基于粒子滤波算法的交通状态估计研究
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摘要
道路交通状态估计是交通安全管理中的重要课题,也是是智能交通系统能够正常运行并发挥作用的前提和基础。交通控制和诱导系统需要对下一时刻乃至以后一些时刻的道路交通状态做出准确的估计和判断,才能做出正确的决策。只有对交通参与者做出及时的控制和诱导,才能有效地确保交通畅通和减少道路安全隐患。另外,准确的交通状态估计也是进行交通事故检测的必要条件。
目前,国内外学者大多采用卡尔曼滤波和扩展卡尔曼滤波等线性方法来解决交通状态估计问题。这些方法能够在一定程度上解决道路交通状态估计问题,并且得到了广泛的应用。然而,由于交通参与者之间存在各种复杂的相互影响,使得交通行为具有高度的非线性。而卡尔曼滤波方法假设系统模型和观测模型服从线性分布,并且系统噪声和观测噪声服从高斯分布。这就使得基于卡尔曼滤波的估计方法存在很大的误差,从而表现出一定的局限性。
粒子滤波是一种通过蒙特卡罗积分仿真来实现对贝叶斯滤波器递推的技术,它不做任何线性高斯假设,是一种非线性的预测方法。本文通过仿真实验对该方法进行了深入的学习和研究,并通过与线性方法EKF滤波器的对比,验证了其在解决非线性问题时的有效性。
另外,针对复杂路段下传统方法的缺陷,本文将粒子滤波方法应用到处理交通状态估计问题中。通过研究二阶宏观随机交通流模型对北京城市快速路建模,并基于Matlab平台进行交通状态估计。实验结果表明,粒子滤波算法能够对道路交通流的参数指标做出较好的估计,具有良好的适用性。
然而,在实验过程中发现,随着迭代次数的增加,只有少数样本具有较大的权值,一些权值较小的粒子会出现退化现象。这不但浪费了大量计算在小权值粒子上,而且也影响了样本粒子的多样化。针对这些问题,本文尝试性地将蚁群算法的思想引入到粒子滤波算法过程中,来优化粒子滤波算法的重采样过程。运用改进后的粒子滤波算法进行实例验证并与基本滤波算法进行对比,实验结果表明,该方法具有良好的准确性和鲁棒性。
Traffic state estimation is an important task of Intelligent Transportation System Management & Traffic Safety, also the presupposition and basis in its operation and functioning. Either traffic control or guidance system requires accurate estimations and assessments for the road traffic state in the next or even following moments. The efficiency of the decision making of the system depends on the accuracy of traffic state estimation. Only when the traffic participants are controlled and guided efficiently, the fluency of the roads and the reduction of hidden accidents can be ensured. In addition, the accurate estimation of traffic flow is a necessary condition for traffic accident detection.
Currently, most literatures adopt linear approaches such as Kalman filter and extended Kalman filter techniques to estimate the traffic state estimation. These techniques can predict traffic state in relatively simple traffic condition, which has been widely used. However, traffic behaviors have higher-order nonlinearity due to the complex interaction among participants. In this case, Kalman filter has some limitations since it assumes the both the system and observation model subject to linear distributions. Moreover, it defines both the system and observation noises obey the Gaussian distribution, which leads to significant errors for the estimation result.
Particle Filter (PF) is a non-linear and non-gaussian estimation technique which realizes the recursive Bayesian Filter via Monte Carlo integration simulation. From the indepth study and investigation of PF via the simulation experiment and the comparison of the PF technique with the linear EKF, we prove that PF is efficient of solving nonlinear problem.
In addition, to remedy the insufficient of the traditional methods under the complex road environment, this report proposes the usage of PF in solving the traffic state estimation problem. The model which combines PF and the second-order macroscopic random traffic flow model is established on the MATLAB Platform. Experiment results based on the real world data from Beijing Loop verify that the proposed technique can estimate the traffic state parameters acutely with good adaptability.
However, PF shows some limitations such as sample poverty, particle degradation, etc. To solve these problems, the thesis innovatively proposes to apply Ant Colony Algorithm (ACO) in the update process of PF and verify the ACO-PF technique with real world data. Experiment results suggest that the proposed technique is superior to the particle filter with higher accuracy and stronger robustness.
目前,国内外学者大多采用卡尔曼滤波和扩展卡尔曼滤波等线性方法来解决交通状态估计问题。这些方法能够在一定程度上解决道路交通状态估计问题,并且得到了广泛的应用。然而,由于交通参与者之间存在各种复杂的相互影响,使得交通行为具有高度的非线性。而卡尔曼滤波方法假设系统模型和观测模型服从线性分布,并且系统噪声和观测噪声服从高斯分布。这就使得基于卡尔曼滤波的估计方法存在很大的误差,从而表现出一定的局限性。
粒子滤波是一种通过蒙特卡罗积分仿真来实现对贝叶斯滤波器递推的技术,它不做任何线性高斯假设,是一种非线性的预测方法。本文通过仿真实验对该方法进行了深入的学习和研究,并通过与线性方法EKF滤波器的对比,验证了其在解决非线性问题时的有效性。
另外,针对复杂路段下传统方法的缺陷,本文将粒子滤波方法应用到处理交通状态估计问题中。通过研究二阶宏观随机交通流模型对北京城市快速路建模,并基于Matlab平台进行交通状态估计。实验结果表明,粒子滤波算法能够对道路交通流的参数指标做出较好的估计,具有良好的适用性。
然而,在实验过程中发现,随着迭代次数的增加,只有少数样本具有较大的权值,一些权值较小的粒子会出现退化现象。这不但浪费了大量计算在小权值粒子上,而且也影响了样本粒子的多样化。针对这些问题,本文尝试性地将蚁群算法的思想引入到粒子滤波算法过程中,来优化粒子滤波算法的重采样过程。运用改进后的粒子滤波算法进行实例验证并与基本滤波算法进行对比,实验结果表明,该方法具有良好的准确性和鲁棒性。
Traffic state estimation is an important task of Intelligent Transportation System Management & Traffic Safety, also the presupposition and basis in its operation and functioning. Either traffic control or guidance system requires accurate estimations and assessments for the road traffic state in the next or even following moments. The efficiency of the decision making of the system depends on the accuracy of traffic state estimation. Only when the traffic participants are controlled and guided efficiently, the fluency of the roads and the reduction of hidden accidents can be ensured. In addition, the accurate estimation of traffic flow is a necessary condition for traffic accident detection.
Currently, most literatures adopt linear approaches such as Kalman filter and extended Kalman filter techniques to estimate the traffic state estimation. These techniques can predict traffic state in relatively simple traffic condition, which has been widely used. However, traffic behaviors have higher-order nonlinearity due to the complex interaction among participants. In this case, Kalman filter has some limitations since it assumes the both the system and observation model subject to linear distributions. Moreover, it defines both the system and observation noises obey the Gaussian distribution, which leads to significant errors for the estimation result.
Particle Filter (PF) is a non-linear and non-gaussian estimation technique which realizes the recursive Bayesian Filter via Monte Carlo integration simulation. From the indepth study and investigation of PF via the simulation experiment and the comparison of the PF technique with the linear EKF, we prove that PF is efficient of solving nonlinear problem.
In addition, to remedy the insufficient of the traditional methods under the complex road environment, this report proposes the usage of PF in solving the traffic state estimation problem. The model which combines PF and the second-order macroscopic random traffic flow model is established on the MATLAB Platform. Experiment results based on the real world data from Beijing Loop verify that the proposed technique can estimate the traffic state parameters acutely with good adaptability.
However, PF shows some limitations such as sample poverty, particle degradation, etc. To solve these problems, the thesis innovatively proposes to apply Ant Colony Algorithm (ACO) in the update process of PF and verify the ACO-PF technique with real world data. Experiment results suggest that the proposed technique is superior to the particle filter with higher accuracy and stronger robustness.
引文
[1]丁蕾,面向城市交通控制的短时交通流预测方法研究,[硕士学位论文],大连理工大学,2009.
[2]Yibing Wang, Markos Papageorgiou, and Albert Messmer, A Real-Time Freeway Network Traffic Surveillance Tool, and Albert Messmer, IEEE transactions on control systems technology, vol.14, no.1, January 2006.
[3]KotsialosA, papageorgiouM, DiakakiC, etal. Traffic flow modeling of large-scale motorway using the macroscopic modeling tool METANET.IEEE Transportations on Intelligent Transportation Systems,2002,3(4):282
[4]Lyudmila Mihaylova, and Ren'eBoel, A Particle Filter for Freeway Traffic Estimation,43rd IEEE Conference on Decision and Control, December 14-17,2004.
[5]KITTAGAWA, G:'Non-Gaussian state-space modelling of nonstationary time series (with discussion)', J. Amer. Statistical Assoc,1987.82, pp.1032-1063
[6]X. Sun, L. Mu-noz, R. Horowitz, Highway Traffic State Estimation Using Improved Mixture Kalman Filters for Effective Ramp Metering Control, Proc. of 42th IEEE Conference on Decision and Control, pp.6333-6338,2003.
[7]CORTES C, VAPN IK V. Support vector networks [J]. Ma ch ineLea rn ing,1995,20 (3): 2732297.
[8]邓乃扬,田英杰.数据挖掘中的新方法—支持向量机[M].北京：科学技术出版社,2004.
[9]姚智胜,基于实时数据的道路网短时交通流预测理论与方法研究,[博士学位论文],北京交通大学,2007.
[10]张敬磊,王晓原,基于非线性组合模型的交通流预测方法,计算机工程,2010(5)：202-204.
[11]唐丽娜,张卫华,短时交通流预测方法的比较研究,中国上海,2007.
[12]王进,史其信,短时交通流预测模型综述,中国公共安全(学术卷),2005(1)：92-98.
[13]刘静,关伟,交通流预测方法综述,公路交通科技.2004(3).82-85.
[14]张晓利,陆化普.非参数回归方法在短时交通流预测中的应用.清华大学学报(自然科学版)2009(9)：39-43.
[15]马君,刘晓东,孟颖,基于神经网络的城市交通流预测研究,电子学报,2009(5)：1092-1094.
[16]王科伟,徐志红.基于混沌时间序列的道路断面短时交通流预测模型.交通运输工程与信息学报.2010(1)：70-73.
[17]D.Gazis, and C.Liu, Kalman Filtering Estimation of Traffic Counts for Two Network Links in Tandem, Transportation ResearchB,Vol.37,No.8,2003,pp.737-745.
[18]Y. Wang, M. Papageorgiou, and A. Messmer, Motorway Traffic State Estimation Based on Extended Kalman Filter, Proc.oftheEuropeanControlConf.,1-3Sept.,2003,UK.
[19]张军辉,粒子滤波跟踪算法研究,[硕士学位论文],河南大学,2009
[20]Gazis D C, Herman P & Potts R B, Car-following theory of steady state flow. Opns.Res.1959, 499-505
[21]Chandler R E, Herman R, Montroll E W.Traffic dynamics:studies in car following. Operations Research,19586,165-184
[22]Herman R, Montroll E W, Potts R B, etal.Traffic dynamics:analysis of stability in car following. Operations Research,19597,86～106
[23]Herman R, Potts R.B. Single lane traffic theory and experiment. In Proceedings of the Labs, General Motors.1959 147～157
[24]Edie L C. Car following and steady state theory for non-congested traffic. Operations Research, 19609,66～76
[25]付传技,交通流模型的研究,[博士学位论文],中国科学技术大学,2007.
[26]张波,基于流体动力学的交通流模型及数值模拟,[硕士学位论文],吉林大学,2007.
[27]林之,基于流体动力学的交通流模型与信号控制仿真软件研制,[硕士学位论文],北方工业大学,2006.
[28]黄乒花,孔令江,刘慕仁,一维元胞自动机随机交通流模型的研究,物理学报,2001(01)：30-36.
[29]葛红霞,祝会兵,戴世强,智能交通系统的元胞自动机交通流模型,物理学报,2005(10)：4621-4626.
[30]蒋景飞,方标新,张建秋,俞承芳,郭涛,二阶宏观交通流模型参数的支持向量回归估计法,中国广西桂林,2009.
[31]Yibing Wang, Markos Papageorgiou, and Albert Messmer, A Real-Time Freeway Network Traffic Surveillance Tool, and Albert Messmer, IEEE transactions on control systems technology, vol.14, no.1,January 2006.
[32]PaPageorgious, M., Blosseville, J.M.,& Haj-Salem, H., Modeling and real-time control of traffic flow on southern Part of Boulevard Peripherique in Paris-Part Ⅰ:modeling[J]. Transportation Research A 24,345-359,1990
[33]姚剑敏,粒子滤波跟踪方法研究,[博士学位论文],中国科学院研究生院(长春光学精密机械与物理研究所),2005.
[34]胡昭华,基于粒子滤波的视频目标跟踪技术研究,[博士学位论文],南京理工大学,2008.
[35]程松,一种利用粒子滤波的实时交通状态估计方法,[硕士学位论文],复旦大学,2008.
[36]Eckhardt R. Stan Ulam, Joln von Neumann, and the Monte Carlo method. Los Alamos Seience.1987,15,131 — 137.
[37]罗瑞,序列蒙特卡罗粒子滤波及其在视频跟踪中的应用,[硕士学位论文],西安电子科技大学,2009.
[38]杨进,基于粒子滤波的多目标跟踪算法研究,[硕士学位论文],上海交通大学,2009.
[39]杨珺,粒子滤波算法研究及应用,[硕士学位论文],西安理工大学,2008.
[40]黄斌,基于粒子滤波的视频目标跟踪方法研究,[硕士学位论文],电子科技大学,2008.
[41]吴宝成,粒子滤波重采样算法研究及其应用,[硕士学位论文],哈尔滨工业大学,2006.
[42]王进,史其信.神经网络模型在短期交通流预测领域应用综述[J].河南科技大学学报(自然科学版),2005,26(2)：22-26.
[43]Cremer, M., Ludwig, J.A fast simulation model for traffic flow on the basis of Booleano Perations[J].MathematicsandComPutersinSimulation.28,297 — 303,198
[44]N. Gordon, D. Salmond, and A. Smith, A Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation, IEEE Proc. on Radar, and Signal Proc, Vol.40, pp.107-113,1993.
[45]KITTAGAWA, G:'Non-Gaussian state-space modelling of nonstationary time series (with discussion)', J. Amer. Statistical Assoc.,1987.82, pp.1032-1063
[46]黄友锐.智能优化算法及其应用[M].北京：国防工业出版社,2008.
[47]T.Stutzle and M.Dorigo, "A short convergence proof for a class of Ant Colony Optimization algorithms," IEEE Transactions on Evolutionary Computation, vol.6, no.4. pp.358-365,2002.
[2]Yibing Wang, Markos Papageorgiou, and Albert Messmer, A Real-Time Freeway Network Traffic Surveillance Tool, and Albert Messmer, IEEE transactions on control systems technology, vol.14, no.1, January 2006.
[3]KotsialosA, papageorgiouM, DiakakiC, etal. Traffic flow modeling of large-scale motorway using the macroscopic modeling tool METANET.IEEE Transportations on Intelligent Transportation Systems,2002,3(4):282
[4]Lyudmila Mihaylova, and Ren'eBoel, A Particle Filter for Freeway Traffic Estimation,43rd IEEE Conference on Decision and Control, December 14-17,2004.
[5]KITTAGAWA, G:'Non-Gaussian state-space modelling of nonstationary time series (with discussion)', J. Amer. Statistical Assoc,1987.82, pp.1032-1063
[6]X. Sun, L. Mu-noz, R. Horowitz, Highway Traffic State Estimation Using Improved Mixture Kalman Filters for Effective Ramp Metering Control, Proc. of 42th IEEE Conference on Decision and Control, pp.6333-6338,2003.
[7]CORTES C, VAPN IK V. Support vector networks [J]. Ma ch ineLea rn ing,1995,20 (3): 2732297.
[8]邓乃扬,田英杰.数据挖掘中的新方法—支持向量机[M].北京：科学技术出版社,2004.
[9]姚智胜,基于实时数据的道路网短时交通流预测理论与方法研究,[博士学位论文],北京交通大学,2007.
[10]张敬磊,王晓原,基于非线性组合模型的交通流预测方法,计算机工程,2010(5)：202-204.
[11]唐丽娜,张卫华,短时交通流预测方法的比较研究,中国上海,2007.
[12]王进,史其信,短时交通流预测模型综述,中国公共安全(学术卷),2005(1)：92-98.
[13]刘静,关伟,交通流预测方法综述,公路交通科技.2004(3).82-85.
[14]张晓利,陆化普.非参数回归方法在短时交通流预测中的应用.清华大学学报(自然科学版)2009(9)：39-43.
[15]马君,刘晓东,孟颖,基于神经网络的城市交通流预测研究,电子学报,2009(5)：1092-1094.
[16]王科伟,徐志红.基于混沌时间序列的道路断面短时交通流预测模型.交通运输工程与信息学报.2010(1)：70-73.
[17]D.Gazis, and C.Liu, Kalman Filtering Estimation of Traffic Counts for Two Network Links in Tandem, Transportation ResearchB,Vol.37,No.8,2003,pp.737-745.
[18]Y. Wang, M. Papageorgiou, and A. Messmer, Motorway Traffic State Estimation Based on Extended Kalman Filter, Proc.oftheEuropeanControlConf.,1-3Sept.,2003,UK.
[19]张军辉,粒子滤波跟踪算法研究,[硕士学位论文],河南大学,2009
[20]Gazis D C, Herman P & Potts R B, Car-following theory of steady state flow. Opns.Res.1959, 499-505
[21]Chandler R E, Herman R, Montroll E W.Traffic dynamics:studies in car following. Operations Research,19586,165-184
[22]Herman R, Montroll E W, Potts R B, etal.Traffic dynamics:analysis of stability in car following. Operations Research,19597,86～106
[23]Herman R, Potts R.B. Single lane traffic theory and experiment. In Proceedings of the Labs, General Motors.1959 147～157
[24]Edie L C. Car following and steady state theory for non-congested traffic. Operations Research, 19609,66～76
[25]付传技,交通流模型的研究,[博士学位论文],中国科学技术大学,2007.
[26]张波,基于流体动力学的交通流模型及数值模拟,[硕士学位论文],吉林大学,2007.
[27]林之,基于流体动力学的交通流模型与信号控制仿真软件研制,[硕士学位论文],北方工业大学,2006.
[28]黄乒花,孔令江,刘慕仁,一维元胞自动机随机交通流模型的研究,物理学报,2001(01)：30-36.
[29]葛红霞,祝会兵,戴世强,智能交通系统的元胞自动机交通流模型,物理学报,2005(10)：4621-4626.
[30]蒋景飞,方标新,张建秋,俞承芳,郭涛,二阶宏观交通流模型参数的支持向量回归估计法,中国广西桂林,2009.
[31]Yibing Wang, Markos Papageorgiou, and Albert Messmer, A Real-Time Freeway Network Traffic Surveillance Tool, and Albert Messmer, IEEE transactions on control systems technology, vol.14, no.1,January 2006.
[32]PaPageorgious, M., Blosseville, J.M.,& Haj-Salem, H., Modeling and real-time control of traffic flow on southern Part of Boulevard Peripherique in Paris-Part Ⅰ:modeling[J]. Transportation Research A 24,345-359,1990
[33]姚剑敏,粒子滤波跟踪方法研究,[博士学位论文],中国科学院研究生院(长春光学精密机械与物理研究所),2005.
[34]胡昭华,基于粒子滤波的视频目标跟踪技术研究,[博士学位论文],南京理工大学,2008.
[35]程松,一种利用粒子滤波的实时交通状态估计方法,[硕士学位论文],复旦大学,2008.
[36]Eckhardt R. Stan Ulam, Joln von Neumann, and the Monte Carlo method. Los Alamos Seience.1987,15,131 — 137.
[37]罗瑞,序列蒙特卡罗粒子滤波及其在视频跟踪中的应用,[硕士学位论文],西安电子科技大学,2009.
[38]杨进,基于粒子滤波的多目标跟踪算法研究,[硕士学位论文],上海交通大学,2009.
[39]杨珺,粒子滤波算法研究及应用,[硕士学位论文],西安理工大学,2008.
[40]黄斌,基于粒子滤波的视频目标跟踪方法研究,[硕士学位论文],电子科技大学,2008.
[41]吴宝成,粒子滤波重采样算法研究及其应用,[硕士学位论文],哈尔滨工业大学,2006.
[42]王进,史其信.神经网络模型在短期交通流预测领域应用综述[J].河南科技大学学报(自然科学版),2005,26(2)：22-26.
[43]Cremer, M., Ludwig, J.A fast simulation model for traffic flow on the basis of Booleano Perations[J].MathematicsandComPutersinSimulation.28,297 — 303,198
[44]N. Gordon, D. Salmond, and A. Smith, A Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation, IEEE Proc. on Radar, and Signal Proc, Vol.40, pp.107-113,1993.
[45]KITTAGAWA, G:'Non-Gaussian state-space modelling of nonstationary time series (with discussion)', J. Amer. Statistical Assoc.,1987.82, pp.1032-1063
[46]黄友锐.智能优化算法及其应用[M].北京：国防工业出版社,2008.
[47]T.Stutzle and M.Dorigo, "A short convergence proof for a class of Ant Colony Optimization algorithms," IEEE Transactions on Evolutionary Computation, vol.6, no.4. pp.358-365,2002.