CN108399741A - A kind of intersection flow estimation method based on real-time vehicle track data - Google Patents

Abstract

The present invention relates to a kind of intersection flow estimation methods based on real-time vehicle track data, include the following steps：1) research period [0, T] is divided into multiple continuous basic time intervals, and classified to basic time interval；2) according to sorted basic time interval, under the conditions of given arrival time, vehicle time of departure likelihood function is calculated according to the corresponding vehicle time of departure conditional probability of different basic time interval types, and calculate final likelihood function；3) vehicle arriving rate obtained in each basic time interval is solved to the likelihood function of vehicle time of departure.Compared with prior art, the present invention has many advantages, such as to adapt to low sample frequency, the data environment of sampling rate and historical data, strong robustness, real-time are high, accuracy is good without merging.

Description

A Method for Estimating Intersection Flow Based on Real-time Vehicle Trajectory Data

technical field

The invention relates to the field of traffic control, in particular to an intersection flow estimation method based on real-time vehicle trajectory data.

Background technique

As the main part of the urban road network, signalized intersections often cause traffic congestion due to the periodic alternation of traffic lights, which greatly restricts the overall operating efficiency of the urban road traffic system. As an important indicator for evaluating intersection operation, cycle flow can be used to indirectly estimate queue length, vehicle delay, parking times, and travel time on the one hand, and can be directly fed back for signal timing optimization on the other hand.

At present, the research on flow estimation at home and abroad is mainly based on fixed-point detectors. The prediction methods include mathematical statistics methods such as filtering algorithms and model analysis methods such as basic graphs and cellular transmission models. The traffic estimation method based on fixed-point detectors mainly has the problems of high equipment layout and maintenance costs and low upload frequency, and the obtained detection indicators such as speed and traffic are based on the average value of the detection step, which cannot reflect the volatility and randomness of traffic flow. sex. Mathematical statistics methods are generally implemented by historical detection data, and most of the model parameters require empirical data calibration; methods based on basic graphs also need to fit the relationship between traffic flow parameters based on historical data, which is less general; and cellular transport models and other model analysis There are specific assumptions in the methods of traffic flow parameters, which abstract the relationship between traffic flow parameters, such as simulated arrival distribution, homogeneity assumptions, etc. Although the random characteristics of traffic flow are considered, the assumptions about the quantitative relationship of traffic flow parameters The scope of application is limited. The research on the use of trajectory for traffic estimation appeared late. Although the trajectory data has the advantages of high precision and strong real-time performance, in practical applications, due to the low capture rate, there are problems of data sparseness and large prediction errors, and the existing methods of using trajectory data The estimation accuracy of the flow estimation method will decrease under the condition of adaptive control. Therefore, establishing a general and applicable periodic flow estimation method has important practical significance for the further application and promotion of trajectory data.

Contents of the invention

The purpose of the present invention is to provide a method for estimating intersection flow based on real-time vehicle trajectory data in order to overcome the above-mentioned defects in the prior art.

The purpose of the present invention can be achieved through the following technical solutions:

A method for estimating traffic flow at an intersection based on real-time vehicle trajectory data, comprising the following steps:

1) Divide the research period [0, T] into multiple continuous basic time intervals, and classify the basic time intervals;

2) According to the classified basic time interval, under the given arrival time condition, calculate the vehicle departure time likelihood function according to the vehicle departure time conditional probability corresponding to different basic time interval types, and calculate the final likelihood function;

3) Solve the likelihood function of the vehicle departure time to obtain the vehicle arrival rate in each basic time interval.

In described step 1), the type of basic time interval includes:

Type I: [r(a _i ), a _i ), from the time when the red light is turned on to the estimated arrival time of the first sampled vehicle in the current period, the vehicles arriving within this basic time interval can arrive at the corresponding effective green light time τ _k =[g(a _i ), bi ₎ , where r(a _i ) is the time when the red light turns on, a _i is the expected arrival time of vehicle i, and bi is the expected departure time of vehicle _i Time, g(a _i ) is the moment when the green light turns on in the current cycle;

Type II: [a _i-1 , a _i ), the expected arrival time interval of two consecutive sampled vehicles in the current cycle, and the corresponding effective green light time τ _k is [b _i-1 , b _i );

Type III: [a _i-1 ,g(a _i-1 )+G), the estimated arrival time of the last vehicle in the current cycle to the end of the green light in the current cycle, where G is the duration of the green light in the current cycle, and its corresponding The effective green light time τ _k is [b _i-1 , g(a _i-1 )+G).

The calculation formula of the estimated arrival time a _i of the vehicle i is:

For queuing vehicles:

Among them, (t _i , d _i ) is the non-queuing track point information of vehicle i at time t, v _f is the free-flow velocity, l is the position of the stop line, and the expected departure time of vehicle i b _i is the time when the vehicle i leaves and stops after the green light is on. line time;

For non-queuing vehicles:

The estimated arrival time is the same as the estimated departure time, which is the moment when vehicle i leaves the stop line after the green light is turned on, namely:

a _i = _bi .

Described step 2) specifically comprises the following steps:

21) Set the arrival of vehicles at the intersection to satisfy the non-homogeneous Poisson distribution;

22) Obtain the joint probability density function L _a of the expected arrival time of all sampled vehicles in the research period, and use it as a given arrival time condition;

23) Under the given arrival time condition, calculate the vehicle departure time conditional probability corresponding to different basic time interval types;

24) Calculate the vehicle departure time likelihood function L _b according to the vehicle departure time conditional probability corresponding to different basic time interval types;

25) Calculate the final likelihood function L.

In the described step 22), the calculation formula of the joint probability density function L _a is:

Among them, n is the number of sampled vehicles in the research period, p is the sampling rate of vehicles in the research period, pλ(a _i ) is the average arrival rate of sampled vehicle i, and λ(a _i ) is the instantaneous arrival rate of vehicles at time a _i , Λ is the arrival intensity, λ(t) is the vehicle arrival rate in the t time interval, λ _k is the vehicle arrival rate in the kth basic time interval, T _k is the duration of the kth basic time interval, K is The total number of base intervals.

In the described step 24), the calculation formula of the vehicle departure time likelihood function L _b is:

The likelihood function of the vehicle departure time is:

Among them, K ₁ represents the set when the basic time interval of type I and type II satisfies a _i < b _i , and K ₂ is the basic time interval of type I and type II when a _i = b _i and the basic time interval of type III The collection of time intervals, h _s is the vehicle’s time away from the saturated headway, M _k is the maximum number of vehicles arriving in the kth basic time interval, is the number of non-sampled vehicles arriving in the basic time interval, and j is the number of vehicles arriving in the basic time interval.

The formula for calculating the final likelihood function L is:

Compared with the prior art, the present invention has the following advantages:

1) It is more practical to release assumptions such as the uniform arrival of known vehicles and historical vehicle patterns in the prior art;

2) Strong real-time performance, capable of realizing flow detection based on periodic rolling, with high accuracy;

3) The method is advanced and robust, and can adapt to the data environment of low sampling frequency and low sampling rate in my country.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Figure 2 is the space-time trajectory diagram of the vehicle.

Fig. 3 is a schematic diagram of the definition of basic time intervals, where Fig. (3a) is Type 1, Fig. (3b) is Type 2, and Fig. (3c) is Type 3.

Fig. 4 is a schematic diagram of the geometric structure of the intersection of the embodiment.

Fig. 5 is a schematic diagram of the space-time trajectory of the vehicle in the embodiment.

Figure 6 is a comparison chart of estimation results, where Figure (6a) is the estimated flow chart during the morning peak period, Figure (6b) is the average absolute percentage error of the flow rate during the morning peak period, and Figure (6c) is the estimated flow chart during the flat peak period, Figure (6d) shows the average absolute percentage error of the flow rate in the normal time period.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Example

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is carried out on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

As shown in Figure 1, due to the periodic replacement of signals at signalized intersections, multiple traffic waves will be formed at the intersection. When the red light is on, the vehicles are forced to stop and join the queue one by one; when the green light is on, the vehicles start to leave the intersection at a saturated flow rate. Based on the time-space trajectory map of the vehicle at the intersection, the expected arrival time and departure time of the vehicle can be accurately known, and then the cycle flow can be estimated.

The present invention provides a method for estimating periodic flow at a signalized intersection based on vehicle trajectory data, comprising the following steps:

1) Calculation of estimated arrival time and departure time of vehicles based on real-time vehicle trajectory data, step 1) specifically includes the following steps:

11) As shown in Figure 2, for the non-queuing track point information (t _i , d _i ) of queuing vehicle i at time t, the free flow velocity v _f and the position of the stop line l, the calculation formula for the estimated arrival time of vehicle i is:

Among them, a _i is the expected arrival time of vehicle i, and the estimated departure time b _i of vehicle i is the moment when the vehicle i leaves the stop line after the green light turns on.

12) For the non-queuing vehicle i+1, its expected arrival time is equal to the expected departure time, which is the time when vehicle i+1 leaves the stop line after the green light turns on:

a _i+2 = b _i+2 ;

2) Basic time interval definition, step 2) specifically includes the following steps:

21) Divide the research period [0,T] into continuous basic time intervals in is the start time of the kth basic time interval, is the end time of the kth basic time interval. According to the expected arrival time of all sampled vehicles and the time when the traffic lights are turned on in each period during the study period, there are three types of basic time intervals, as shown in Figure 3.

Step 21) specifically comprises the following steps:

211) Type 1: [r(a _i ), a _i ), from the time when the red light turns on to the estimated arrival time of the first sampled vehicle in the current period. Where r(a _i ) is the moment when the red light turns on in the current cycle. Correspondingly, vehicles arriving within the basic time interval can leave the intersection within the corresponding effective green light time [g(a _i ), b _i ), where g(a _i ) is the moment when the green light is turned on in the current cycle such as Figure 3a shows.

212) Type 2: [a _i-1 , a _i ), the expected arrival time interval between two consecutive sampled vehicles in the current cycle. The corresponding effective green light time is [bi _-1 , _bi ) as shown in Figure 3b.

213) Type 3: [a _i-1 ,g(a _i-1 )+G), the estimated arrival time of the last vehicle in the current cycle to the end of the green light in the current cycle. Among them, G is the green light duration of the current cycle i-1. The corresponding effective green light time is [b _i-1 , g(a _i-1 )+G) as shown in Fig. 3c.

22) Assuming that the arrival of vehicles at the intersection satisfies the non-homogeneous Poisson distribution, the average arrival rate of vehicles in each basic time interval can be expressed as:

Among them, λ _k is the average vehicle arrival rate of the k-th basic time interval, T _k is the duration of the k-th basic time interval, equal to

3) Estimated vehicle arrival time likelihood function estimation, step 3) specifically includes the following steps:

Assuming that the vehicle sampling rate is p during the study period, the average arrival rate of the sampled vehicles is pλ(t). Based on the characteristics of the non-homogeneous Poisson distribution, the joint probability density function of the expected arrival time of all sampled vehicles within the study time is:

where n is the number of sampled vehicles in the study period,

4) Under the condition of the expected arrival time of the given vehicle, the likelihood function estimation of the departure time of the vehicle, step 4) specifically includes the following steps:

41) For the k-th basic time interval, the unsampled vehicles N _k follow a Poisson distribution with mean (1-p)λ _k T _k . At the same time, due to the limitation of the arrival time of saturated vehicles, the maximum number of vehicles arriving in the kth basic time interval is Then the probability function of the non-sampling vehicle N _k can be expressed as:

in,

According to the three different types of basic time intervals in step 2, there are three situations for the conditional probability of vehicle departure time given the vehicle's expected arrival time.

Step 41) specifically includes the following steps:

411) Case 1: For Type 1 and Type 2, if a _i < b _i , it means that the sampled vehicle i is a queuing vehicle, and within the corresponding basic time interval, all non-sampled vehicles are queuing vehicles. Therefore, the number of non-sampled vehicles arriving in this basic time interval is: Where τ _k is the effective green light time of the kth basic time interval. Then the corresponding vehicle departure time conditional probability is:

Among them, h _d is the headway distance from saturation.

412) Case 2: For type 1 and type 2, if a _i = b _i , it means that the sampled vehicle i is a non-queuing vehicle, then the maximum number of non-sampled vehicles arriving in the kth basic time interval is: Where τ _k is the effective green light time of the kth basic time interval. Then the corresponding vehicle departure time conditional probability is:

413) Case 3: For type 3, specify that i-1 is the last sampled vehicle in the current period, then the maximum number of non-sampled vehicles arriving in the k-th basic time interval is: Wherein, τ _k =g(a _i-1 )+Gb _i-1 . Then the corresponding vehicle departure time conditional probability is:

42) Based on the three situations in step 41), it can be obtained that the likelihood function of the departure time of the vehicle under the given expected arrival time of the sampled vehicle is:

Among them, K ₁ represents the set of basic time intervals satisfying case 1, and K ₂ is the set of basic time intervals satisfying cases 2 and 3. Finally, the following likelihood function can be obtained:

5) The calculation of vehicle arrival rate in each basic time interval includes the following steps:

Suppose λ(a _i )=λ _k when When equal to a _i , the following first-order partial derivative of λ _k can be obtained:

Embodiments of the present invention are as follows:

(1) Data preprocessing

In the present invention, the accuracy of the traffic estimation method is verified by using the trajectory data of straight vehicles at the north entrance of the intersection of Huanggang Road and Fuzhong, the main road in Shenzhen, as shown in FIG. 4 . The verification period is the morning peak period from 7:00 to 8:15 on April 13, 2017 and the off-peak period from 9:30 to 12:00, including six different timing schemes. The corresponding trajectory capture rate and timing information are shown in the table 1. After preprocessing the vehicle trajectory data, the space-time trajectory diagram of the vehicle is obtained, as shown in Figure 5, and then the estimated arrival time and departure time of the vehicle are extracted to estimate the periodic flow rate, and the estimated result is verified by the mean absolute error percentage (MAPE).

Table 1 Signal timing information and vehicle sampling rate

(2) Analysis of results

Fig. 6 is a schematic diagram of the estimation results of the method of the present invention and the method of Zheng et al. in the morning peak period from 7:00 to 8:15 o'clock and the peak period from 9:30 to 12 o'clock.

As shown in Figure 6a, for the morning peak hours, both methods can capture the periodic flow fluctuations well, and achieve better flow estimation. Under the cycle aggregation time interval, the MAPE of the present invention is 15.23%, while that of Zheng et al. is 16.17%. And along with the increase of time aggregation interval, the MAPE of two kinds of methods all declines, from 10-min, 30-min and hour aggregation time interval, PAPE of the present invention is respectively 12.94%, 8.87% to8.85%, While the MAPE of Zheng et al.'s method is 13.52%, 11.60% to 5.06%.

In the flat peak period, it can be seen from Fig. 6c that the method of the present invention is still able to detect the change of the step cycle flow rate very well, while the estimated result of the Zheng et al. method is always greater than the observed flow rate. Under the cycle, 10-min, 30-min and hour aggregate time intervals, the MAPE of the present invention are 15.64%, 8.94%, 5.85% and 6.29%, respectively, while the MAPE of Zheng et al.’s method are 20.12%, 19.63%, 19.11% % and 18.94%.

The above results show that the periodic flow estimation method proposed by the present invention is better than the estimation method proposed by Zheng et al. Moreover, the present invention does not need to rely on any historical data, has good robustness, and has wider application scenarios.

Claims (7)

1. A method for estimating flow at an intersection based on real-time vehicle trajectory data, is characterized in that, comprises the following steps: 1) Divide the research period [0, T] into multiple continuous basic time intervals, and classify the basic time intervals; 2) According to the classified basic time interval, under the given arrival time condition, calculate the vehicle departure time likelihood function according to the vehicle departure time conditional probability corresponding to different basic time interval types, and calculate the final likelihood function; 3) Solve the likelihood function of the vehicle departure time to obtain the vehicle arrival rate in each basic time interval. 2. a kind of intersection flow estimation method based on real-time vehicle track data according to claim 1, is characterized in that, in described step 1), the type of basic time interval comprises: Type I: [r(a _i ), a _i ), from the time when the red light is turned on to the estimated arrival time of the first sampled vehicle in the current period, the vehicles arriving within this basic time interval can arrive at the corresponding effective green light time τ _k =[g(a _i ), bi ₎ , where r(a _i ) is the time when the red light turns on, a _i is the expected arrival time of vehicle i, and bi is the expected departure time of vehicle _i Time, g(a _i ) is the moment when the green light turns on in the current cycle; Type II: [a _i-1 , a _i ), the expected arrival time interval of two consecutive sampled vehicles in the current cycle, and the corresponding effective green light time τ _k is [b _i-1 , b _i ); Type III: [a _i-1 ,g(a _i-1 )+G), the estimated arrival time of the last vehicle in the current cycle to the end of the green light in the current cycle, where G is the duration of the green light in the current cycle, and its corresponding The effective green light time τ _k is [b _i-1 , g(a _i-1 )+G). 3. a kind of intersection flow estimation method based on real-time vehicle trajectory data according to claim 2, is characterized in that, the computing formula of the expected arrival time a of described vehicle _i is: For queuing vehicles: Among them, (t _i , d _i ) is the non-queuing track point information of vehicle i at time t, v _f is the free-flow velocity, l is the position of the stop line, and the expected departure time of vehicle i b _i is the time when the vehicle i leaves and stops after the green light is on. line time; For non-queuing vehicles: The estimated arrival time is the same as the estimated departure time, which is the moment when vehicle i leaves the stop line after the green light is turned on, namely: a _i = _bi . 4. a kind of intersection flow estimation method based on real-time vehicle trajectory data according to claim 2, is characterized in that, described step 2) specifically comprises the following steps: 21) Set the arrival of vehicles at the intersection to satisfy the non-homogeneous Poisson distribution; 22) Obtain the joint probability density function L _a of the expected arrival time of all sampled vehicles in the research period, and use it as a given arrival time condition; 23) Under the given arrival time condition, calculate the vehicle departure time conditional probability corresponding to different basic time interval types; 24) Calculate the vehicle departure time likelihood function L _b according to the vehicle departure time conditional probability corresponding to different basic time interval types; 25) Calculate the final likelihood function L. 5. a kind of intersection flow estimation method based on real-time vehicle trajectory data according to claim 4, is characterized in that, in described step 22), the computing formula of joint probability density function _L is: Among them, n is the number of sampled vehicles in the research period, p is the sampling rate of vehicles in the research period, pλ(a _i ) is the average arrival rate of sampled vehicle i, and λ(a _i ) is the instantaneous arrival rate of vehicles at time a _i , Λ is the arrival intensity, λ(t) is the vehicle arrival rate in the t time interval, λ _k is the vehicle arrival rate in the kth basic time interval, T _k is the duration of the kth basic time interval, K is The total number of base intervals. 6. a kind of intersection flow estimation method based on real-time vehicle trajectory data according to claim 5, is characterized in that, in described step 24), the computing formula of vehicle departure time likelihood function L _b is: The likelihood function of the vehicle departure time is: Among them, K ₁ represents the set when the basic time interval of type I and type II satisfies a _i < b _i , and K ₂ is the basic time interval of type I and type II when a _i = b _i and the basic time interval of type III The collection of time intervals, h _s is the vehicle’s time away from the saturated headway, M _k is the maximum number of vehicles arriving in the kth basic time interval, is the number of non-sampled vehicles arriving in the basic time interval, and j is the number of vehicles arriving in the basic time interval. 7. a kind of intersection flow estimation method based on real-time vehicle trajectory data according to claim 6, is characterized in that, the computing formula of described final likelihood function L is: