CN102629418B

CN102629418B - Fuzzy kalman filtering-based traffic flow parameter prediction method

Info

Publication number: CN102629418B
Application number: CN201210102006.0A
Authority: CN
Inventors: 郭海锋; 方良君; 张贵军; 俞立; 朱炯; 张志建; 汪建仙
Original assignee: Zhejiang University of Technology ZJUT
Current assignee: Zhejiang University of Technology ZJUT
Priority date: 2012-04-09
Filing date: 2012-04-09
Publication date: 2014-10-29
Anticipated expiration: 2032-04-09
Also published as: CN102629418A

Abstract

The invention discloses a fuzzy kalman filtering-based traffic flow parameter prediction method, which is characterized by comprising the following steps of: laying a detector in each lane on the upstream of a road section and in each lane on the downstream of the road section to acquire real-time traffic flow parameter data; acquiring contemporaneous historical traffic flow parameter data of the detector in each lane; constructing a dynamic kalman filtering traffic flow parameter prediction model by using a kalman filtering technology; obtaining a kalman filtering parameter prediction result through a kalman filtering time updating equation and a state updating equation; introducing a historical contemporaneous average traffic flow parameter into a formula (2) and constructing a fuzzy kalman filtering traffic flow parameter prediction model; and predicting the traffic flow parameter of a next time interval and behind the next time interval according to the real-time traffic flow parameter acquired by the detector and the historical contemporaneous average traffic flow parameter.

Description

Traffic Flow Prediction Method Based on Fuzzy Kalman Filter

技术领域technical field

本发明涉及一种交通流预测方法。The invention relates to a traffic flow prediction method.

背景技术Background technique

短时交通流参数预测是以检测设备获得的实时交通数据为基础，通过构建的模型和方法预测下一时段的交通流参数。该预测结果通常用于实时交通信号控制系统和动态诱导系统中。因此短时交通流参数的预测将直接影响上述系统的实时效果。The short-term traffic flow parameter prediction is based on the real-time traffic data obtained by the detection equipment, and predicts the traffic flow parameters in the next period through the constructed model and method. The prediction results are usually used in real-time traffic signal control systems and dynamic guidance systems. Therefore, the prediction of short-term traffic flow parameters will directly affect the real-time effect of the above-mentioned system.

从预测模型看，短时交通流预测可分为两类：第一类是以数理统计和微积分等传统数学和物理方法为基础的预测模型，主要包括时间序列模型、卡尔曼滤波模型、参数回归模型、指数平滑模型等；第二类是以现代科学技术和方法为主要研究手段而形成的预测模型，其特点是所采用的模型和方法不追求严格意义上的数学推导和明确的物理意义，而更重视对真实交通流现象的拟合效果，主要包括非参数回归模型、KARIMA算法、基于小波理论的方法、基于多维分形的方法、谱分析法、状态空间重构模型和多种与神经网络相关的复合预测模型等。From the perspective of forecasting models, short-term traffic flow forecasting can be divided into two categories: the first category is based on traditional mathematical and physical methods such as mathematical statistics and calculus, mainly including time series models, Kalman filter models, parameter Regression model, exponential smoothing model, etc.; the second type is a prediction model formed by modern scientific technology and methods as the main research method, and its characteristic is that the models and methods adopted do not pursue strict mathematical derivation and clear physical meaning , and pay more attention to the fitting effect of real traffic flow phenomena, mainly including non-parametric regression model, KARIMA algorithm, method based on wavelet theory, method based on multidimensional fractal, spectral analysis method, state space reconstruction model and a variety of neural networks Network-related composite forecasting models, etc.

在上述预测模型中，卡尔曼滤波预测模型因其具有精度较高，鲁棒性较强的优点被广泛使用，而且较IWAO OKUTANI和VYTHOTKAS P C通过卡尔曼滤波模型预测交通流参数发现，其预测结果优于著名的UTCS-2预测方法的预测结果。但是已有的卡尔曼滤波预测模型预测输出值存在几个时间段的延迟，即存在一定的滞后性，影响了预测参数在动态实时控制和在诱导系统中的广泛应用。Among the above prediction models, the Kalman filter prediction model is widely used because of its high precision and strong robustness. Compared with IWAO OKUTANI and VYTHOTKAS PC, it is found that the Kalman filter model predicts traffic flow parameters. The results are better than those of the well-known UTCS-2 forecasting method. However, the existing Kalman filter prediction model predicts the output value to be delayed for several periods of time, that is, there is a certain hysteresis, which affects the wide application of prediction parameters in dynamic real-time control and in induction systems.

发明内容Contents of the invention

本发明要克服已有的卡尔曼滤波预测模型预测输出值存在滞后性的缺点，提供一种能够弥补滞后性问题的基于模糊卡尔曼滤波的交通流参数预测方法。The present invention overcomes the disadvantage of hysteresis in the predicted output value of the existing Kalman filter prediction model, and provides a fuzzy Kalman filter-based traffic flow parameter prediction method that can compensate for the hysteresis problem.

本发明所述的基于模糊卡尔曼滤波的交通流参数预测方法包括以下步骤：The traffic flow parameter prediction method based on fuzzy Kalman filter of the present invention comprises the following steps:

1)在路段上游各车道和路段下游各车道布设检测器采集实时交通流参数数据；1) Arrange detectors in each lane upstream of the road section and each lane downstream of the road section to collect real-time traffic flow parameter data;

2)获取各车道检测器同期历史交通流参数数据；2) Obtain the historical traffic flow parameter data of each lane detector in the same period;

3)采用卡尔曼滤波技术构建动态卡尔曼滤波交通流参数预测模型，所述动态卡尔曼滤波交通流参数预测模型描述如式(1)所示：3) The dynamic Kalman filter traffic flow parameter prediction model is constructed by using the Kalman filter technology, and the description of the dynamic Kalman filter traffic flow parameter prediction model is as shown in formula (1):

$\overset{&LeftRightArrow; &LeftRightArrow;}{Q Q} L L ((τ τ + + k k)) = = {H h}_{00} V V ((τ τ)) + + {H h}_{11} V V ((τ τ - - 11)) + + \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot + + {H h}_{n no - - 11} V V ((τ τ - - n no + + 11)) + + ω ω ((τ τ)) - - - - - - ((11))$

式中：为τ时刻后k个时间段的路段L上的交通流参数向量，它与路段两端出入口的交通流参数有关；V(τ)＝[v₁(τ),v₂(τ),…,v_m(τ)]^T是在时段((τ-1)T,τT]各出入口的交通流参数向量，其中v_m(τ)是在时段((τ-1)T,τT]某个入口或出口的交通流参数，它包含对交通流参数预测一些有用的预测因子，可以通过检测器直接观测到，V(τ-1)是在时段((τ-1)T,τT]前一个时段((τ-2)T,(τ-1)T]各出入口的交通流参数向量；H₀,H₁,…,H_n-1为参数矩阵，H_k＝[c₁′(τ),c′₂(τ),…,c′_m(τ)]，c′_m(τ)为状态变量；m为路段上入口和出口所考虑的检测器总数；ω(τ)为观测噪声，假定为期望为零的白噪声，它的协方差矩阵为R(τ)；In the formula: is the traffic flow parameter vector on the road section L of k time periods after time τ, which is related to the traffic flow parameters at the entrances and exits at both ends of the road section; V(τ)=[v ₁ (τ),v ₂ (τ),…, v _m (τ)] ^T is the traffic flow parameter vector of each entrance and exit in the time period ((τ-1)T,τT], where v _m (τ) is a certain entrance in the time period ((τ-1)T,τT] Or the traffic flow parameters of the exit, it contains some useful predictors for the prediction of traffic flow parameters, which can be directly observed by the detector, V(τ-1) is a period before the period ((τ-1)T,τT] ((τ-2)T,(τ-1)T] The traffic flow parameter vectors of each entrance and exit; H ₀ , H ₁ ,...,H _n-1 are parameter matrices, H _k =[c ₁ ′(τ), c′ ₂ (τ),…,c′ _m (τ)], c′ _m (τ) is the state variable; m is the total number of detectors considered at the entrance and exit of the road section; ω(τ) is the observation noise, assuming is expected to be zero white noise, its covariance matrix is R(τ);

4)在步骤3)基础上，通过卡尔曼滤波时间更新方程和状态更新方程，得到卡尔曼滤波参数预测结果如(2)所示：4) On the basis of step 3), through the Kalman filter time update equation and the state update equation, the Kalman filter parameter prediction result is obtained as shown in (2):

$\overset{^^}{Q Q} L L ((τ τ + + k k)) = = A A ((τ τ)) \overset{^^}{X x} ((τ τ | | τ τ - - 11)) - - - - - - ((22))$

式中：为τ时刻后k个时间段路段L上所预测的交通流参数向量；In the formula: is the predicted traffic flow parameter vector on the road segment L of k time segments after time τ;

为状态估计向量；A(τ)＝[V^T(τ),V^T(τ-1),V^T(τ-2)]为交通流参数的观测向量； is the state estimation vector; A(τ)=[V ^T (τ), V ^T (τ-1), V ^T (τ-2)] is the observation vector of traffic flow parameters;

5)将历史同期平均交通流参数引入式(2)中，构建模糊卡尔曼滤波交通流参数预测模型如式(3)所示：5) Introduce the historical average traffic flow parameters into formula (2), and construct the fuzzy Kalman filter traffic flow parameter prediction model as shown in formula (3):

$\overset{&OverBar; &OverBar;}{Q Q} L L ((τ τ + + k k)) = = ((11 - - γ γ)) \overset{^^}{Q Q} L L ((τ τ + + k k)) + + γ γ \overset{&OverBar; &OverBar;}{QL QL} ((τ τ + + k k)) - - - - - - ((33))$

其中，为预测的最终结果，为同时期历史平均参数；为卡尔曼滤波的预测结果；γ为历史值权重系数；in, For the predicted final result, is the historical average parameter of the same period; is the prediction result of Kalman filter; γ is the historical value weight coefficient;

6)将检测器采集到的实时交通流参数和历史同期平均交通流参数输入到式(3)中，对下一时间间隔及之后的交通流参数进行预测。6) Input the real-time traffic flow parameters collected by the detector and the historical average traffic flow parameters in the same period into formula (3), and predict the traffic flow parameters in the next time interval and after.

所述检测器包括但不限于环形感应线圈检测器、视频检测器、微波检测器、雷达检测器、无线传感器节点；The detectors include, but are not limited to, loop induction coil detectors, video detectors, microwave detectors, radar detectors, wireless sensor nodes;

所述交通流参数是指交通流量和/或占有率和/或速度和/或密度和/或饱和度；The traffic flow parameters refer to traffic flow and/or occupancy and/or speed and/or density and/or saturation;

所述下一时间间隔是指5分钟或15分钟或30分钟或60分钟。Said next time interval refers to 5 minutes or 15 minutes or 30 minutes or 60 minutes.

所述卡尔曼滤波时间更新方程为：The Kalman filter time update equation is:

$\overset{^^}{X x} ((τ τ | | τ τ - - 11)) = = B B ((τ τ)) \overset{^^}{X x} ((τ τ - - 11)) - - - - - - ((44))$

P(τ|τ-1)＝Q(τ-1)+B(τ-1)P(τ-1)B^T(τ-1) (5)P(τ|τ-1)＝Q(τ-1)+B(τ-1)P(τ-1)B ^T (τ-1) (5)

状态更新方程为：The state update equation is:

K(τ)＝P(τ|τ-1)A^T(τ)[A(τ)P(τ|τ-1)A^T(τ)+R(τ)]^-1 (6)K(τ)＝P(τ|τ-1)A ^T (τ)[A(τ)P(τ|τ-1)A ^T (τ)+R(τ)] ^-1 (6)

$\overset{^^}{X x} ((τ τ)) = = \overset{^^}{X x} ((τ τ | | τ τ - - 11)) + + K K ((τ τ)) [[z z ((τ τ)) - - A A ((τ τ)) \overset{^^}{X x} ((τ τ | | τ τ - - 11))]] - - - - - - ((77))$

P(τ)＝[I-K(τ)A(τ)]P(τ|τ-1) (8)P(τ)＝[I-K(τ)A(τ)]P(τ|τ-1) (8)

式中：为状态向量，为状态估计向量；B(τ)为状态转移矩阵，B(τ)＝I；P(τ)为误差协方差，P(τ|τ-1)为估计协方差；K(τ)为卡尔曼增益；z(τ)为实际获取的交通流参数，其值等于R(τ)为期望为零的白噪声。In the formula: is the state vector, is the state estimation vector; B(τ) is the state transition matrix, B(τ)=I; P(τ) is the error covariance, P(τ|τ-1) is the estimated covariance; K(τ) is the Kalman gain; z(τ) is the actual obtained traffic flow parameter, and its value is equal to R(τ) is white noise expected to be zero.

所述历史值权重系数γ由模糊逻辑确定；The historical value weight coefficient γ is determined by fuzzy logic;

所述模糊规则：以相对误差，平均相对误差，平均绝对相对误差，作为模糊综合判断的指标，参数γ越大，则当前交通流变化趋势更接近历史平均；反之，则当前交通流变化趋势更接近卡尔曼滤波模块的预测值。The fuzzy rule: using relative error, average relative error, and average absolute relative error as indicators for fuzzy comprehensive judgment, the larger the parameter γ, the closer the current traffic flow trend is to the historical average; otherwise, the current traffic flow trend is closer Close to the predicted value of the Kalman filter module.

本发明将同期历史数据和卡尔曼滤波模块用于短时交通流参数预测，利用模糊逻辑算法将两者进行组合，其输出值作为最终交通流参数预测值。本发明能够对交通流参数做出较为准确的预测，能够用于实时交通信号控制系统和动态诱导系统中，也可对交通管理部门的管理提供有效的保障。本发明充分利用卡尔曼滤波模型精度高，鲁棒性强的特点，结合城市道路交通流的日相似性特点，从而提高预测精度。The invention uses the historical data of the same period and the Kalman filter module for short-term traffic flow parameter prediction, uses fuzzy logic algorithm to combine the two, and its output value is used as the final traffic flow parameter prediction value. The invention can make relatively accurate predictions on traffic flow parameters, can be used in real-time traffic signal control systems and dynamic guidance systems, and can also provide effective guarantee for the management of traffic management departments. The invention makes full use of the characteristics of high precision and strong robustness of the Kalman filter model, and combines the characteristics of daily similarity of urban road traffic flow, thereby improving the prediction accuracy.

本发明的优点是：无滞后性、精确度高。The invention has the advantages of no hysteresis and high precision.

附图说明Description of drawings

图1是路段动态交通流示意图Figure 1 is a schematic diagram of dynamic traffic flow on road sections

图2是本发明工作原理Fig. 2 is the working principle of the present invention

具体实施方式Detailed ways

参照附图：Referring to the attached picture:

其中，为预测的最终结果，为同时期历史平均参数；为卡尔曼滤波的预测结果；γ为历史值权重系数in, For the predicted final result, is the historical average parameter of the same period; is the prediction result of Kalman filter; γ is the weight coefficient of historical value

所述检测器包括但不限于环形感应线圈检测器、视频检测器、微波检测器、雷达检测器、无线传感器节点；The detectors include but are not limited to loop induction coil detectors, video detectors, microwave detectors, radar detectors, wireless sensor nodes;

状态更新方程为：The state update equation is:

P(τ)＝[I-K(τ)A(τ)]P(τ|τ-1) (8)P(τ)＝[I-K(τ)A(τ)]P(τ|τ-1) (8)

具体实施时，设置检测器布置如图1所示，图中d_n为置于道路中的检测器，每天24小时监测并记录该监测器的车辆，以一个固定时间5min汇总一次，存储一周的交通流参数，将其分为工作日与非工作日流参数。按工作日与非工作日对不同日同时段求均值，并折算成小时交通流参数，作为历史交通流参数标本。During the specific implementation, the layout of the detectors is shown in Figure 1. In the figure, d _n is the detector placed on the road, and the vehicles of the monitor are monitored and recorded 24 hours a day. Traffic flow parameters are divided into working day and non-working day flow parameters. According to working days and non-working days, the average value is calculated for the same period of different days, and converted into hourly traffic flow parameters, as a sample of historical traffic flow parameters.

预测时，建立交通流预测模型：When forecasting, establish a traffic flow forecasting model:

$\overset{&LeftRightArrow; &LeftRightArrow;}{Q Q} L L ((τ τ + + 11)) = = {H h}_{00} V V ((τ τ)) + + {H h}_{11} V V ((τ τ - - 11)) + + . . . . . . + + {H h}_{n no - - 11} V V ((τ τ - - n no + + 11)) + + ω ω ((τ τ))$

其中，为观测路段在时段(τT,(τ+1)T]内的交通流参数预测值，其中，τ＝1,2,…,n，T为预测周期，一般取值为5-15min,H₀,H₁,…,H_n+1为参数矩阵，H_k＝[c₁′(τ),c′₂(τ),…,c′_m(τ)]，c′_m(τ)为状态变量；V(τ)＝[v₁(τ),v₂(τ),…,v_m(τ)]^T为时段((τ-1)T,τT]内路段各出入口的交通流参数向量，v_m(τ)是时段((τ-1)T,τT]内路段出入的交通流参数；ω(τ)为观测噪声，假定为期望为零的白噪声，它的协方差矩阵为R(τ)。in, is the predicted value of the traffic flow parameters of the observed road section in the time period (τT,(τ+1)T], where τ=1,2,...,n, T is the prediction period, generally the value is 5-15min, H ₀ ,H ₁ ,…,H _n+1 is the parameter matrix, H _k =[c ₁ ′(τ),c′ ₂ (τ),…,c′ _m (τ)], c′ _m (τ) is the state Variable; V(τ)＝[v ₁ (τ),v ₂ (τ),...,v _m (τ)] ^T is the traffic flow parameter vector of each entrance and exit of the road section in the time period ((τ-1)T,τT] , v _m (τ) is the traffic flow parameter of the road section in and out of the time period ((τ-1)T,τT]; ω(τ) is the observation noise, which is assumed to be white noise with zero expectation, and its covariance matrix is R (τ).

将式(1)作以下变换：Transform formula (1) as follows:

X(τ)＝(H₀,H₁,H₂)^T X(τ)＝(H ₀ ,H ₁ ,H ₂ ) ^T

A(τ)＝[V^T(τ),V^T(τ-1),V^T(τ-2)]A(τ)＝[V ^T (τ), V ^T (τ-1), V ^T (τ-2)]

$z z ((τ τ)) = = \overset{&LeftRightArrow; &LeftRightArrow;}{Q Q} L L ((τ τ + + 11))$

交通流参数预测模型可变为：The traffic flow parameter prediction model can be changed to:

X(τ)＝B(τ)X(τ-1)+v(τ-1)X(τ)=B(τ)X(τ-1)+v(τ-1)

z(τ)＝A(τ)X(τ)+ω(τ)z(τ)=A(τ)X(τ)+ω(τ)

式中：z(τ)为观测向量；X(τ)为状态向量；A(τ)为观测矩阵；B(τ)为状态转移矩阵，B(τ)＝I；v(τ-1)为模型噪声，假定为期望为零的白噪声，它的协方差矩阵为Q(τ-1)。In the formula: z(τ) is the observation vector; X(τ) is the state vector; A(τ) is the observation matrix; B(τ) is the state transition matrix, B(τ)=I; v(τ-1) is Model noise, assumed to be white noise with zero expectation, has a covariance matrix of Q(τ-1).

将每个时间段检测上来的交通流参数输入卡尔滤波模型中，按图2所示过程推算，图2为卡尔曼滤波预测模型具体推算过程，它可分为两个部分：时间更新方程和状态更新方程。时间更新方程负责及时向前推算当前状态变量和误差协方差估计的值，以便为下一个时间状态构造先验估计。状态更新方程利用实际获取的测量值对先验估计做出纠正得到后验估计。图2中，为状态向量，为状态估计向量；B(τ)为状态转移矩阵，B(τ)＝I；P(τ)为误差协方差，P(τ|τ-1)为估计协方差；K(τ)为卡尔曼增益；z(τ)为实际获取的交通流参数，其值等于R(τ)为期望为零的白噪声。Input the traffic flow parameters detected in each time period into the Kalman filter model, and calculate according to the process shown in Figure 2. Figure 2 shows the specific calculation process of the Kalman filter prediction model, which can be divided into two parts: time update equation and state Update the equation. The temporal update equation is responsible for extrapolating the values of the current state variables and error covariance estimates forward in time in order to construct prior estimates for the next temporal state. The state update equation uses the measured values actually obtained to correct the prior estimate to obtain the posterior estimate. In Figure 2, is the state vector, is the state estimation vector; B(τ) is the state transition matrix, B(τ)=I; P(τ) is the error covariance, P(τ|τ-1) is the estimated covariance; K(τ) is the Kalman gain; z(τ) is the actual obtained traffic flow parameter, and its value is equal to R(τ) is white noise expected to be zero.

得到预测结果的数学表达式为：The mathematical expression to get the predicted result is:

$\overset{^^}{Q Q} L L ((τ τ + + 11)) = = A A ((τ τ)) \overset{^^}{X x} ((τ τ | | τ τ - - 11))$

其中，为卡尔曼滤波预测模型的输出，代表观某测路段在时段(τT,(τ+1)T]内卡尔曼滤波预测模型的交通流参数预测值；为前一时段的状态矩阵。in, For the output of the Kalman filter prediction model, it represents the traffic flow parameter prediction value of the Kalman filter prediction model in the time period (τT, (τ+1)T] of a certain measured road section; is the state matrix of the previous period.

采用一种模糊逻辑算法，将获取的同期历史平均值和卡尔曼滤波预测模型的输出作组合，建立基于模糊卡尔曼滤波的短时交通流预测方法，数学表达式为：A fuzzy logic algorithm is used to combine the obtained historical average value and the output of the Kalman filter prediction model to establish a short-term traffic flow prediction method based on fuzzy Kalman filter. The mathematical expression is:

$\overset{&OverBar; &OverBar;}{Q Q} L L ((τ τ + + 11)) = = ((11 - - γ γ)) \overset{^^}{Q Q} L L ((τ τ + + 11)) + + γ γ \overset{&OverBar; &OverBar;}{QL QL} ((τ τ + + 11))$

其中：为模糊组合模型的输出，代表观某测路段在时段(τT,(τ+1)T]内交通流参数的预测值；为卡尔曼滤波预测模型的输出，代表观某测路段在时段(τT,(τ+1)T]内卡尔曼滤波模块的交通流参数预测值；为在已知时段(τT,(τ+1)T]历史平均值；γ为权重系数，γ∈[0,1]，模糊组合γ调整算法的模糊规则的基本规则为：以相对误差，平均相对误差，平均绝对相对误差，作为模糊综合判断的指标，参数γ越大，则当前交通流参数变化趋势更接近历史平均；反之，则当前交通流参数变化趋势更接近卡尔曼滤波预测模型的预测值。in: is the output of the fuzzy combination model, which represents the predicted value of the traffic flow parameters in the period (τT,(τ+1)T] of a measured road section; is the output of the Kalman filter prediction model, representing the traffic flow parameter prediction value of the Kalman filter module in the time period (τT, (τ+1)T] of the observed road section; is the historical average value in the known period (τT,(τ+1)T]; γ is the weight coefficient, γ∈[0,1], the basic rule of the fuzzy rule of the fuzzy combination γ adjustment algorithm is: with relative error, the average Relative error, average absolute relative error, as an indicator of fuzzy comprehensive judgment, the larger the parameter γ, the closer the current traffic flow parameter change trend is to the historical average; otherwise, the current traffic flow parameter change trend is closer to the prediction of the Kalman filter prediction model value.

预测结果主要用于路网协调控制实施。被控区域内如图1所示，在交叉口出入口和关键路段埋有车辆检测器，用于实时监测交通流参数，检测到信息通过专用网络传输到交通信息库中。The prediction results are mainly used for the implementation of road network coordination control. As shown in Figure 1 in the controlled area, vehicle detectors are buried at the intersection entrances and key road sections for real-time monitoring of traffic flow parameters, and the detected information is transmitted to the traffic information database through a dedicated network.

Claims

1. The traffic flow prediction method based on fuzzy Kalman filter, it is characterized in that comprising the following steps:

1) Arrange detectors in each lane upstream of the road section and each lane downstream of the road section to collect real-time traffic flow parameter data;

2) Obtain the historical traffic flow parameter data of each lane detector in the same period;

3) The dynamic Kalman filter traffic flow parameter prediction model is constructed by using the Kalman filter technology, and the description of the dynamic Kalman filter traffic flow parameter prediction model is as shown in formula (1):

\overset{&LeftRightArrow; &LeftRightArrow;}{Q Q} L L ((τ τ + + k k)) = = {H h}_{00} V V ((τ τ)) + + {H h}_{11} V V ((τ τ - - 11)) + + \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {+ + H h}_{n no - - 11} V V ((τ τ - - n no + + 11)) + + ω ω ((τ τ)) - - - - - - ((11))

In the formula: is the traffic flow parameter vector on the road section L of k time periods after time τ, which is related to the traffic flow parameters at the entrances and exits at both ends of the road section; V(τ)=[v ₁ (τ),v ₂ (τ),…, v _m (τ)] ^T is the traffic flow parameter vector of each entrance and exit in the time period ((τ-1)T,τT], where v _m (τ) is a certain entrance in the time period ((τ-1)T,τT] Or the traffic flow parameters of the exit, it contains some useful predictors for the prediction of traffic flow parameters, which can be directly observed by the detector, V(τ-1) is a period before the period ((τ-1)T,τT] ((τ-2)T,(τ-1)T] The traffic flow parameter vectors of each entrance and exit; H ₀ , H ₁ ,...,H _n-1 are parameter matrices, H _k =[c ₁ ′(τ), c′ ₂ (τ),…,c′ _m (τ)], c′ _m (τ) is the state variable; m is the total number of detectors considered at the entrance and exit of the road section; ω(τ) is the observation noise, assuming is expected to be zero white noise, its covariance matrix is R(τ);

4) On the basis of step 3), through the Kalman filter time update equation and the state update equation, the Kalman filter parameter prediction result is obtained as shown in (2):

\overset{^^}{Q Q} L L ((τ τ + + k k)) = = A A ((τ τ)) \overset{^^}{X x} ((τ τ | | τ τ - - 11)) - - - - - - ((22))

In the formula: is the predicted traffic flow parameter vector on the road segment L of k time segments after time τ;

is the state estimation vector; A(τ)=[V ^T (τ), V ^T (τ-1), V ^T (τ-2)] is the observation vector of traffic flow parameters;

The Kalman filter time update equation is:

\overset{^^}{X x} ((τ τ | | τ τ - - 11)) = = B B ((τ τ)) \overset{^^}{X x} ((τ τ - - 11)) - - - - - - ((44))

P(τ|τ-1)＝Q(τ-1)+B(τ-1)P(τ-1)B ^T (τ-1) (5)

The state update equation is:

K(τ)＝P(τ|τ-1)A ^T (τ)[A(τ)P(τ|τ-1)A ^T (τ)+R(τ)] ^-1 (6)

\overset{^^}{X x} ((τ τ)) = = \overset{^^}{X x} ((τ τ | | τ τ - - 11)) + + K K ((τ τ)) [[z z ((τ τ)) - - A A ((τ τ)) \overset{^^}{X x} ((τ τ | | τ τ - - 11)) - - - - - - ((77))

P(τ)＝[I-K(τ)A(τ)]P(τ|τ-1) (8)

In the formula: is the state vector, is the state estimation vector; B(τ) is the state transition matrix, B(τ)=I; P(τ) is the error covariance, P(τ|τ-1) is the estimated covariance; K(τ) is the Kalman gain; z(τ) is the actual obtained traffic flow parameter, and its value is equal to R(τ) is expected to be zero white noise, Q(τ-1) is the covariance matrix of model noise;

5) Introduce the historical average traffic flow parameters into formula (2), and construct the fuzzy Kalman filter traffic flow parameter prediction model as shown in formula (3):

\overset{&OverBar; &OverBar;}{Q Q} L L ((τ τ + + k k)) = = ((11 - - γ γ)) \overset{^^}{Q Q} L L ((τ τ + + k k)) + + γ γ \overset{&OverBar; &OverBar;}{QL QL} ((τ τ + + k k)) - - - - - - ((33))

in, For the predicted final result, is the historical average parameter of the same period; is the prediction result of Kalman filter; γ is the historical value weight coefficient;

6) Input the real-time traffic flow parameters collected by the detector and the historical average traffic flow parameters in the same period into formula (3), and predict the traffic flow parameters in the next time interval and after.

2. The method of claim 1, wherein:

The detectors include, but are not limited to, loop induction coil detectors, video detectors, microwave detectors, radar detectors, wireless sensor nodes;

The traffic flow parameters refer to traffic flow and/or occupancy and/or speed and/or density and/or saturation;

Said next time interval refers to 5 minutes or 15 minutes or 30 minutes or 60 minutes.

3. The method of claim 1, wherein:

The historical value weight coefficient γ is determined by fuzzy logic;

The fuzzy rule: using relative error, average relative error, and average absolute relative error as indicators for fuzzy comprehensive judgment, the larger the parameter γ, the closer the current traffic flow trend is to the historical average; otherwise, the current traffic flow trend is closer Close to the predicted value of the Kalman filter module.