基于多源异质检测数据的道路交通流参数估计问题研究
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摘要
道路交通拥堵疏解主要措施是提高交通供给的同时适度限制交通需求,试图通过缩小供给与需求两者差距,在期望服务水平下,使交通基础设施供给与交通出行需求达到某种均衡。随着传感技术、通信技术、计算机技术和信息化技术等不断发展,交通检测的手段不断提高和丰富,为交通管理者提供了更多高质量和高可靠的检测数据。基于这些检测数据可及大地提高交通流组织管理水平,使已有交通基础设施的供给能力最大化。但是,出于经济成本和其他因素等考虑,无法实现交通检测器的全路网覆盖。因而,深入研究如何有效的利用少量有限的多源检测数据,来合理的对整个路网交通流运行状态进行估计是提高交通流组织管理效率的关键所在。
本论文从交通流运动波模型出发,研究多源异质检测数据的融合机制,探讨几种典型的交通流参数估计问题。具体来说,本论文研究工作主要有以下几个方面：
(1)将三检测器模型推广应用于宏观和微观交通流状态估计。与传统的交通流运动波模型不同,三检测器模型以累积车流量为系统状态量,直接显现地建立了路段内部状态量与路段上下游边界状态量的最小化函数关系。基于理想边界条件假设,本论文不仅研究了宏观交通流参数,如路段行程时间、流量和密度的时空演化谱等估计方法,而且研究了微观交通流参数,如车辆行驶轨迹的估计方法。
(2)在三检测器模的基础上,提出随机三检测器模型。实际中,检测数据是对交通系统的一种测量,测量误差不可避免,且检测技术采样频率有限,难以提供连续的检测数据。测量误差和检测数据非连续性决定边界条件是非理想的。本论文将该非理想边界条件建模成一个随机边界条件,边界向量中每个元素是一个符合正态分布的随机变量。借助随机路径选择问题上广泛使用的Probit模型,可建立内部状态量与随机边界状态量的最小化函数关系,进一步利用Clark的逼近理论估计内部交通流参数的均值和误差大小。
(3)将多源异质检测数据建模成系列线性测量方程,并利用Kalman滤波融合到随机三检测器模型中。多源异质检测数据包括路段内部线圈传感器提供的车流量、占有率和瞬时速度信息、AVI旅行时间数据和GPS移动位置数据。利用随机三检测器模型,上述检测量均可以建模成以随机边界的累积车流量为状态量的线性测量方程。在Kalman滤波框架下,可利用建立的线性测量方程输出一个最佳增益量,来更新随机边界的累积车流量和累积车流量误差的方差-协方差矩阵,得到随机边界的最佳估计。基于该最佳随机边界估计,利用随机三检测器模型可估计内部交通流参数及其估计误差大小。
(4)基于信息价值理论,将各种检测数据对交通流参数估计的贡献大小建模成信息价值量。上述研究内容建立了检测数据与边界状态量估计误差大小的关系,基于信息价值理论误差大小可建模成信息量。然而,检测数据据参数的变化影响误差大小,故可建立检测数据参数与信息量的关系。
(5)基于约束最小二乘法,将快速路走廊的交通流参数估计问题建模成一个非线性的优化模型。基于三检测理论的前置波和后置波理念,将三检测器模型的最小化函数建模成两个不等式来描述交通流动态变化的约束。基于合流点和分流点的累积进口车流量和累积出口车流量守恒规则,将主干道与上匝道口或下匝道口的系统状态量建模成等式约束。走廊各关键节点的通行能力限制可建模成系列不等式约束。优化模型的目标是系统状态真实值与检测量差距最小化。考虑的检测量包括固定式检测器的车流量和AVI设备的旅行时间等检测数据等。
For road traffic system, the main principle of mitigating the traffic congestion is to take both traffic supply and traffic demand in consideration. Particularly, the capacity of the traffic infrastructure shall be fully utilized and the traffic demand shall be controlled in a sense to keep the traffic system running in a driver-satisfied level of service. Now, the soaring development of sensing technology, communication technology, information technology and computer technology takes traffic surveillance technology into the threshold of multi-sensors based detecting period. These traffic surveillance technologies can produce massive data sources, which can be used to advancethe efficiency of traffic system by modern traffic management or traffic flow organization. The advance of efficiency of traffic system will make the capacity of infrastructureto be maximized. However, caused by the economy cost, privacy concerns and bad weather condition, etc., the traffic sensing devices could not be installed enough to fully cover the traffic network. Thus, the traffic state estimation technology is used to know the traffic state based on the limited partly covered data sources.
Based on the traffic kinematic wave theory, this dissertation studies the traffic state estimation problem in the highway or freeway segment by following aspects:
(1)Estimating the microscopic and macroscopic traffic states using the famous three-detector theory. Be different from the classified kinematic wave theory, which adopts the flow or density as the system sate variable, the Three-detector theory adopts the cumulative flow count as the system state variable. By doing this, the traffic state inside the boundary and along the boundary can be explicitly modeled, rather than by a cell-by-cell transfer framework like the cell transmission model. Under the perfect boundary condition, this study not only can estimate the macroscopic traffic states such as link based travel time as well as the evolution of flow or density along the segment of interest, but also the microscopic traffic states such as individual vehicle trajectory as well as the vehicle fuel consumption or emission;
(2)Proposing a stochastic boundary based three-detector model. In the real world, the traffic state measurement error is inevitable and the sampling frequency is limited, which imply that the assumed perfect boundary is hard to satisfy in current sensing condition. Thus, this imperfect boundary, namely the measurements are discontinuous and noised, is necessary to modeled in the traffic state estimation framework. By assuming the measurement noise as a white noise and designing a linear interpolation algorithm, this study models the imperfect boundary a stochastic boundary, which is constructed by a cumulative flow count vector and error variance-covariance matrix. In this stochastic boundary condition, the system process equation is modified as the minimization of two normal distributed random variables, rather than the minimization of two deterministic variables. The classical Probit model, which is extensively used in the field of random route choice, can produce the minimization or maximization of multiple random variable based the Clark's approximation theory. This study employs the notion of Probit model and Clark's approximation to approximate the cumulative flow count at any point inside the boundary as a normally distributed random variable, the mean and variance of which are calculated by the mean and variance of the related cumulative flow count at the boundary. This modeling notion is very plausible to quantify the estimation uncertainty.
(3)Modeling the observations of heterogeneous data sources as a series of linear measurement equations in a Kalman filter framework. The considered heterogeneous data sources are includingthe flow, occupancy and instantaneousspeed of the loop detectors, the travel time observation from the automatic vehicle identification surveillance technology, and the semi-continuous vehicle trajectory from the global position system based surveillance technology. Under the framework of the proposed stochastic three-detector model, all the aforementioned observations can be modeled or transferred as cumulative flow count observations. Along this way, the linear measurement equation of each kind of observation can be built. In the Kalman framework, based on the measurement equation and the system process equation (from the stochastic three-detector model), an optimal Kalman gain can be calculated and further the prior traffic state estimation can be updated to a posterior traffic state estimation including an optimal traffic state estimation and a posterior error variance-covariance matrix. The posterior error variance-covariance describes the range of estimation uncertainty. Theoretically, the more the observations are, the less estimation uncertainty is.
(4)Estimating the value of information of each observation based on the informationtheory.Above studies build the relationship between each observation and the traffic state estimation uncertainty, such as density estimation uncertainty, and the uncertainty can be quantified using the trace of the error variance-covariance matrix. The inverse of the uncertainty can be used to calculate the value of information. Thus, we can calculate the value of information for each observation, which is very useful for the traffic engineer to decide the sensing configurations. Particularly, this study focus on the value of information of different sampling frequency of the middle loop detector, the market penetration rate of automatic vehicle identification based surveillance technology, and the market penetration rate of global position system based surveillance technology.
(5)Modeling the traffic state estimation problem of a typical freeway corridor as a non-linear optimization problem under a constrained least squares framework. The minimization function of the three-detector theory can be equally transformed as two inequalities constraints to describe the traffic flow propagation, particularly the forward and backward shockwave propagation. Based on the flow conservation at merge or diverge point, the total inflow and total outflow are modeled as an equality constraint. The capacity limit of any point along the corridor can be model as an inequality constraint. The objective of the optimization problem is constructed by the total least squares of the difference between measurements and system variable in the notion of cumulative flow count. In addition, the travel time observation can be weighted into the objective to reflect the real link based traffic states.
本论文从交通流运动波模型出发,研究多源异质检测数据的融合机制,探讨几种典型的交通流参数估计问题。具体来说,本论文研究工作主要有以下几个方面：
(1)将三检测器模型推广应用于宏观和微观交通流状态估计。与传统的交通流运动波模型不同,三检测器模型以累积车流量为系统状态量,直接显现地建立了路段内部状态量与路段上下游边界状态量的最小化函数关系。基于理想边界条件假设,本论文不仅研究了宏观交通流参数,如路段行程时间、流量和密度的时空演化谱等估计方法,而且研究了微观交通流参数,如车辆行驶轨迹的估计方法。
(2)在三检测器模的基础上,提出随机三检测器模型。实际中,检测数据是对交通系统的一种测量,测量误差不可避免,且检测技术采样频率有限,难以提供连续的检测数据。测量误差和检测数据非连续性决定边界条件是非理想的。本论文将该非理想边界条件建模成一个随机边界条件,边界向量中每个元素是一个符合正态分布的随机变量。借助随机路径选择问题上广泛使用的Probit模型,可建立内部状态量与随机边界状态量的最小化函数关系,进一步利用Clark的逼近理论估计内部交通流参数的均值和误差大小。
(3)将多源异质检测数据建模成系列线性测量方程,并利用Kalman滤波融合到随机三检测器模型中。多源异质检测数据包括路段内部线圈传感器提供的车流量、占有率和瞬时速度信息、AVI旅行时间数据和GPS移动位置数据。利用随机三检测器模型,上述检测量均可以建模成以随机边界的累积车流量为状态量的线性测量方程。在Kalman滤波框架下,可利用建立的线性测量方程输出一个最佳增益量,来更新随机边界的累积车流量和累积车流量误差的方差-协方差矩阵,得到随机边界的最佳估计。基于该最佳随机边界估计,利用随机三检测器模型可估计内部交通流参数及其估计误差大小。
(4)基于信息价值理论,将各种检测数据对交通流参数估计的贡献大小建模成信息价值量。上述研究内容建立了检测数据与边界状态量估计误差大小的关系,基于信息价值理论误差大小可建模成信息量。然而,检测数据据参数的变化影响误差大小,故可建立检测数据参数与信息量的关系。
(5)基于约束最小二乘法,将快速路走廊的交通流参数估计问题建模成一个非线性的优化模型。基于三检测理论的前置波和后置波理念,将三检测器模型的最小化函数建模成两个不等式来描述交通流动态变化的约束。基于合流点和分流点的累积进口车流量和累积出口车流量守恒规则,将主干道与上匝道口或下匝道口的系统状态量建模成等式约束。走廊各关键节点的通行能力限制可建模成系列不等式约束。优化模型的目标是系统状态真实值与检测量差距最小化。考虑的检测量包括固定式检测器的车流量和AVI设备的旅行时间等检测数据等。
For road traffic system, the main principle of mitigating the traffic congestion is to take both traffic supply and traffic demand in consideration. Particularly, the capacity of the traffic infrastructure shall be fully utilized and the traffic demand shall be controlled in a sense to keep the traffic system running in a driver-satisfied level of service. Now, the soaring development of sensing technology, communication technology, information technology and computer technology takes traffic surveillance technology into the threshold of multi-sensors based detecting period. These traffic surveillance technologies can produce massive data sources, which can be used to advancethe efficiency of traffic system by modern traffic management or traffic flow organization. The advance of efficiency of traffic system will make the capacity of infrastructureto be maximized. However, caused by the economy cost, privacy concerns and bad weather condition, etc., the traffic sensing devices could not be installed enough to fully cover the traffic network. Thus, the traffic state estimation technology is used to know the traffic state based on the limited partly covered data sources.
Based on the traffic kinematic wave theory, this dissertation studies the traffic state estimation problem in the highway or freeway segment by following aspects:
(1)Estimating the microscopic and macroscopic traffic states using the famous three-detector theory. Be different from the classified kinematic wave theory, which adopts the flow or density as the system sate variable, the Three-detector theory adopts the cumulative flow count as the system state variable. By doing this, the traffic state inside the boundary and along the boundary can be explicitly modeled, rather than by a cell-by-cell transfer framework like the cell transmission model. Under the perfect boundary condition, this study not only can estimate the macroscopic traffic states such as link based travel time as well as the evolution of flow or density along the segment of interest, but also the microscopic traffic states such as individual vehicle trajectory as well as the vehicle fuel consumption or emission;
(2)Proposing a stochastic boundary based three-detector model. In the real world, the traffic state measurement error is inevitable and the sampling frequency is limited, which imply that the assumed perfect boundary is hard to satisfy in current sensing condition. Thus, this imperfect boundary, namely the measurements are discontinuous and noised, is necessary to modeled in the traffic state estimation framework. By assuming the measurement noise as a white noise and designing a linear interpolation algorithm, this study models the imperfect boundary a stochastic boundary, which is constructed by a cumulative flow count vector and error variance-covariance matrix. In this stochastic boundary condition, the system process equation is modified as the minimization of two normal distributed random variables, rather than the minimization of two deterministic variables. The classical Probit model, which is extensively used in the field of random route choice, can produce the minimization or maximization of multiple random variable based the Clark's approximation theory. This study employs the notion of Probit model and Clark's approximation to approximate the cumulative flow count at any point inside the boundary as a normally distributed random variable, the mean and variance of which are calculated by the mean and variance of the related cumulative flow count at the boundary. This modeling notion is very plausible to quantify the estimation uncertainty.
(3)Modeling the observations of heterogeneous data sources as a series of linear measurement equations in a Kalman filter framework. The considered heterogeneous data sources are includingthe flow, occupancy and instantaneousspeed of the loop detectors, the travel time observation from the automatic vehicle identification surveillance technology, and the semi-continuous vehicle trajectory from the global position system based surveillance technology. Under the framework of the proposed stochastic three-detector model, all the aforementioned observations can be modeled or transferred as cumulative flow count observations. Along this way, the linear measurement equation of each kind of observation can be built. In the Kalman framework, based on the measurement equation and the system process equation (from the stochastic three-detector model), an optimal Kalman gain can be calculated and further the prior traffic state estimation can be updated to a posterior traffic state estimation including an optimal traffic state estimation and a posterior error variance-covariance matrix. The posterior error variance-covariance describes the range of estimation uncertainty. Theoretically, the more the observations are, the less estimation uncertainty is.
(4)Estimating the value of information of each observation based on the informationtheory.Above studies build the relationship between each observation and the traffic state estimation uncertainty, such as density estimation uncertainty, and the uncertainty can be quantified using the trace of the error variance-covariance matrix. The inverse of the uncertainty can be used to calculate the value of information. Thus, we can calculate the value of information for each observation, which is very useful for the traffic engineer to decide the sensing configurations. Particularly, this study focus on the value of information of different sampling frequency of the middle loop detector, the market penetration rate of automatic vehicle identification based surveillance technology, and the market penetration rate of global position system based surveillance technology.
(5)Modeling the traffic state estimation problem of a typical freeway corridor as a non-linear optimization problem under a constrained least squares framework. The minimization function of the three-detector theory can be equally transformed as two inequalities constraints to describe the traffic flow propagation, particularly the forward and backward shockwave propagation. Based on the flow conservation at merge or diverge point, the total inflow and total outflow are modeled as an equality constraint. The capacity limit of any point along the corridor can be model as an inequality constraint. The objective of the optimization problem is constructed by the total least squares of the difference between measurements and system variable in the notion of cumulative flow count. In addition, the travel time observation can be weighted into the objective to reflect the real link based traffic states.
引文
[1]中华人民共和国国家统计局.中国统计年鉴[M].北京,中国统计出版社,2007.
[2]张文奇.简述中国经济发展与交通运输的关系[J].城市交通,2001,3：1-7.
[3]Glen Weisbrod, Don Vary, George Treyz. Measuring Economic Costs of Urban Traffic Congestion to Business[J]. Transportation Research Record,2007,1839:03-3234.
[4]徐吉谦,主编.交通工程总论[M].人民交通出版社,1991.
[5]吕力生.城市交通阻塞分析[J].上海大学学报,1998,(6).
[6]Christian Claudel.Convex formulations of inverse modeling problems on systems modeled by Hamilton-Jacobi equations:applications to traffic flow engineering[D].University of California, Berkeley.2011:5-20.
[7]Zhou, X. and List, G. An Information-Theoretic Sensor Location Model for Traffic Origin-Destination Demand Estimation Applications. Transportation Science.2010,44:254-273.
[8]刘栋,穆晓霞,宋国杰等.基于浮动车数据的城市交通状态估计研究[J].河南师范大学学报(自然科学版).2011,39(3)：162-166.
[9]史文欢,孔庆杰,刘允才等.基于出租车跟踪的市区路网交通状态估计方法[J].交通信息与安全.2009,27(5)：29-32.
[10]袁月明,关伟,吴建平等.基于视频检测技术的城市快速路交通状态分析研究[J].2008,26(4)：1-3.
[11]徐涛,杨晓光,徐爱功,张明月.面向城市道路交通状态估计的数据融合研究[J].计算机工程与应用,2011,47(7)：218-221.
[12]龙建成.城市道路交通拥堵传播规律及消散控制策略研究[D].北京交通大学.2009.
[13]贾斌,高自友,李克平,李新刚.基于元胞自动的交通系统建模与模拟[M].科学出版社.2007.
[14]程松,陈光梦.一种利用粒子滤波的实时交通状态估计方法.微型电脑应用.2008,24(2)：13-17.
[15]Ashok, K., Ben-Akiva, M.E. Alternative approaches for real-time estimation and prediction of time-dependent origin-destination flows[J]. Transportation Science.2000,34(1),21-36.
[16]Zhou, X., List, G.F.,2010. An information-theoretic sensor location model for traffic origin-destination demand estimation applications. Transportation Science 44(2),254-273.
[17]Coifman, B.,2002. Estimating travel times and vehicle trajectories on freeways using dual loop detectors. Transportation Research Part A 36(4),351-364.
[18]Daganzo, C. F.,1994. The cell transmission model:a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B 28(4),269-287.
[19]Newell, G.F.,1993. A simplified theory of kinematic waves in highway traffic, part I:General Theory. Transportation Research Part B 27(4),281-297.
[20]John Wiley.Kalman Filtering Theary and practice using matlab[M].A Wiley-interscience.2001
[21]任淑云.基于粒子滤波算法的交通状态估计研究[D].北京交通大学.2010.
[22]Mufioz, L., Sun, X., Horowitz, R., Alvarez, L.,2003. Traffic density estimation with the cell transmission model. In:proceedings of the American control conference. Denver, Colorado, USA, pp.3750-3755.
[23]Sun, X., Munoz, L., Horowitz, R.,2003. Highway traffic state estimation using improved mixture Kalman filters for effective ramp metering control. In:Proceedings of the 42nd IEEE Conference on Decision and Control. Hawaii, USA,6333-6338.
[24]Sumalee, A., Zhong, X., Pan, L., Szeto, Y.,2011. Stochastic cell transmission model (SCTM):A stochastic dynamic traffic model for traffic state surveillance and assignment. Transportation Research Part B 45(3),507-533.
125] Nanthawichit, C., Nakatsuji, T., Suzuki, H.,2003. Application of probe-vehicle data for real-time traffic-state estimation and short-term travel-time prediction on a freeway. Transportation Research Record 1855,49-59.
[26]Work, D. B., Blandin, S., Tossavainen, O.-P., Piccoli, B., Bayen, A. M.,2010. A traffic model for velocity data assimilation. Appl. Math. Res. Express 2010(1),1-35.
[27]Herrera, J. C., Bayen, A. M.,2010. Incorporation of Lagrangian measurements in freeway traffic state estimation. Transportation Research Part B 44(4),269-287.
[28]Wang, Y., Papageorgiou, M.,2005. Real-time freeway traffic state estimation based on extended Kalman filter:a general approach. Transportation Research Part B 39(2),141-167.
[29]Wang, Y., Papageorgiou, M., Messmer, A.,2007. Real-time freeway traffic state estimation based on extended Kalman filter. Transportation Science 41 (2),167-181.
[30]http://en.wikipedia.org/wiki/Extended_Kalman_filter.
[31]Mihaylova, L., Boel, R., Hegyi, A.,2007. Freeway traffic estimation within particle filtering framework. Automatica 43 (2),290-300.
[32]Payne, H.J., Brown, D., and Cohen, S.L. Improved Techniques for Freeway Surveillance, Transportation Research Record 1112, TRB, National Research Council, Washington, D.C.,1987, pp.52-60.
[33]http://en.wikipedia.org/wiki/Ensemble_Kalman_filter.
[34]http://en.wikipedia.org/wiki/Monte_Carlo.
[35]Treiber, M., Helbing, D.,2002. Reconstructing the spatio-temporal traffic dynamics from stationary detector data. Cooper@tive Tr@nsport@tion Dyn@mics 1,3.1-3.24.
[36]Mehran, B., Kuwahara. M., Naznin, F.,2011, Implementing kinematic wave theory to reconstruct vehicle trajectories from fixed and probe sensor data. Proceeding of the 19th International Symposium on Transportation and Traffic Theory, Berkeley, USA, vol.17, pp. 247-268.
[37]Wasson, J.S., Sturdevant, J.R., Bullock, D.M.,2008. Real-time travel time estimates using MAC address matching. Institute of Transportation Engineers Journal,78(6),20-23.
[38]Haghani, A., Hamedi, M., Sadabadi, K. F., Young, S., Tarnoff, P.,2010. Data collection of freeway travel time ground truth with Bluetooth sensors. Transportation Research Record, 2160,60-68.
[39]Zhou, X., Mahmassani, H.,2006. Dynamic OD demand estimation using automatic vehicle identification data. IEEE Transactions on Intelligent Transportation Systems 7(1), 105-114.
[40]姜桂艳.道路交通状态判别技术与应用[M].人民出版社.2004.
[41]Cassidy, M., Coifinan, B.,1997, Relation among average speed, flow, and density and the analogous relation between density and occupancy, Transportation Research Record 1591,1-6.
[42]Edie, LC. Discussion of traffic stream measurements and definitions. Proc Int Symp. Onthe Theory of Traffic Flow J. Almond (ed) Paris:OECD,1965:139-154.
[43]Daganzo, CF 1997 Fundamentals of transportation and traffic operations. New York:Elsevier.
[44]彭春华,刘建业,刘岳峰,晏磊,郑江华.车辆检测传感器综述[J].传感器与微系统.2007,26(6)：4-7,11.
[45]FHWA.,2008. The next generation simulation (NGSIM).http://www.ngsim.fhwa.dot.gov/>.
[46]吴平衡.基于浮动车的交通信息获取关键技术及应用分析[M].西南交通大学.2009.
[47]Wardrop, J. G. and G. Charlesworth (1954). A Method of Estimating Speed and Flow of Traffic from a Moving Vehicle. Proceedings of the Institution of Civil Engineers, part II,Vol.3,pp.158-171.
[48]盛鹏,赵树龙,宋万忠,刘怡光,杨梦龙等.基于旅行时间检测系统的交通应用研究[J].计算机信息.2007(11)：2634：2636
[49]陈思.基于GPS/GIS浮动车技术的旅行时间预测模型[D].北京交通大学.2007.
[50]Transportation Research Board Traffic flow monograph [M].1964,1975,2009.
[51]Greenshields,B.D.,.A Study of Traffic Capacity[J].Proceeding 14th Annual Meeting Highway Research Board.1935:448-477.
[52]Greenberg, H., An analysis of traffic flow[J]. Operation esearch.1959.7(1):79-85.
[53]Underwood,R.T.,Speed,volume and density relationships,In quality and theory of traffic flow.Bureau of Highway Traffic,Yale University,newHaven,Conn.1961:141-187.
[54]Newell, G. F.,2002. A simplified car-following theory:a lower order model. Transportation Research Part B,36(3),195-205.
[55]Hurdle, V.F., Son, B.,2000. Road test of a freeway model. Transportation Research Part A 34(7),537-564.
[56]G. Dervisoglu, G. Gomes, J. Kwon, and P. Varaiya. Automatic calibration of the fundamentaldiagram and empirical observations on capacity. Presented at Transportation Research Board 88th Annual Meeting,2009.
[57]http://pems.dot.ca.gov/.
[58]Randall J.LeVeque. Numerical Methods for Conservation Laws [M]. Mathematics of Computation,1991,57(196):44-48.
[59]Xiaoyun Lu,Alexander Skabardonis.Freeway traffic shockwave analysis:exploring the NGSIM trajectory data[J].Washington,D.C.2007.86th Annual Meeting Transportation Research Board.
[60]Nicholoas J.Garber,Lester A.Hoel.Traffic and highway engineering [M].Fourth Edition.PWS Publishing Company, Boston.2009::231:243.
[61]Lighthill, M.J., Whitham, G.B.,1955. On kinematic waves:Ⅱ. A theory of traffic flow on long crowded roads, In:Proc. Royal Society, vol.229 (1178) of A, pp.317-345.
[62]Richards, P.I.,1956. Shock waves on the highway. Operations Research 4(1),42-51.
[63]S.K.Godunov.Mat.Sb.,47.1959:271.
[64]J.P.Lebacque.The Godunov scheme and what it means for first order traffic flow models[J].International symposium on transportation and traffic theory,Lyon,France.1996:647-677.
[65]Three-detector problem and Newell's method. On Wikipedia: http://en.wikipedia.org/wiki/Three-detector_problem_and_Newell's_method.
[66]Daganzo, C. F.,2003. A variational formulation of kinematic waves:solution methods. Transportation Research Part B 39(10),934-950.
[67]Daganzo, C. F.,2005. A variational formulation of kinematic waves:basic theory and complex boundary conditions. Transportation Research Part B 39(2),187-196.
[68]Tie-Qiao Tang.S.C.Wong. Hai-Jun Huang.Peng Zhang.Macroscopic Modeling of Lane-changing for Two-lane Traffic Flow[J].Journal of Advanced Transportation.2008.43(3):245-273.
[69]Sun, Z., Ban, X. Vehicle Trajectory Reconstruction for Signalized Intersections Using Variational Formulation of Kinematic Waves. Presentedat the 90th Transportation Research Board Annual Meeting.2010.
[70]Transportation Network Modeling Committee.Dynamic Traffic Assignment:A Primer.Transportation Research Circular E-C153.2011:16-21.
[71]Yibing Wang.,Markos papageorgiou.,Albert Messmer.RENAISSANCE-A unified macroscopic model-based approach to real-time freeway network traffic surveillance[J].Transportation Research part C.2006.14:190-212.
[72]Ashok, K.,1996. Estimation and prediction of time-dependent origin-destination flows, Ph.D. Dissertation, MIT.143-149.
[73]Daganzo, C. F.,1979. Multinomial probit:The theory and its application to demand forecasting. Academic Press, New York.118-125.
[74]Clark, C. E.,1961. The greatest of a finite set of random variables. Operations Research 9(2), 145-162.
[75]Daganzo, C.F., Bouthelier F., Sheffi, Y.,1977. Multinomial probit and Qualitative Choice:A Computationally Efficient Algorithm. Transportation Science 11(4),338-358.
[76]Horowitz, J.L., Sparmann, J. M., Daganzo, C. F.,1982. Investigation of accuracy of Clark approximation for multinomial probit Model. Transportation Science 16(3),382-401.
[77]Yegor Malinovskiy, Un-Kun Lee, Yao-Jan Wu and Yinhai Wang (2010), "Investigation ofBluetooth-Based Travel Time Estimation Error on a Short Corridor," Presented at the 90th Annual Meeting of the Transportation Research Board, Washington, D.C.
[78]Gazis, D. C. and Szeto, M. W. (1972). Application of Kalman Filtering to the Surveillance and Control of Traffic Systems. Transportation Science,6(4):419-439.
[79]Cremer, M. and Papageorgiou, P. (1981) Parameter Identification for a Traffic Flow Model. Automatica,17, pp.837-843.
[80]Sherali, H.D., Desaia, J., Rakhab, H.,2006. A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times. Transportation Research Part B 40(10),857-871.
[81]Okutani, I. and Stephanedes, Y. (1984) Dynamic Prediction of Traffic Volume Through Kalman Filtering Theory. Transportation Research 18B(1),1-11.
[82]sites.google.com/site/dtalite/.
[83]http://www.gams.com/.
[84]Juan Carlos Munoz., Carlos F.Danganzo.Fingerpringting Traffic from static freeway sensors.Cooperative transportation dyanmaic 1.2002.1.1-1.11.
[2]张文奇.简述中国经济发展与交通运输的关系[J].城市交通,2001,3：1-7.
[3]Glen Weisbrod, Don Vary, George Treyz. Measuring Economic Costs of Urban Traffic Congestion to Business[J]. Transportation Research Record,2007,1839:03-3234.
[4]徐吉谦,主编.交通工程总论[M].人民交通出版社,1991.
[5]吕力生.城市交通阻塞分析[J].上海大学学报,1998,(6).
[6]Christian Claudel.Convex formulations of inverse modeling problems on systems modeled by Hamilton-Jacobi equations:applications to traffic flow engineering[D].University of California, Berkeley.2011:5-20.
[7]Zhou, X. and List, G. An Information-Theoretic Sensor Location Model for Traffic Origin-Destination Demand Estimation Applications. Transportation Science.2010,44:254-273.
[8]刘栋,穆晓霞,宋国杰等.基于浮动车数据的城市交通状态估计研究[J].河南师范大学学报(自然科学版).2011,39(3)：162-166.
[9]史文欢,孔庆杰,刘允才等.基于出租车跟踪的市区路网交通状态估计方法[J].交通信息与安全.2009,27(5)：29-32.
[10]袁月明,关伟,吴建平等.基于视频检测技术的城市快速路交通状态分析研究[J].2008,26(4)：1-3.
[11]徐涛,杨晓光,徐爱功,张明月.面向城市道路交通状态估计的数据融合研究[J].计算机工程与应用,2011,47(7)：218-221.
[12]龙建成.城市道路交通拥堵传播规律及消散控制策略研究[D].北京交通大学.2009.
[13]贾斌,高自友,李克平,李新刚.基于元胞自动的交通系统建模与模拟[M].科学出版社.2007.
[14]程松,陈光梦.一种利用粒子滤波的实时交通状态估计方法.微型电脑应用.2008,24(2)：13-17.
[15]Ashok, K., Ben-Akiva, M.E. Alternative approaches for real-time estimation and prediction of time-dependent origin-destination flows[J]. Transportation Science.2000,34(1),21-36.
[16]Zhou, X., List, G.F.,2010. An information-theoretic sensor location model for traffic origin-destination demand estimation applications. Transportation Science 44(2),254-273.
[17]Coifman, B.,2002. Estimating travel times and vehicle trajectories on freeways using dual loop detectors. Transportation Research Part A 36(4),351-364.
[18]Daganzo, C. F.,1994. The cell transmission model:a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B 28(4),269-287.
[19]Newell, G.F.,1993. A simplified theory of kinematic waves in highway traffic, part I:General Theory. Transportation Research Part B 27(4),281-297.
[20]John Wiley.Kalman Filtering Theary and practice using matlab[M].A Wiley-interscience.2001
[21]任淑云.基于粒子滤波算法的交通状态估计研究[D].北京交通大学.2010.
[22]Mufioz, L., Sun, X., Horowitz, R., Alvarez, L.,2003. Traffic density estimation with the cell transmission model. In:proceedings of the American control conference. Denver, Colorado, USA, pp.3750-3755.
[23]Sun, X., Munoz, L., Horowitz, R.,2003. Highway traffic state estimation using improved mixture Kalman filters for effective ramp metering control. In:Proceedings of the 42nd IEEE Conference on Decision and Control. Hawaii, USA,6333-6338.
[24]Sumalee, A., Zhong, X., Pan, L., Szeto, Y.,2011. Stochastic cell transmission model (SCTM):A stochastic dynamic traffic model for traffic state surveillance and assignment. Transportation Research Part B 45(3),507-533.
125] Nanthawichit, C., Nakatsuji, T., Suzuki, H.,2003. Application of probe-vehicle data for real-time traffic-state estimation and short-term travel-time prediction on a freeway. Transportation Research Record 1855,49-59.
[26]Work, D. B., Blandin, S., Tossavainen, O.-P., Piccoli, B., Bayen, A. M.,2010. A traffic model for velocity data assimilation. Appl. Math. Res. Express 2010(1),1-35.
[27]Herrera, J. C., Bayen, A. M.,2010. Incorporation of Lagrangian measurements in freeway traffic state estimation. Transportation Research Part B 44(4),269-287.
[28]Wang, Y., Papageorgiou, M.,2005. Real-time freeway traffic state estimation based on extended Kalman filter:a general approach. Transportation Research Part B 39(2),141-167.
[29]Wang, Y., Papageorgiou, M., Messmer, A.,2007. Real-time freeway traffic state estimation based on extended Kalman filter. Transportation Science 41 (2),167-181.
[30]http://en.wikipedia.org/wiki/Extended_Kalman_filter.
[31]Mihaylova, L., Boel, R., Hegyi, A.,2007. Freeway traffic estimation within particle filtering framework. Automatica 43 (2),290-300.
[32]Payne, H.J., Brown, D., and Cohen, S.L. Improved Techniques for Freeway Surveillance, Transportation Research Record 1112, TRB, National Research Council, Washington, D.C.,1987, pp.52-60.
[33]http://en.wikipedia.org/wiki/Ensemble_Kalman_filter.
[34]http://en.wikipedia.org/wiki/Monte_Carlo.
[35]Treiber, M., Helbing, D.,2002. Reconstructing the spatio-temporal traffic dynamics from stationary detector data. Cooper@tive Tr@nsport@tion Dyn@mics 1,3.1-3.24.
[36]Mehran, B., Kuwahara. M., Naznin, F.,2011, Implementing kinematic wave theory to reconstruct vehicle trajectories from fixed and probe sensor data. Proceeding of the 19th International Symposium on Transportation and Traffic Theory, Berkeley, USA, vol.17, pp. 247-268.
[37]Wasson, J.S., Sturdevant, J.R., Bullock, D.M.,2008. Real-time travel time estimates using MAC address matching. Institute of Transportation Engineers Journal,78(6),20-23.
[38]Haghani, A., Hamedi, M., Sadabadi, K. F., Young, S., Tarnoff, P.,2010. Data collection of freeway travel time ground truth with Bluetooth sensors. Transportation Research Record, 2160,60-68.
[39]Zhou, X., Mahmassani, H.,2006. Dynamic OD demand estimation using automatic vehicle identification data. IEEE Transactions on Intelligent Transportation Systems 7(1), 105-114.
[40]姜桂艳.道路交通状态判别技术与应用[M].人民出版社.2004.
[41]Cassidy, M., Coifinan, B.,1997, Relation among average speed, flow, and density and the analogous relation between density and occupancy, Transportation Research Record 1591,1-6.
[42]Edie, LC. Discussion of traffic stream measurements and definitions. Proc Int Symp. Onthe Theory of Traffic Flow J. Almond (ed) Paris:OECD,1965:139-154.
[43]Daganzo, CF 1997 Fundamentals of transportation and traffic operations. New York:Elsevier.
[44]彭春华,刘建业,刘岳峰,晏磊,郑江华.车辆检测传感器综述[J].传感器与微系统.2007,26(6)：4-7,11.
[45]FHWA.,2008. The next generation simulation (NGSIM).http://www.ngsim.fhwa.dot.gov/>.
[46]吴平衡.基于浮动车的交通信息获取关键技术及应用分析[M].西南交通大学.2009.
[47]Wardrop, J. G. and G. Charlesworth (1954). A Method of Estimating Speed and Flow of Traffic from a Moving Vehicle. Proceedings of the Institution of Civil Engineers, part II,Vol.3,pp.158-171.
[48]盛鹏,赵树龙,宋万忠,刘怡光,杨梦龙等.基于旅行时间检测系统的交通应用研究[J].计算机信息.2007(11)：2634：2636
[49]陈思.基于GPS/GIS浮动车技术的旅行时间预测模型[D].北京交通大学.2007.
[50]Transportation Research Board Traffic flow monograph [M].1964,1975,2009.
[51]Greenshields,B.D.,.A Study of Traffic Capacity[J].Proceeding 14th Annual Meeting Highway Research Board.1935:448-477.
[52]Greenberg, H., An analysis of traffic flow[J]. Operation esearch.1959.7(1):79-85.
[53]Underwood,R.T.,Speed,volume and density relationships,In quality and theory of traffic flow.Bureau of Highway Traffic,Yale University,newHaven,Conn.1961:141-187.
[54]Newell, G. F.,2002. A simplified car-following theory:a lower order model. Transportation Research Part B,36(3),195-205.
[55]Hurdle, V.F., Son, B.,2000. Road test of a freeway model. Transportation Research Part A 34(7),537-564.
[56]G. Dervisoglu, G. Gomes, J. Kwon, and P. Varaiya. Automatic calibration of the fundamentaldiagram and empirical observations on capacity. Presented at Transportation Research Board 88th Annual Meeting,2009.
[57]http://pems.dot.ca.gov/.
[58]Randall J.LeVeque. Numerical Methods for Conservation Laws [M]. Mathematics of Computation,1991,57(196):44-48.
[59]Xiaoyun Lu,Alexander Skabardonis.Freeway traffic shockwave analysis:exploring the NGSIM trajectory data[J].Washington,D.C.2007.86th Annual Meeting Transportation Research Board.
[60]Nicholoas J.Garber,Lester A.Hoel.Traffic and highway engineering [M].Fourth Edition.PWS Publishing Company, Boston.2009::231:243.
[61]Lighthill, M.J., Whitham, G.B.,1955. On kinematic waves:Ⅱ. A theory of traffic flow on long crowded roads, In:Proc. Royal Society, vol.229 (1178) of A, pp.317-345.
[62]Richards, P.I.,1956. Shock waves on the highway. Operations Research 4(1),42-51.
[63]S.K.Godunov.Mat.Sb.,47.1959:271.
[64]J.P.Lebacque.The Godunov scheme and what it means for first order traffic flow models[J].International symposium on transportation and traffic theory,Lyon,France.1996:647-677.
[65]Three-detector problem and Newell's method. On Wikipedia: http://en.wikipedia.org/wiki/Three-detector_problem_and_Newell's_method.
[66]Daganzo, C. F.,2003. A variational formulation of kinematic waves:solution methods. Transportation Research Part B 39(10),934-950.
[67]Daganzo, C. F.,2005. A variational formulation of kinematic waves:basic theory and complex boundary conditions. Transportation Research Part B 39(2),187-196.
[68]Tie-Qiao Tang.S.C.Wong. Hai-Jun Huang.Peng Zhang.Macroscopic Modeling of Lane-changing for Two-lane Traffic Flow[J].Journal of Advanced Transportation.2008.43(3):245-273.
[69]Sun, Z., Ban, X. Vehicle Trajectory Reconstruction for Signalized Intersections Using Variational Formulation of Kinematic Waves. Presentedat the 90th Transportation Research Board Annual Meeting.2010.
[70]Transportation Network Modeling Committee.Dynamic Traffic Assignment:A Primer.Transportation Research Circular E-C153.2011:16-21.
[71]Yibing Wang.,Markos papageorgiou.,Albert Messmer.RENAISSANCE-A unified macroscopic model-based approach to real-time freeway network traffic surveillance[J].Transportation Research part C.2006.14:190-212.
[72]Ashok, K.,1996. Estimation and prediction of time-dependent origin-destination flows, Ph.D. Dissertation, MIT.143-149.
[73]Daganzo, C. F.,1979. Multinomial probit:The theory and its application to demand forecasting. Academic Press, New York.118-125.
[74]Clark, C. E.,1961. The greatest of a finite set of random variables. Operations Research 9(2), 145-162.
[75]Daganzo, C.F., Bouthelier F., Sheffi, Y.,1977. Multinomial probit and Qualitative Choice:A Computationally Efficient Algorithm. Transportation Science 11(4),338-358.
[76]Horowitz, J.L., Sparmann, J. M., Daganzo, C. F.,1982. Investigation of accuracy of Clark approximation for multinomial probit Model. Transportation Science 16(3),382-401.
[77]Yegor Malinovskiy, Un-Kun Lee, Yao-Jan Wu and Yinhai Wang (2010), "Investigation ofBluetooth-Based Travel Time Estimation Error on a Short Corridor," Presented at the 90th Annual Meeting of the Transportation Research Board, Washington, D.C.
[78]Gazis, D. C. and Szeto, M. W. (1972). Application of Kalman Filtering to the Surveillance and Control of Traffic Systems. Transportation Science,6(4):419-439.
[79]Cremer, M. and Papageorgiou, P. (1981) Parameter Identification for a Traffic Flow Model. Automatica,17, pp.837-843.
[80]Sherali, H.D., Desaia, J., Rakhab, H.,2006. A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times. Transportation Research Part B 40(10),857-871.
[81]Okutani, I. and Stephanedes, Y. (1984) Dynamic Prediction of Traffic Volume Through Kalman Filtering Theory. Transportation Research 18B(1),1-11.
[82]sites.google.com/site/dtalite/.
[83]http://www.gams.com/.
[84]Juan Carlos Munoz., Carlos F.Danganzo.Fingerpringting Traffic from static freeway sensors.Cooperative transportation dyanmaic 1.2002.1.1-1.11.