提出了基于竞争机制的粒子初始化方法,根据初始阶段有效粒子数原理选择准确度高的粒子,从而改善其滤波效果。粒子滤波最大的困难是粒子退化,现有两种类型的方法以改善粒子退化问题:优化重要密度函数,重采样;然而它们在使用范围与计算量等方面还有待改善。针对这一情况,本文提出了一种新算法:一步采样粒子滤波方法,该方法与重采样方法出发点相同——即利用新的采样方法改善退化现象,不同点在于:这种方法完全摒弃了“一群粒子在空间中传播”的思维模式,通过滤波均值与方差产生粒子,本方法在计算量与滤波效果方面均优于重采样方法。
概率数据互联(PDA)算法是解决目标数据关联的最常用的方法之一,属于贝叶斯的滤波算法。最优的贝叶斯方法需要对当前时刻以前的所有确认量测集合进行研究,并给出每一个量测序列的概率;而PDA只对最新的确认量测集合进行研究,因此是次优的贝叶斯方法。实验证明:与次优的贝叶斯方法相比,最优贝叶斯方法性能更为优越,但计算量也大得多,很难工程化实现。为在计算量容许的情况下进一步提高PDA算法的性能,本文将历史统计得到的目标速度、航向信息引入PDA算法过程中,仿真实验证明新方法可有效提高数据关联精度和可靠性。
For its good detection performance in long distance and extensive areas, High Frequency Surface Wave Radar (HFSWR) has been in important application in some areas. However, some kinds of shortcomings, like low detection rate, low detection accuracy in angle, may happen with the different characters of targets or with the difference of surroundings, which makes the target tracking much more difficult.
Facing the request to ship target tracking of HFSWR, this paper brings up or improves methods for data processing. The main point is focused on the multi-ships tracking in complex backgrounds and track initiation of targets in long distance. Firstly the paper introduces the basic knowledge about the state estimation in radar target tracking. The classic filtering method in target tracking is Kalman Filter, the paper shows its basic theory and its algorithm process. The traditional filtering method of non-linear filtering is Extend Kalman Filtering (EKF), it extends the Kalman Filter into the non-linear areas through linearization, and the paper shows both the values and the limitations of EKF. When the target is maneuvering, the equation of motion is also non-linear, then the interacting multi-model (IMM) algorithm is one of the most valuable methods, this paper introduces the theory of IMM and brings up a new selection method of transfer probability matrix between multi-models, which improves the performance of the algorithm.
In data processing of HFSWR, a target that is further from the radar will lead to bigger tangential location error, which makes the track initiation difficult. What’s more, relatively low detection probability degreades the data rate, which further adds the indefinability. Aiming at this problem, based on the theory of information entropy, and taking advantage of the non-correlation between the angle error and the range error, this paper brings up a new track initiation method for the far targets, through research on the radial information (range and radial velocity) and tangential information (angle), the track initiation problem is transferred into a process of entropy decrese. The method also shows the calculation of entrapy and the determinant method of temporary tracks, affirmative tracks and false tracks. In the end, both the imitations and the real datas approve the validity of the method.
For the HFSWR, the measurement equation is non-linear and the motion is sometimes non-linear too. Traditional method to solve the non-linear filtering is to approcimate through linearization, while this approcimation will surely bring up the linearization error, and the error accumulation will reduce the performance of filtering and even make the filtering diverge. A substitution of the method is to sampling according to the current state, and the sampling“particles”can show the distribution of current state, there are two kinds of methods based on sampling methods: the confirmed sampling (as the unscented filtering) and the random sampling (as the particle filtering).
Unscented filtering (UF) provides a new way to solve the non-linear problem. The paper firstly introduces the basic principle of unscented filtering——unscented transform, and shows the basic algorithm process. Through compared with EKF, UKF costs a little more in calculation, while shows much better performance in precision for the maneuvering target.
Particle filtering (PF) achieves the recursive Bayes filtering through Monte-Carlo method, which is applicable to target tracking of non-linear and non-Gaussian background, the essence of PF is to seek random samples that spread in the state space, and the precision of initiation affects the filtering performance a lot. Aiming at the problem of initiation in target tracking, this paper brings up the particle filtering initiation method, which is based on the effective numbers of initial particles, in the new method, the filtering performance is improved for the more precise particles are selected. The most difficult problem of PF is particle degeneracy, two main kinds of methods to deal with degeneracy are: (1) optimize selection method of importance density function; (2) resampling. Although importance density function matters a lot to PF, there is still no perfect selection method in general circumstance. Resampling alleviates particle degeneracy, but it takes much calculation, and can hardly satisfy real-time operation. What’s more, resampling decreases diversity of particles hence make algorithm unrobust. Aiming at this problem, the paper brings up a new method: one-step particle filtering method, as well as the resampling method, the new method aims at solving the degeneracy through new sampling method; while the difference is that the new method sample particles not through the particles of prior time, but based on the mean and coviance of prior filtering results. This method shows better performance in both precision and calculation amount.
Probability data association (PDA) algorithm, which belongs to Bayes algorithm, is one of the most useful methods in target tracking. The optimal Bayes method need consider all affirmative measurements and calculate the probability of every measurement sequence, while the PDA algorithm only considers the current affirmative measurements, hence it is sub-optimal Bayes algorithm. It has been proved that at the cost of much more calculation, the optimal Bayes method shows better performance than the sub-optimal Bayes algorithm, while it is difficult in engineerring. To increase the performance of PDA at the condition of proper calculation, this paper leads into the velocity estimation and course estimation which is based on the history information, Simulations show that the new PDA algorithm combined with velocity and course information can improve the accuracy of association.
引文
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43 Julier, Simon J. and H. F. Durrant-Whyte. Navigation and Parameter Estimationof High Speed Road Vehicles. In Robotics and Automation Conference, 1995: 101~105
44 E. A. Wan, R. Van Der Merwe. The Unscented Kalman Filter for Nonlinear Estimation. Proc. of IEEE Symposium 2000, Lake Louise, Alberta, Canada, 2000:1256~1260
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46 R. Van Der Merwe, Nando De Freitas, Arnaud Doucet, Eric Wan. The Unscented Particle Filter. Advance Neural Inform, Process. 2000: 1596~1603
47 Van der Merwe, R. and E. A. Wan. Effcient Derivative-Free Kalman Filters for Online Learning. European Symposium on Artificial Neural Networks, Bruges,Belgium, 2001: 205~210
48 Peihua, Li and Tianwen Zhang. Unscented Kalman Filter for Visual Curve Tracking. Proceedings of Statistical Methods in Video Processing, 2004,22(2):157~164
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32刘晨,冯新喜.基于IPDA的机动目标航迹起始算法.弹箭与制导学报, 2006,26(1):117~122
33刘晋霞,李定主,杨瑞光.基于边扫描边跟踪系统的多目标航迹起始相关.火力与指挥控制. 2005, 30(4): 125~130
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35王丽珍,刘慧霞,潘广林,梁彦,潘泉.天波超视距雷达的混合多模型PDA航迹起始仿真分析.中国电子科学研究院学报. 2006, 1(2): 130~136
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44 E. A. Wan, R. Van Der Merwe. The Unscented Kalman Filter for Nonlinear Estimation. Proc. of IEEE Symposium 2000, Lake Louise, Alberta, Canada, 2000:1256~1260
45 R. Van Der Merwe, E. A. Wan. the Square-Root unscented Kalman Filter for State and Parameter Estimation. International Conterence on Aacoustics, Speech, and Signal Processing. SaltLake City. 2001: 3461~3464
46 R. Van Der Merwe, Nando De Freitas, Arnaud Doucet, Eric Wan. The Unscented Particle Filter. Advance Neural Inform, Process. 2000: 1596~1603
47 Van der Merwe, R. and E. A. Wan. Effcient Derivative-Free Kalman Filters for Online Learning. European Symposium on Artificial Neural Networks, Bruges,Belgium, 2001: 205~210
48 Peihua, Li and Tianwen Zhang. Unscented Kalman Filter for Visual Curve Tracking. Proceedings of Statistical Methods in Video Processing, 2004,22(2):157~164
49 Stenger, B., P. R. S. Mendonc, and R. Cipolla. Model-Based Hand Tracking Using an Unscented Kalman Filter. In Proceedings of the British Machine Vision Conference, 2001: 63~72
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51 Arnaud Doucet, Nando de Freitas, Neil Gordon. Sequential Monte Carlo in Practice, Springer-Verlag. 2001: 1291~1298
52 Sanjeev Arulampalam, Simon Maskell, Neil Gordan, Tim Clapp, A Tutorial on Particle Filters for Online Non-linear/Non-gaussian Bayesian Tracking. IEEE Transaction on Signal Processing, 2002,50(2) : 174~188
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55 A. Doucet, S. Godsill and C. Andrieu. On Sequential Monte Carlo SamplingMethods for Bayesian Filtering, Statistics and Computing, 2000, 10(3): 197~208
56 Bruno, Marcelo G.S. Improved Sequential Monte Carlo Filtering for Ballistic Target Tracking. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(3): 1103~1108
57 Deng, Xiaolong, Xie, Jianying. Nonlinear Target Tracking Based on Particle Filter. Proceedings of the World Congress on Intelligent Control and Automation, 2004, 2: 1618~1620
58 G.. Kitagawa. Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models. [J]. J of Computational and Graphical Statistics, 1996, 5(1): 1~25
59 Bruno, G. S. Marcelo, Pavlov and Anton. Improved Particle Filters for Ballistic Target Tracking. Proc of IEEE International Conference on Acoustics, Speech and Signal Processing, 2004, 2: 705~708
60李涛,薛祖瑞,胡小平.一种使用非等权值粒子的确定性粒子滤波算法.国防科技大学学报, 2004, 26(1): 72~76
61朱志宇,姜长生.机动目标跟踪的高斯_厄米特粒子滤波算法.系统工程与电子技术. 2007, 29(10): 1596~1599
62邓小龙,谢剑英,杨煌普.基于交互式多模型的粒子滤波算法.系统仿真学报. 2005, 17(10): 2360~2363
63左东广,韩崇昭,卞树檀,郑林,朱洪艳.闪烁噪声机动目标跟踪的模型集交互跟踪算法.系统仿真学报. 2004, 76(4): 767~771
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