WO2020216386A1

WO2020216386A1 - Low penetration vehicle trajectory data-based intersection queue length estimation method and apparatus

Info

Publication number: WO2020216386A1
Application number: PCT/CN2020/097598
Authority: WO
Inventors: 孙剑; 殷炬元; 胡祥旺; 唐克双
Original assignee: 同济大学
Priority date: 2019-04-26
Filing date: 2020-06-23
Publication date: 2020-10-29
Also published as: CN110335459A

Abstract

A low penetration vehicle trajectory data-based intersection queue length estimation method and apparatus, said method comprising: step S1: converting original estimation data into a distance-time graph, and recording a vehicle state of each trajectory point in the distance-time graph, wherein vehicle states comprise a moving state and a queuing state; step S2: identifying queue key points on the basis of changes in the vehicle states, wherein queue key points comprise a queue joining point and a queue leaving point; step S3: periodically dividing the various queue key points; step S4: estimating a queue dissipation wave and a queue formation wave, and obtaining a maximum queue length. Compared to the prior art, the present invention has advantages such as a wide application range.

Description

Intersection queue length estimation method and device based on low-permeability vehicle trajectory data

Technical field

The invention relates to a traffic control technology, in particular to a method and a device for estimating the length of the intersection queue length based on low-permeability vehicle trajectory data.

Background technique

Urban traffic plays a vital role in the development of the entire society. However, the problem of traffic congestion has become increasingly prominent and has become a major obstacle to the further development of cities. As the throat of urban traffic, the operation of intersections has always attracted attention. At present, most of the vehicle operation information at intersections comes from manual surveys and traffic detection equipment of the signal control system, such as fixed-point detectors buried under the parking line of the intersection or under the ground upstream of the entrance road. These equipment can detect the flow of vehicles, Information such as speed and occupancy rate provides a basis for the monitoring of the operation status of the intersection and the optimization of signal timing. Due to the high construction cost and damage rate of fixed-point detectors and the difficulty of subsequent maintenance, in the context of the "Internet +" era, this method of obtaining traffic flow information is in urgent need of change.

With the widespread use of smart phones and various APPs, smart phone devices equipped with GPS can efficiently obtain the space-time location information of the phone. Apps related to travel services, such as taxi apps and navigation apps, have also become common tools for people to travel. Such APP software continuously records the spatio-temporal location information of the vehicle where the mobile phone is located in the background, forming vehicle trajectory data. How to effectively apply vehicle trajectory data to the transportation field has become the research focus of the transportation industry in the "Internet +" era. Among them, the use of vehicle trajectory data for traffic state estimation, such as the estimation of traffic state parameters such as queue length, delay and flow at intersections, is A hot spot in recent years. Most of the existing related researches are based on the assumption that they can obtain sufficiently high or even full-sample vehicle trajectory data. However, the reality is that the drivers who use this type of APP within a certain time and space often only account for a small part of the total, such as less than 10% The data that can be used is called low-permeability vehicle trajectory data. Since the penetration rate is closely related to the accuracy and even the feasibility of the traffic state estimation, the realization of the traffic state estimation in the low penetration rate vehicle trajectory data environment is a major challenge posed by actual needs.

Summary of the invention

The purpose of the present invention is to provide a method and device for estimating the queuing length at intersections based on low-permeability 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:

An intersection queue length estimation method based on low-permeability vehicle trajectory data, including:

Step S1: Convert the original estimated data into a distance-time graph, and record the vehicle state at each track point in the distance-time graph, where the vehicle state includes a traveling state and a queue state;

Step S2: Identify the key points in the queuing based on the change of the vehicle status, wherein the key points in the queuing include joining the queuing point and leaving the queuing point;

Step S3: Periodically divide each queuing key point;

Step S4: Estimate the queuing dissipation wave and the queuing formation wave, and obtain the maximum queuing length.

The identification of the vehicle status in the step S1 specifically includes: setting a speed threshold, and using the vehicle status corresponding to the track point whose speed is greater than the speed threshold as the traveling status, and vice versa as the queuing status.

The joining queuing point is a trajectory point where the vehicle state changes from a traveling state to a queuing state, and the leaving queuing point is a trajectory point where the vehicle state changes from the queuing state to the traveling state;

And according to the intersection to be passed through corresponding to the current trajectory, the queuing point is divided into the queuing point for the first time and the queuing point again.

The step S3 specifically includes:

Step S31: Estimate the start time of the green light corresponding to each departure queuing point by using the projection method, and determine the period to which each departure queuing point belongs;

Step S32: According to the pairing relationship between the leaving queuing point and the joining queuing point, each joining queuing point is divided into the period to which the corresponding leaving queuing point belongs.

The step S4 specifically includes:

Step S41: construct a queued dissipation wave;

Step S42: Establish a queue formation state space model, and construct a queue formation wave based on the queue formation state space model;

Step S43: Obtain the intersection point of the queuing dissipated wave and the queuing forming wave, and obtain the maximum queue length based on the obtained intersection point.

The queuing dissipated wave is a straight line fitted by leaving the queuing point, specifically:

x = β ₀ + β ₁ ·t

Among them: x is the distance coordinate from the queuing point, t is the time, β ₀ and β ₁ are the parameters of the queuing dissipation wave;

The queue formation state space model is specifically:

Among them: QX _k is the tail position of the queue at time _k , VF _k is the queue formation speed at time k, T is the length of time between k and k-1, and QX _k-1 is the tail position of the queue at k-1 , VF _k-1 is the queue formation speed at k-1, and a _k is the queue formation acceleration.

The queuing forming wave is a piecewise function, and each section has a different slope. The specific estimation methods include:

Step S421: Select the first added queuing point as input, and obtain each segment point by using a Kalman filter;

Step S422: Obtain a queue formation wave based on the obtained segment points.

The step S43 is specifically to obtain the intersection point of the queuing evanescent wave and the end of the queuing wave, and obtain the maximum queuing length based on the obtained intersection point.

An intersection queue length estimation device based on low-permeability vehicle trajectory data, including a memory, a processor, and a program stored in the memory and executed by the processor. The processor implements the following steps when the program is executed :

Step S3: Periodically divide each queuing key point;

Compared with the prior art, the present invention has the following beneficial effects:

1) Only vehicle trajectory data is required as the single input of the method. On the one hand, it replaces traditional fixed-point detection data, which greatly reduces the construction, operation and maintenance costs of signal control system detection equipment. On the other hand, it does not require signal timing, flow and arrival. The applicability of information necessary for similar methods such as models has been expanded.

2) Kalman filter combined with shock wave theory to estimate the queue. Compared with the traditional statistical regression method, it not only uses the observed trajectory data, but also increases the use of the system correlation between the current state and the historical state, and comprehensively considers the observation error and The system error makes a more reasonable estimate and improves the estimation accuracy.

3) In a low-penetration data environment, it is more common that there is only one trajectory in a certain period. The traditional statistical regression method cannot be used in this case, but the method of the present invention can be estimated in this case, which expands the application condition;

4) Kalman filter is estimated step by step in a recursive manner, and it can be used in both offline and online environments, thereby expanding its use in intersection online supervision and adaptive control.

Description of the drawings

Figure 1 A flowchart of the main steps of the method of the present invention;

Figure 2 Vehicle trajectory distance-time diagram of a through lane at an intersection;

Figure 3 Queue key points and period division;

Figure 4 Estimation of queuing dissipated wave, forming wave and maximum period queue;

Figure 5 Channelization diagram and implementation area of the case intersection;

Figure 6 Scattered points of Didi vehicle trajectories in the implementation area of the case;

Figure 7 Case trajectory distance-time diagram and queuing key point identification;

Figure 8: Case queuing key point cycle division.

Detailed ways

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

The purpose of the present invention is to propose a method for estimating the queuing length of each flow direction and period of the intersection by using low-permeability vehicle trajectory data within the range of the intersection. For vehicles equipped with mobile phone positioning APP, the positioning information includes: user ID, longitude, latitude, recording time and instantaneous speed and other information are recorded at a higher frequency to form vehicle trajectory data. The method of the present invention uses these data as a single input, combines the traffic flow theory with the filter theory, and designs a complete process from the processing of the original trajectory to the establishment of the shock wave model to the Kalman filter to estimate the queue length.

An intersection queue length estimation method based on low-permeability vehicle trajectory data, which is implemented by a computer system in the form of a computer program. The computer system is an estimation device, including a memory, a processor, and stored in the memory and executed by the processor. For the executed program, for each flow direction (or lane group) of the intersection, the specific steps of this method are as follows: As shown in Figure 1, the processor implements the following steps when executing the program:

Step S1: Convert the original estimated data into a distance-time graph, and record the vehicle state at each track point in the distance-time graph, where the vehicle state includes the traveling state and the queuing state, and the vehicle state identification is specifically: set one For the speed threshold, the state of the vehicle corresponding to the track point whose speed is greater than the speed threshold is regarded as the traveling state, and vice versa as the queuing state.

That is, step 1: Convert the original vehicle trajectory data into a distance-time (xt) graph. For each flow direction, a certain upstream position is selected as the zero point of the distance, and the stop line position is recorded as x _xtop . The zero position should be selected to ensure that the queue length does not usually exceed x _xtop . For example, the upstream exit is the starting point of the entrance Is zero. Using the original data to calculate the cumulative travel distance of the vehicle from the zero point at each time point, the original trajectory of each vehicle is transformed into a series of time and space points, namely

with

They are the time and distance of the i-th vehicle and the k-th trajectory point. The trajectory points of all vehicles are plotted on the same distance-time diagram, as shown in Figure 2.

Then step 2: Identify the movement state of the vehicle at each track point. The movement state of the i-th vehicle and the k-th track point is recorded as

It is defined as two types: traveling state and queuing state. The two states compare the instantaneous speed of the track point

With speed threshold

To determine the size, as in formula (1)

Step S2: Identify queuing key points based on the change of vehicle status, where the queuing key points include joining queuing points and leaving queuing points, joining queuing points are the track points where the vehicle state changes from the traveling state to the queuing state, and leaving the queuing point is the vehicle state The trajectory point that changes from the queuing state to the traveling state; and according to the intersection to be passed corresponding to the current trajectory, the queuing point is divided into the first queuing point and the queuing point again.

Specifically, Step 3: Identify key points in the queue. The queuing key points refer to two types of track points: joining queuing points and leaving queuing points. Joining the queuing point refers to the trajectory point when the vehicle changes from the traveling state to the queuing state, that is, the trajectory point at the moment when it joins the queue. Since a group of queuing queues may not be able to pass through the intersection in one signal cycle, that is, a car may experience more than one queuing when passing through an intersection, and further divide the queuing points into two types: joining the queue for the first time and joining again Queuing point. Therefore, if you use

To represent the type of the i-th vehicle and the k-th trajectory point, then

There are four possible scenarios: non-queuing critical point (NCP), leaving the queuing point (LP), joining the queuing point for the first time (PJP) and joining the queuing point again (SJP). For a certain track point, use the vehicle motion state at that point

And an auxiliary variable

To judge

Specifically, give

with

Initialize when k=1,

Then use equations (2) and (3) to judge the situation after k>1 one by one. When all the track points of a car are judged

The value of queuing key point identification is completed.

Step S3: Periodically divide each key point in the queue, including:

Specifically, in step 4, for a certain departure queue point (t, x), VD _{default is} projected to the stop line position at a certain rate. The time of this projection point is the estimated green light start time GS, which is determined by the formula (4 ) Calculation. Since most of the vehicles in each cycle leave the queue at a stable saturated flow rate, the leaving queuing points in each cycle are obviously linearly distributed, and the slope difference is not large (mostly in the range of 4-6m/s), this value is VD _default , Can be preset as a constant, such as VD _default = 5m/s.

For the departure queuing points in the same cycle, the corresponding estimated green light start time should be close enough, and whether it is close or not is described by a preset threshold ε, that is, if the absolute value of the difference is less than ε, it is close enough, as in equation (5). Using this feature, it can be judged whether adjacent leaving queuing points belong to the same cycle, that is, for the k and k-1 leaving queuing points (t ^(k) ,x ^(k) ) and (t ^(k-1) ,x ^{( k-1)} ), k≥2. If formula (5) is satisfied, it means that the two estimated green lights are close enough at the start time, then (t ^(k) ,x ^(k) ) and (t ^(k-1) ,x ^{( k-1)} ) belong to the same period, otherwise, belong to different periods.

|GS ^(k) -GS ^(k-1) |＜ε (5)

According to this characteristic, first arrange all departure queue points in chronological order to obtain {(t ^(k) ,x ^(k) )|k=1, 2,...,N}, and calculate the corresponding green light start time , Get {GS ^(k) |k=1,2,...,N}; for the first exit queue point (t ⁽¹⁾ ,x ⁽¹⁾ ), let it belong to the first cycle; then judge (t ⁽²⁾ ,x ⁽²⁾ ) and (t ⁽¹⁾ ,x ⁽¹⁾ ) belong to the same cycle, if not, then (t ⁽²⁾ ,x ⁽²⁾ ) belong to the next cycle; By analogy, all departure queue points can be divided into corresponding periods.

According to the characteristics of vehicles passing through the intersection, parking (queuing) and starting (traveling) must occur in sequence, that is, each joining queuing point (no matter joining the queuing point for the first time or again) must have a leaving queuing point to pair with it. Therefore, after the period division of leaving the queuing point is over, according to the pairing relationship, each joining queuing point can be easily divided into the period of the corresponding leaving queuing point, as shown in Figure 3.

Step S4: Estimate the queuing dissipation wave and queuing formation wave, and obtain the maximum queuing length, which specifically includes:

Step S41: That is, the fifth step is to construct the queuing dissipated wave. The queuing dissipated wave is a straight line fitted by leaving the queuing point, specifically:

x = β ₀ + β ₁ ·t

According to the shock wave theory, vehicles arrive at the intersection and stop at a red light to join the queue, forming a wave that propagates to the end of the queue, that is, the queue forms a wave; correspondingly, the vehicles leave the queue in order after the green light starts, forming a wave propagating at the end of the queue , That is, the queuing dissipated wave; within a period, the point where the two waves meet is the maximum queuing point of the period. Therefore, the queue forming wave and the evanescent wave in each cycle are constructed to estimate the maximum queue length of each cycle.

The queuing dissipated wave is expressed as a straight line fitted by leaving the queuing point. Therefore, the estimation of the queuing dissipated wave is the expression of the straight line calculated by the least square method. β ₀ and β ₁ are queuing evanescent wave parameters, which are also parameters to be estimated. The estimated value is expressed as

with

On the basis of completing the fourth step of this method, the departure queue points that are divided in a certain period are expressed as {(t ⁽¹⁾ ,x ⁽¹⁾ ),(t ⁽²⁾ ,x ⁽²⁾ ),... ,(t ^(N) ,x ^(N) )}, where N represents the number of points, it can be divided into three situations: ①N≥2, and all the time to leave the queue (t ⁽¹⁾ ,t ⁽²⁾ , ...,t ^(N) ) are not all equal, ②N≥2, and all the time to leave the queue are all equal (t ⁽¹⁾ = t ⁽²⁾ =...=t ^(N) ), ③N=1( According to step 4, there is no case where N=0). For situation ①, the least squares problem represented by equation (6) can be calculated, and the estimated

with

For situations ② and ③,

Replace with VD _default , and then calculate according to formula (7)

The estimated queuing dissipated wave is shown as the thick black dashed line in Figure 4.

Step S42: Establish a queue formation state space model, and construct a queue formation wave based on the queue formation state space model,

That is, the sixth step is to establish a state-space model for queue formation. The state-space model consists of the state equations and observation equations shown in equations (8) and (9), which is the basis for the use of Kalman filters.

X _k =Φ _k|k-1 X _k-1 +w _k (8)

Z _k = H _k X _k + v _k (9)

w _k and v _k satisfy formulas (10)～(13)

E[w _k ]=0 (10)

E[v _k ]=0 (11)

Among them, X _k is the state vector, Z _k is the observation vector, Φ _k|k-1 is the state transition matrix, H _k observation matrix, w _k system noise vector, v _k is the observation noise vector, Q _k and R _k are respectively The covariance matrix of w _k and v _k .

Due to the randomness of vehicles arriving at the intersection, the formation of the queue is regarded as a discrete random system. The state variable X k at time _k is described by two quantities: the position of the tail of the queue QX _k and the formation speed VF _{k of the} queue. The randomness is characterized by the queuing formation acceleration a _k . From the randomness formed by queuing, a _k is a Gaussian white noise with the characteristics shown in equations (14) and (15)

E[a _k ]=0 (14)

According to the dynamic characteristics of queue formation, the system state equation shown in equation (16) is established

which is

Among them, q is the covariance strength of a _k , and T is the sampling interval.

QX _k is the tail position of the queue at time _k , VF _k is the queue formation speed at time k, T is the length of time between k and k-1, QX _k-1 is the tail position of the queue at k-1, VF _k-1 is the queue formation speed at k-1, and a _k is the queue formation acceleration.

The queuing forming wave is a piecewise function, and each segment has a different slope. The specific estimation method includes: Step S421: Select the first added queuing point as input, and use Kalman filter to obtain each segment point; Step S422: Based on the obtained Each segment point gets lined up to form a wave.

Specifically, the seventh step is different from the queuing dissipated wave represented by a fitted straight line. Due to the randomness of vehicle arrival, the queuing forming wave in each cycle is segmented, and each segment may have a different slope (ie, queuing Forming wave speed), estimating the queue forming wave is to estimate each segment point on the queue forming wave, that is, to estimate the state vector X _k in the state space model. As mentioned above, the joining queuing point is further divided into the first joining queuing point and rejoining the queuing point. The reason is that when the queuing formation wave is constructed, only the first joining queuing point is selected as input, because only the first joining queuing point reflects the natural arrival of vehicles. characteristic.

Before using the queuing points for the first time for estimation, in order to reduce the estimation error, these points are grouped first. All the points that joined the queue for the first time are sorted by time and expressed as ((t ⁽¹⁾ ,x ⁽¹⁾ ),(t ⁽²⁾ ,x ⁽²⁾ ),...,(t ^(N) ,x ^(N) )} and after step 4, the period of each point is known. For two adjacent points, (t ^(k) ,x ^(k) ) and (t ^(k-1) ,x ^(k-1) ), assuming that (t ^(k-1) ,x ^(k-1) ) belongs to the group Ω ⁽ⁿ⁾ , there are the following rules: ①If (t ^(k) ,x ^(k) ) and (t ^{(k- 1)} ,x ^(k-1) ) belong to different periods, then (t ^(k) ,x ^(k) ) belong to the group Ω ⁽ⁿ⁺¹⁾ ; ②(t ^(k) ,x ^(k) ) and (t ^(k-1) ,x ^(k-1) ) belong to the same period. If formula (17) is satisfied, then (t ^(k) ,x ^(k) ) belong to the group Ω ⁽ⁿ⁺¹⁾ , otherwise, (t ^{( k)} ,x ^(k) ) belong to the group Ω ⁽ⁿ⁾ .

among them,

with

It is a preset threshold for grouping.

According to the above rules, let the first queuing point (t ⁽¹⁾ ,x ⁽¹⁾ ) belong to the first group Ω ⁽¹⁾ , and then judge (t ⁽²⁾ ,x ⁽²⁾ ) and (t ^{( 1)} Whether ,x ⁽¹⁾ ) belong to the same group, if not, (t ⁽²⁾ ,x ⁽²⁾ ) belong to Ω ⁽²⁾ ; and so on, all the first joining queue points can be divided into each group.

After the regrouping is completed, the centroids of all points in each group will be used as the input to construct the queue forming wave, that is, the observation input of Kalman filter. For Ω ^(k) , its centroid (τ ^k , ξ ^k ) is calculated according to equation (18), Kalman filter will be updated at τ ^k , and ξ ^{k will be taken} as the observation input of Kalman filter, that is, Z _k = ξ ^k . Since ξ ^k is the observed value of QX _k , it is obvious that the observation matrix H _k can be determined, that is, H _k =[1 0].

Given the initialization parameters of the Kalman filter, namely VF ₁ , P ₁ , R, q, the Kalman filter is updated according to the following rules:

For k=1, that is, at the first update point (τ ¹ , ξ ¹ ), the observation input Z ₁ =ξ ¹ , let QX ₁ =Z ₁ , then the state vector for k=1 is

For k＞1, the sampling interval T=τ ^k -τ ^k-1 , the observation input Z _k =ξ ^k , according to whether (τ ^k ,ξ ^k ) and (τ ^k-1 ,ξ ^k-1 ) belong to the same period There are two situations:

Case 1: (τ ^k ,ξ ^k ) and (τ ^k-1 ,ξ ^k-1 ) belong to the same period, and calculate the state vector at time k according to equations (19)～(23)

And the error matrix P _k . Case 1 is shown in the estimation at t _{k in} Figure 4, the observation input points corresponding to t _k and t _k-1 belong to the same period n.

P _k|k-1 =Φ _k|k-1 P _k-1 Φ _k|k-1 ^T +Q _k-1 (20)

K _k = P _k|k-1 H _k ^T (H _k P _k|k-1 H _k ^T + R _k ) ^-1 (21)

P _k =(IK _k H _k )P _k|k-1 (IK _k H _k ) ^T + K _k R _k K _k ^T (23)

Case 2: (τ ^k ,ξ ^k ) and (τ ^k-1 ,ξ ^k-1 ) belong to different periods, and the queued wave is cut off by the queued dissipation wave at the end of the period of (τ ^k-1 ,ξ ^k-1 ) , And re-generated at the beginning of the period of (τ ^k ,ξ ^k ), therefore, it is equivalent to re-initializing the state vector in the new period

And the error matrix P _k , namely

P _k =P _k-1 . Case 2 is shown in the estimation at t _k+1 in Fig. 4, the observation input points corresponding to t _k+1 and t _k belong to different periods, and they belong to period n+1 and period n respectively.

For the above two cases, (τ ^k ,QX _k ) is the estimated queuing forming wave segmentation point, as shown by the black circle in Figure 4.

Step S43: Obtain the intersection point of the queuing dissipated wave and the queue forming wave, and obtain the maximum queuing length based on the obtained intersection point, specifically obtaining the intersection of the queuing dissipated wave and the queue forming wave end segment, and obtain the maximum queuing length based on the obtained intersection point.

Specifically, in step 8, according to the shock wave theory, the maximum periodic queue appears at the intersection of the queue forming wave and the dissipated wave. Therefore, estimating the maximum periodic queue length is also estimating the intersection. Since the queuing forming wave is segmented, its intersection with the queuing dissipated wave must appear at the end of the queuing forming wave in each cycle, that is, in step 7 case 2 (τ ^k-1 ,ξ ^k-1 ) The line after the dot forms a wave. According to case 2 in step 7, the estimated state vector at (τ ^k-1 ,ξ ^k-1 ) is

Then (τ ^k-1 , ξ ^k-1 ) the line equation of the queue forming wave is equation (24); according to step 5, the line equation of the period of queue dissipation wave is equation (25).

x=VF _k-1 (t-τ ^k-1 )+QX _t-1 (24)

Combine the two formulas to obtain the intersection point (t ^* ,x ^* ) of the queuing dissipated wave and the queuing forming wave of the period, then the maximum queuing length of the period is

MQL=x _stop -x ^* (26)

The estimation of the maximum queuing period is shown in Figure 4.

Similarly, the remaining cycles are operated in accordance with step 8, and the maximum queue length of each cycle can be estimated.

The above is the detailed steps for estimating the maximum queuing length in each cycle using the vehicle trajectory data of a certain flow at an intersection. These steps are applicable to any flow direction at the intersection. Therefore, the maximum queuing length in each cycle for all flow directions at the intersection can be estimated. .

The following takes the straight flow direction of the north entrance road at the intersection of Huanggang Road and Fuzhong Road in Shenzhen (4 straight lanes in total) as the object, using the GPS trajectory data of the Didi Travel APP as input, and it is estimated that the flow will go to the morning peak period of a certain working day The queue length of each cycle.

The channelization diagram and implementation area of the case intersection are shown in Figure 5.

During the implementation period, Didi vehicles accounted for 7.4% of the total number of vehicles, and the trajectory sampling interval was about 3 seconds. The scattered points of Didi vehicle trajectories in the implementation area are shown in Figure 6.

According to the first step of the present invention, the zero point is selected at 280m upstream from the parking line, that is, the position of the parking line is x _xtop = 280m, and the cumulative travel distance of each trajectory point is calculated based on the original trajectory data of the Didi vehicle and plotted as time-distance Figure, that is, the trajectory of each vehicle is represented by the gray dashed line in Figure 7.

According to the second and third steps of the present invention, the vehicle motion state of each track point is first determined, and then the key points of the queue are identified, as shown in Fig. 7.

Figure 7 shows the situation of a certain period of time during the implementation period. The joining queue points and leaving queue points on each track are paired one by one, a total of 19 pairs of key points will be added to the queue points (in this example, all are the first joining queue points , So collectively referred to as joining queuing points) are numbered in chronological order, and the space-time coordinates of all key points are shown in Table 1:

Table 1 Time and space coordinates of key points in the queue

According to the fourth step of the present invention, first use the projection method to project all leaving queue points to the parking line position by pressing VD _default (5m/s according to experience), and calculate the corresponding green light start time GS according to formula (4). Small (according to equation (5), ε may be 50 based on experience) leaving the queue points are divided into the same cycle. As shown in Figure 8, the two groups of departure queue points are respectively clustered near the two arrows, that is, the two black solid line areas belong to the fifth and sixth cycles respectively. Then, according to the one-to-one pairing relationship between the leaving queuing point and the joining queuing point, each joining queuing point is divided into the period of the leaving queuing point on the same trajectory, as shown in Figure 8. The realization area belongs to the same cycle.

According to the fifth step of the present invention, in each cycle, since the leaving queuing point belongs to the case 1 in step 5, the leaving queuing point is fitted according to the least squares method to obtain the linear equation of the queuing dissipation wave, as shown in Figure 9. . The estimated results of the queued evanescent wave in the fifth and sixth cycles in Fig. 9 are respectively equations (27) and (28), that is, the two black dotted lines in Fig. 9.

x=2719.6-3.9t (27)

x=4501.7-5.2t (28)

According to the sixth step, establish the state space model shown in equation (16), and set the required initial parameters according to the field survey. In this example, q = 0.0075, R = 237.5, VF ₁ = -1.5m/s( Note that taking the driving direction as the positive direction, and the negative values of VF and VD _default indicate that the queue formation wave and the dissipated wave propagate backward), and

According to the seventh step of the present invention, the joining queue points are grouped first. According to formula (17), the 19 queuing points in the 5th and 6th periods are divided into 7 groups, and the centroid of the group, that is, the average time and position of all points in the group, is used as the estimated queuing forming wave segment point Input, for example, the 1st to 3rd joining queuing points are divided into a group (numbered 1), the centroid of the group is the time and space average of these three points, ie (550.7,265), then at t=550.7 In s, 265m is used as the observation input, that is, Z _k = 265, and the Kalman filter is used to estimate X _k . Since this point belongs to Case 2 in step 7, the estimated QX is 265m, that is, the centroid of the group coincides with the estimated point ; For the 4th queuing point, it is a single group and belongs to the situation 1 in step 7, then Kalman filter takes Z _k =241.7 at t=596s, and estimates X _k according to equations (19)～(23) , The result is QX=238.5m. The estimation of each segment point of the queue forming wave is shown in Figure 9, and the detailed results are shown in Table 2 below.

According to the eighth step of the present invention, the line segment after group 4 and group 7 is the last segment of the queue forming wave in the 5th and 6th cycles, respectively. Therefore, according to the X _k estimation results and the queue dissipation wave at groups 4 and 7, Solve the intersection of two straight lines as the maximum queuing point of the period. The X _k estimation results of group 4 and group 7 are

with

That is to say, the equation of the two-period queuing to form the wave terminal is

x-189.3=-1.1653(t-630.5) (29)

x-112.3=-1.8333(t-835) (30)

Combining the equations (27) and (28) of the queuing dissipation wave, the maximum queuing points of the two periods are (668,145.6) and (850,84.8) respectively, as shown in Figure 9, that is, the maximum queuing length of the period is 280-145.6. =134.4m and 280-84.8=195.2m.

Similarly, the queue length of the remaining periods in this case can be estimated according to the method of the present invention.

Claims

An intersection queue length estimation method based on low-permeability vehicle trajectory data, characterized in that it includes:

Step S1: Convert the original estimated data into a distance-time graph, and record the vehicle state at each track point in the distance-time graph, where the vehicle state includes a traveling state and a queue state;

Step S2: Identify the key points in the queuing based on the change of the vehicle status, wherein the key points in the queuing include joining the queuing point and leaving the queuing point;

Step S3: Periodically divide each queuing key point;

Step S4: Estimate the queuing dissipation wave and the queuing formation wave, and obtain the maximum queuing length.
The method for estimating the queuing length at intersections based on low-permeability vehicle trajectory data according to claim 1, wherein the identification of the vehicle status in step S1 specifically includes: setting a speed threshold, and setting the corresponding speed to be greater than The vehicle state at the trajectory point of the speed threshold is regarded as the traveling state, and vice versa, as the queue state.
The method for estimating the length of queuing at intersections based on low-permeability vehicle trajectory data according to claim 1, wherein the queuing point is the trajectory point where the vehicle state changes from the traveling state to the queuing state, and the leaving The queuing point is the track point where the vehicle state changes from the queuing state to the traveling state;

And according to the intersection to be passed through corresponding to the current trajectory, the queuing point is divided into the queuing point for the first time and the queuing point again.
The method for estimating the queuing length at intersections based on low-permeability vehicle trajectory data according to claim 1, wherein said step S3 specifically comprises:

Step S31: Estimate the start time of the green light corresponding to each departure queuing point by using the projection method, and determine the period to which each departure queuing point belongs;

Step S32: According to the pairing relationship between the leaving queuing point and the joining queuing point, each joining queuing point is divided into the period to which the corresponding leaving queuing point belongs.
The method for estimating the queuing length at intersections based on low-permeability vehicle trajectory data according to claim 1, wherein said step S4 specifically comprises:

Step S41: construct a queued dissipation wave;

Step S42: Establish a queue formation state space model, and construct a queue formation wave based on the queue formation state space model;

Step S43: Obtain the intersection point of the queuing dissipated wave and the queuing forming wave, and obtain the maximum queue length based on the obtained intersection point.
The method for estimating the queuing length at intersections based on low-permeability vehicle trajectory data according to claim 5, wherein the queuing dissipated wave is a straight line fitted by leaving the queuing point, specifically:

x = β 0 + β 1 ·t

Among them: x is the distance coordinate from the queuing point, t is the time, β 0 and β 1 are the parameters of the queuing dissipation wave;
The method for estimating the length of the intersection queue length based on low-permeability vehicle trajectory data according to claim 5, wherein the queue formation state space model is specifically:

Among them: QX k is the tail position of the queue at time k , VF k is the queue formation speed at time k, T is the length of time between k and k-1, and QX k-1 is the tail position of the queue at k-1 , VF k-1 is the queue formation speed at k-1, and a k is the queue formation acceleration.
The method for estimating the queuing length at intersections based on low-permeability vehicle trajectory data according to claim 7, wherein the queuing forming wave is a piecewise function, and each section has a different slope. The specific estimation method is include:

Step S421: Select the first added queuing point as input, and obtain each segment point by using a Kalman filter;

Step S422: Obtain a queue formation wave based on the obtained segment points.
The method for estimating the queuing length at intersections based on low-permeability vehicle trajectory data according to claim 8, characterized in that, in step S43, specifically, obtaining the intersection point of the queuing dissipated wave and the queuing forming wave end segment, and The maximum queue length is obtained based on the obtained intersection point.
An intersection queue length estimation device based on low-permeability vehicle trajectory data, which is characterized by comprising a memory, a processor, and a program stored in the memory and executed by the processor, and the processor executes the program When implementing the following steps:

Step S1: Convert the original estimated data into a distance-time graph, and record the vehicle state at each track point in the distance-time graph, where the vehicle state includes a traveling state and a queue state;

Step S2: Identify the key points in the queuing based on the change of the vehicle status, where the key points in the queuing include joining and leaving the queuing points;

Step S3: Periodically divide each queuing key point;

Step S4: Estimate the queuing dissipated wave and the queuing forming wave, and obtain the maximum queuing length.