CN105575113A - Sensing method of traffic running states - Google Patents

Abstract

The invention discloses a sensing method of traffic running states and belongs to the field of intelligent traffic systems. For a specific road, traffic state distribution is different in different periods in a day, and traffic state distribution characteristics of morning peaks and midnights are obviously different. Thus, different periods should be differentiated during researching of the traffic state distribution, thereby modeling the traffic state distribution. In order to estimate parameters in a model, a traffic state model expression in practical application should be solved, so the proportion of each kind of traffic states can be obtained and corresponding states of data can be judged, thereby achieving an objective of traffic state sensing. According to the invention, by combining a normal theme model, modeling of the traffic running state distribution in any period of the road is achieved; by use of the obtained model, traffic states of the road can be judged in real time; and a disadvantage of difficulties in carrying out sensing in different roads at different time in a traditional traffic state sensing algorithm is overcome.

Description

A kind of traffic circulation state aware method

Technical field

The invention belongs to intelligent transportation system scope, particularly a kind of traffic circulation state aware method.

Background technology

The domestic and international method about traffic circulation state aware emerges in an endless stream at present, and traffic circulation state aware is also popular studying a question in intelligent transportation system.Existing traffic circulation state aware algorithm can roughly be divided into four classes:

(1) direct comparison algorithm, wherein McMaster algorithm and exponential smoothing algorithm most representative.

(2) spatio-temporal prediction algorithm, as Celltransmissionmodel and GaussianMixtureHiddenMarkovModel based on state-space model.

(3) algorithm for pattern recognition, algorithm for pattern recognition to have employed in pattern-recognition the method that conventional algorithm classifies to traffic circulation state as Bayes's linear discriminant, support vector machine etc.

(4) intelligent algorithm, intelligent algorithm is generally carry out unsupervised learning based on traffic data thus the algorithm of classifying to traffic circulation state.

The method of existing traffic behavior perception, major part is all by carrying out cluster to existing traffic data, then classifies to new data according to the class models obtained, judges traffic circulation state.These class methods are just merely classified from the angle of data to traffic behavior, do not consider the relation of section and traffic behavior, also do not consider the real physical characteristics of traffic flow.In addition, these class methods can only merely be classified to traffic behavior, cannot realize the functions such as further traffic flow forecasting according to training pattern, and the scope of application is wideless.

Summary of the invention

The object of the invention is to propose a kind of traffic circulation state aware method, it is characterized in that, comprising:

1) traffic state model modeling

For concrete section, the Different periods that its traffic behavior is distributed in one day is different, the traffic behavior distribution characteristics at morning peak and midnight obviously makes a big difference, therefore need the different periods separately to treat when the distribution of research traffic behavior, thus modeling is carried out to traffic behavior distribution; The step of traffic behavior distribution being carried out to modeling is as follows:

(1) for certain section, if divided different time sections according to 2 hours, so this section just can be divided into 12 research objects, and wherein there is the traffic behavior distributed data of its uniqueness each time period, and the research unit that this is the most basic is defined as time section; Meanwhile, definition data point is certain concrete traffic data that traffic detector detects, defines in model the various parameters needing to use, as shown in table 1,

The various parameters used are needed in table 1 model

(2) simulate the generation of the traffic data of forward, suppose that each time section has K kind traffic behavior and can select, for a data point w, should first determine its traffic behavior; Then according to the traffic behavior determination traffic data of this data point; So, to be the probability of t be just the traffic data of this data point w:

Wherein, ∑ kp (w=t|z=k) is a multinomial distribution, and be distribution when selecting data point z=k from traffic behavior, p (z=k) is the traffic behavior of this data point is the probability of k;

Suppose distribution p (the z|d=m)=θ m of the traffic behavior z on time section m, first determine concrete traffic behavior distribution θ m according to hyper parameter α, then from distribution θ m, sampling just can obtain the traffic behavior zm of each data point, n; Suppose for traffic behavior zm, n, its traffic data t is distributed as p (t|z=k)=φ k; Similarly, need first to determine the traffic data distribution phi that each traffic behavior is corresponding then to obtain the traffic data of this data point from φ k stochastic sampling according to hyper parameter β; From distribution θ m, sampling obtains the traffic behavior of all data points, is formed the set of the traffic data in a section with this with in this model, the traffic behavior distribution of data point is multinomial distribution; Equally, the distribution in traffic data point of traffic data is also multinomial distribution;

(3) according to above-described model, obtain the probability that whole data set generates, be expressed as all hyper parameter provided and the joint distribution needing estimated parameter to form:

formula (1)

In formula, and p (Φ | β) be the traffic data distribution that each traffic behavior is corresponding, this distribution is unique for a time section; P (wm, n| φ zm, n) p (zm, n| θ m) p (θ m| α) obtains traffic behavior corresponding to each data point to from time section, and then sampling obtains the process of the traffic data of each data point; All data point probability of occurrence sums are exactly the probability that whole data set occurs; And for some specific data points, the probability of its traffic data wm, n=t is:

formula (2)

Formula (1) above, formula (2) are the traffic behavior sensor model of foundation, describe the probability that various types of traffic data occurs;

2) traffic state model expression formula solves

Want the parameter in estimation model, just need to know the definite expression formula of above-mentioned joint distribution when practical application, when estimating traffic state model, if at the traffic behavior zm that each data point is corresponding, n is known, θ m and φ k can by the traffic data wm of each data point, n and traffic behavior zm, the mode of n statistics is calculated, and therefore only needs the traffic behavior zm estimating each traffic data point when actual estimated, n; Estimate that the Gibbs sampling method of zm, n is called gibbs sampler of collapsing, only needing to estimate zm, n, time, then formula (1) is write as simply:

P (w, z| α, β)=p (w|z, β) p (z| α) formula (3)

In formula, Section 1 and α have nothing to do, and Section 2 and β have nothing to do, and therefore can be considered respectively for these two;

First to derive Section 1, consider Probability p (w|z, Φ) represent be the distribution Φ of traffic data under known often kind of traffic behavior time the process of all traffic data points that obtains, it is a multinomial distribution, now, Φ is the Study first of this distribution, and distribution p (Φ | β) is the prior distribution of multinomial distribution, so then has:

P (w|z, β)=∫ p (w|z, Φ) p (Φ | β) d Φ formula (4)

Here, the prior distribution choosing Phi is Di Li Cray (Dirichlet) distribution, due to the conjugate gradient descent method that Dirichlet distribute is multinomial distribution, therefore when calculating, the form of the Posterior distrbutionp that we obtain also is Dirichlet distribute, and this just greatly simplifies final mathematical computations; Due to

formula (5)

Substitute into formula (4) above, finally obtain:

formula (6)

Wherein Δ (β) represents that parameter is the Dirichlet distribute of β, n _k ^(t)represent the number of times that traffic data t occurs under traffic behavior k; n _z ^(t)represent the number of times that traffic data t occurs under traffic behavior Z; Similarly, Section 2 p (z| α) can be written as

P (z| α)=∫ p (z| Θ) p (Θ | α) d Θ formula (7)

And p (z| Θ) wherein can be write as all θ m equally, the form that k is multiplied, wherein, n _m ^(k)on expression time section m, the number of times that traffic behavior k occurs; Equally,

formula (8)

Substitution formula (7), can obtain the result similar with formula (6):

formula (9)

Convolution (7) and formula (9), the joint distribution that we can obtain describing traffic circulation state is:

formula (10)

The expression of the probability distribution having had traffic data to occur, Gibbs sampling algorithm is used to estimate the parameter in model, just can estimate parameter θ m and φ m according to existing traffic data, thus set up the model that describes traffic behavior;

3) model parameter estimation

Gibbs sampler (Gibbssampling) is a kind of conventional Markov monte carlo method (MCMCmethod), in Gibbs sampling, only sample to dimension xi when other dimensions are constant, constant dimension is defined as at every turn the process of whole Gibbs sampling is as follows:

(1) dimension i is selected

(2) pass through to xi sampling, wherein, following formula can be used to calculate:

When using the parameter in the above-mentioned traffic state model of Gibbs sampled-data estimation, formula of sampling first should be determined make i=(m, n) be the subscript of a traffic data, in Gibbs sampling, have with according to the character that result obtained above and Dirichlet distribute, sampling formula can be obtained as follows:

After Gibbs sampling convergence, just can obtain the sampled result of the traffic behavior z of all traffic datas point; Due to parameter θ m and φ k corresponding be multinomial distribution, and the conjugate gradient descent method that its prior distribution is chosen is Dirichlet distribution, and therefore, the Posterior distrbutionp of parameter θ m and φ k is also Dirichlet distribution:

formula (11),

Wherein nm is the sight gauge numerical value of traffic behavior on time section m, and nk is the sight gauge numerical value of traffic data in traffic behavior k;

Posterior distrbutionp due to parameter θ m and φ k is also Dirichlet distribution, and according to the character of Dirichlet distribution, can obtain its estimated value is

formula (12),

Wherein, n _k ^(t)represent the number of times that traffic data t occurs under traffic behavior k; n _m ^(k)on expression time section m, the number of times that traffic behavior k occurs;

After the sampling of Gibbs algorithm terminates, the traffic behavior that we can obtain each data point distributes z, and parameter Θ and Φ, parameter Θ and Φ describes the distribution of traffic data point in the distribution of traffic behavior on each time section and each traffic behavior, is the key parameter describing traffic circulation state; The probability that each traffic behavior on a time section occurs and the probability that data point occurs under corresponding traffic behavior just can be known by Θ and Φ; After completing the modeling of Gibbs sampling to traffic circulation state, whenever traffic detector collects new traffic data, only need to think that the distribution Φ of traffic data point is constant in traffic behavior, the Θ using Gibbs sampling to reappraise data of newly arriving can estimate Θ, just can obtain the ratio that often kind of traffic behavior accounts for wherein, just can judge the traffic behavior that these data are corresponding, thus realize the object of traffic behavior perception.

The invention has the beneficial effects as follows that topic model conventional in unified with nature Language Processing of the present invention achieves the modeling of the traffic circulation distributions to section random time section, and utilize the traffic behavior in the model real-time judge section obtained; Make up and be difficult to neatly for different time in conventional traffic state aware algorithm, different sections of highway carries out the shortcoming of perception.

Accompanying drawing explanation

Fig. 1 is each traffic behavior change schematic diagram in moon in water booth East Road one day.

Fig. 2 is the speed of a motor vehicle of 4 and the statistics of vehicle flowrate in morning of Fig. 1.

Fig. 3 is the average speed of 9 and the statistics of vehicle flowrate in morning of Fig. 1.

Embodiment

The present invention proposes a kind of traffic circulation state aware method, is explained the present invention below in conjunction with the drawings and specific embodiments.

First illustrate, for concrete section, it is different that its traffic behavior is distributed in intraday Different periods, and the traffic behavior distribution characteristics at morning peak and midnight obviously makes a big difference, and therefore needs the different periods separately to treat when the distribution of research traffic behavior, for certain section, if divided different time sections according to 2 hours, so this section just can be divided into 12 research objects, and wherein there is the traffic behavior distributed data of its uniqueness each time period, and the research unit that this is the most basic is defined as time section, simultaneously, definition data point is certain concrete traffic data that traffic detector detects, this traffic data is the numerical value of the traffic data that traffic detector collects, it should be noted that, same traffic data may occur repeatedly on a time section, a traffic data as defined every 5km/h, so the speed of a motor vehicle is greater than all data that 45km/h is less than 50km/h and all calculates same traffic data, but these data are different data points, this is just as the word in document, in a document, same word may occur repeatedly, occur being exactly a data point each time, this word is then a traffic data, thus modeling is carried out to traffic behavior distribution, by calculating the probability that whole data set generates, be expressed as all hyper parameter provided and the joint distribution needing estimated parameter to form:

formula (1)

In formula, and p (Φ | β) be the traffic data distribution that each traffic behavior is corresponding, this distribution is unique for a time section; P (wm, n| φ zm, n) p (zm, n| θ m) p (θ m| α) obtains traffic behavior corresponding to each data point to from time section, and then sampling obtains the process of the traffic data of each data point; All data point probability of occurrence sums are exactly the probability that whole data set occurs; And for some specific data points, the probability of its traffic data wm, n=t is:

formula (2)

Formula (1) above, formula (2) are the traffic behavior sensor model of foundation, describe the probability that various types of traffic data occurs;

Next solves traffic state model expression formula,

Want the parameter in estimation model, just need to know the definite expression formula of above-mentioned joint distribution when practical application, when estimating traffic state model, if at the traffic behavior zm that each data point is corresponding, n is known, θ m and φ k can by the traffic data wm of each data point, n and traffic behavior zm, the mode of n statistics is calculated, and therefore only needs the traffic behavior zm estimating each traffic data point when actual estimated, n;

Sampled by Gibbs algorithm, the traffic behavior that can obtain each data point distributes z, and parameter Θ and Φ, parameter Θ and Φ describe the distribution of traffic data point in the distribution of traffic behavior on each time section and each traffic behavior, it is the key parameter describing traffic circulation state; The probability that each traffic behavior on a time section occurs and the probability that data point occurs under corresponding traffic behavior just can be known by Θ and Φ; After completing the modeling of Gibbs sampling to traffic circulation state, whenever traffic detector collects new traffic data, only need to think that the distribution Φ of traffic data point is constant in traffic behavior, the Θ using Gibbs sampling to reappraise data of newly arriving can estimate Θ, just can obtain the ratio that often kind of traffic behavior accounts for wherein, just can judge the traffic behavior that these data are corresponding, thus realize the object of traffic behavior perception;

Under concrete sampling process is shown in:

Embodiment

The data on Haining City moon in water booth East Road, Zhejiang Province are used to verify model.Moon in water booth East Road is positioned at northeast, center, Haining City city, is the strategic road connecting Haining City center and Haining City northeast.

We have intercepted from 0:00 to 23:59 on Dec 10th, 2014 on Dec 1st, 2014 data analysis of totally 10 days, these data are collected by the microwave traffic detector on moon in water booth East Road, once, the data of collection comprise total vehicle flowrate in eight tracks, moon in water booth East Road in a minute, average speed and occupation rate in collection per minute.

First time division section.In order to more accurately describe the traffic on moon in water booth East Road, we were the division interval in time section with 15 minutes.

Therefore, moon in water booth East Road at one day traffic in one direction we use 96 time sections to describe, within one day, there are 15 data in each time section, within 10 days, on each time section, have 150 data.Add up the traffic data in each time section, the traffic data in section is at the same time put together, as training set.Wherein, the line number of the first behavior training data is also the number in time section.Because moon in water booth East Road has both direction, therefore time section has 2*96=192.Every a line below the first row is the traffic data occurred in a time section, and its form is: 100* flow+speed of a motor vehicle.As 240 represent altogether through two cars in 1 minute, the average speed of two cars is 40km/h; 1332 represent altogether through 13 cars in 1 minute, and the average speed of these 13 cars is 32km/h.Because moon in water booth East Road is positioned at busiest section, center, city, speed limit 60km/h, can use this numeral to represent flow and the speed of a motor vehicle simultaneously.Certainly, flow and the speed of a motor vehicle also can have other method for expressing, because the concrete numerical value in training data in LDA can't affect training result (in topic model, training data is word), therefore the form of training data is very flexible, brings easy greatly to training.

Setting traffic behavior number is 3, represent unimpeded, normal, block up three kinds of traffic behaviors.The traffic circulation state model training that we obtain before using this training set, the major parameter obtained after training and implication thereof are in table 2.Wherein, Θ is the matrix of a 192*3, and every a line represents the traffic behavior distribution in a time section, and the numerals of three row are probability that three kinds of traffic behaviors occur in section at this moment separately.Φ is the matrix of 3 row, and its columns is equal to the number of traffic data, and wherein each element represents the probability that corresponding traffic data occurs in often kind of traffic behavior.Φ is also used to the key matrix carrying out traffic behavior perception.Θ, Φ implication is as shown in table 2.

Table 2 Θ, Φ implication

By Θ, moon in water booth East Road is described to the traffic on moon in water booth East Road, in moon in water booth East Road one day, Fig. 1 is shown in each traffic behavior change

Can see in the morning before six thirty, represent normal blue line and represent that the ratio of traffic behavior shared by the red line that blocks up is all very little, far below representing unimpeded green line; And at 7:00 to the 8:00 of morning peak and evening peak and 17:00 to 18:00, represent that the red line blocked up all has a peak, this and actual traffic conditions are identical, illustrate that this model can describe the situation of change of traffic behavior in moon in water booth East Road one day well.

There is the model of description traffic circulation state obtained above, for the new traffic data that traffic detector detects, can use and train the parameter obtained to carry out resampling to its traffic behavior, thus estimate its traffic behavior.Use the traffic data of first 5 days to model training, then use the traffic data of latter five days to test.For early 4 and the early result of 9, be the speed of a motor vehicle of 4 and the statistics of vehicle flowrate in morning as shown in Figure 2, Fig. 3 is the average speed of 9 and the statistics of vehicle flowrate in morning.Can see, when morning 4, the traffic behavior of most data point is all judged as unimpeded, and when morning 9, be judged as when average speed is less, vehicle flowrate is larger and block up, and being judged as normal when average speed is comparatively large, vehicle flowrate is also large, rare occasion is judged as unimpeded.This also conforms to the direct feel of these two time periods with us.From experimental result, can the running status of perception Current traffic effectively by model, there is extraordinary effect.Certainly, the step of above judgement can complete full automation on computers, and therefore this algorithm can be used to, in the traffic circulation state aware module of intelligent transportation system, to have very strong Practical significance.

Claims (1)

1. a traffic circulation state aware method, is characterized in that, comprising:

1) traffic state model modeling

For concrete section, the Different periods that its traffic behavior is distributed in one day is different, the traffic behavior distribution characteristics at morning peak and midnight obviously makes a big difference, therefore need the different periods separately to treat when the distribution of research traffic behavior, thus modeling is carried out to traffic behavior distribution; The step of traffic behavior distribution being carried out to modeling is as follows:

(1) for certain section, if divided different time sections according to 2 hours, so this section just can be divided into 12 research objects, and wherein there is the traffic behavior distributed data of its uniqueness each time period, and the research unit that this is the most basic is defined as time section; Meanwhile, definition data point is certain concrete traffic data that traffic detector detects, defines in model the various parameters needing to use, as shown in table 1,

The various parameters used are needed in table 1 model

(2) simulate the generation of the traffic data of forward, suppose that each time section has K kind traffic behavior and can select, for a data point w, should first determine its traffic behavior; Then according to the traffic behavior determination traffic data of this data point; So, to be the probability of t be just the traffic data of this data point w:

$p(w=t)=\underset{k}{\Σ}p(w=t|z=k)p(z=k),\underset{k}{\Σ}p(z=k)=1,$

Wherein, ∑ kp (w=t|z=k) is a multinomial distribution, and be distribution when selecting data point z=k from traffic behavior, p (z=k) is the traffic behavior of this data point is the probability of k;

Suppose distribution p (the z|d=m)=θ m of the traffic behavior z on time section m, first determine concrete traffic behavior distribution θ m according to hyper parameter α, then from distribution θ m, sampling just can obtain the traffic behavior zm of each data point, n; Suppose for traffic behavior zm, n, its traffic data t is distributed as p (t|z=k)=φ k; Similarly, need first to determine the traffic data distribution phi that each traffic behavior is corresponding then to obtain the traffic data of this data point from φ k stochastic sampling according to hyper parameter β; From distribution θ m, sampling obtains the traffic behavior of all data points, is formed the set of the traffic data in a section with this with in this model, the traffic behavior distribution of data point is multinomial distribution; Equally, the distribution in traffic data point of traffic data is also multinomial distribution;

(3) according to above-described model, obtain the probability that whole data set generates, be expressed as all hyper parameter provided and the joint distribution needing estimated parameter to form:

formula (1)

In formula, and p (Φ | β) be the traffic data distribution that each traffic behavior is corresponding, this distribution is unique for a time section; P (wm, n| φ zm, n) p (zm, n| θ m) p (θ m| α) obtains traffic behavior corresponding to each data point to from time section, and then sampling obtains the process of the traffic data of each data point; All data point probability of occurrence sums are exactly the probability that whole data set occurs; And for some specific data points, the probability of its traffic data wm, n=t is:

formula (2)

Formula (1) above, formula (2) are the traffic behavior sensor model of foundation, describe the probability that various types of traffic data occurs;

2) traffic state model expression formula solves

Want the parameter in estimation model, just need to know the definite expression formula of above-mentioned joint distribution when practical application, when estimating traffic state model, if at the traffic behavior zm that each data point is corresponding, n is known, θ m and φ k can by the traffic data wm of each data point, n and traffic behavior zm, the mode of n statistics is calculated, and therefore only needs the traffic behavior zm estimating each traffic data point when actual estimated, n; Estimate that the Gibbs sampling method of zm, n is called gibbs sampler of collapsing, only needing to estimate zm, n, time, then formula (1) is write as simply:

P (w, z| α, β)=p (w|z, β) p (z| α) formula (3)

In formula, Section 1 and α have nothing to do, and Section 2 and β have nothing to do, and therefore can be considered respectively for these two;

First to derive Section 1, consider Probability p (w|z, Φ) represent be the distribution Φ of traffic data under known often kind of traffic behavior time the process of all traffic data points that obtains, it is a multinomial distribution, now, Φ is the Study first of this distribution, and distribution p (Φ | β) is the prior distribution of multinomial distribution, so then has:

P (w|z, β)=∫ p (w|z, Φ) p (Φ | β) d Φ formula (4)

Here, the prior distribution choosing Phi is Di Li Cray (Dirichlet) distribution, due to the conjugate gradient descent method that Dirichlet distribute is multinomial distribution, therefore when calculating, the form of the Posterior distrbutionp that we obtain also is Dirichlet distribute, and this just greatly simplifies final mathematical computations; Due to

formula (5)

Substitute into formula (4) above, finally obtain:

formula (6)

Wherein Δ (β) represents that parameter is the Dirichlet distribute of β, n _k ^(t)represent the number of times that traffic data t occurs under traffic behavior k; n _z ^(t)represent the number of times that traffic data t occurs under traffic behavior Z; Similarly, Section 2 p (z| α) can be written as

P (z| α)=∫ p (z| Θ) p (Θ | α) d Θ formula (7)

And p (z| Θ) wherein can be write as all θ m equally, the form that k is multiplied, wherein, n _m ^(k)on expression time section m, the number of times that traffic behavior k occurs; Equally,

$p\left(z\right|\mathrm{\Θ})=\underset{m=1}{\overset{M}{\mathrm{\Π}}}\underset{k=1}{\overset{K}{\mathrm{\Π}}}p(z_i=k|d_i=m)=\underset{m=1}{\overset{M}{\mathrm{\Π}}}\underset{k=1}{\overset{K}{\mathrm{\Π}}}{\mathrm{\θ}}_{m,k}^{n_m^{\left(k\right)}}$ Formula (8)

Substitution formula (7), can obtain the result similar with formula (6):

$\begin{array}{c}p\left(z\right|\mathrm{\α})=\∫p\left(z\right|\mathrm{\Θ})p\left(\mathrm{\Θ}\right|\mathrm{\α})d\mathrm{\Θ}\\ =\∫\underset{m=1}{\overset{M}{\mathrm{\Π}}}\frac{1}{\mathrm{\α}}\underset{k=1}{\overset{K}{\mathrm{\Π}}}{\mathrm{\θ}}_{m,k}^{n_m^{\left(k\right)}+{\mathrm{\α}}_k-1}{\mathrm{d\θ}}_m\\ =\underset{m=1}{\overset{M}{\mathrm{\Π}}}\frac{\mathrm{\Δ}(n_m+\mathrm{\α})}{\mathrm{\Δ}\left(\mathrm{\α}\right)},n_m={\left\{n_m^{\left(k\right)}\right\}}_{k=1}^K\end{array}$ Formula (9)

Convolution (7) and formula (9), the joint distribution that we can obtain describing traffic circulation state is:

$p(w,z|\mathrm{\α},\mathrm{\β})=\underset{z=1}{\overset{K}{\mathrm{\Π}}}\frac{\mathrm{\Δ}(n_z+\mathrm{\β})}{\mathrm{\Δ}\left(\mathrm{\β}\right)}\·\underset{m=1}{\overset{M}{\mathrm{\Π}}}\frac{\mathrm{\Δ}(n_m+\mathrm{\α})}{\mathrm{\Δ}\left(\mathrm{\α}\right)}$ Formula (10)

The expression of the probability distribution having had traffic data to occur, Gibbs sampling algorithm is used to estimate the parameter in model, just can estimate parameter θ m and φ m according to existing traffic data, thus set up the model that describes traffic behavior;

3) model parameter estimation

Gibbs sampler (Gibbssampling) is a kind of conventional Markov monte carlo method (MCMCmethod), in Gibbs sampling, only sample to dimension xi when other dimensions are constant, constant dimension is defined as at every turn the process of whole Gibbs sampling is as follows:

(1) dimension i is selected

(2) pass through to xi sampling, wherein, following formula can be used to calculate:

When using the parameter in the above-mentioned traffic state model of Gibbs sampled-data estimation, formula of sampling first should be determined

make i=(m, n) be the subscript of a traffic data, in Gibbs sampling, have with according to the character that result obtained above and Dirichlet distribute, sampling formula can be obtained as follows:

After Gibbs sampling convergence, just can obtain the sampled result of the traffic behavior z of all traffic datas point; Due to parameter θ m and φ k corresponding be multinomial distribution, and the conjugate gradient descent method that its prior distribution is chosen is Dirichlet distribution, and therefore, the Posterior distrbutionp of parameter θ m and φ k is also Dirichlet distribution:

$p\left({\mathrm{\θ}}_m\right|z_m,\mathrm{\α})=\frac{1}{Z_{{\mathrm{\θ}}_m}}\underset{n=1}{\overset{N}{\mathrm{\Π}}}p\left(z_{m,n}\right|{\mathrm{\θ}}_m)\·p\left({\mathrm{\θ}}_m\right|\mathrm{\α})=\mathrm{\Δ}\left({\mathrm{\θ}}_m\right|n_m+\mathrm{\α})$

formula (11),

Wherein nm is the sight gauge numerical value of traffic behavior on time section m, and nk is the sight gauge numerical value of traffic data in traffic behavior k;

Posterior distrbutionp due to parameter θ m and φ k is also Dirichlet distribution, and according to the character of Dirichlet distribution, can obtain its estimated value is

${\mathrm{\θ}}_{m,k}=\frac{n_m^{\left(k\right)}+{\mathrm{\α}}_k}{{\mathrm{\Σ}}_{k=1}^K{n}_m^{\left(k\right)}+{\mathrm{\α}}_k}$ Formula (12),

Wherein, n _k ^(t)represent the number of times that traffic data t occurs under traffic behavior k; n _m ^(k)on expression time section m, the number of times that traffic behavior k occurs;

After the sampling of Gibbs algorithm terminates, the traffic behavior that we can obtain each data point distributes z, and parameter Θ and Φ, parameter Θ and Φ describes the distribution of traffic data point in the distribution of traffic behavior on each time section and each traffic behavior, is the key parameter describing traffic circulation state; The probability that each traffic behavior on a time section occurs and the probability that data point occurs under corresponding traffic behavior just can be known by Θ and Φ; After completing the modeling of Gibbs sampling to traffic circulation state, whenever traffic detector collects new traffic data, only need to think that the distribution Φ of traffic data point is constant in traffic behavior, the Θ using Gibbs sampling to reappraise data of newly arriving can estimate Θ, just can obtain the ratio that often kind of traffic behavior accounts for wherein, just can judge the traffic behavior that these data are corresponding, thus realize the object of traffic behavior perception.