Highway traffic state robust estimation method based on connected vehicle trajectory data

Abstract

The application discloses a kind of based on the robust estimation method of highway traffic state of network-connected vehicle trajectory data, comprising: constructing virtual oblique grid;Calculate the representative value of traffic state in each oblique grid unit, construct traffic state observation matrix;Traffic state estimation is converted into low-rank matrix completion problem;Establish the robust traffic state estimation model based on low-rank and sparse matrix recovery;Introduce auxiliary variable to retain original state observation information, convert the robust traffic state estimation model into multivariable optimization problem, use alternating direction multiplier method to decompose multivariable optimization problem into multiple sub-variable optimization problems, and update multiple sub-variables iteratively.The application has high-precision, reliable estimation performance, provides more reliable support for fine active traffic management and control application, improves the robustness of traffic state estimation model in real application scenario, and has higher computational efficiency when facing large-scale road network scene.

Description

Technical Field

[0001] This invention belongs to the field of traffic state estimation technology, specifically relating to a robust estimation method for highway traffic state based on connected vehicle trajectory data. Background Technology

[0002] Traffic state estimation refers to the complete and accurate estimation of all-temporal and spatial traffic conditions (such as traffic speed) based on partial traffic state observation data collected from fixed or mobile sensors (such as connected vehicles). In reality, although data collected from fixed or mobile detectors can provide fragmented spatiotemporal traffic state observations, these field-collected traffic state observations are often sparse, limited, and noisy. Fixed cross-section detectors are costly and mostly deployed on specific, limited road cross-sections, often with limited spatial coverage, making it impossible to accurately detect traffic conditions between two cross-sections. Benefiting from the rapid development of vehicle-to-everything (V2X) technology, mobile detectors can provide more complete spatial traffic state observations, but due to the limited penetration of connected vehicles, their temporal distribution is sparse. Therefore, estimating complete and accurate all-temporal and spatial traffic conditions of highways from limited and noisy observation data remains a challenging task that urgently needs to be addressed in current Intelligent Transportation Systems (ITS) applications. Connected vehicle trajectory data has advantages such as high resolution and wide spatiotemporal coverage, which can support refined highway active traffic management and control applications. Existing technologies also include some methods for estimating traffic conditions using connected vehicle trajectory data. For example, patent publication number CN116311945A discloses a method for constructing a holographic traffic condition dataset based on multi-source information fusion; patent publication number CN115641712B discloses a road traffic condition estimation method; patent publication number CN113851006B discloses a method and system for estimating real-time traffic conditions at intersections based on multi-source data fusion; and patent publication number CN114333335A discloses a lane-level traffic condition estimation method based on trajectory data.

[0003] In summary, existing methods for estimating highway traffic conditions can be mainly divided into two categories:

[0004] (1) Physical model-driven methods mainly consider the physical traffic flow characteristics to construct traffic flow models for traffic state estimation. They typically have the advantages of strong physical interpretability and small data requirements. Representative methods include those based on the LWR model and its higher-order extension, the ARZ model. However, physical model-driven methods are often limited by the capabilities of the physical traffic flow model and the assumptions made during the data assimilation process. In addition, for large-scale road network applications, the parameter calibration process of model-driven methods is time-consuming and laborious.

[0005] (2) Data-driven methods primarily use various learning frameworks to capture and learn the spatiotemporal dependencies of traffic states from traffic data to estimate traffic states. These methods offer advantages such as strong adaptability and high estimation accuracy. Representative methods include those based on adaptive smoothing, Gaussian processes, deep learning, and low-rank matrix / tensor completion. The most common approach in data-driven methods is to discretize the estimated spatiotemporal region into an orthogonal rectangular network and incorporate traffic state observation datasets collected by fixed and moving detectors into the grid. Grid-based data-driven methods are easy to implement and readily capture high-dimensional spatiotemporal dependencies of traffic states. However, data-driven methods are highly dependent on data and often require additional training data. Furthermore, their estimation results have poor physical interpretability. The specific disadvantages of existing grid-based data-driven methods include:

[0006] (1) The traffic state matrix is ​​constructed using an orthogonal grid-based method. The matrix is ​​divided vertically and horizontally in the spatiotemporal plane, which is inconsistent with the oblique propagation direction of the traffic wave, resulting in non-homogeneous traffic state observation.

[0007] (2) The model assumes data purity but does not consider potential abnormal data. In actual applications, traffic condition observations may contain anomalies due to erroneous records from fixed detectors or network attacks on connected vehicles. The assumption of data purity may lead to insufficient robustness of the estimation model.

[0008] (3) The computational complexity is high. In addition to being related to the problem size itself, it is also related to the number of model hyperparameters and the amount of observation data. When it is applied to large-scale applications, it will generate high computational costs. Summary of the Invention

[0009] Technical problem solved: This invention discloses a robust estimation method for highway traffic state based on connected vehicle trajectory data. It still has high accuracy and reliable estimation performance under the condition of extremely sparse state observation data, providing more reliable support for refined active traffic management and control applications, improving the robustness of traffic state estimation models in real-world application scenarios, and having higher computational efficiency for large-scale road network scenarios.

[0010] Technical solution:

[0011] A robust estimation method for highway traffic state based on connected vehicle trajectory data, comprising the following steps:

[0012] S1: Utilizing traffic wave priors, the estimated spatiotemporal region is discretized into a grid along the time direction and the reverse spatial propagation direction of the traffic wave to construct a virtual oblique grid; acquire connected vehicle trajectory data, and assign each trajectory point to an oblique grid cell according to the temporal and spatial attributes of the connected vehicle trajectory data; by aggregating the trajectory points within the oblique grid cell, calculate the representative value of traffic state within each oblique grid cell, and construct a traffic state observation matrix;

[0013] S2: Minimize the rank of the traffic state observation matrix constructed in step S1, transforming traffic state estimation into a low-rank matrix completion problem; introduce a sparse matrix to accommodate potential outliers in traffic state observations, and transform outlier detection into a sparse matrix recovery problem by applying regularization constraints to the sparse matrix, thus establishing a robust traffic state estimation model based on low-rank and sparse matrix recovery.

[0014] S3: Based on the robust traffic state estimation model constructed in step S2, auxiliary variables are introduced to retain the original state observation information. An augmented Lagrangian objective function is constructed to transform the robust traffic state estimation model into a multivariate optimization problem. The alternating direction multiplier method is used to decompose the multivariate optimization problem into multiple sub-variable optimization problems. Multiple sub-variables are iteratively updated until the preset convergence condition is met, and the traffic state matrix and the traffic state observation outlier matrix are output.

[0015] Furthermore, the traffic state observation matrix M includes three types of information: trajectory point location, trajectory acquisition time, and traffic speed.

[0016] Furthermore,

[0017] Step S1, the process of constructing the traffic state observation matrix includes the following sub-steps:

[0018] Given the traffic status observation data of connected vehicles in a given spatiotemporal region (s i , t i x i ), i = 1, ..., N, where s i and t i Traffic state variables x i Spatial and temporal coordinates: N is the total number of connected vehicle trajectory points with traffic status observations;

[0019] Introducing prior information about traffic waves, the grid is discretized along the time direction and the reverse spatial propagation direction of the traffic waves to construct a virtual oblique grid and calculate the traffic state variable x. i Time coordinates and spatial coordinates

[0020]

[0021]

[0022] Where Δs and Δt are the spatial and temporal resolutions used in the traffic grid, respectively, θ is the tilt angle of the direction of reverse traffic wave propagation, θ = arccot(v / 3.6), v is the reverse traffic wave velocity in km / h, 1, ∈ [-10, -20], b is the intercept constant, b = S·tan(θ), S is the spatial length of the traffic state estimation area;

[0023] Step S12: Obtain the representative value of traffic state (taking traffic speed as an example) for each oblique grid cell (l, t) by collecting the traffic state trajectory data observed within the oblique grid cell.

[0024]

[0025] Where, N l，t It is the total number of observation points in the oblique grid cell (l, t);

[0026] Step S13: Traffic state representative values ​​for all oblique grid units calculated in S12 Construct a traffic condition observation matrix M.

[0027] 4. The robust traffic state estimation method for highways based on connected vehicle trajectory data according to claim 1, characterized in that, in step S2, the process of establishing a robust traffic state estimation model based on low-rank and sparse matrix recovery includes the following sub-steps:

[0028] Step S21: Based on the given traffic state observation matrix M, construct the objective function of the low-rank tensor completion model based on rank minimization:

[0029] min rank(L)stP Ω (L)=P Ω (M)

[0030] Where L is the low-rank traffic state matrix for target recovery, Ω is the observation index set of spatiotemporal traffic data, M is the traffic state observation matrix, and the constraint means that the low-rank matrices L and M have the same value at the observation set Ω; rank(L) represents the rank of matrix L; P Ω (L)=P Ω (M) denotes the constraint that low-rank matrices L and M have the same value at the observation set Ω; P Ω (L) represents the value of the low-rank matrix L at the observation set Ω, P Ω (M) represents the value of the observation matrix M at the observation set Ω;

[0031] Step S22: Using the non-convex truncated nuclear norm as the rank function of the matrix, the traffic state estimation problem is described as the following optimization problem by minimizing the rank of the traffic state observation matrix:

[0032] min||L|| r，* stP Ω (L)=P Ω (M)

[0033] Among them, ||L|| r，* It is the truncated nuclear norm of the low-rank matrix L;

[0034] Step S23: Introduce a sparse matrix S to accommodate potential anomalies in traffic state observations. By applying L1 regularization constraints to the sparse matrix S, outlier detection is transformed into a sparse matrix recovery problem, and a robust traffic state estimation model based on low-rank and sparse matrix recovery is constructed.

[0035] min||L|| r，* +λ||S||1s.tP Ω (L+S)=P Ω (M)

[0036] Where ||S||1 is the l1 norm of the sparse matrix S, λ is the weight parameter balancing low rank and sparse regularization, and the constraint indicates that the traffic state observations consist of two parts: low-rank traffic state and sparse state observation anomalies.

[0037] 5. The robust estimation method for highway traffic state based on connected vehicle trajectory data according to claim 1, characterized in that, in step S3, the process of outputting the traffic state matrix and the traffic state observation outlier matrix includes the following steps:

[0038] Step S31: Introduce an auxiliary matrix W to preserve the original information of the traffic state observation matrix M during the iterative update process.

[0039] min||L|| r，* +λ||S||1s.tW=L+S,P Ω (W)=P Ω (M);

[0040] In the formula, P Ω (M) represents the value of the observation matrix M at the observation set Ω;

[0041] Step S32: Construct the augmented Lagrangian function of the robust traffic state estimation model:

[0042]

[0043] Where <·, ·> denote the inner product, and Y denotes the Lagrange multiplier. ρ represents the penalty parameter, ρ > 0; n1 and n2 represent the number of spatial and temporal oblique grids in the state estimation region; the size of matrices L, M, Y, and S is n1 × n2;

[0044] Step S33: Based on the alternating direction multiplier method framework, the multivariate optimization problem of the robust traffic state estimation model is decomposed into iteratively solving the following four univariate sub-optimization problems:

[0045]

[0046]

[0047]

[0048] Y l+1 =Y l +ρ(W l+1 -L l+1 -S l+1 )

[0049] Where l represents the l-th iteration, L l+1 S l+1 W l+1 and Y l+1 These are the (l+1)th iteration results of sub-variables L, S, W, and the Lagrange multiplier Y, respectively. l W l and Y l These are the l-th iteration results for sub-variable S, sub-variable W, and Lagrange multiplier Y:

[0050] Step S34: Using the traffic state observation matrix M, weight parameter λ, and truncation parameter r constructed in step S1 as inputs to the robust traffic state estimation model, initialize the variables as follows:

[0051]

[0052] in, M is a matrix where all elements are 0; Ω- M represents the values ​​of the traffic state observation matrix in the complement of the observation location set (i.e., locations without observations); Ω The mean(M) represents the values ​​of the traffic condition observation matrix within the observation location set. Ω () represents the mean of all values ​​taken by the traffic condition observation matrix at the observation location;

[0053] Step S35: Remove irrelevant terms. Based on the initial tensor, describe the update process of matrices L, S, and W as solving a minimization subproblem. In each iteration, alternately update the four variables until the preset convergence condition is reached.

[0054] S351: Update subvariable L:

[0055]

[0056] in, For weighted singular value thresholding operators;

[0057] S352: Update subvariable S:

[0058]

[0059] in, The dot-wise product operator is represented by sgn(·), and the sign function is represented by sgn(·).

[0060] S353: Update subvariable W:

[0061]

[0062] Among them, P Ω (W l+1 ) = P Ω (M), Ω is the spatiotemporal traffic state observation set;

[0063] S354: Repeat steps S351 to S353 until the convergence condition is met. ε represents the convergence condition value, which is typically taken as 10. -4 ;

[0064] Step S36: Output the converged traffic state matrix L and anomaly matrix.

[0065] Beneficial effects:

[0066] First, the robust estimation method for highway traffic state based on connected vehicle trajectory data of the present invention, based on the low-rank traffic matrix of oblique grid, helps to capture the directional propagation characteristics of traffic waves and the spatial dependence of traffic state. It still has high accuracy and reliable estimation performance under the condition of extremely sparse state observation data, providing more reliable support for refined active traffic management and control applications.

[0067] Second, the robust estimation method for highway traffic state based on connected vehicle trajectory data of the present invention does not require data cleaning and preprocessing. The constructed sparse matrix has the ability to detect and eliminate potential abnormal traffic state observations, thereby improving the robustness of the traffic state estimation model in real-world application scenarios.

[0068] Third, the robust highway traffic state estimation method based on connected vehicle trajectory data of this invention is based on matrix recovery, and its computational complexity is only related to the time and spatial length of the state estimation region, thus exhibiting higher computational efficiency in large-scale road network scenarios. The proposed method can be rapidly deployed on a large scale with low implementation costs. Attached Figure Description

[0069] Figure 1 This is a flowchart of the robust estimation method for highway traffic state based on connected vehicle trajectory data of the present invention;

[0070] Figure 2 A schematic diagram illustrating the construction of a traffic state matrix based on oblique grids;

[0071] Figure 3 The diagram shows the traffic state estimation results under a 5% connected vehicle penetration rate scenario; where (a) is a true value diagram, (b) is a 5% connected vehicle trajectory input diagram, (c) is a traffic state estimation result obtained using the ASM method, (d) is a traffic state estimation result obtained using the STH-RTC method, (e) is a traffic state estimation result obtained using the MC method, and (f) is a traffic state estimation result obtained using the method described in this invention.

[0072] Figure 4 The diagrams show the traffic state estimation results under the scenario of 5% connected vehicle penetration rate and including outliers; where (a) is a true value diagram, (b) is a diagram of the trajectory input of 10% connected vehicles, (c) is a diagram of the traffic state estimation results obtained using the ASM method, (d) is a diagram of the traffic state estimation results obtained using the STH-RTC method, (e) is a diagram of the traffic state estimation results obtained using the method of the present invention without traffic state outliers, and (f) is a diagram of the traffic state estimation results obtained using the method of the present invention with traffic state outliers. Detailed Implementation

[0073] The following embodiments are provided to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.

[0074] The following is an explanation of the terms involved in this invention:

[0075] Connected vehicle trajectory data: Intelligent connected vehicles equipped with on-board units (OBU) transmit vehicle trajectory data (V2I) to the roadside and center in real time during driving, including information such as vehicle position, heading and speed.

[0076] Traffic state estimation: Accurately estimate the complete traffic state (such as traffic speed) in all time and space based on sparse, limited and noisy traffic state observations collected from fixed and mobile detectors.

[0077] See Figure 4 This invention discloses a robust estimation method for highway traffic state based on connected vehicle trajectory data. The robust estimation method for highway traffic state includes the following steps:

[0078] S1: Utilizing traffic wave priors, the estimated spatiotemporal region is discretized into a grid along the time direction and the reverse spatial propagation direction of the traffic wave to construct a virtual oblique grid; acquire connected vehicle trajectory data, and assign each trajectory point to an oblique grid cell according to the temporal and spatial attributes of the connected vehicle trajectory data; by aggregating the trajectory points within the oblique grid cell, calculate the representative value of traffic state within each oblique grid cell, and construct a traffic state observation matrix;

[0079] S2: Minimize the rank of the traffic state observation matrix constructed in step S1, transforming traffic state estimation into a low-rank matrix completion problem; introduce a sparse matrix to accommodate potential outliers in traffic state observations, and transform outlier detection into a sparse matrix recovery problem by applying regularization constraints to the sparse matrix, thus establishing a robust traffic state estimation model based on low-rank and sparse matrix recovery.

[0080] S3: Based on the robust traffic state estimation model constructed in step S2, auxiliary variables are introduced to retain the original state observation information. An augmented Lagrangian objective function is constructed to transform the robust traffic state estimation model into a multivariate optimization problem. The alternating direction multiplier method is used to decompose the multivariate optimization problem into multiple sub-variable optimization problems. Multiple sub-variables are iteratively updated until the preset convergence condition is met, and the traffic state matrix and the traffic state observation outlier matrix are output.

[0081] This invention utilizes trajectory data collected from connected vehicles, including information such as collection time, vehicle location, and vehicle speed. First, based on traffic wave priors, an oblique grid is constructed to transform traffic state observation data into a traffic state observation matrix, capturing traffic flow propagation characteristics and spatial dependencies of traffic states. This transforms the traffic state estimation problem into a low-rank matrix completion task. Second, an anomaly-tolerant module based on sparse matrices is constructed to detect and remove potentially abnormal data from traffic state observations. Next, a low-rank and sparse matrix completion model based on connected vehicle trajectory data is established. Finally, using the Alternating Direction Multiplier Method (ADMM) framework, the multivariate optimization problem is transformed into multiple sub-variable optimization problems, and iterative solutions are used to obtain the estimated complete traffic state matrix and the state observation outlier matrix.

[0082] The specific process of step 1 is as follows:

[0083] Step S11: The traffic state matrix contains three types of information: trajectory point location, trajectory acquisition time, and traffic speed. Given the connected vehicle traffic state observation data (s) for a given spatiotemporal region... i , t i x i ), i = 1, ..., N, where s i and t i Traffic state variables x i The spatial and temporal coordinates of the trajectory data are reconstructed. To improve the accuracy of traffic state estimation and avoid the problem of missing matrix columns, prior information of traffic waves is introduced. The grid is discretized along the temporal direction and the reverse spatial propagation direction of the traffic waves to construct a virtual oblique grid, thus reconstructing the temporal and spatial coordinates of the trajectory data.

[0084]

[0085] Where Δs and Δt are the spatial and temporal resolutions used in the traffic grid, respectively, θ is the tilt angle of the direction of reverse traffic wave propagation, θ = arccot(v / 3.6), where v is the reverse traffic wave velocity in km / h, v∈[-10, -20], and b is the intercept constant, b = S·tan(θ).

[0086] Step S12: Obtain the representative traffic state value for each grid cell (l, t) by collecting the traffic state trajectory data observed within the oblique grid cells:

[0087]

[0088] Where, N l，t It represents the total number of observation points in cell (l, t).

[0089] Step S13: As Figure 2 As shown, the representative value of the calculated speed The traffic condition observation matrix M is constructed by filling the matrix.

[0090] The specific process of step 2 is as follows:

[0091] Step S21: Given a partial traffic state matrix, construct the objective function of a low-rank tensor completion model based on rank minimization as follows:

[0092] min rank(L)stP Ω (L)=P Ω (M)

[0093] Where Ω is the observation index set of spatiotemporal traffic data, M is the traffic state matrix of partial observations, and the constraint means that the low-rank matrices L and M take the same value at the observation set Ω.

[0094] Step S22: Minimizing the rank of the objective function is an NP-hard problem, and a non-convex truncated kernel norm is used as the rank function of the matrix. By minimizing the rank of the observation matrix, the traffic state estimation problem can be described as the following optimization problem:

[0095] min||L|| r，* stP Ω (L)=P Ω (M)

[0096] Among them, ||L|| r，* It is the truncated nuclear norm of the low-rank matrix L.

[0097] Step S23: To mitigate the adverse impact of potential anomalies in traffic state observations on model performance, assuming that the potential outlier data is random and sparsely distributed, a sparse matrix S is introduced to accommodate potential outliers in the traffic state observations. By applying L1 regularization constraints to the sparse matrix, outlier detection is transformed into a sparse matrix recovery problem, and a robust traffic state estimation model based on low-rank and sparse matrix recovery (TW-LSMC) is constructed.

[0098] min||L|| r，* +λ||S||1s.tP Ω (L+S)=P Ω (M)

[0099] Where ||S||1 is the l1 norm of the sparse matrix S, λ is the weight parameter balancing low rank and sparse regularization, and the constraint indicates that the traffic state observations consist of two parts: low-rank traffic state and sparse state observation anomalies.

[0100] The specific process of step 3 is as follows:

[0101] Step S31: Considering the solution efficiency and computational complexity of the model, an auxiliary matrix W is introduced to retain the original information of the traffic state observation matrix M during the iterative update process.

[0102] min||L|| r，* +λ||S||1s.tW=L+S,P Ω (W)=P Ω (M).

[0103] Step S32: To handle equality constraints, construct the augmented Lagrangian function of the TW-LSMC model:

[0104]

[0105] Where <·, ·> represent the inner product. Let ρ denote the Lagrange multiplier, and ρ > 0 denote the penalty parameter.

[0106] Step S33: Based on the ADMM framework, the multivariate optimization problem of the model can be decomposed into iteratively solving the following four univariate sub-optimization problems:

[0107]

[0108]

[0109]

[0110] Y l+1 =Y l +ρ(W l+1 -L l+1 -S l+1 )

[0111] Where l represents the l-th iteration.

[0112] Step S34: Using the traffic state matrix M, weight parameter λ, and truncation parameter r constructed in step S1 as model input, initialize the variables as follows:

[0113]

[0114] in, It is a matrix in which all elements are 0.

[0115] Step S35: Remove irrelevant terms. Based on the initial tensor, describe the update process of matrices L, S, and W as solving the following minimization subproblem. In each iteration, the four variables are updated alternately until the preset convergence condition is reached.

[0116] (1) Update subvariable L:

[0117]

[0118] in, This is a weighted singular value threshold operator.

[0119] (2) Update sub-variable S:

[0120]

[0121] in, The dot-wise product operator is represented by sgn(·), which represents the sign function, i.e.

[0122] (3) Update sub-variable W:

[0123]

[0124] Among them, P Ω (Wl+1 ) = P Ω (M), where Ω is the spatiotemporal traffic state observation set.

[0125] (4) Repeat steps (1) to (3) until the convergence condition is met. Then it will terminate.

[0126] Step S36: Output the converged traffic state matrix L and anomaly matrix S.

[0127] Case Analysis

[0128] This example uses high-precision vehicle trajectory data from the second lane of U.S. Highway 101 in the NGSIM dataset to experimentally verify the proposed method.

[0129] This example simulates real-world traffic state estimation scenarios using two scenarios: sparse data without outliers and sparse data with outliers. Connected vehicle penetration rates of 3%, 5%, 10%, and 15% are set to simulate real-world traffic state observation data collection scenarios. In each scenario, vehicle trajectory data is randomly selected as the observation input, and the experiment is repeated 20 times to test the traffic state estimation performance of the proposed method.

[0130] This experiment employed several mainstream traffic state estimation methods, namely ASM, STH-LRTC, and MC, and compared the proposed TW-LSMC model with existing solutions. RMSE and MAE were used as evaluation metrics to assess the performance of different models under various traffic state scenarios. Table 1 compares the estimation errors of different traffic state estimation methods under different penetration rate scenarios.

[0131] Table 1. Comparison of estimation errors (mean ± standard deviation) of different traffic state estimation methods in different scenarios.

[0132]

[0133] Figure 3 The results show the traffic state estimation results of the proposed method and existing methods in a scenario with a 5% connected vehicle penetration rate. The proposed method recovers the complete traffic wave, including fine-grained features such as accurate wavelength and clear wave boundaries, and exhibits high robustness to sparse data. Figure 3 In the diagram, (a) is a truth diagram, (b) is a diagram of the trajectory input of 5% connected vehicles, (c) is a diagram of the traffic state estimation result obtained by the ASM method, (d) is a diagram of the traffic state estimation result obtained by the STH-RTC method, (e) is a diagram of the traffic state estimation result obtained by the MC method, and (f) is a diagram of the traffic state estimation result obtained by the method described in this invention.

[0134] Figure 4 The results show the traffic state estimation of the proposed method and existing methods in a scenario with a 10% connected vehicle penetration rate and outliers in traffic state observations. Experimental results show that the proposed method accurately estimates the complete structured traffic state using a low-rank matrix, and the sparse matrix successfully detects outliers in traffic state observations, demonstrating the robustness of the proposed traffic state estimation method. Figure 4 In the diagram, (a) is a true value diagram, (b) is a diagram of the trajectory input of 10% connected vehicles, (c) is a diagram of the traffic state estimation result obtained using the ASM method, (d) is a diagram of the traffic state estimation result obtained using the STH-RTC method, (e) is a diagram of the traffic state estimation result obtained using the method of the present invention without traffic state outliers, and (f) is a diagram of the traffic state estimation result obtained using the method of the present invention with traffic state outliers.

[0135] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A robust estimation method of highway traffic state based on trajectory data of connected vehicles, characterized in that, The expressway traffic state robust estimation method comprises the following steps: S1: using traffic wave prior, discretizing the estimated space-time region along the time direction and the reverse traffic wave space propagation direction, constructing a virtual oblique grid; obtaining network-connected vehicle trajectory data, assigning each trajectory point to the oblique grid unit according to the time and space attributes of the network-connected vehicle trajectory data; calculating the traffic state representative value in each oblique grid unit by aggregating the trajectory points in the oblique grid unit, and constructing a traffic state observation matrix; S2: minimizing the rank of the traffic state observation matrix constructed in step S1, converting the traffic state estimation into a low-rank matrix completion problem; introducing a sparse matrix compatible with the potential outliers in the traffic state observation, converting the outlier detection into a sparse matrix recovery problem by regularizing the sparse matrix, and establishing a robust traffic state estimation model based on low-rank and sparse matrix recovery; S3: on the basis of the robust traffic state estimation model constructed in step S2, introducing auxiliary variables to retain the original state observation information, constructing an augmented Lagrangian objective function, converting the robust traffic state estimation model into a multivariable optimization problem, using the alternating direction multiplier method to decompose the multivariable optimization problem into multiple sub-variable optimization problems, and iteratively updating the multiple sub-variables until the preset convergence condition is met, and outputting the traffic state matrix and the traffic state observation outlier matrix; In step S1, the process of constructing the traffic state observation matrix comprises the following sub-steps: Connected vehicle traffic state observation data of a given spatiotemporal region wherein, and are spatial coordinates and temporal coordinates of traffic state variables respectively; is the total number of connected vehicle trajectory points with traffic state observations; The traffic wave prior information is introduced, the grid is discretized along the time direction and the reverse traffic wave space propagation direction, a virtual oblique grid is constructed, and traffic state variables are calculated time coordinates and space coordinates : ； ； wherein, are the spatial resolution and the temporal resolution used in the traffic grid, respectively, is the slope angle of the backward traffic wave propagation direction, , is the backward traffic wave speed in [km / h], , , is the intercept constant, S is the spatial length of the traffic state estimation area. Step S12: Obtain the representative value of the traffic state of each oblique grid cell by aggregating the observed traffic state trajectory data within the oblique grid cell :​ ； wherein is an oblique grid cell the total number of observation points; Step S13: Calculate the traffic state representative value of all diagonal grid units based on the result of S12 , construct the traffic state observation matrix .

2. The robust estimation method of highway traffic state based on connected vehicle trajectory data according to claim 1, characterized in that, The traffic state observation matrix It includes three types of information: trajectory point position, time of trajectory collection, and traffic speed.

3. The robust estimation method of highway traffic state based on connected vehicle trajectory data according to claim 1, characterized in that, In step S2, the process of establishing the robust traffic state estimation model based on low-rank and sparse matrix recovery comprises the following sub-steps: Step S21: constructing a low-rank tensor completion model objective function based on a given traffic state observation matrix , a low-rank tensor completion model objective function based on rank minimization is constructed: ； wherein, is a low-rank traffic state matrix of interest, is a set of observation indices of the spatio-temporal traffic data, is a traffic state observation matrix, the constraint means that the low-rank matrix and takes the same value at the observation set ; denotes the rank of the matrix L; = denotes the low-rank matrix and the constraint that the values at the observation set are equal; denotes the low-rank matrix the values at the observation set , denotes the values of the observation matrix at the observation set ; In step S22, a non-convex truncated nuclear norm is used as the rank function of the matrix, and the traffic state estimation problem is described as the following optimization problem by minimizing the rank of the traffic state observation matrix: ； wherein is the truncated nuclear norm of the low-rank matrix H. Step S23: Introducing sparse matrix With the compatibility of potential anomalies in traffic state observation, by the sparse matrix Regularization constraints, convert the outlier detection into sparse matrix recovery problem, construct a robust traffic state estimation model based on low rank and sparse matrix recovery:​ ； wherein is a sparse matrix of norm, is a weight parameter balancing low-rank and sparsity regularization, and the constraint indicates that the observations of traffic states are composed of both low-rank traffic states and sparse state observation outliers.

4. The robust estimation method of highway traffic state based on connected vehicle trajectory data according to claim 1, characterized in that, In step S3, the process of outputting the traffic state matrix and the traffic state observation outlier matrix comprises the following steps: Step S31: Introducing the auxiliary matrix Preserving the original information of the traffic state observation matrix in the iterative updating process: ； wherein represents an observation matrix at the observation set value; In step S32, the augmented Lagrangian function of the robust traffic state estimation model is constructed: ； wherein, denotes an inner product, denotes a Lagrange multiplier, , denotes a penalty parameter, ; and denote the number of spatial and temporal skew grid points within the state estimation region, respectively; In step S33, based on the alternating direction multiplier method framework, the multivariable optimization problem of the robust traffic state estimation model is decomposed into four single-variable sub-optimization problems solved iteratively: ； ； ； ； wherein denotes the l+1th iteration, , , and are the l+1th iteration results of the sub-variables , the sub-variables , the sub-variables and the Lagrange multiplier , , and are the lth iteration results of the sub-variables , the sub-variables and the Lagrange multiplier ; Step S34: Constructing the traffic state observation matrix with step S1 , weight parameter , truncation parameter As an input of the robust traffic state estimation model, each variable is initialized as follows: ； wherein, is a matrix of zeros for all elements; denotes the values of the traffic state observation matrix at the complement of the set of observation locations; denotes the values of the traffic state observation matrix at the set of observation locations; denotes the mean of all values of the traffic state observation matrix at the set of observation locations; Step S35: Removing irrelevant terms, according to the initial tensor, the matrix The update process of is described as solving a minimization subproblem, in which four variables are updated alternately in each iteration until a preset convergence condition is reached: S351: update sub-variables : ； wherein is a weighted singular value thresholding operator; S352: update sub-variables : ； wherein , denotes the pointwise product operator, denotes the sign function, ; S353: update sub-variables : ； wherein , is a spatiotemporal traffic state observation set; S354: repeat steps S351 to S353 until a convergence condition is satisfied ; denotes a convergence condition value; Step S36: output the converged traffic state matrix and the anomaly matrix .

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