Reconstruction method of intersection vehicle cumulative arrival curve based on license plate recognition data

Abstract

The application discloses a kind of based on the intersection vehicle cumulative arrival curve reconstruction method of license plate identification data, comprising: obtaining the license plate data of upstream and downstream intersections, extracting the observation value of arrival curve at upstream intersection exit section;Based on Gaussian process, construct the interpolation model of arrival curve, with part of the observation value of arrival curve as input, the upstream arrival information of unmatched vehicle is inferred;Maximum minimum inclination method is used to simplify the distribution of parameters in the interpolation model of arrival curve, and the parameters in the interpolation model of arrival curve are estimated by maximum likelihood, and the arrival curve at the section of upstream intersection is reconstructed.The application can automatically capture the nonlinearity and uncertainty of vehicle arrival, so that the reconstructed arrival curve has physical meaning in practical application, and provides a reliable scheme for accurate reconstruction of arrival curve.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent transportation systems, and particularly relates to a method for reconstructing a cumulative arrival curve of vehicles at an intersection based on license plate recognition data. BACKGROUND

[0002] In the intelligent transportation system, the cumulative arrival-departure curve of vehicles provides a strong foundation and guarantee for traffic flow modeling and traffic state estimation. The departure information of vehicles passing through the intersection can be directly obtained by detectors, while the arrival information is often difficult to obtain directly due to factors such as driver differences, vehicle lane changing, queuing, etc. With the gradual popularization of intelligent and networked vehicles, the accuracy requirements of intelligent transportation control for traffic state estimation are also increasing, which further challenges the accuracy reconstruction of the cumulative arrival curve. There are two key points for accurate reconstruction of the arrival curve: (1) a large amount of vehicle arrival information is needed as the data basis for curve reconstruction; (2) due to factors such as driver differences, road complexity, and detector defects, the vehicle arrival process has nonlinear and uncertain characteristics, so it is necessary to model the nonlinear and uncertain vehicle arrival process and describe the nonlinear and uncertain characteristics of vehicle arrival.

[0003] Fixed detectors and mobile detectors are two main ways to obtain vehicle arrival information. Fixed detectors are usually arranged at a certain section of the road and can directly obtain vehicle arrival information. Traditional fixed detectors mainly include magnetic coils, radars, infrared sensors, etc. Mobile detectors record vehicle trajectory data by being installed on vehicles, indirectly providing vehicle arrival information, and mainly include floating cars, networked cars, etc. In recent years, due to the need for high-precision traffic state estimation, as a new type of fixed detector, video detectors have been widely used in obtaining a large amount of vehicle arrival information. Among them, the license plate recognition (LPR) system is a typical representative of video detectors. By installing LPR cameras at different intersections, the license plate information of vehicles passing through the intersection can be captured. LPR systems are widely deployed on important road sections and intersections in cities to record the arrival information of all vehicles at the observation section, and have relatively stable data collection characteristics. By matching these license plate information, the movement of vehicles between different intersections can be tracked. Based on LPR data, a large number of observed values required for arrival curve reconstruction can be obtained, providing good data support for arrival curve reconstruction.

[0004] Current arrival curve reconstruction methods and their defects mainly include:

[0005] (1) Based on the traditional fixed detector, the vehicle arrival information is directly obtained by reasonable layout, so as to realize the reconstruction of the arrival curve. However, the arrival curve reconstruction method based on the traditional fixed detector has the defects of small coverage range and difficult acquisition of time and space information of the whole road section. At the same time, due to the queuing and lane changing behavior of vehicles, the installation position of the fixed detector affects the accuracy of the vehicle arrival information acquisition, which easily causes the inaccurate reconstruction of the arrival curve.

[0006] (2) Based on the mobile detector, the turning points of the queue profile are estimated considering the arrival information of vehicles in different driving states, so as to realize the reconstruction of the arrival curve of the stable cycle. The partial vehicle trajectory data obtained by sampling is used to model the arrival process of the vehicle, the connection points of the queue queue are estimated based on the statistical model assuming that the vehicle arrival obeys a certain distribution, or the queue profile is directly fitted by using the piecewise linear method, and the maximum likelihood estimation, kernel density and other parameter estimation methods are used to solve the model, so as to reconstruct the complete arrival curve. The mobile detector has a larger coverage range than the fixed detector, and can obtain rich traffic space-time information. However, at present, the penetration rate of the mobile detector is not high, the spatial distribution is uneven, and the reconstruction method of the arrival curve based on the mobile detector is prone to large local deviation. Assuming that the vehicle arrival process in the cycle is stable arrival or assuming that the cycle information (such as cycle length, signal phase, etc.) is known can compensate for the defect of low penetration rate, but in actual application, it is difficult to capture the uncertainty of the vehicle arrival process for the signal control intersection with time-varying cycle information (such as adaptive signal control).

[0007] (3) Although the license plate recognition (LPR) system has relatively stable data acquisition characteristics, it usually uses piecewise linear arrival flow rate or assumes that the vehicle arrival obeys a certain distribution to describe the nonlinear arrival process of the vehicle. In actual application, due to the existence of a large number of assumptions, it is difficult to dynamically depict the nonlinear arrival process of the vehicle. SUMMARY

[0008] The technical problem solved by the present application is that the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data can automatically capture the nonlinearity and uncertainty of vehicle arrival, so that the reconstructed arrival curve has physical meaning in actual application, and provides a reliable scheme for accurate reconstruction of the arrival curve.

[0009] TECHNICAL SCHEME

[0010] An intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data, the intersection vehicle cumulative arrival curve reconstruction method comprises the following steps:

[0011] S1, obtaining license plate data of upstream and downstream intersections, and extracting observation values of the arrival curve at the section of the exit lane of the upstream intersection:

[0012] According to the departure information of the vehicle in the LPR data, the cumulative departure curve of the vehicle at the stop line of the upstream and downstream intersections is obtained; taking the vehicle departure curve at the stop line of the downstream intersection as a reference, the arrival vehicles at the section of the exit lane of the upstream intersection are matched by license plate, and the partial observation values of the arrival curve are obtained according to the matched vehicle information;

[0013] S2, constructing an arrival curve interpolation model based on a Gaussian process, taking the partial observation values of the arrival curve as input, and inferring the upstream arrival information of the unmatched vehicles; wherein, in the Gaussian process, the periodic kernel function and the square exponential kernel function are combined, and the local periodic kernel function obtained after the combination is used to automatically capture the dynamic periodic change of the arrival curve, and a monotonically increasing constraint is added in the arrival curve interpolation model;

[0014] S3, simplifying the distribution of the parameters in the arrival curve interpolation model by using the maximum and minimum inclination method, estimating the parameters in the arrival curve interpolation model by using maximum likelihood, and reconstructing the arrival curve at the section of the upstream intersection.

[0015] Further, in step S1, the process of obtaining the license plate data of the upstream and downstream intersections and extracting the observation values of the arrival curve at the section of the exit lane of the upstream intersection includes the following steps:

[0016] S11, obtaining the time stamp sequence t of all vehicles departing from the stop line according to the license plate recognition data of the adjacent two intersections; sorting the time stamp sequence t to obtain the corresponding cumulative number of vehicles, and the points on the vehicle departure curve of the upstream and downstream intersections are represented as and wherein, is the time stamp of the a-th vehicle departing from the upstream intersection, is the cumulative number of vehicles at the upstream intersection when the a-th vehicle departs; is the time stamp of the b-th vehicle departing from the downstream intersection, is the cumulative number of vehicles at the downstream intersection when the b-th vehicle departs; a = 1, 2, …, m U , b = 1, 2, …, n D , m U and n D are the number of vehicles at the upstream and downstream intersections, respectively;

[0017] S12, considering the first-in first-out principle, taking the vehicle departure curve of the downstream intersection as a reference, matching the arrival vehicles at the section of the exit lane of the upstream intersection by license plate, and obtaining the observation values of the arrival curve g is the number of matched vehicles.

[0018] For the ith departure observation, if its license plate is successfully matched in the upstream arrival, the ith departure observation is taken as the matched vehicle and as an observation of the arrival curve, denoted as:

[0019]

[0020]

[0021] wherein, is the timestamp of the matched vehicle leaving the upstream stop line, is the cumulative vehicle number when the matched vehicle leaves the downstream stop line.

[0022] Further, in step S2, the arrival curve interpolation model is constructed based on the Gaussian process, and the process of inferring the upstream arrival information of the unmatched vehicle based on the partial observations of the arrival curve includes the following steps:

[0023] S21, based on the partial observations of the arrival curve, an arrival curve interpolation model based on the Gaussian process is constructed, and the specific steps are as follows:

[0024] S211, taking the arrival timestamp and the cumulative vehicle number of the matched vehicle as the input variables of the Gaussian process, for a lane, the cumulative vehicle number y and the arrival timestamp x satisfy the following mathematical relationship:

[0025] y = f(x) + ε

[0026] wherein, ε is Gaussian distributed noise with mean value 0 and variance f(x) is a multidimensional Gaussian distribution N(m(x), K(x, x)) with mean function m(x) = E[f(x)] and covariance matrix K(x, x) = COV[f(x), f(x)];

[0027] S212, define the mean function m(x), and set the mean function m(x) = 0;

[0028] S213, construct the covariance matrix K(x, x):

[0029]

[0030] S214, take the cumulative vehicle number y * of the unmatched vehicle on the arrival curve as a new observation input in the Gaussian process, and estimate the arrival timestamp x * of the unmatched vehicle, and the joint Gaussian distribution of all arrival vehicles is represented as:

[0031]

[0032] Wherein, the marginal distribution f * It still follows a Gaussian distribution, with a posterior mean m. * (x * ) and covariance C * They are respectively:

[0033] m * (x * )=m(x * )+K(x * ,x)K(x,x) -1 (f(x)-m(x))

[0034] C * =K(x) * x * )-K(x * ,x)K(x,x) -1 K(x, x) * );

[0035] S22, the periodic kernel function Sum-squared kernel function By combining these components, we obtain the local periodic kernel function k. lp (x, x′):

[0036]

[0037] Where, σ 2 and σ′ 2 Let Variance be the variance of the periodic kernel function and the SE kernel function, respectively. It is the combined kernel variance; p The length parameter of the periodic kernel is used to determine the correlation between two input variables x and x′; eq is the length parameter of the squared exponential kernel, p is the period; the parameters of the arrival curve interpolation model are...

[0038] S23, add a monotonically increasing constraint to the Gaussian process model to make the arrival curve reflect the increasing characteristics of the cumulative vehicle count curve; in the arrival curve interpolation model, the monotonically increasing constraint is expressed as follows:

[0039]

[0040] in, It is a linear operator in a constrained Gaussian process;

[0041] The constrained arrival curve interpolation model is represented as follows:

[0042]

[0043] where {X υ} is a finite point set of s virtual observation point positions, are virtual observation point positions; a(·) and b(·) are constraint region restriction functions;

[0044] The posterior distribution of the arrival curve interpolation model is expressed as:

[0045]

[0046]

[0047] where m * and m υ are the posterior mean functions of x * and X υ , respectively, V is a virtual position random variable with a truncated Gaussian distribution τ , which indicates that all virtual observation points satisfy the constraint condition; coefficients A, A1, B, B1 and ∑ are defined as follows:

[0048]

[0049]

[0050]

[0051] B2=K(x * , x * )-A2K(x, x * )

[0052]

[0053]

[0054]

[0055] where I is an identity matrix, A2, B2 and B3 are intermediate parameters.

[0056] Further, in step S3, the maximum-minimum inclination method is used to simplify the distribution of the parameters in the arrival curve interpolation model, the maximum likelihood is used to estimate the parameters in the arrival curve interpolation model, and the process of reconstructing the arrival curve at the upstream intersection section includes the following steps:

[0057] S31, the maximum likelihood is used to estimate the parameters in the arrival curve interpolation model , and the form of the likelihood function is expressed as:

[0058] L(θ)=p(x, x* , X υ |θ)=p(x,x * |θ)p(X υ |x,x * , θ)

[0059] where p(x,x * |θ) is the likelihood probability without constraints; p(X υ |x,x * , θ) is the probability value of the virtual observation point X υ reaching the curve incrementally when the constraints are met;

[0060] The log-likelihood function is represented as l(θ)=ln p(x,x * |θ)+ln p(X υ |x,x * , θ), which is the sum of the unconstrained and constrained log-likelihood values.

[0061] S32, using the maximum minimum inclination method to simplify the complex truncated Gaussian distribution, and then using maximum likelihood estimation to estimate the parameters of the arrival curve interpolation model after simplification, and reconstructing the arrival curve at the upstream intersection section.

[0062] Beneficial effects:

[0063] First, the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data can automatically capture the nonlinearity and uncertainty of vehicle arrival; the periodic kernel function is used in the Gaussian process to describe the periodicity of the arrival curve, and the assumption of piecewise linearity of vehicle arrival is released.

[0064] Second, the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data is completely data-driven, avoiding the negative effects of model overfitting caused by the strong assumption of piecewise linearity, and improving the universality and stability of the arrival curve interpolation model.

[0065] Third, the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data does not require the input of periodic information in the arrival curve interpolation model, releasing the premise assumption that the periodic information is known; the periodic kernel function with dynamic changes in periodicity further expands the application range of the arrival curve interpolation model to signal control intersections with time-varying periodic information, such as different signal timing schemes for morning and evening peak hours, and inductive signal control.

[0066] Fourthly, the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data of the present application meets the traffic physical meaning of the arrival curve, adds a monotonically increasing constraint in the Gaussian process, further improves the accuracy of the arrival curve interpolation model, and makes the reconstructed curve have physical meaning in actual application, thereby providing a reliable scheme for accurate reconstruction of the arrival curve. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 Lane and LPR system layout schematic diagram of the embodiment of the present application;

[0068] Figure 2 Effect result schematic diagram of the LP kernel and the monotonically increasing constraint on the arrival curve reconstruction; wherein (a) is the arrival curve reconstruction effect comparison result of the model using only the LP periodic kernel function under different license plate matching rates; (b) is the arrival curve reconstruction effect comparison result of the model adding only the monotonically increasing constraint under different license plate matching rates; (c) is the arrival curve reconstruction effect comparison result of the model using both the LP periodic kernel function and the monotonically increasing constraint under different license plate matching rates;

[0069] Figure 3 Arrival curve reconstruction result schematic diagram of time periods 2, 3 and 4;

[0070] Figure 4 Arrival curve reconstruction result schematic diagram during time period conversion;

[0071] Figure 5 Flow chart of the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data of the present application. DETAILED DESCRIPTION

[0072] The following examples can enable a person skilled in the art to more fully understand the present application, but do not limit the present application in any way.

[0073] The terms related to the present application are explained as follows:

[0074] License plate recognition data refers to all vehicle information collected by a license plate recognition system at a certain section, including the license plate, arrival time, speed and the like of the vehicle.

[0075] Vehicle cumulative arrival curve refers to the cumulative arrival vehicle number curve of a certain section of a road over time.

[0076] Reference Figure 5 The embodiment of the present application discloses an intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data, which comprises the following steps:

[0077] S1, obtain the license plate data of the upstream and downstream intersections, and extract the observed values of the arrival curve at the cross section of the exit lane of the upstream intersection:

[0078] According to the departure information of the vehicle in the LPR data, the cumulative departure curve of the vehicle at the stop line of the upstream and downstream intersections is obtained; the vehicle departure curve at the stop line of the downstream intersection is taken as a reference, the arrival vehicles at the cross section of the exit lane of the upstream intersection are matched by license plates, and the partial observed values of the arrival curve are obtained according to the matched vehicle information;

[0079] S2, based on the Gaussian process, an arrival curve interpolation model is constructed, the partial observed values of the arrival curve are taken as input, and the upstream arrival information of the unmatched vehicle is inferred; wherein, in the Gaussian process, the periodic kernel function and the square exponential kernel function are combined, the local periodic kernel function obtained after the combination is automatically captured to the dynamic periodic change of the arrival curve, and a monotonically increasing constraint is added to the arrival curve interpolation model, so as to ensure the physical characteristics of the arrival curve as the cumulative vehicle number change curve;

[0080] S3, for the complex distribution of the parameters in the model, the maximum minimum inclination method is used to simplify the distribution of the parameters in the arrival curve interpolation model, so as to accelerate the maximum likelihood estimation speed and avoid falling into a local optimal solution; then the maximum likelihood is used to estimate the parameters in the arrival curve interpolation model, and finally the arrival curve at the cross section of the upstream intersection is reconstructed.

[0081] The specific process of step 1 is as follows:

[0082] S11, according to the license plate recognition data of the adjacent two intersections, the time stamp sequence of all vehicles leaving the stop line is obtained. The time stamp sequence t is sorted, and the corresponding cumulative vehicle number N of all vehicles can be directly obtained. Therefore, the points on the vehicle departure curve of the upstream and downstream intersections are respectively represented as and m U and n D are the number of vehicles at the upstream and downstream, respectively.

[0083] S12, considering the first-in first-out (F[FO) principle, the vehicle departure curve of the downstream intersection is taken as a reference, the arrival vehicles at the cross section of the exit lane of the upstream intersection are matched by license plates, and the observed values of the arrival curve are obtained g is the number of matched vehicles. For the i-th departure observed value, if its license plate can be matched in the upstream arrival, the i-th departure observed value is the matched vehicle, that is, the observed value of the arrival curve, which can be specifically represented as:

[0084]

[0085]

[0086] wherein, is the timestamp of the matched vehicle leaving the upstream stop line, is the cumulative vehicle number at the time of the matched vehicle leaving the downstream stop line.

[0087] The specific process of step 2 is as follows:

[0088] S21, based on the partial observation values of the arrival curve, a Gaussian process-based arrival curve model is constructed. Gaussian process is widely used in regression and classification problems in machine learning, especially for complex nonlinear processes. In Gaussian process, prediction and uncertainty estimation are performed by calculating the conditional probability distribution of the output variable. The specific steps are as follows:

[0089] (1) The arrival timestamp and the cumulative vehicle number of the matched vehicle are taken as the input variables of the Gaussian process. For a lane, the cumulative vehicle number y and the arrival timestamp x satisfy the following mathematical relationship:

[0090] y=f(x)+ε

[0091] wherein, ε is Gaussian distributed noise with mean 0 and variance ; f(x) is a multidimensional Gaussian distribution N(m(x), K(x, x')) with mean m(x)=E[f(x)] and covariance matrix K(x, x')=COV[f(x), f(x')].

[0092] (2) Define the mean function m(x). In order to release the premise assumption of piecewise linearity, the mean function is set to m(x)=0, and the model reflects the arrival curve characteristics through the covariance matrix.

[0093] (3) Construct the covariance matrix K(x, x'). The covariance matrix is one of the keys to affect the estimation effect of Gaussian process, and its effect depends on whether the kernel function k(x, x') matched with the curve characteristics is used. The covariance matrix is represented as:

[0094]

[0095] (4) Construct the joint Gaussian distribution. The cumulative vehicle number y * of the unmatched vehicle on the arrival curve is taken as a new observation input in the Gaussian process, and its arrival timestamp x * is estimated. Therefore, the joint Gaussian distribution of all arrival vehicles is represented as:

[0096]

[0097] where the edge distribution f * is still Gaussian, whose posterior mean m * (x * ) and covariance C * are respectively:

[0098] m * (x * ) = m(x * ) + K(x * , x)K(x, x) -1 (f(x) - m(x))

[0099] C * = K(x * , x * ) - K(x * , x)K(x, x) -1 K(x, x * ).

[0100] S22, a specific periodic kernel function is adopted in the covariance matrix of the Gaussian process to characterize the dynamic periodicity of the arrival curve. The periodic kernel function is combined with the squared exponential (SE) kernel function , which can guarantee the periodicity of the curve to change with the distance while capturing the periodic trend of the arrival curve. This combined kernel is called the local periodic (LP) kernel function, which is mathematically expressed as follows:

[0101]

[0102] where σ 2 and σ' 2 are the variances of the periodic kernel function and the SE kernel function, respectively, is the variance of the combined kernel, l p is the length parameter of the periodic kernel, which determines the correlation between two input variables x and x', l eq is the length parameter of the squared exponential kernel, and p is the period. Therefore, the model parameters are

[0103] S23, in order to further improve the accuracy of the reconstruction of the arrival curve, a monotonically increasing constraint is added to the Gaussian process model to ensure the increasing property of the arrival curve as the cumulative vehicle number curve. In the arrival curve model, the monotonically increasing constraint is expressed as follows:

[0104]

[0105] where is the linear operator in the constrained Gaussian process.

[0106] To guarantee the increasing property of the reconstructed curve, a method of virtual observation points is adopted. The main idea is to find a finite point set {X υ} and constrain the estimates at these points so that the whole curve satisfies the increasing constraint with a large probability. The finite point set {X υ} is the virtual observation points. Thus, the constrained arrival curve model is represented as follows:

[0107] f|x, X υ := f|f(x) + ε = y,

[0108] where, is the virtual observation point position; a(·) and b(·) are the constraint region limit functions.

[0109] Therefore, the posterior distribution of the model can be represented as:

[0110]

[0111]

[0112] where m * and m υ are the mean functions of x * and X υ , respectively. The virtual position random variable V with constraint satisfies a truncated Gaussian distribution τ, which means that all virtual observation points satisfy the constraint condition. The coefficients A, A1, B, B1 and ∑ are defined as follows:

[0113]

[0114]

[0115]

[0116] B2 = K(x * , x * ) - A2K(x, x * )

[0117]

[0118]

[0119]

[0120] where I is the identity matrix.

[0121] The specific process of the step 3 is as follows:

[0122] S31, For the arrival curve model constructed in this paper, the purpose of parameter estimation is to obtain the most likely arrival curve from the posterior distribution. Maximum likelihood estimation is used to estimate the parameters θ={σ} in the arrival curve model. 2 , l p p, l eq The likelihood function is estimated as follows:

[0123] L(θ) = p(x, x) * X υ |θ)=p(x,x * |θ)p(X υ |x,x * ,θ)

[0124] Where p(x, x) * |θ) is the likelihood probability without constraints; p(X) υ |x,x * θ) represents the virtual observation point X υ The probability value of reaching the increasing curve when the constraints are met.

[0125] Therefore, the log-likelihood function is expressed as l(θ) = ln p(x, x). * |θ)+ln p(X υ |x,x * ,θ), which is the sum of the logarithmic probability values ​​of the unconstrained and constrained logarithms.

[0126] S32, due to the constraint functions a(·) and b(·), the posterior distribution of the arrival curve model exhibits a complex truncated Gaussian distribution. To improve the efficiency of parameter estimation and avoid the estimation problem getting trapped in local optima, the maximum-minimum tilt method is used to simplify the complex truncated Gaussian distribution. After simplification, maximum likelihood estimation is used again to estimate the model's parameters, ultimately obtaining the reconstructed arrival curve.

[0127] Case Analysis

[0128] (1) The layout of the test road section lanes and LPR system in step S1 is as follows: Figure 1 As shown.

[0129] (2) The signal timing scheme for the upstream intersection of the experimental section in step S1 is shown in Table 1.

[0130] Table 1. Signal Timing Scheme for the Upstream Intersection (24 Hours)

[0131]

[0132] (3) The effect of the LP kernel and monotonically increasing constraint in step S2 on the arrival curve reconstruction is as follows: Figure 2 As shown.

[0133] From Figure 2 It can be seen that, for different matching rates, in the arrival curve reconstruction model, only using the LP kernel function can automatically capture the periodic characteristics of the arrival curve even when the matching rate is low, but the curve will have sudden rising and falling fluctuations. Compared with the LP kernel function, adding only the monotone increasing constraint in the model can significantly reduce the sudden rising and falling fluctuations of the curve, but when the matching rate is low, due to the influence of the convergence speed of the model, the monotone increasing constraint tends to reconstruct an approximately increasing straight line, which cannot better reflect the periodic characteristics of the arrival curve. Therefore, by fusing the LP kernel function and the monotone increasing constraint and adding them to the arrival curve model, the periodic characteristics of the arrival curve can be automatically captured, and the stability of the change trend of the reconstructed curve can be ensured, thereby enhancing the robustness of the model. Figure 2 In the figure, (a) is the comparison result of the arrival curve reconstruction effect of the model using only the LP periodic kernel function under different license plate matching rates; (b) is the comparison result of the arrival curve reconstruction effect of the model using only the monotone increasing constraint under different license plate matching rates; (c) is the comparison result of the arrival curve reconstruction effect of the model using both the LP periodic kernel function and the monotone increasing constraint under different license plate matching rates. It can be found from the three pictures in Figure 2 that the accuracy of the arrival curve reconstruction is gradually improved.

[0134] (4) The arrival curve reconstruction results of time periods 2, 3, and 4 in step S3 are shown in Figure 3 .

[0135] Early morning peak, flat peak, and late evening peak are selected from time periods 2, 3, and 4 respectively for 15 minutes to show the reconstruction effect of the arrival curve. It can be seen from Figure 3 that the reconstructed arrival curve can better capture the periodicity and increasing trend, and has a low reconstruction error.

[0136] (5) The arrival curve reconstruction results during the time period conversion in step S3 are shown in Figure 4 .

[0137] It can be seen from Figure 4 that when the cycle length changes, the arrival curve reconstruction model can also capture the change of the cycle, and can quickly adapt to the new signal timing scheme, further demonstrating that the proposed arrival curve reconstruction method has good robustness.

[0138] In summary, the intersection vehicle cumulative arrival curve reconstruction method based on license plate recognition data of the application establishes a specific Gaussian process model to reconstruct the cumulative arrival curve at the section of the exit lane of the upstream intersection. The reconstruction method regards the reconstruction of the arrival curve as an interpolation problem based on the Gaussian process according to the partial observation values of the arrival curve, adopts a specific periodic kernel function, adds a monotonically increasing constraint in the model, constructs the arrival curve model, and simultaneously simplifies the complex distribution parameters in the arrival curve interpolation model by using the maximum minimum tilt method, and estimates the parameters of the arrival curve interpolation model by using the maximum likelihood, so as to obtain the reconstructed complete arrival curve.

[0139] The above is only the preferred embodiment of the application, and the protection scope of the application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the application shall fall within the protection scope of the application. It should be noted that some improvements and refinements of the application without departing from the principles of the application shall be considered as the protection scope of the application.

Claims

1. A method for reconstructing cumulative arrival curve of intersection vehicles based on license plate recognition data, characterized in that, The intersection vehicle cumulative arrival curve reconstruction method comprises the following steps: S1, obtaining the license plate data of the upstream and downstream intersections, and extracting the observation value of the arrival curve at the section of the exit lane of the upstream intersection: According to the departure information of the vehicle in the LPR data, the cumulative departure curve of the vehicle at the stop line of the upstream and downstream intersections is obtained; the vehicle departure curve at the stop line of the downstream intersection is taken as the reference, the arrival vehicles at the section of the exit lane of the upstream intersection are matched by license plate, and the partial observation value of the arrival curve is obtained according to the matched vehicle information; S2, constructing an arrival curve interpolation model based on a Gaussian process, taking the partial observation value of the arrival curve as the input, and inferring the upstream arrival information of the unmatched vehicles; wherein, in the Gaussian process, the periodic kernel function and the square exponential kernel function are combined, the local periodic kernel function obtained after the combination is used to automatically capture the dynamic periodic change of the arrival curve, and a monotonically increasing constraint is added to the arrival curve interpolation model; S3, simplifying the distribution of the parameters in the arrival curve interpolation model by using the maximum minimum tilt method, estimating the parameters in the arrival curve interpolation model by using the maximum likelihood, and reconstructing the arrival curve at the section of the upstream intersection; In step S2, the process of constructing an arrival curve interpolation model based on a Gaussian process, taking the partial observation value of the arrival curve as the input, and inferring the upstream arrival information of the unmatched vehicles comprises the following steps: S21, constructing an arrival curve interpolation model based on a Gaussian process based on the partial observation value of the arrival curve, and the specific steps are as follows: S211, match the arrival timestamp of the vehicle and the cumulative number of vehicles As the input variables of the Gaussian process, for a lane, the cumulative number of vehicles y and the arrival timestamp x satisfy the following mathematical relationship: y=f(x)+ε where ε is a Gaussian distributed noise with mean 0 and variance f(x) is a multi-dimensional Gaussian distribution N(m(x), K(x, x)) with mean function m(x) = E[f(x)] and covariance matrix K(x, x) = COV[f(x), f(x)]; S212, defining a mean function m(x), and setting the mean function m(x)=0; S213, constructing a covariance matrix K(x,x): S214, cumulative number of vehicles y that did not match on the arrival curve * Consider the new observation input as a Gaussian process with arrival timestamp x * Estimate, the joint Gaussian distribution of all arriving vehicles is represented as: where the edge distribution f * is still Gaussian, with posterior mean m * (x * ) and covariance C * respectively: m * (x * )=m(x * )+K(x * ,x)K(x,x) -1 (f(x)-m(x)) C * = K(x * ,x * ) - K(x * ,x) K(x,x) -1 K(x,x * ) S22, combine the periodic kernel function and the square exponential kernel function to obtain a local periodic kernel function k lp (x, x') : where σ 2 and σ′ 2 are the variances of the periodic kernel and the SE kernel, respectively, is the combined kernel variance; l p is the length parameter of the periodic kernel, which determines the correlation between two input variables x and x′; l eq is the length parameter of the square exponential kernel, and p is the periodicity; the parameters of the arrival curve interpolation model are S23, adding a monotonically increasing constraint to the Gaussian process model to make the arrival curve as an increasing curve of the cumulative vehicle number; in the arrival curve interpolation model, the monotonically increasing constraint is represented as follows: wherein is a linear operator in the band constrained Gaussian process; The arrival curve interpolation model with the constraint is represented as follows: where {X υ} is a finite point set of s virtual observation point positions, are virtual observation point positions; a(·) and b(·) are constraint region restriction functions; The posterior distribution of the arrival curve interpolation model is represented as: where m * and m v are the posterior mean functions of x * and X υ respectively, V is a constrained virtual location random variable following a truncated Gaussian distribution τ, indicating that all virtual observation points satisfy the constraint condition; the coefficients A, A1, B, B1 and Σ are defined as follows: B2 = K(x * ,x * )- A2K(x,x * ) Wherein, I is a unit matrix, A2, B2 and B3 are intermediate parameters.

2. The method of reconstructing cumulative arrival curve of intersection vehicles based on license plate recognition data according to claim 1, wherein, In step S1, the process of obtaining the license plate data of the upstream and downstream intersections and extracting the observation value of the arrival curve at the section of the exit lane of the upstream intersection comprises the following steps: S11, according to the number plate recognition data of the adjacent two intersections, obtaining the time stamp sequence t of all vehicles in each lane of the upstream and downstream intersections when the vehicles leave the stop line; sorting the time stamp sequence t to obtain the corresponding cumulative vehicle number of all vehicles, and the points on the vehicle leaving curve of the upstream and downstream intersections are respectively represented as and wherein, is the time stamp when the a-th vehicle leaves the upstream intersection, is the cumulative vehicle number of the upstream intersection when the a-th vehicle leaves; is the time stamp when the b-th vehicle leaves the downstream intersection, is the cumulative vehicle number of the downstream intersection when the b-th vehicle leaves; a = 1, 2, …, m U , b = 1, 2, …, n D , m U and n D are the number of vehicles upstream and downstream, respectively; S12, considering the first-in first-out principle, taking the vehicle driving-off curve of the downstream intersection as a reference benchmark, performing license plate matching on the arriving vehicles at the cross-section of the exit lane of the upstream intersection, and obtaining the observation value of the arrival curve i = 1, 2, …, g, g is the number of matched vehicles; For the i-th departure observation value, if the license plate thereof is successfully matched in the upstream arrival, the i-th departure observation value is taken as the matched vehicle and as the observation value of the arrival curve, and is specifically represented as: wherein, is the timestamp of the vehicle leaving the upstream parking line, is the cumulative number of vehicles at the time of the vehicle leaving the downstream parking line.

3. The method of reconstructing cumulative arrival curve of intersection vehicles based on license plate recognition data according to claim 1, wherein, In step S3, the process of simplifying the distribution of the parameters in the arrival curve interpolation model by using the maximum minimum tilt method, estimating the parameters in the arrival curve interpolation model by using the maximum likelihood, and reconstructing the arrival curve at the section of the upstream intersection comprises the following steps: S31, using maximum likelihood to estimate parameters in the arrival curve interpolation model The estimation is performed, and the likelihood function is expressed in the form L(θ) = p(x, x * | θ) = p(x, x v | θ) = p(x, x * | θ) = p(x, x v | θ) = p(x, x * , θ) where p(x, x * |θ) is the likelihood probability without constraints; p(x, x v |θ) is the likelihood probability without constraints; p(x, x * |θ) is the likelihood probability without constraints; p(x, x v |θ) is the likelihood probability without constraints; p(x, x The log-likelihood function is expressed as l(0) = ln p(x, x * | 0) + ln p(x v | x, x * , 0), which is the sum of the unconstrained and constrained log-probability values. S32, simplifying the complex truncated Gaussian distribution by using the maximum minimum tilt method, estimating the parameters of the arrival curve interpolation model again by using the maximum likelihood estimation after simplification, and reconstructing the arrival curve at the section of the upstream intersection.

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