CN108399741A - A kind of intersection flow estimation method based on real-time vehicle track data - Google Patents
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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
Technical Field
The invention relates to the field of traffic control, in particular to an intersection flow estimation method based on real-time vehicle track data.
Background
Signal intersections are used as main components of urban road networks, and due to the periodic alternation of traffic lights, traffic jam often occurs, so that the overall operation efficiency of an urban road traffic system is greatly restricted. The periodic flow is used as an important index for evaluating the operation of the intersection, and can be used for indirectly estimating indexes such as queuing length, vehicle delay, parking times, travel time and the like on 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 realized based on a fixed point detector, and the prediction method comprises a mathematical statistic method such as a filtering algorithm and a model analysis method such as a basic graph and a cellular transmission model. The flow estimation method based on the fixed point detector mainly has the problems of high equipment layout and maintenance cost and low uploading frequency, and the obtained detection indexes such as speed, flow and the like are average values based on detection step length and cannot reflect the volatility and randomness of traffic flow. The mathematical statistical method is generally realized by historical detection data, and most model parameters need empirical data calibration; the method based on the basic diagram is also required to fit the relation of traffic flow parameters based on historical data, and the generality is poor; however, the methods for analyzing models such as cellular transmission models have specific assumptions, and abstract the relationship between traffic flow parameters, such as simulated arrival distribution, homogenization assumptions, and the like. The research of utilizing the track to carry out flow estimation is late, although the track data has the advantages of high precision and strong real-time performance, the problems of data sparseness and large prediction error exist in practical application due to low capture rate, and the estimation precision of the existing flow estimation method utilizing the track data is reduced under the condition of self-adaptive control. Therefore, establishing a periodic flow estimation method with strong generality and applicability has important practical significance for further application and popularization of the trajectory data.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an intersection flow estimation method based on real-time vehicle trajectory data.
The purpose of the invention can be realized by the following technical scheme:
an intersection flow estimation method based on real-time vehicle track data comprises the following steps:
1) dividing the study period [0, T ] into a plurality of continuous basic time intervals, and classifying the basic time intervals;
2) according to the classified basic time intervals, under the condition of given arrival time, calculating a vehicle driving-off time likelihood function according to vehicle driving-off time conditional probabilities corresponding to different basic time interval types, and calculating a final likelihood function;
3) and solving the likelihood function of the vehicle driving-away time to obtain the vehicle arrival rate in each basic time interval.
In step 1), the types of the basic time interval include:
type I: [ r (a)i),ai) The estimated arrival time of the first sampled vehicle in the current period from the red light starting time, and the vehicles arriving in the basic time interval can be in corresponding effective green light time tauk＝[g(ai),bi) Drive-in from the intersection, where r (a)i) For the red light on, aiPredicted arrival time of vehicle i, biIs the predicted departure time of vehicle i, g (a)i) Turning on the green light in the current period;
type II: [ a ] Ai-1,ai) Two consecutive sampled vehicles in the current cycle are expected to arrive at a time interval corresponding to the effective green time taukIs [ b ]i-1,bi)；
Type III: [ a ] Ai-1,g(ai-1) + G) of the last vehicle predicted arrival time of the current cycle to the green light end time of the current cycle, where G is the green light duration of the current cycle with its corresponding effective green light time τkIs [ b ]i-1,g(ai-1)+G)。
Predicted arrival time a of the vehicle iiThe calculation formula of (2) is as follows:
for a queued vehicle:
wherein (t)i,di) Is the non-queuing track point information v of the vehicle i at the time tfPredicted departure time b for free flow velocity, l for parking line position, vehicle iiWhen the vehicle leaves the stop line after the green light is turned on;
for non-queued vehicles:
the estimated arrival time is the same as the estimated driving-away time, and is the time when the vehicle i leaves the stop line after the green light is turned on, namely:
ai＝bi。
the step 2) specifically comprises the following steps:
21) setting vehicles at the intersection to reach the non-homogeneous Poisson distribution;
22) obtaining a joint probability density function L of the predicted arrival times of all sampled vehicles within a study periodaAnd using the condition as a given arrival time condition;
23) under the condition of given arrival time, calculating the vehicle driving-away time conditional probability corresponding to different basic time interval types;
24) calculating a vehicle driving-off time likelihood function L according to vehicle driving-off time conditional probabilities corresponding to different basic time interval typesb；
25) The final likelihood function L is calculated.
In the step 22), the probability density function L is combinedaThe calculation formula of (A) is as follows:
where n is the number of sampled vehicles in the study period, p is the vehicle sampling rate in the study period, p λ (a)i) To sample the average arrival rate of vehicle i, λ (a)i) Is aiThe instantaneous arrival rate of the vehicle at a time, lambda being the arrival intensity, lambda (t) being the arrival rate of the vehicle in the time interval t, lambdakIs the vehicle arrival rate, T, in the k basic time intervalkIs the duration of the kth elementary time interval, K being the total number of elementary time intervals.
Said step 24), the vehicle leaving time likelihood function LbThe calculation formula of (A) is as follows:
the vehicle drive-off time likelihood function is:
wherein, K1The basic time interval representing type I and type II satisfies ai＜biSet of cases, and K2Satisfies a for the basic time intervals of type I and type IIi＝biSet of time and basic time interval case of type III, hsFor vehicles travelling away from a saturated headway, MkThe 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 vehicle arriving in the basic time interval.
The final likelihood function L is calculated as:
compared with the prior art, the invention has the following advantages:
1) the assumptions of uniform arrival of the known vehicles, historical vehicle modes and the like in the prior art are released, so that the method is more practical;
2) the real-time performance is strong, the flow detection based on the periodic rolling can be realized, and the accuracy is high;
3) the method is advanced, has strong robustness, and can adapt to the data environment with low sampling frequency and low sampling rate in China.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a vehicle spatiotemporal trajectory diagram.
Fig. 3 is a diagram illustrating basic time interval definition, wherein fig. 3a is type 1, fig. 3b is type 2, and fig. 3c is type 3.
FIG. 4 is a schematic diagram of an embodiment intersection geometry.
FIG. 5 is a schematic view of an embodiment vehicle spatiotemporal trajectory.
Fig. 6 is a comparison graph of the estimation results, in which (6a) is an early peak time period estimated flow rate graph, (6b) is an early peak time period average absolute percentage error, (6c) is a flat peak time period estimated flow rate graph, and (6d) is a flat time period average absolute percentage error.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, the intersection can develop multiple traffic waves due to the periodic replacement of signalized intersection signals. When the red light is turned on, vehicles are forced to stop, and the vehicles are sequentially added into the queue; at the instant the green light is on, the vehicle starts to drive off the intersection at a saturated flow rate. Based on the space-time trajectory diagram of the vehicle at the intersection, the estimated arrival time and the driving-away time of the vehicle can be accurately obtained, and further the estimation of the periodic flow is realized.
The invention provides a signalized intersection periodic flow estimation method based on vehicle track data, which comprises the following steps:
1) calculating the predicted arrival time and the driving-away time of the vehicle based on the real-time vehicle track data, wherein the step 1) specifically comprises the following steps:
11) as shown in FIG. 2, non-queued trace point information at time t for a queued vehicle i (t)i,di) Velocity v of free flowfAnd a stop line position l, the calculation formula of the predicted arrival time of the vehicle i is as follows:
wherein, aiPredicted arrival time for vehicle i, and predicted departure time b for vehicle iiWhen the vehicle leaves the stop line after the green light is turned on.
12) For a non-queued vehicle i +1, the predicted arrival time is equal to the predicted departure time, and the time when the vehicle i +1 leaves the stop line after the green light is turned on is as follows:
ai+2＝bi+2；
2) defining a basic time interval, wherein the step 2) specifically comprises the following steps:
21) will study time period [0, T]Divided into successive elementary time intervalsWherein Is the start time of the kth elementary time interval,is the end time of the kth elementary time interval. These three types of basic time intervals are shown in fig. 3, based on the estimated arrival times of all sampled vehicles within the study time and the turn-on time of the traffic lights in each period.
Step 21) specifically comprises the following steps:
211) type 1: [ r (a)i),ai) And the predicted arrival time of the first sampling vehicle in the current period from the red light starting time. Wherein r (a)i) And starting the red light of the current period. Accordingly, vehicles arriving within the base time interval may be at the corresponding valid green time [ g (a)i),bi) Drive-in from the intersection, where g (a)i) The green light on time for the current cycle is shown in fig. 3 a.
212) Type 2: [ a ] Ai-1,ai) And continuously sampling the predicted arrival time interval of the vehicles in two times in the current period. With a corresponding effective green time of [ bi-1,bi) As shown in fig. 3 b.
213) Type 3: [ a ] Ai-1,g(ai-1) + G), the expected arrival time of the last vehicle of the current cycle to the end of the green light of the current cycle. Where G is the green duration of the current cycle i-1. With a corresponding effective green time of [ bi-1,g(ai-1) + G) is shown in FIG. 3 c.
22) Assuming that the vehicle arrival at the intersection satisfies the non-homogeneous poisson distribution, the average arrival rate of the vehicles in each basic time interval can be expressed as:
wherein λ iskAverage vehicle arrival rate, T, for the k-th fundamental time intervalkIs the duration of the kth basic time interval, equal to
3) The estimation of the likelihood function of the estimated arrival time of the vehicle, step 3) specifically comprises the following steps:
assuming a vehicle sampling rate p over the study period, the average arrival rate of the sampled vehicles is p λ (t). Based on the characteristics of the non-homogeneous poisson distribution, the joint probability density function of the predicted arrival time of all sampled vehicles in the research time is as follows:
wherein n is the number of sampled vehicles within the study period,
4) under the condition of the estimated arrival time of the given vehicle, estimating the driving-away time likelihood function of the vehicle, wherein the step 4) specifically comprises the following steps:
41) for the kth basic time interval, non-sampled vehicle NkObeying a mean value of (1-p) lambdakTkPoisson distribution of (a). Meanwhile, due to the limitation of the arrival time distance of the saturated vehicles, the maximum number of the vehicles arriving in the kth basic time interval isThen the non-sampled vehicle NkThe probability function of (a) can be expressed as:
wherein,
according to the three different types of basic time intervals in the step 2, the vehicle driving-away time conditional probability has three conditions under the condition of the estimated arrival time of the given vehicle.
Step 41) specifically comprises the following steps:
411) case 1: for type 1 and type 2, if ai＜biExplanation sampling vehicleIf vehicle i is a queued vehicle, then all non-sampled vehicles are queued vehicles within the corresponding base time interval. Thus, the number of non-sampled vehicles arriving in this basic time interval is:wherein tau iskThe effective green time for the kth basic time interval. Then the corresponding vehicle drive-off time conditional probability is:
wherein h isdTo drive away from the saturated headway.
412) Case 2: for type 1 and type 2, if ai＝biIf the sampled vehicle i is a non-queued vehicle, the maximum number of non-sampled vehicles arriving in the kth basic time interval is:wherein tau iskThe effective green time for the kth basic time interval. Then the corresponding vehicle drive-off time conditional probability is:
413) case 3: for type 3, say i-1 is the last sampled vehicle in the current cycle, then the maximum number of non-sampled vehicles arriving in the kth fundamental time interval is:wherein, tauk＝g(ai-1)+G-bi-1. Then the corresponding vehicle drive-off time conditional probability is:
42) based on 41) three cases, the vehicle departure time likelihood function given the sampled estimated vehicle arrival time can be found as:
wherein, K1Represents that the basic time interval satisfies the set of case 1, and K2The set of cases 2 and 3 is satisfied for the base time interval. The following likelihood functions are finally obtained:
5) the vehicle arrival rate calculation in each basic time interval specifically comprises the following steps:
let λ (a)i)＝λkWhen in useIs equal to aiThen, the following can be obtained with respect to λkFirst order partial derivatives of (1):
the examples of the invention are as follows:
(1) data pre-processing
The method adopts the trajectory data of the straight-ahead vehicles at the north entrances of the Huang post road and the Fuzhong intersection of the main road in Shenzhen city to carry out precision verification on the flow estimation method, as shown in FIG. 4. The verification period is from 7 o ' clock to 8:15 o ' clock at 13 o ' clock in 2017 and from 9:30 o ' clock to 12 o ' clock, and comprises six different timing schemes, and the corresponding track capture rate and timing information are shown in table 1. And (3) preprocessing vehicle track data to obtain a vehicle space-time track diagram, as shown in fig. 5, further extracting the estimated arrival time and the driving-away time of the vehicle to carry out periodic flow estimation, and verifying an estimation result by adopting a mean absolute error percentage (MAPE).
TABLE 1 Signal timing information and vehicle sampling Rate
(2) Analysis of results
FIG. 6 is a diagram illustrating the estimation results of the early peak period from 7 to 8:15 and the flat peak period from 9:30 to 12 according to the method of the present invention and the method of Zheng et al.
As shown in fig. 6a, both methods can capture the fluctuation of the periodic traffic well for the early peak period, and better achieve the traffic estimation. At periodic set time intervals, the MAPE of the present invention was 15.23%, whereas that of ZHEN et al was 16.17%. And as the time set interval increased, the MAPE decreased for both methods, from 10-min,30-min and the hour set interval, the PAPE of the present invention was 12.94%, 8.87% to 8.85%, respectively, while the MAPE of the method of ZHEN et al was 13.52%, 11.60% to 5.06%.
In the peak-flattening period, as can be seen from fig. 6c, the method of the present invention can still well step the periodic flow change, and the estimation result of the Zheng et al method is always larger than the observed flow. At cycles, 10-min,30-min and hourly time intervals, the MAPEs of the invention were 15.64%, 8.94%, 5.85% and 6.29%, respectively, while the methods of Zheng et al had MAPEs of 20.12%, 19.63%, 19.11% and 18.94%.
The results show that the periodic flow estimation method provided by the invention is superior to the estimation method provided by Zheng et al. In addition, the method does not need to depend on any historical data, has good robustness and has wider application scenes.
Claims (7)
1. An intersection flow estimation method based on real-time vehicle track data is characterized by comprising the following steps:
1) dividing the study period [0, T ] into a plurality of continuous basic time intervals, and classifying the basic time intervals;
2) according to the classified basic time intervals, under the condition of given arrival time, calculating a vehicle driving-off time likelihood function according to vehicle driving-off time conditional probabilities corresponding to different basic time interval types, and calculating a final likelihood function;
3) and solving the likelihood function of the vehicle driving-away time to obtain the vehicle arrival rate in each basic time interval.
2. The intersection traffic estimation method based on the real-time vehicle trajectory data according to claim 1, characterized in that in the step 1), the types of the basic time intervals comprise:
type I: [ r (a)i),ai) The estimated arrival time of the first sampled vehicle in the current period from the red light starting time, and the vehicles arriving in the basic time interval can be in corresponding effective green light time tauk＝[g(ai),bi) Drive-in from the intersection, where r (a)i) For the red light on, aiPredicted arrival time of vehicle i, biIs the predicted departure time of vehicle i, g (a)i) Turning on the green light in the current period;
type II: [ a ] Ai-1,ai) Two consecutive sampled vehicles in the current cycle are expected to arrive at a time interval corresponding to the effective green time taukIs [ b ]i-1,bi)；
Type III: [ a ] Ai-1,g(ai-1) + G) of the last vehicle predicted arrival time of the current cycle to the green light end time of the current cycle, where G is the green light duration of the current cycle with its corresponding effective green light time τkIs [ b ]i-1,g(ai-1)+G)。
3. The intersection traffic estimation method based on real-time vehicle trajectory data according to claim 2, characterized in that the predicted arrival time a of the vehicle iiThe calculation formula of (2) is as follows:
for a queued vehicle:
wherein (t)i,di) Is the non-queuing track point information v of the vehicle i at the time tfPredicted departure time b for free flow velocity, l for parking line position, vehicle iiWhen the vehicle leaves the stop line after the green light is turned on;
for non-queued vehicles:
the estimated arrival time is the same as the estimated driving-away time, and is the time when the vehicle i leaves the stop line after the green light is turned on, namely:
ai＝bi。
4. the intersection traffic estimation method based on the real-time vehicle trajectory data according to claim 2, wherein the step 2) specifically comprises the following steps:
21) setting vehicles at the intersection to reach the non-homogeneous Poisson distribution;
22) obtaining a joint probability density function L of the predicted arrival times of all sampled vehicles within a study periodaAnd using the condition as a given arrival time condition;
23) under the condition of given arrival time, calculating the vehicle driving-away time conditional probability corresponding to different basic time interval types;
24) calculating a vehicle driving-off time likelihood function L according to vehicle driving-off time conditional probabilities corresponding to different basic time interval typesb；
25) The final likelihood function L is calculated.
5. The intersection traffic estimation method based on real-time vehicle trajectory data according to claim 4, characterized in that in the step 22), a probability density function L is combinedaThe calculation formula of (A) is as follows:
wherein n is the number of sampled vehicles in the study period, and p is the number of vehicles in the study periodSampling rate, p λ (a)i) To sample the average arrival rate of vehicle i, λ (a)i) Is aiThe instantaneous arrival rate of the vehicle at a time, lambda being the arrival intensity, lambda (t) being the arrival rate of the vehicle in the time interval t, lambdakIs the vehicle arrival rate, T, in the k basic time intervalkIs the duration of the kth elementary time interval, K being the total number of elementary time intervals.
6. The intersection traffic estimation method based on real-time vehicle trajectory data according to claim 5, characterized in that in the step 24), the vehicle driving-off time likelihood function LbThe calculation formula of (A) is as follows:
the vehicle drive-off time likelihood function is:
wherein, K1The basic time interval representing type I and type II satisfies ai＜biSet of cases, and K2Satisfies a for the basic time intervals of type I and type IIi＝biSet of time and basic time interval case of type III, hsFor vehicles travelling away from a saturated headway, MkThe 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 vehicle arriving in the basic time interval.
7. The intersection flow estimation method based on the real-time vehicle trajectory data according to claim 6, characterized in that the final likelihood function L is calculated by the following formula:
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| CN112201037A (en) * | 2020-09-27 | 2021-01-08 | 同济大学 | Intersection arrival rate estimation method based on sampling trajectory data |
| CN113506453A (en) * | 2021-09-10 | 2021-10-15 | 华砺智行(武汉)科技有限公司 | Bus priority signal control method, device, equipment and readable storage medium |
| CN113506453B (en) * | 2021-09-10 | 2022-02-22 | 华砺智行(武汉)科技有限公司 | Bus priority signal control method, device, equipment and readable storage medium |
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| CN115100875A (en) * | 2022-06-06 | 2022-09-23 | 东南大学 | Green wave traveling speed uncertainty quantification method based on internet vehicle track data |
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