A method for estimating traffic state of urban road section considering bus moving bottleneck effect

Abstract

The application discloses a kind of urban road section traffic state estimation methods considering bus moving bottleneck effect, bus speed influence term is extended to quadratic function form from linear relationship, and physical boundary condition constraint is introduced, and road section traffic capacity constraint model considering bus moving bottleneck effect is established;Based on bus operation trajectory, internal boundary condition of road section is constructed, and combined with subsection recursion mechanism, bus moving bottleneck influence can continuously spread in space-time domain;At the same time, the Sigmoid function is used to smooth the approximation of the step reading process in the motion wave model, and the differentiable traffic state solving process is constructed, and the upstream arrival, downstream departure and bus internal boundary constraint are unified into the calculation graph framework, so as to realize the real-time dynamic estimation of road section density, queue length and vehicle delay and other traffic states under the condition of bus mixed traffic flow.

Description

Technical Field

[0001] This invention belongs to the field of intelligent transportation technology, specifically relating to a method for estimating traffic conditions on urban road sections that considers the bottleneck effect of public transportation. Background Technology

[0002] With increasing pressure on urban traffic, accurately grasping the traffic conditions of urban road segments has become a crucial foundation for congestion identification, queue length assessment, vehicle delay evaluation, and signal control optimization. Current urban traffic condition perception primarily relies on fixed detectors, checkpoint videos, and geomagnetic coils. While these devices can acquire cross-sectional observation information such as vehicle arrivals, departures, flow rates, and speeds, their deployment and detection range limit their ability to fully reflect the continuous movement of vehicles within a road segment. Particularly in urban roads with dense bus routes and high departure frequencies, buses, due to their large size, weak acceleration and deceleration capabilities, and low operating speeds, and the processes of entering, stopping, and merging, exert constraints on following vehicles, causing them to follow, change lanes, slow down, and queue, thus altering the local capacity and traffic flow propagation of the road segment. Therefore, relying solely on upstream and downstream cross-sectional data and treating road segment traffic flow as typical passenger car traffic flow is insufficient to accurately depict the true traffic operation under the influence of public transportation.

[0003] Existing technologies mainly include traffic state estimation methods based on motion wave models or simplified Newell models, capacity calculation methods based on the theory of moving bottlenecks in public transport, and parameter learning methods for traffic flow models based on computational graphs. Among them, motion wave models and simplified Newell models can infer the traffic state within a road segment using upstream arrival curves and downstream departure curves, and have advantages such as clear physical meaning and high computational efficiency. However, they are usually geared towards homogeneous traffic flow and do not adequately consider the local capacity changes caused by low-speed bus operation, stop stops, and departures. Existing studies on moving bottlenecks in public transport usually describe the constraint effect of low-speed vehicles on the traffic flow behind them through relative reference frames, bottleneck graphs, or capacity reduction models. However, most methods are still at the level of public transport impact analysis or local capacity calculation and have not been fully integrated with the real-time traffic state estimation process of urban road segments.

[0004] Furthermore, existing bus mobility bottleneck capacity models mostly use linear approximations to describe the relationship between bus speed and capacity, making it difficult to reflect the nonlinear changes between the two under complex urban traffic conditions. Additionally, some models lack physical boundary constraints for typical bus states such as stationary and free-flowing operations, affecting model accuracy and interpretability. Existing traffic state estimation methods typically do not transform bus trajectories into computationally applicable internal boundary conditions, making it difficult to describe the continuous propagation process of bus mobility bottleneck impacts in the spatiotemporal domain. Meanwhile, traditional motion wave models involve step judgment, propagation delay, and discontinuous fusion calculations, resulting in insufficient differentiability and limiting their ability to be fused and optimized with real-time detection data and bus trajectory data. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a method for estimating traffic conditions on urban road sections that considers the bottleneck effect of public transport. The aim is to transform the bus trajectory into the internal movement boundary in the traffic flow model, and combine the bottleneck constraint of public transport with a dynamic recursive estimation method to solve the problem of inaccurate perception of traffic conditions on urban road sections under the influence of public transport, thereby improving the accuracy and real-time performance of traffic condition estimation.

[0006] The first aspect of this invention provides a method for estimating traffic conditions on urban road sections considering the bottleneck effect of public transport movement, the method comprising: S1: Obtain traffic operation data for the urban road segment to be estimated. The traffic operation data includes: the upstream vehicle arrival sequence, the downstream vehicle departure sequence, the bus trajectory data, and the road segment geometric parameters.

[0007] S2: Establish a basic traffic state propagation model for urban road segments based on the motion wave model. Construct a basic cumulative vehicle count matrix based on the upstream vehicle arrival sequence and the downstream vehicle departure sequence to describe the traffic flow propagation state without considering the impact of public transport bottlenecks.

[0008] S3: Based on the bus operation trajectory data, determine the mobile bottleneck constraints formed during the operation of the bus, and establish a local capacity constraint model that considers the impact of bus operation status, so as to obtain the traffic flow constraint conditions corresponding to different bus operation statuses.

[0009] S4: Divide the bus running trajectory into multiple trajectory segments according to a preset time interval, and generate the corresponding internal boundary cumulative vehicle count based on the bus position, running speed and the local traffic capacity constraint model corresponding to each trajectory segment, and use the internal boundary cumulative vehicle count as the internal movement boundary condition in the motion wave model.

[0010] S5: Determine the bus mobility bottleneck impact area based on the internal mobility boundary conditions, and calculate the candidate cumulative vehicle number matrix corresponding to the bus mobility bottleneck impact area.

[0011] S6: According to the time sequence of the bus operation trajectory segments, the candidate cumulative vehicle count matrix corresponding to each trajectory segment is recursively merged into the basic cumulative vehicle count matrix to obtain the target cumulative vehicle count matrix considering the impact of bus mobility bottlenecks.

[0012] S7: Calculate the urban road segment traffic state parameters based on the target cumulative vehicle count matrix. The traffic state parameters include road segment traffic density, queue length, and vehicle delay.

[0013] According to an embodiment of the present invention, in step S3, the local capacity constraint model considering the bus mobility bottleneck effect includes a bus operating speed influence term, which is expressed in the form of a nonlinear function to describe the nonlinear relationship between changes in bus operating speed and the degree of mobility bottleneck constraint.

[0014] According to an embodiment of the present invention, the local accessibility calculation model satisfies preset physical boundary constraints, including: When buses are stationary, the local capacity is reduced to the capacity after buses have occupied road resources. When buses are moving at free-flow speed, the bottleneck effect disappears, and the local capacity recovers to the capacity level corresponding to the condition without the influence of a bus bottleneck.

[0015] According to one embodiment of the present invention, the trajectory segment further includes spatiotemporal coordinate information corresponding to the spatial location of the bus, and the cumulative number of vehicles at the internal boundary under the corresponding time and spatial location is calculated based on the trajectory segment.

[0016] According to an embodiment of the present invention, in step S5, the area affected by the bus bottleneck is divided into the following regions based on the spatial relationship between the target calculated location and the bus bottleneck trajectory: Forward impact area is used to describe the traffic impact generated by the bus movement bottleneck along the free-flow propagation direction; The backward impact area is used to describe the traffic impact caused by the upstream propagation of public transport bottlenecks through congestion waves. The central area of ​​impact is used to describe the traffic recovery process after the bottleneck effect of public transportation ends.

[0017] According to one embodiment of the present invention, the composition of the influence area is determined according to different bus stop types. For example, for straight-line bus stops, the internal movement boundary condition is jointly determined by the cumulative number of candidate vehicles corresponding to the forward and backward influence areas. For bay-type bus stops, in addition to the forward and backward impact areas, the candidate cumulative vehicle count corresponding to the central impact area is further introduced to describe the dissipation process of the impact after the bus leaves the main lane.

[0018] According to one embodiment of the present invention, the basic traffic state propagation model adopts a traffic flow state expression method based on the cumulative number of vehicles. The cumulative number of vehicles at any spatiotemporal location is jointly determined by the propagation results of the upstream boundary, the propagation results of the downstream boundary, and the propagation results of the internal movement boundary of the public transport.

[0019] According to an embodiment of the present invention, the recursive update process in step S6 includes: Bus trajectory segments were selected sequentially according to the bus operating time. The cumulative vehicle count matrix of the candidate internal moving boundary corresponding to the current bus trajectory segment is merged with the cumulative vehicle count matrix of the current traffic state; Update the current cumulative vehicle count matrix using the fusion results; Repeat the above process until all bus trajectory segments are recursively calculated to obtain the target cumulative vehicle count matrix.

[0020] According to one embodiment of the present invention, in the traffic state estimation process, the discontinuous calculation process in the motion wave model is made continuous, including: The cumulative number of candidate vehicles at the boundary is calculated using the continuous weighting function. The cumulative number of candidate vehicles at the boundary includes the cumulative number of candidate vehicles at the upstream boundary, the cumulative number of candidate vehicles at the downstream boundary, and the cumulative number of candidate vehicles at the internal moving boundary.

[0021] According to one embodiment of the present invention, the traffic state estimation process after continuous processing is constructed in a computational graph framework, which includes traffic flow propagation nodes, public transport mobility bottleneck constraint nodes, and boundary condition propagation nodes, and updates the traffic flow model parameters and public transport mobility bottleneck parameters through backpropagation.

[0022] According to one embodiment of the present invention, the learnable parameters include: free flow velocity, congestion wave propagation velocity, congestion density, differentiable smoothing parameters, and bus mobility bottleneck capacity model parameters.

[0023] According to one embodiment of the present invention, the traffic state estimation method includes an offline training phase and an online estimation phase: During the offline training phase, based on historical traffic detection data and bus operation trajectory data, the traffic flow model parameters and bus movement bottleneck parameters are optimized under the condition of satisfying the physical constraints of traffic flow. During the online estimation phase, the target cumulative vehicle count matrix is ​​calculated using real-time traffic detection data and bus operation trajectory data under calibrated parameter conditions, and traffic state parameters are output in real time.

[0024] A second aspect of the present invention provides a traffic state estimation system for urban road sections that considers the bottleneck effect of public transport movement, the system comprising: The data acquisition module acquires upstream vehicle arrival sequences, downstream vehicle departure sequences, bus trajectory data, and road segment geometric parameters for urban road segments. The basic state propagation module constructs a basic cumulative vehicle count matrix based on the kinematic wave model, using the upstream and downstream vehicle arrival sequences. The bus mobility bottleneck constraint calculation module determines the local capacity constraints of bus mobility bottlenecks based on bus trajectories. The internal boundary construction module generates the internal boundary cumulative vehicle count and forms the internal mobility boundary conditions based on the location, speed, and local capacity constraints of the bus trajectory segments. The influence area determination module divides the influence area into forward influence area, backward influence area, and central influence area based on the spatial relationship between the bus mobility bottleneck trajectory and the target calculation location.

[0025] The recursive calculation module is used to recursively calculate the cumulative vehicle count matrix based on the motion wave model and the internal movement boundary conditions of the bus. The status output module is used to output the road segment density, queue length, and vehicle delay based on the cumulative vehicle count matrix.

[0026] According to one embodiment of the present invention, the recursive calculation module includes: a differentiable calculation unit, used to convert the propagation delay reading process in the motion wave model into a continuously differentiable calculation process.

[0027] The computational graph training unit is used to update traffic flow parameters and bus mobility bottleneck parameters based on the loss function and backpropagation algorithm.

[0028] The technical effects achieved by this invention are as follows: First, by incorporating the bus vehicle trajectory into the traffic state estimation process and describing the mobile bottleneck effect caused by the bus's low-speed operation, stop at stations, and departure as internal constraints of the road segment, this invention overcomes the problem of traditional methods relying solely on upstream and downstream cross-sectional data and ignoring bus disturbances within the road segment. It can more accurately estimate state parameters such as road segment density, queue length, and vehicle delay under mixed bus traffic flow conditions.

[0029] Secondly, by dividing the bus route into multiple route segments and constructing corresponding internal movement boundaries, combined with the influence area division and segmented recursive mechanism, the local capacity changes caused by bus movement bottlenecks can be continuously propagated in time and space, thereby providing a more precise description of the formation, propagation and recovery process of traffic flow during bus operation.

[0030] Furthermore, a nonlinear capacity constraint model considering the impact of bus operating speed is established, and physical boundary conditions such as bus stationary state and free-flow operating state are introduced, so that the model can reflect the dynamic relationship between bus operating state and road segment capacity, avoiding the problem of large calculation deviations in traditional linear reduction models under complex traffic environments, and improving the applicability and physical consistency of the model.

[0031] Finally, differentiable computation methods are used to transform the discontinuous computation process in the motion wave model into an optimizable computation process, and a computational framework integrating traffic detection data and bus trajectory data is constructed to realize the training and updating of model parameters and online state estimation. While maintaining the physical interpretability of the traffic flow model, the model's adaptability to real-time traffic changes is improved. Attached Figure Description

[0032] Figure 1 This is a flowchart of a method for estimating traffic conditions on urban road sections that considers the bottleneck effect of public transport, as disclosed in an embodiment of the present invention. Figure 2 This is a schematic diagram of the envelope surface composed of capacity lines in the urban road segment traffic state estimation method considering the public transport mobility bottleneck effect disclosed in an embodiment of the present invention. Figure 3 This is the basic triangle diagram in the urban road segment traffic state estimation method considering the public transport mobility bottleneck effect disclosed in the embodiments of the present invention; Figure 4 This is a surface plot of the cumulative number of vehicles passing through in an urban road segment traffic state estimation method that considers the bottleneck effect of public transport, as disclosed in an embodiment of the present invention. Figure 5 This is a flowchart of a differentiable calculation based on a motion wave model in an urban road segment traffic state estimation method that considers the bottleneck effect of public transport, as disclosed in an embodiment of the present invention. Figure 6 This is a schematic diagram of the division of the bus mobility bottleneck influence area in the urban road segment traffic state estimation method considering the bus mobility bottleneck effect disclosed in the embodiment of the present invention. Figure 7(a) is a spatiotemporal distribution map of road segment density estimation in a single bus operation scenario with a straight-line bus stop, in the urban road segment traffic state estimation method considering the bottleneck effect of bus movement disclosed in an embodiment of the present invention. Figure 7(b) is a spatiotemporal distribution map of road segment density estimation in a single bus operation scenario at a bay-type bus stop, in the urban road segment traffic state estimation method considering the bottleneck effect of bus movement disclosed in an embodiment of the present invention. Figure 7(c) is a spatiotemporal distribution map of road segment density estimation in a multi-bus operation scenario with bay-type bus stops in an urban road segment traffic state estimation method considering the bus mobility bottleneck effect disclosed in an embodiment of the present invention. Figure 8 This is a block diagram of an urban road segment traffic state estimation system that considers the bottleneck effect of public transport mobility, as disclosed in an embodiment of the present invention. Detailed Implementation

[0033] Unless otherwise expressly stated, throughout the specification and claims, the term "comprising" or its variations such as "including" or "comprises" shall be understood to include the stated elements or components without excluding other elements or other components.

[0034] The technical solution of the present invention is illustrated below through specific embodiments. It should be understood that the one or more steps mentioned in the present invention do not preclude the existence of other methods and steps before or after the combined steps, or that other methods and steps may be inserted between these explicitly mentioned steps. It should also be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Unless otherwise stated, the numbering of each method step is only for the purpose of identifying each method step, and not for limiting the order of each method or limiting the scope of the present invention. Changes or adjustments to their relative relationships, without substantial changes to the technical content, can also be considered as within the scope of the present invention.

[0035] The raw materials and instruments used in the examples are not subject to any specific restrictions on their source; they can be purchased from the market or prepared according to conventional methods known to those skilled in the art.

[0036] The first aspect of this invention discloses a method for estimating traffic conditions on urban road sections that considers the bottleneck effect of public transport mobility, such as... Figure 1 As shown, it includes: S1: Obtain traffic operation data for the urban road segment to be estimated. The traffic operation data includes: the upstream vehicle arrival sequence, the downstream vehicle departure sequence, the bus trajectory data, and the road segment geometric parameters.

[0037] S2: Establish a basic traffic state propagation model for urban road segments based on the motion wave model. Construct a basic cumulative vehicle count matrix based on the upstream vehicle arrival sequence and the downstream vehicle departure sequence to describe the traffic flow propagation state without considering the impact of public transport bottlenecks.

[0038] S3: Based on the bus operation trajectory data, determine the mobile bottleneck constraints formed during the operation of the bus, and establish a local capacity constraint model that considers the impact of bus operation status, so as to obtain the traffic flow constraint conditions corresponding to different bus operation statuses.

[0039] S4: Divide the bus running trajectory into multiple trajectory segments according to a preset time interval, and generate the corresponding internal boundary cumulative vehicle count based on the bus position, running speed and the local traffic capacity constraint model corresponding to each trajectory segment, and use the internal boundary cumulative vehicle count as the internal movement boundary condition in the motion wave model.

[0040] S5: Determine the bus mobility bottleneck impact area based on the internal mobility boundary conditions, and calculate the candidate cumulative vehicle number matrix corresponding to the bus mobility bottleneck impact area.

[0041] S6: According to the time sequence of the bus operation trajectory segments, the candidate cumulative vehicle count matrix corresponding to each trajectory segment is recursively merged into the basic cumulative vehicle count matrix to obtain the target cumulative vehicle count matrix considering the impact of bus mobility bottlenecks.

[0042] S7: Calculate the urban road segment traffic state parameters based on the target cumulative vehicle count matrix. The traffic state parameters include road segment traffic density, queue length, and vehicle delay.

[0043] Specifically, step S2 is implemented through the following steps: S21: Establish a basic triangular diagram representation. Use a basic triangular diagram to describe the relationship between traffic flow and density in urban road segments. Assume the free-flow velocity is... The backward propagation speed of the congestion wave is The blockage density is The critical density is Then the flow-density relationship under free-flow and congested conditions can be expressed as: (1) The critical density can be obtained from the intersection of the free-flow branch and the congested branch: (2) in, For free flow velocity, The absolute value of the backward propagation speed of the congestion wave. For blocking density, This represents the critical density. The basic diagram of the triangle is shown below. Figure 2 As shown, it is used to determine the direction of free flow propagation and the direction of congestion wave reverse propagation in the motion wave model.

[0044] S22: Establish the basic cumulative vehicle count representation for the Newell simplified motion wave model. (Based on the cumulative vehicle count...) Assuming the road segment length is a variable representing the traffic state of the road segment. Spatial location Starting from the upstream boundary, the cumulative arrival curve upstream is: The downstream cumulative departure curve is Then any point in spacetime The cumulative number of vehicles at a given location is determined by both the upstream and downstream boundary conditions.

[0045] The cumulative number of candidate vehicles determined by the upstream arrival at the boundary is: (3) The candidate cumulative number of vehicles determined by the downstream departure boundary is: (4) Therefore, the basic cumulative number of vehicles without considering the influence of the internal boundaries of the public transport system can be expressed as: (5) in, This indicates that the vehicle propagates from the upstream boundary to the location at a free-flow velocity. The time required This indicates that the congestion wave propagates backward from the downstream boundary to the location. The required time. The cumulative number of vehicles can be determined by spatial location. and time For a three-dimensional surface representation of the independent variable, such as Figure 3 As shown.

[0046] S23: Construct a differentiable propagation delay readout function. In the original Newell model, and The cumulative curve needs to be read using a time index based on the propagation delay. This process involves step detection and discrete indexing, which is inconvenient for gradient calculation and backpropagation. Therefore, this invention uses the Sigmoid function to perform a continuously differentiable approximation of the step reading process, with the following form: (6) in, For input variables, This is a smoothing parameter used to control the width of the 0-1 step transition interval; The smaller the value, the closer the sigmoid function is to the original step function. The larger the value, the smoother the transition process.

[0047] For any spatial location and the current calculation time Construct differentiable weight functions for the upstream and downstream boundaries respectively: (7) (8) in, For discrete-time indexing, This indicates the effect of the upstream arriving sequence on the spatiotemporal point under the influence of free-flow propagation delay. Contribution weight, This indicates the effect of the downstream departure sequence on the spatiotemporal points under the influence of the back propagation delay of the congestion wave. The contribution weight. When When the weight is close to 1; when When the weight is close to 0, a smooth approximation of the step reading process is achieved.

[0048] S24: Calculate the cumulative number of upstream and downstream candidate vehicles using a differentiable weighting function. Let... and Let represent the number of upstream arriving vehicles and the number of downstream departing vehicles within a unit time interval, respectively. Then, the differentiable cumulative number of upstream candidate vehicles is: (9) The number of downstream candidate vehicles after minimization is: (10) Therefore, the basic cumulative number of vehicles can be written as: (11) In the computational graph implementation, the upstream arrival sequence and downstream departure sequence obtained in step S1 are transformed into a sliding time window matrix, the spatial sampling points are expanded into spatial position vectors, and the differentiable weight matrix and candidate cumulative vehicle count matrix are computed in parallel through upstream and downstream branches. Subsequently, the upstream and downstream candidate cumulative vehicle count matrices are fused element-wise to obtain the basic cumulative vehicle count matrix: (12) The overall differentiable computation process is as follows: As shown. Through the above processing, the original non-differentiable propagation delay reading process based on index query is transformed into a continuous weighted summation process, which reduces the free-flow velocity. Congestion wave speed Blocking density and smoothing parameters All of these can be used as parameters to be calibrated or learnable parameters to participate in training, providing a foundation for subsequent integration of the internal boundaries of public transportation mobility bottlenecks and updating model parameters.

[0049] The specific process for establishing the local capacity constraint model that considers the impact of bus operation status in step S3 is as follows: S31: Constructing a two-parameter model for the capacity of a moving bottleneck due to public transportation. Considering that changes in bus speed in urban road sections constrain the passage of other vehicles, and that the relationship between bus speed and bottleneck capacity is not a simple linear one, this invention extends the influence of bus speed on the relative capacity of the moving bottleneck from a linear form to a quadratic function form. Let the maximum capacity of the road section without bus interference be... The bus operating speed is The free-flow speed of the road section is The number of lanes on the road is Then, the two-parameter capacity model considering the bottleneck effect of public transport mobility is: (13) in, Relative throughput capacity under the constraints of public transport mobility bottlenecks; This represents the maximum traffic capacity of the road segment when there is no impact from public transportation. For bus operating speed; The free-flow velocity of the road segment; This refers to the number of lanes on the road. and Here are the parameters to be calibrated. In the formula, This indicates the reduction in the effective traffic capacity of a road segment caused by a bus occupying or restricting a lane.

[0050] S32: Introducing physical boundary conditions to constrain model parameters. To avoid unreasonable values ​​for model parameters due to complete reliance on data fitting, this invention further introduces typical physical boundary conditions during bus operation.

[0051] When the bus is stationary, that is Buses occupy one lane, reducing the available traffic capacity of the road segment to: (14) When the bus is running at free-flow speed, that is When there is no longer a significant relative speed difference between buses and other vehicles, the traffic bottleneck effect disappears, and at this point: (15) Boundary conditions We can obtain: (16) Substituting this into the two-parameter capacity model, we obtain the single-parameter bus mobility bottleneck capacity model: (17) This model retains the nonlinear expressive power of quadratic functions while reducing the number of parameters to be calibrated, and ensures that the model has a clear physical meaning under two boundary states: the bus is stationary and the bus is moving at free-flow speed. Its geometric meaning is as follows: Figure 5 As shown, the capacity lines corresponding to different bus speeds form an envelope on the flow-density plane.

[0052] S33: Perform model parameter calibration and model selection. Using observational data on the impact of public transport bottlenecks extracted from the microscopic simulation scenario, calibrate the parameters in the single-parameter model. Calibration is performed. To determine the capacity constraint model suitable for subsequent traffic state estimation, the original linear model, the two-parameter quadratic model, and the single-parameter quadratic model can be used as candidate models. The root mean square error, coefficient of determination, and adjusted coefficient of determination are used to comprehensively evaluate the fitting effect, number of parameters, and physical boundary constraints of the candidate models. Based on the evaluation results, the single-parameter quadratic model with better fitting effect, simpler parameter form, and clear physical boundary meaning is selected as the local capacity constraint model for the public transport mobility bottleneck in subsequent traffic state estimation.

[0053] The specific implementation process of step S4 is as follows: S41: Construct bus trajectory segments. Discretize the continuous running trajectory of the bus within the study section according to a set time interval. The trajectory segment. For the first... Let there be a trajectory segment, with its start and end times recorded as follows: and The starting and ending positions are respectively and The average velocity of the segment is The local capacity constraint obtained from step S2 is: Then the first A single bus trajectory segment can be represented as: (18) In introducing the first Before each bus trajectory segment, let the current cumulative vehicle count matrix be... Then the cumulative number of vehicles at the starting point of this segment is: (19) in, Indicates the first The cumulative number of vehicles at the starting point of each bus trajectory segment's internal boundary. When the starting point of the bus trajectory segment does not completely coincide with the discrete spatiotemporal grid node, interpolation between adjacent grid points can be used to obtain the cumulative number of vehicles. This ensures a continuous recursive relationship between adjacent bus trajectory segments.

[0054] S42: Establish candidate cumulative vehicle counts for the internal boundary of the public transport mobility bottleneck. Based on the Lax-Hopf variational principle, the bus trajectory is considered as the internal mobility boundary in the spatiotemporal domain of the road segment. For the... The internal boundary conditions of a bus trajectory segment can be expressed as follows: (20) For any point in time and space within the road segment affected by this bus movement bottleneck The cumulative number of candidate vehicles generated by the internal boundary conditions is: (twenty one) in, For the first Local traffic capacity constraints corresponding to each segment; This indicates that the traffic wave propagates from the bus trajectory to the target spatiotemporal point. Time required; This represents the wave velocity term in the corresponding propagation direction; The critical density is defined by this formula. This formula describes the local constraint effect on the cumulative vehicle count surface of a road segment when the public transport bottleneck is used as an internal boundary.

[0055] S43: Delineate the impact domain of the bus bottleneck and calculate its propagation time. Based on the relative position between the target spatiotemporal point and the bus bottleneck trajectory, the impact area of ​​the bus bottleneck is divided into a forward domain, a backward domain, and a central domain. The forward domain is located downstream of the bus bottleneck trajectory and describes the process of the bottleneck's impact propagating downstream along the free flow direction. The backward domain is located upstream of the bus bottleneck trajectory and describes the process of the bottleneck propagating upstream through congestion waves and inducing queuing. The central domain is located after the bus bottleneck activity ends, defined by a characteristic line emanating from the trajectory's endpoint, and describes the process of traffic recovery after the bottleneck's impact dissipates. The bus bottleneck impact area is divided as follows: Figure 6 As shown.

[0056] For the For each bus trajectory segment, the bus location is linearly extrapolated within a local time range to obtain the location for propagation time calculation: (twenty two) To determine whether the target point is upstream or downstream of the bus trajectory, the influence domain is further defined to determine its location: (twenty three) set up For spatial discretization vectors, For the first The local time discretization vector corresponding to each segment To prevent extremely small positive numbers with a denominator of zero, the forward propagation time matrix and the backward propagation time matrix are as follows: (twenty four) (25) in, This indicates the time required for the impact of the public transport bottleneck to propagate downstream in the free flow direction. This indicates the time required for the impact of the public transport bottleneck to propagate upstream in the direction of the congestion wave. For free flow velocity, This represents the absolute value of the backward propagation speed of the congestion wave.

[0057] Based on the aforementioned propagation time matrix, candidate cumulative vehicle count matrices for the inner boundaries of the forward and backward domains can be constructed respectively: (26) S44: Determine the candidate matrix of the internal boundary based on the bus stop type. For straight-line stops and general driving sections, where buses are located in the main lane or continuously affect the main lane's traffic capacity, the candidate matrix of the internal boundary is jointly determined by the candidate solutions from the forward domain and the backward domain: (27) For bay-type bus stops, once a bus enters the bay, it can be considered to have temporarily left the main lane, and its stationary parking process is no longer considered a continuous moving bottleneck constraint on the main lane. In this case, based on the candidate solutions in the forward and backward domains, a central domain candidate solution is further introduced. This is used to describe the dissipation process of the impact after the bottleneck effect ends. The cumulative number of candidate vehicles in the central domain can be represented as: (28) When considering the central region, the first The candidate matrix of internal boundaries for each bus trajectory segment can be expanded as follows: (29) in, Indicates the first The final internal boundary candidate cumulative vehicle count matrix is ​​formed by the bus trajectory segments. Therefore, straight-line bus stops and bay-type bus stops can be distinguished by different internal boundary construction methods.

[0058] S45: Connect adjacent bus trajectory segments using a segmented recursive mechanism. First, let the basic cumulative vehicle count matrix, without considering the influence of internal bus boundaries, be: (30) Then, following the time sequence of the bus trajectory segments, the candidate solutions for the internal boundaries of each segment are embedded one by one into the current cumulative vehicle count matrix, and recursively updated: (31) When all After recursively calculating each bus trajectory segment, we obtain the predicted cumulative vehicle count matrix considering the bottleneck effect of bus movement: (32) in, This is the basic cumulative vehicle count matrix obtained by considering only the upstream and downstream boundary conditions; To be included in the The cumulative vehicle count matrix after constraining each bus trajectory segment; For the first The internal boundary candidate solution matrix corresponding to each bus trajectory segment; This is the final prediction result. The above segmented recursive mechanism ensures that each bus trajectory segment acts on the cumulative vehicle count matrix that already includes the influence of preceding buses, thereby achieving the continuous propagation of the impact of bus mobility bottlenecks in the spatiotemporal domain.

[0059] In step S5, based on the spatial relationship between the target calculated location and the bus moving bottleneck trajectory, the bus moving bottleneck influence area is divided into: The forward impact area describes the traffic impact generated by the bus bottleneck along the free-flow propagation direction; the backward impact area describes the traffic impact formed by the bus bottleneck propagating upstream through congestion waves; and the central impact area describes the traffic recovery process after the bus bottleneck ends.

[0060] Specifically, S51: Construct the forward propagation layer. This forward propagation layer is used to organize the upstream and downstream boundary conditions, the internal boundary conditions of the bus trajectory, and the segmented recursive process into a differentiable computational graph. Based on step S2, the cumulative vehicle count matrix at the upstream and downstream boundaries is calculated. Perform differentiability calculations; based on step S4, calculate the candidate solution matrix of the internal boundary of each bus trajectory segment. Perform matrix calculations; and based on the segmented recursive mechanism described in step S4 (S45), update the cumulative vehicle count matrix according to the time sequence of the bus trajectory segments to obtain the final predicted cumulative vehicle count matrix. .

[0061] S52: Construct the supervised loss layer. This involves converting the cumulative vehicle count matrix obtained from the model predictions... At the detection section location The predicted traffic flow is extracted, and the cumulative vehicle count error and traffic flow error are combined into the loss function. The location of the detection section is then determined. The predicted flow rate at the location is calculated as follows: (33) The model's total loss function is a weighted combination of cumulative vehicle loss and traffic loss: (34) The cumulative loss in the number of vehicles is as follows: (35) The traffic loss is: (36) The traffic loss is: (37) in, For detecting cross-section Predicted flow at the location, For time step, and These represent the cumulative number of vehicles observed and the observed traffic flow at the detection section, respectively. and For loss weighting coefficients, To detect the set of cross-sections, This represents the total number of time steps.

[0062] S53: The gradients of the learnable parameters of the model are calculated through backpropagation, and the parameters are updated using the Adam optimizer. The learnable parameters include the free-flow velocity. Blocking density Congestion wave speed Smoothing parameters Bus mobility bottleneck capacity model parameters Etc. Let the first... The model parameters at the next iteration are: The gradient of the loss function with respect to the parameters is The Adam optimizer update process is as follows: (38) in, For the first Model parameters after the next iteration For learning rate, and These are the first-order moment estimate and the second-order moment estimate of the gradient, respectively. and These are the first-order moment estimates and second-order moment estimates after bias correction, respectively. and The attenuation coefficient is... To prevent division by zero of small positive numbers, the above-described forward propagation, supervised loss calculation, and parameter back-update process enables joint training of traffic flow basic graph parameters, differentiable smoothing parameters, and public transport mobility bottleneck capacity parameters.

[0063] The specific process of the real-time application method that combines offline training with online estimation is as follows: S61: Offline Training Phase. Historical traffic detection data and bus trajectory data are preprocessed into the input format of the computational graph model and discretized at uniform time intervals. A cumulative vehicle entry curve is constructed based on upstream detection data, and a cumulative vehicle departure curve is constructed based on downstream detection data. Simultaneously, bus trajectory data is organized into a sequence of trajectory segments containing location, speed, and operating status. This data is input into the computational graph-based road segment traffic state estimation model. The cumulative vehicle count matrix for the road segment is solved through forward propagation, and the model output is compared with the observation data from fixed detection sections within the road segment to calculate the loss. Subsequently, backpropagation and gradient descent algorithms are used to update the model parameters. After multiple iterations, basic traffic flow graph parameters, bus mobility bottleneck capacity parameters, and differentiable computational parameters suitable for the study road segment are obtained.

[0064] S62: Online Estimation Phase. In online applications, the model no longer undergoes a complete retraining of all parameters; instead, it utilizes the model parameters obtained during the offline training phase. At each estimation time, real-time traffic detection data and bus trajectory data within the current time window are read and organized into upstream / downstream boundary inputs and bus internal boundary inputs. Under given model parameters, the cumulative vehicle count matrix for the current road segment is quickly calculated via forward propagation of the computational graph, enabling dynamic updates to the traffic state within the road segment.

[0065] S63: Online extraction of traffic state indicators. Based on the cumulative vehicle count matrix obtained in step S62, road segment density, flow rate, and speed are calculated using finite difference calculus. Furthermore, queuing areas are identified, and queue lengths and vehicle delays are calculated. The formulas for calculating traffic state indicators are as follows: (39) After obtaining the density and velocity fields, queuing regions are identified by combining velocity and density thresholds, and the upstream position of the queuing region is taken as the tail position. Let the downstream stop line position be... The last position of the line is The queue length is: (40) Vehicle delays are calculated based on the correspondence between vehicle numbers in the cumulative vehicle count curve. For the... Let the time when the vehicle leaves the downstream boundary of the study section be . The time of arrival at the upstream boundary of the research section is The time required to pass through the research section under free-flow conditions. As a baseline, the vehicle delay is: (41) in, For spacetime points Traffic density at the location For traffic, For speed, For spatial step size, For time step, Queue length This is the downstream stop line position. This is the end of the queue. For the first The delay of the vehicle and The first The departure and arrival times of the vehicle. For the length of the road segment, This represents the free-flow velocity.

[0066] To verify the effectiveness of the method of this invention, typical urban roads in the central urban area of ​​Taizhou City were selected as the verification object. Based on actual road traffic operation data, a mixed traffic flow operation scenario for public transport was constructed using the SUMO microscopic traffic simulation platform. According to the acquired bus trajectory data and traffic detection data, the relevant parameters in the bus mobility bottleneck constraint model were determined, and the method of this invention was used to estimate the traffic conditions of road segments in the experimental scenario. The effectiveness of the method was evaluated through indicators such as road segment traffic density, queue length, and vehicle delay.

[0067] Two main urban roads in Taizhou City, Donghai Avenue and Tiyuguan Road, were selected as the research subjects. The study sections were both 900 m long, with 0-50 m as the upstream buffer zone, 50-650 m as the observation zone, and 650-900 m as the queuing buffer zone. Experiments were conducted in two-lane and three-lane scenarios, and two types of bus stops—straight-line stops and bay stops—were set up for each lane number scenario.

[0068] The free-flow speed for private vehicles is set according to the "Code for Design of Urban Road Engineering" (CJJ 37-2012), with 50 km / h for a two-lane scenario and 60 km / h for a three-lane scenario; the free-flow speed for buses is set at 8 gradients within the range of 30-44 km / h. The vehicle attribute parameter settings are shown in Table 1.

[0069] Table 1 Traffic detection data is sourced from license plate recognition devices upstream and downstream of the road segment. The training set uses data from the morning rush hour (8:00-9:00) on weekdays from December 15th to 18th, while the test set uses data from the same time period on December 19th. Bus trajectory data is obtained from bus operation records in the simulation scenario.

[0070] The single-parameter quadratic function capacity model proposed in step S3 was calibrated. Using observed capacity data under the influence of public transport bottlenecks extracted from simulation scenarios, the original linear model, the two-parameter quadratic model, and the single-parameter quadratic model were fitted respectively, and evaluated using root mean square error (RMSE), coefficient of determination (R²), and adjusted coefficient of determination (R²_adj). The calibration results are shown in Table 2. To improve the clarity of the table layout, "linear," "two-parameter," and "single-parameter" in the table correspond to the original linear model, the two-parameter quadratic model, and the single-parameter quadratic model, respectively.

[0071] Table 2 As shown in Table 2, the R² of the original linear model is negative in both two-lane and three-lane scenarios, indicating that the linear reduction model is insufficient to effectively describe the nonlinear relationship between bus operating speed and bottleneck capacity. The R² of both the two-parameter quadratic model and the one-parameter quadratic model exceeds 0.83, demonstrating significantly better fitting performance than the original linear model. Considering that the RMSE difference between the one-parameter and two-parameter models is less than 5%, and that the one-parameter model has the advantages of fewer parameters and clearer physical boundary constraints, this invention selects the one-parameter quadratic model as the bus moving bottleneck capacity constraint model for subsequent traffic state estimation.

[0072] To verify the traffic state estimation performance of this invention under mixed bus traffic flow conditions, a method based on a motion wave model was selected as a comparison method. This comparison method only utilizes upstream and downstream boundary detection data for state estimation, without considering the impact of moving bottlenecks formed by buses within road segments. The method of this invention, however, further introduces internal boundaries of bus trajectories and local capacity constraints based on the motion wave model. The two methods were evaluated from three aspects: road segment density, queue length, and vehicle delay. Evaluation metrics included mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE).

[0073] The road segment density estimation results are shown in Table 3. In different scenarios, including two-lane and three-lane roads, straight-line bus stops, and bay-type bus stops, the MAE, RMSE, and MAPE of the method in this invention are all lower than those of the method based on the motion wave model. In particular, in the two-lane straight-line bus stop scenario, the road segment density MAPE decreased from 22.48% to 12.92%, indicating that after introducing the bus movement bottleneck constraint, the model can more accurately characterize the local density increase phenomenon caused by bus stopping and leaving.

[0074] Table 3 The queue length estimation results are shown in Table 4. Compared with the method based on the motion wave model, the method of the present invention can reduce the queue length estimation error in various scenarios. In the two-lane straight-line bus stop scenario, the queue length MAPE decreased from 32.85% to 13.74%; in the three-lane bay-type bus stop scenario, the queue length MAPE decreased from 18.36% to 7.74%. This indicates that the method of the present invention can more effectively describe the impact of bus mobility bottlenecks on the upstream queue formation and dissipation process.

[0075] Table 4 The vehicle delay estimation results are shown in Table 5. The results demonstrate that the method of this invention is also superior to the comparative methods in terms of vehicle delay estimation. For the scenario of a two-lane straight-line bus stop where bus interference is strong, the vehicle delay MAPE decreased from 33.84% to 14.36%; for the scenario of a three-lane bay-type bus stop where bus interference is relatively weak, the vehicle delay MAPE decreased from 19.91% to 7.73%. This indicates that the method of this invention can not only improve the estimation of road segment state variables but also improve the estimation accuracy of vehicle operating efficiency indicators.

[0076] Table 5 To further illustrate the spatiotemporal distribution characteristics of the estimation results, Figures 7(a), 7(b), and 7(c) present the road segment density estimation results under a two-lane scenario. It can be seen that, considering the impact of buses, the model can more clearly identify the local high-density areas formed during bus deceleration, stopping, and departure, and can characterize the propagation process of this local disturbance to the upstream queuing area and the downstream recovery area. Therefore, compared with the motion wave model that does not consider the impact of buses, the method of this invention has a better descriptive ability for the density evolution, queuing changes, and vehicle delays in bus-mixed road segments.

[0077] Considering the improvement in MAPE across the three traffic state indicators, the method described in this invention achieves higher estimation accuracy compared to the baseline method that does not consider the impact of public transport. The MAPE for road segment density estimation decreased by an average of 11.53 percentage points, for queue length estimation by an average of 14.32 percentage points, and for vehicle delay estimation by an average of 15.85 percentage points. These results demonstrate that transforming bus trajectories into internal moving boundaries of road segments and incorporating the local capacity constraints caused by bus movement bottlenecks into the traffic state estimation process can effectively improve the accuracy of traffic state estimation under mixed public transport conditions.

[0078] The comparative results across different scenarios demonstrate that the method of this invention exhibits stable error reduction effects in two-lane, three-lane, straight-line bus stops, and bay-type bus stops, indicating its good applicability to various road conditions and bus stop types. Particularly in the two-lane straight-line bus stop scenario, where bus arrival and departure processes cause the strongest interference to mainline traffic, the improvement effect after introducing the bus movement bottleneck effect is even more significant, reducing the MAPE of road segment density, queue length, and vehicle delay by approximately 10, 19, and 20 percentage points, respectively. Even in the three-lane bay-type bus stop scenario where bus interference is relatively weak, all indicators are still improved, further demonstrating that the method of this invention is not only applicable to scenarios with significant bus interference but can also improve state estimation accuracy in general bus-mixed road sections.

[0079] The spatiotemporal distribution results of road segment density estimation show that the method of the present invention can accurately characterize the local high-density areas formed during bus deceleration, stopping and departure, and can describe the process of the local disturbance propagating to the upstream queuing area and the downstream recovery area. It is not only superior to the baseline method in terms of error index, but also has better physical interpretation and applicability in characterizing the spatiotemporal evolution of traffic flow.

[0080] A second aspect of the present invention provides a traffic state estimation system for urban road sections that considers the bottleneck effect of public transport movement, such as... Figure 8 The system includes: a data acquisition module for acquiring upstream vehicle arrival sequences, downstream vehicle departure sequences, bus trajectory data, and road segment geometric parameters; a basic state propagation module for constructing a basic cumulative vehicle count matrix based on the upstream and downstream vehicle departure sequences using a motion wave model; a bus mobility bottleneck constraint calculation module for determining local capacity constraints of bus mobility bottlenecks based on bus trajectories; an internal boundary construction module for generating internal boundary cumulative vehicle counts and forming internal mobility boundary conditions based on the location, speed, and local capacity constraints of bus trajectory segments; and an influence area determination module for dividing the influence area into a forward influence area, a backward influence area, and a central influence area based on the spatial relationship between the bus mobility bottleneck trajectory and the target calculation location.

[0081] The recursive calculation module is used to recursively calculate the cumulative vehicle count matrix based on the motion wave model and the internal movement boundary conditions of the bus. The status output module is used to output the road segment density, queue length, and vehicle delay based on the cumulative vehicle count matrix.

[0082] According to one embodiment of the present invention, the recursive calculation module includes: a differentiable calculation unit, used to convert the propagation delay reading process in the motion wave model into a continuously differentiable calculation process.

[0083] The computational graph training unit is used to update traffic flow parameters and bus mobility bottleneck parameters based on the loss function and backpropagation algorithm.

[0084] The technical effects achieved by this invention are as follows: First, by incorporating the bus vehicle trajectory into the traffic state estimation process, and describing the mobile bottleneck effect caused by the bus's low-speed operation, stop at stations, and departure as internal constraints of the road segment, this invention overcomes the problem of traditional methods relying solely on upstream and downstream cross-sectional data and ignoring bus disturbances within the road segment. It can more accurately estimate state parameters such as road segment density, queue length, and vehicle delay under mixed bus traffic flow conditions.

[0085] Secondly, by dividing the bus route into multiple route segments and constructing corresponding internal movement boundaries, combined with the influence area division and segmented recursive mechanism, the local capacity changes caused by bus movement bottlenecks can be continuously propagated in time and space, thereby providing a more precise description of the formation, propagation and recovery process of traffic flow during bus operation.

[0086] Furthermore, a nonlinear capacity constraint model considering the impact of bus operating speed is established, and physical boundary conditions such as bus stationary state and free-flow operating state are introduced, so that the model can reflect the dynamic relationship between bus operating state and road segment capacity, avoiding the problem of large calculation deviations in traditional linear reduction models under complex traffic environments, and improving the applicability and physical consistency of the model.

[0087] Finally, differentiable computation methods are used to transform the discontinuous computation process in the motion wave model into an optimizable computation process, and a computational framework integrating traffic detection data and bus trajectory data is constructed to realize the training and updating of model parameters and online state estimation. While maintaining the physical interpretability of the traffic flow model, the model's adaptability to real-time traffic changes is improved.

[0088] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. A method for estimating traffic conditions on urban road segments considering the bottleneck effect of public transport mobility, characterized in that, The method includes: S1: Obtain traffic operation data for the urban road segment to be estimated. The traffic operation data includes the upstream vehicle arrival sequence, downstream vehicle departure sequence, bus trajectory data, and road segment geometric parameters. S2: Establish a basic traffic state propagation model for urban road segments based on the motion wave model. Construct a basic cumulative vehicle number matrix based on the upstream vehicle arrival sequence and the downstream vehicle departure sequence to describe the traffic flow propagation state without considering the impact of public transport bottlenecks. S3: Determine the mobile bottleneck constraints formed during the operation of the buses based on the bus operation trajectory data, and establish a local capacity constraint model that considers the impact of bus operation status in order to obtain traffic flow constraint conditions corresponding to different bus operation statuses. S4: Divide the bus running trajectory into multiple trajectory segments according to a preset time interval, and generate the corresponding internal boundary cumulative vehicle count based on the bus position, running speed and the local traffic capacity constraint model corresponding to each trajectory segment, and use the internal boundary cumulative vehicle count as the internal movement boundary condition in the motion wave model. S5: Determine the bus mobility bottleneck impact area based on the internal mobility boundary conditions, and calculate the candidate cumulative vehicle number matrix corresponding to the bus mobility bottleneck impact area; S6: According to the time sequence of the bus operation trajectory segments, the candidate cumulative vehicle number matrix corresponding to each trajectory segment is recursively merged into the basic cumulative vehicle number matrix to obtain the target cumulative vehicle number matrix considering the impact of bus mobility bottlenecks. S7: Calculate the urban road segment traffic state parameters based on the target cumulative vehicle count matrix. The traffic state parameters include road segment traffic density, queue length, and vehicle delay.

2. The urban road segment traffic state estimation method according to claim 1, characterized in that, In step S3, the local capacity constraint model considering the bus mobility bottleneck effect includes a bus operating speed influence term, which is expressed in the form of a nonlinear function to describe the nonlinear relationship between changes in bus operating speed and the degree of mobility bottleneck constraint.

3. The urban road segment traffic state estimation method according to claim 2, characterized in that, The local traffic capacity calculation model satisfies preset physical boundary constraints, including: When the bus is stationary, the local traffic capacity is reduced to the traffic capacity after the bus occupies the road resources. When buses are running at free-flow speed, the mobile bottleneck effect disappears, and the local capacity is restored to the capacity level corresponding to the condition without the influence of the bus mobile bottleneck.

4. The urban road segment traffic state estimation method according to claim 1, characterized in that, The trajectory segment also includes spatiotemporal coordinate information corresponding to the spatial location of the bus, and calculates the cumulative number of vehicles at the internal boundary under the corresponding time and spatial location based on the trajectory segment.

5. The urban road segment traffic state estimation method according to claim 1, characterized in that, In step S5, based on the spatial relationship between the target calculated location and the bus moving bottleneck trajectory, the bus moving bottleneck influence area is divided into: Forward impact area is used to describe the traffic impact generated by the bus movement bottleneck along the free-flow propagation direction; The backward impact area is used to describe the traffic impact caused by the upstream propagation of public transport bottlenecks through congestion waves. The central area of ​​impact is used to describe the traffic recovery process after the bottleneck effect of public transportation ends.

6. The urban road segment traffic state estimation method according to claim 5, characterized in that, The composition of the affected area is determined according to the different bus stop patterns.

7. The urban road segment traffic state estimation method according to claim 1, characterized in that, The basic traffic state propagation model adopts a traffic flow state expression method based on the cumulative number of vehicles. The cumulative number of vehicles at any time and space location is jointly determined by the propagation results of the upstream boundary, the downstream boundary, and the internal movement boundary of the public transport.

8. The method for estimating traffic conditions on urban road sections according to claim 1, characterized in that, The recursive update process in step S6 includes: Bus trajectory segments were selected sequentially according to the bus operating time. The cumulative vehicle count matrix of the candidate internal moving boundary corresponding to the current bus trajectory segment is fused with the cumulative vehicle count matrix of the current traffic state; Update the current cumulative vehicle count matrix using the fusion results; Repeat the above process until all bus trajectory segments are recursively calculated to obtain the target cumulative vehicle count matrix.

9. The method for estimating traffic conditions on urban road sections according to claim 1, characterized in that, In the traffic state estimation process, the discontinuous calculation process in the motion wave model is made continuous, including: The cumulative number of candidate vehicles at the boundary is calculated using the continuous weighting function. The cumulative number of candidate vehicles at the boundary includes the cumulative number of candidate vehicles at the upstream boundary, the cumulative number of candidate vehicles at the downstream boundary, and the cumulative number of candidate vehicles at the internal moving boundary.

10. The urban road segment traffic state estimation method according to claim 9, characterized in that, The traffic state estimation process after continuous processing is constructed in a computational graph framework, which includes traffic flow propagation nodes, public transport mobility bottleneck constraint nodes, and boundary condition propagation nodes. The traffic flow model parameters and public transport mobility bottleneck parameters are updated through backpropagation.

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