Signal lamp countdown estimation method fusing traffic wave space-time propagation law

Abstract

The invention discloses a traffic wave space-time propagation law-fused signal lamp countdown estimation method, which comprises the following steps of: (1) dividing a target road section into a plurality of road section units at equal intervals, and dispersing a time axis into a plurality of time periods, so that the space-time is divided into a plurality of space-time grids; (2) calculating a grid state value used for representing the moving state of each detection vehicle on each space-time grid according to the instantaneous speed of each detection vehicle on each space-time grid; (3) establishing a signal lamp countdown estimation model fused with a traffic wave space-time propagation rule; (4) adding constraint conditions for the signal lamp countdown estimation model; and (5) solving the signal lamp countdown estimation model to obtain the optimal value of the decision variable, and calculating the signal lamp countdown according to the optimal value of the decision variable. The method is wider in application scene.

Description

Technical Field

[0001] The invention relates to traffic technology, and in particular to a signal light countdown estimation method integrating the space-time propagation law of traffic waves. Background Art

[0002] Traffic signal timing information, including cycle length, red and green light duration, etc., plays a key role in the efficient operation of urban traffic. It can help drivers adjust vehicle speed and reduce unnecessary stops and starts, thereby reducing fuel consumption and gas emissions by 10%-20%. In the context of autonomous driving and connected vehicles, this information is also an important basis for safe and efficient driving, and helps navigation systems to more accurately estimate travel times and develop better route planning. However, there are many obstacles to obtaining this information directly from the traffic signal system. For safety reasons, access to traffic signal system interfaces is strictly restricted to prevent hackers from using the interfaces to manipulate traffic signals, causing traffic chaos or other adverse consequences. At the same time, the diversity of traffic signal systems in different regions and the restrictions of local regulations make it difficult to share information between management organizations. Although some map service providers have obtained and displayed signal timing information in some areas, the coverage is limited and mainly concentrated at central signal intersections.

[0003] At present, the traffic signal timing information estimation methods are mainly divided into two categories. The method based on trajectory reconstruction uses vehicle trajectory data for estimation. For example, the signal timing information is determined by tracking the time when the vehicle passes the stop line. This method has high requirements for data sampling frequency and penetration. With the development of sensor technology, some studies use data collected by detection vehicles or other sensors for estimation, such as using bus data to reconstruct trajectories to infer signal timing. However, such methods generally have assumptions, such as vehicles traveling at a constant speed, constant acceleration and deceleration, etc., which oversimplify the actual traffic dynamics and driving behavior and are greatly restricted in practical applications. The method based on shock waves estimates signal timing information based on the formation and dissipation process of traffic shock waves. For example, the boundary of congestion events is approximated by triangles, or the timing is determined by fitting shock waves with piecewise linear functions. However, these methods have limitations. On the one hand, only specific geometric shapes can be used to approximate the boundary of shock waves, and the scope of application is narrow; on the other hand, they are mainly aimed at signal timing with fixed cycle durations, and it is difficult to apply them to intersections with different timing plans. In addition, there are some studies using statistical or machine learning techniques. Although they can use past observation data to predict the remaining waiting time, they also have limitations and cannot handle complex and changing traffic scenarios well. Summary of the invention

[0004] In view of the problems existing in the prior art, the purpose of the present invention is to provide a traffic light countdown estimation method which integrates the spatiotemporal propagation laws of traffic waves and has a wider range of practical application scenarios.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions: A signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves comprises the following steps: (1) Divide the target road section into several road section units at equal intervals, discretize the time axis into several time periods, and thus divide the space-time into several space-time grids; (2) calculating a vehicle grid observation state value of each space-time grid according to the instantaneous speed of each detection vehicle on each space-time grid, wherein the vehicle grid observation state value is used to characterize the observed movement state of each detection vehicle on each space-time grid; (3) Establish a traffic light countdown estimation model that integrates the spatiotemporal propagation law of traffic waves. The traffic light countdown estimation model is specifically as follows: , In the formula, K represents the number of detected vehicles, is the space-time grid ( ) of the vehicle grid recovery state, when the space-time grid ( ) when stationary =1, otherwise =0; is the variable indicating the actual state of the grid, Represents a space-time grid ( ) of the vehicle grid observation state value, They represent the road section unit number and time period number of the detection vehicle k respectively; is the red light start time indicator variable. When t is the red light start time of a cycle, ,otherwise , is the green light start time indicator variable. When t is the green light start time of a cycle, ,otherwise ; Pair indicator variables for traffic lights. When the red light and green light start time of the same cycle ,otherwise ; is a continuous red light indicator variable. When the red light starts at two consecutive cycles ,otherwise ; represents a period classification indicator variable, when The two periodic signals of the red light start at the same time ,otherwise ; is an arbitrary time period number, and , ; (4) Adding constraints to the traffic light countdown estimation model; (5) Solve the traffic light countdown estimation model and obtain the decision variables The optimal value of The optimal value of is calculated to get the traffic light countdown.

[0006] Furthermore, step (2) specifically includes: (2.1) Obtain the instantaneous speed of each detection vehicle on each space-time grid; (2.2) According to the instantaneous speed, the grid state value used to characterize the movement state of each detection vehicle on each space-time grid is calculated according to the following formula: , In the formula, when It is considered that the detection vehicle k is in the space-time grid ( ) is in a stationary state, at this time, , otherwise it is considered to be in a moving state. ,s k represents the instantaneous speed of the detection vehicle k, s th Indicates the speed threshold.

[0007] Furthermore, the constraints include red light start time constraint, green light start time constraint, red and green light start time pairing constraint, continuous cycle identification constraint, shock wave spatiotemporal propagation constraint, vehicle waiting time reduction constraint, signal cycle classification constraint, cycle length range constraint and decision variable constraint.

[0008] Furthermore, the red light start time constraint is specifically: ; ; ; The green light start time constraint is specifically: ; ; ; In the formula, , are the grid actual state indicator variables when the value of i is 1 at the time instant of the space-time grid (1, t) and (1, t-1), and T represents the number of time periods.

[0009] Furthermore, the traffic light start time pairing constraint is specifically: , ; , ; , ; , ; In the formula, T represents the number of time periods, for The value of t is the value when t1. for The value when t is t2.

[0010] Furthermore, the continuous cycle identification constraint is specifically: , ; , ; , ; , ; In the formula, T represents the number of time periods, for The value of t is the value when t1. for The value when t is t3.

[0011] Furthermore, the shock wave spatiotemporal propagation constraints are specifically: ; ; The vehicle waiting time decreasing constraint is specifically: , ; In the formula, , They are all indicator variables of the actual state of the grid, I represents the number of road section units, and T represents the number of time periods.

[0012] Furthermore, the signal period classification constraint is specifically: ; ; ; ; ; ; ; ; ; , , , ; ; ; ; ; In the formula, , are the absolute value of the difference between the two cycles of the red light starting at time t1 and time t3, and the absolute value of the difference between the two cycles of the red light starting at time t1 and time t3, They are , Auxiliary variables used to assist in determining , The values ​​of are all binary decision variables, taking values ​​of 0 or 1. , , They represent the period length and duration of the red light when the red light starts at t1. , , , They represent the cycle length and duration of the red light when the red light starts at t3, t4 and t5 are the time period numbers. is the continuous red light indicator variable, is the traffic light pairing indicator variable, M is a positive number greater than the preset threshold, represents the signal period, and T represents the number of time periods.

[0013] Furthermore, the cycle length range constraint is specifically: , The decision variable constraints are specifically: ; ; ; ; ; ; ; ; ; ; In the formula, , They represent the minimum and maximum cycle lengths respectively, T represents the number of time periods, and I represents the number of road section units.

[0014] Furthermore, according to The steps of calculating the optimal value of the signal light countdown specifically include: (5.1) According to The optimal value of extracts the following key signal timing parameters: Red light start time series: from The optimal value is 1. , set the value to 1 The time point corresponding to the time period serial number t is taken as the red light start time point of a cycle. The red light start time points of all cycles are arranged in chronological order as follows: , They represent the red light start time points of the 1st, kth, and Nth cycles after sorting, respectively, and N is the total number of cycles; Green light start time: from The optimal value is 1. , set the value to 1 The time point corresponding to the time period serial number t is taken as the green light start time of a cycle; Cycle length and red light duration: according to The optimal value of is calculated as follows: , , In the formula, They represent the period length and duration of the red light when the red light starts at t1. The two cycles are of the same type, that is, the cycle length is the same as the red light duration; (5.2) Locate the period to which the current time belongs according to the following formula , and obtain the cycle length of the cycle and red light duration : ; In the formula, represents the current time, m represents the time period number, Indicates the start time of the red light in the mth cycle; (5.3) Calculate the traffic light countdown according to the following formula: , In the formula, Countdown to the red light, Countdown to the green light, Indicates The red light start time of each cycle.

[0015] Compared with the prior art, the present invention has the following beneficial effects: the present invention can estimate the most likely traffic light timing information from noise interference and sparse data. The model integrates the spatiotemporal propagation law of traffic waves, takes the position and speed of the detected vehicle on the signal-controlled road section as input, and outputs signal light timing information including signal cycle length, red light and green light duration, etc. Compared with the existing methods, the present invention does not need to preset the specific shape of the queue contour in the time-space diagram of the signal intersection, and can distinguish different types of signal cycles, where the same type of cycles have the same signal light timing scheme, so as to estimate the signal light timing information more accurately. Under appropriate assumptions, the present invention can achieve unbiased estimation, and solving the model is equivalent to performing maximum likelihood estimation, which is the first time in the existing literature. Numerical results based on simulation data and actual data show that even in the case of low penetration and high sampling interval, the present invention can still obtain satisfactory estimation accuracy. The present invention can be applied to signal timing with different non-fixed cycle durations, has a wider range of applications, and can well handle complex and changeable traffic scenes. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves provided by an embodiment of the present invention; Figure 2 It is a schematic diagram of the traffic signal timing at a signalized intersection and the corresponding queue contour diagram in the time-space diagram; Figure 3 It is a schematic diagram showing the gradual decrease of vehicle waiting time from downstream to upstream in a single cycle; Figure 4 It is a schematic diagram of the estimated signal timing of the NGSIM dataset with 10% penetration and 30-second sampling interval. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0018] Before introducing the present invention, the relevant terms used in the present invention are explained as follows: Traffic signal timing information: refers to parameters such as the cycle duration, red light duration, and green light duration of traffic lights. It is crucial to the intelligent transportation system and can help drivers optimize driving behavior, reduce fuel consumption and emissions, and improve the performance of autonomous driving and navigation systems. However, it is difficult to obtain directly from the traffic signal system due to policy barriers and safety concerns.

[0019] Detection vehicle: A vehicle equipped with sensors that can collect data such as its own position and speed. Its data can be used to estimate traffic signal timing information, but there are data sparsity and noise problems. This paper distinguishes the state of the detection vehicle data points (divided into static and moving states based on the speed and threshold comparison) and uses it as the model input to estimate the signal timing.

[0020] Traffic wave propagation: Traffic wave propagation refers to the phenomenon of traffic flow propagating on the road, which is similar to the wave in the fluid. By establishing a mathematical programming model, the temporal and spatial impact range of traffic accidents can be estimated, and the output of the model can meet the propagation law of traffic waves.

[0021] The embodiment of the present invention provides a signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves, such as Figure 1 As shown, specifically including: (1) Divide the target road section into several road section units at equal intervals, discretize the time axis into several time periods, and thus divide the space-time into several space-time grids.

[0022] Specifically, the target road section is equally divided into I road section units, and the time axis is discretized into T time periods, so that the time and space are divided into I×T time-space grids.

[0023] (2) According to the instantaneous speed of each detection vehicle on each space-time grid, a vehicle grid observation state value of each space-time grid is calculated, where the vehicle grid observation state value is used to characterize the observed movement state of each detection vehicle on each space-time grid.

[0024] This step specifically includes: (2.1) Obtain the instantaneous speed of each detection vehicle on each space-time grid; (2.2) According to the instantaneous speed, the grid state value used to characterize the movement state of each detection vehicle on each space-time grid is calculated according to the following formula: , In the formula, when It is considered that the detection vehicle k is in the space-time grid ( ) is in a stationary state, at this time, , otherwise it is considered to be in a moving state. ,s k represents the instantaneous speed of the detection vehicle k, s thIndicates the speed threshold, which is set to 2km / h in this embodiment.

[0025] In addition, the error compensation term can be introduced Establish a fault-tolerant mapping relationship between the observed state and the real state , effectively eliminating sensor noise interference; at the same time, constructing a coverage matrix to identify data sparse areas, and using a constraint-driven state reasoning mechanism to complete data for uncovered grid cells. As an input variable construction method, it realizes the multi-dimensional feature analysis and noise-resistant characterization of traffic flow status, and provides a structured input with both spatiotemporal correlation and robustness for the subsequent optimization model. The technical effect is significantly better than the traditional continuous variable processing method.

[0026] (3) Establish a traffic light countdown estimation model that integrates the spatiotemporal propagation laws of traffic waves.

[0027] When constructing the objective function of the traffic light countdown estimation model, the core purpose is to use the detection vehicle data to accurately estimate the traffic signal timing information, while fully considering the challenges brought by data sparsity and noise interference. The construction of the objective function follows the principle of making the model output highly consistent with the actual observation data. The specific construction process is as follows: 1. Establish the construction purpose: Aim to accurately infer traffic signal timing information from noisy and sparse detection vehicle data, including key factors such as cycle length, red light and green light duration. k Due to the characteristics of the signal timing plan P, it is difficult to accurately derive the signal timing plan P based on these data. Therefore, the construction of the objective function focuses on how to efficiently use the existing data and improve the accuracy of the estimation.

[0028] 2. Define key elements: Based on the detection vehicle data, according to the speed threshold s th Divide the data point states into static and moving states, and define the binary indicators for discrimination To characterize the observed cell state.

[0029] The final established signal light countdown estimation model is as follows: , In the formula, K represents the number of detected vehicles, is the space-time grid ( ) of the vehicle grid recovery state, when the space-time grid ( ) when stationary =1, otherwise =0; is the variable indicating the actual state of the grid, Represents a space-time grid ( ) of the vehicle grid observation state value, They represent the road section unit number and time period number of the detection vehicle k respectively; is the red light start time indicator variable. When t is the red light start time of a cycle, ,otherwise , is the green light start time indicator variable. When t is the green light start time of a cycle, ,otherwise ; Pair indicator variables for traffic lights. When the red light and green light start time of the same cycle ,otherwise ; is a continuous red light indicator variable. When the red light starts at two consecutive cycles ,otherwise ; represents a period classification indicator variable, when The two periodic signals of the red light start at the same time ,otherwise ; is an arbitrary time period number, and , .

[0030] In this objective function, when , that is, when the cell is observed to be in a stationary state, the expected decision variable Also 1, ensuring that the state restored by the model is consistent with the actual observed state; otherwise, Ideally, should be 0. By minimizing the difference between the two, it can ensure that the cell state restored by the model is consistent with the actual observation data to the greatest extent. This enables the model to estimate traffic signal timing information based on more accurate cell state analysis, thereby improving the reliability and accuracy of the estimation results. The decision variables are optimized, which comprehensively covers the identification and matching of the start time of red and green lights in the traffic signal cycle, the classification of cycle types, and the recovery of cell states, etc., which fully reflects the comprehensive needs of the model for estimating traffic signal timing information. and Cooperate with each other to accurately describe the starting time points of red and green lights in the signal cycle; in complex time series with multiple cycles, It can effectively identify the pairing relationship between the start time of red and green lights in the same cycle, providing the necessary conditions for determining the cycle length and red light duration; The continuity of the start time of different cycles is clarified, combined with , the cycle length and red light duration can be accurately calculated, thus completely describing the time characteristics of the signal cycle; Used to restore the actual state of the grid cells in the space-time graph. In the analysis based on the space-time graph, it is difficult to judge the state of the grid cells due to the sparse data points and noise interference; The introduction of variables can accurately identify the grid cell status according to the actual traffic status, providing a reliable basis for the subsequent estimation of traffic signal timing information based on the cell status. Considering that the data of a single cycle is limited and the timing of adjacent time periods has a certain stability, Classifying signal cycles can effectively integrate data from multiple cycles and improve the model's estimation accuracy of signal timing information, especially in adaptive signal timing intersection scenarios, which can better adapt to dynamic changes in traffic conditions.

[0031] In summary, this objective function closely revolves around the core task of accurately estimating traffic signal timing information using detection vehicle data. By minimizing the difference between observed and restored cell states, it effectively integrates various decision variables in the model, providing a key guarantee for achieving high-precision signal timing information estimation.

[0032] (4) Add constraints to the traffic light countdown estimation model.

[0033] Among them, the constraints include red light start time constraint, green light start time constraint, red and green light start time pairing constraint, continuous cycle identification constraint, shock wave spatiotemporal propagation constraint, vehicle waiting time reduction constraint, signal cycle classification constraint, cycle length range constraint and decision variable constraint.

[0034] The red light start time constraint is specifically: ;(1) ;(2) ;(3) Among them, constraint (1) means that when time t corresponds to the start time of a red light in a certain cycle, that is, When , the first cell <1,t> located at the stop line must be at rest, so it is required , this constraint ensures this condition. The principle is that when the red light is on, the vehicle will stop before the stop line, making the vehicle corresponding to the cell stationary.

[0035] Constraint (2) indicates that the red light start time also corresponds to time t In the case of , the cell <1,t-1> at the stop line at the previous moment should be in a moving state where the vehicle can drive normally, that is This is because vehicles can pass normally before the red light comes on, which is in line with the actual traffic scenario.

[0036] Constraint (3) is used to reversely verify whether time t is the start time of the red light. and According to the actual traffic logic, t should be the start time of the red light, that is, , this constraint guarantees this logical judgment.

[0037] The green light start time constraint is specifically: ;(4) ;(5) ;(6) In the formula, When i is 1 The value of , T represents the number of time periods.

[0038] Constraint (4) indicates that when time t corresponds to the start time of a green light cycle, the vehicle in the cell <1, t> at the stop line should be in the moving state of starting to drive, so .

[0039] Constraint (5) indicates that time t is the green light start time At this time, the vehicles in the cell <1, t-1> at the stop line at the previous moment should be in a stationary state waiting for the green light, that is, This is consistent with the actual situation that vehicles wait at the stop line before the green light comes on.

[0040] Constraint (6) is used to reversely determine whether time t is the green light start time. and At this time, according to common traffic rules, t should be the start time of the green light, that is, , this constraint guarantees the judgment of this logical relationship.

[0041] The traffic light start time pairing constraint is specifically: , ; (7) , ; (8) , ; (9) , ; (10) In the formula, T represents the number of time periods, for The value of t is the value when t1. for The value when t is t2.

[0042] Constraint (7) indicates that when t1 is the red light start time ( ), t2 is the green light start time ( ) and there are no other red and green light start times between t1 and t2 ( ), according to the definition of traffic signal cycle, it can be inferred that t1 and t2 correspond to the start time of the red light and green light in the same cycle, that is, .

[0043] Constraints (8), (9), and (10) together indicate that if the condition of constraint (7) is not satisfied, that is, ,or ,or ,It can be determined that t1 and t2 do not correspond to the start time of the red light and the start time of the green light in the same cycle, that is, .

[0044] The continuous cycle identification constraint is specifically: , ;(11) , ;(12) , ; (13) , ;(14) In the formula, T represents the number of time periods, for The value of t is the value when t1. for The value when t is t3.

[0045] Constraint (11) indicates that when t1 and t3 are the start times of the red lights in two cycles ( ), and there is no other red light start time between t1 and t3 ( ), according to the continuity of the traffic signal cycle, it can be inferred that t1 and t3 correspond to two consecutive cycles, that is, .

[0046] Constraints (12), (13), and (14) together indicate that if the condition of constraint (11) is not satisfied, that is, ,or ,or , we know that t1 and t3 do not correspond to consecutive cycles, that is, .

[0047] The shock wave spatiotemporal propagation constraints are specifically: ;(15) ;(16) The vehicle waiting time decreasing constraint is specifically: , ;(17) In the formula, , are all indicator variables of the actual state of the grid, I represents the number of road section units, and T represents the number of time periods. Figure 2 Figure shows a signalized intersection with various cycle types and the corresponding queue profiles in a time-space diagram.,The horizontal axis represents time while the vertical axis represents the distance to the stop line.

[0048] Constraint (15) indicates that in the space-time graph, the propagation of traffic shock waves has a specific law.<i,t> When in a stationary state, according to the continuity and directionality of shock wave propagation, its adjacent cells are required to<i-1,t> or<i,t-1> , or both must be at rest ( ,or , or both are 1).

[0049] Constraint (16) indicates that, also based on the law of shock wave propagation, when the unit cell<i-1,t> and<i,t-1> are all in a stationary state ( ), according to the propagation characteristics of the shock wave, the unit cell<i,t> It must also be at rest ( ).

[0050] Constraint (17) indicates that within a signal cycle, starting from the time the red light comes on, vehicles downstream of the stop line will wait longer than vehicles upstream.

[0051] The signal period classification constraints are specifically: ; (18) ; (19) ; (20) ;(twenty one) ; (twenty two) ;(twenty three) ;(twenty four) ; (25) ; (26) , , , ;(27) ;(28) ;(29) ;(30) ;(31) In the formula, , are the absolute value of the difference between the two cycles of the red light starting at time t1 and time t3, and the absolute value of the difference between the two cycles of the red light starting at time t1 and time t3, They are , Auxiliary variables used to assist in determining , The values ​​of are all binary decision variables, taking values ​​of 0 or 1. , , They represent the period length and duration of the red light when the red light starts at t1. , , , They represent the cycle length and duration of the red light when the red light starts at t3, t4 and t5 are the time period numbers. is the continuous red light indicator variable, is the traffic light pairing indicator variable, M is a positive number greater than the preset threshold, represents the signal period, and T represents the number of time periods.

[0052] Constraints (18) to (27) together indicate that when t1 and t3 correspond to the start time of the red light in two consecutive cycles ( = 1), and their signal timing plans are the same ( , = ), according to the signal cycle classification rules, these two cycles belong to the same type ( =1), by And the variables introduced , , A set of constraints are constructed to achieve this classification.

[0053] Constraints (28) to (30) together indicate that if ,as well as as well as = These prerequisites, namely ,or ,or , the two cycles will not be classified as the same type, i.e. =0.

[0054] Constraint (31) indicates that we can and To determine the signal period This constraint helps to further analyze the distribution of different cycle types and provide an important basis for the optimization of traffic signal timing.

[0055] The cycle length range constraint is specifically: , (32) The decision variable constraints are specifically: ; (33) ; (34) ; (35) ; (36) ; (37) ; (38) ; (39) ; (40) ; (41) ; (42) In the formula, They represent the minimum and maximum cycle lengths respectively, T represents the number of time periods, and I represents the number of road section units.

[0056] Constraints (33) to (37) together represent that, in order to ensure the consistency and solvability of the model calculation, the decision variables are restricted to binary.

[0057] Constraints (38) to (42) together indicate that, for a given spatiotemporal boundary condition, when the subscripts of decision variables exceed the normal range, these decision variables are assigned a value of 0 in order to ensure the rationality and stability of the model.

[0058] (5) Solve the traffic light countdown estimation model and obtain the decision variables The optimal value of The optimal value of is calculated to get the traffic light countdown.

[0059] This step specifically includes: (5.1) According to The optimal value of extracts the following key signal timing parameters: Red light start time series: from The optimal value is 1. , set the value to 1 The time point corresponding to the time period serial number t is taken as the red light start time point of a cycle. The red light start time points of all cycles are arranged in chronological order as follows: , It indicates the starting time point of the red light in the 1st, kth, and Nth cycles after sorting, where N is the total number of cycles; Green light start time: from The optimal value is 1. , set the value to 1 The time point corresponding to the time period serial number t is taken as the green light start time of a cycle; Cycle length and red light duration: according to The optimal value of is calculated as follows: , , In the formula, They represent the period length and duration of the red light when the red light starts at t1. The two cycles are of the same type, that is, the cycle length is the same as the red light duration; (5.2) Locate the period to which the current time belongs according to the following formula , and obtain the cycle length of the cycle and red light duration : ; In the formula, represents the current time, m represents the time period number, Indicates the start time of the red light in the mth cycle; (5.3) Calculate the traffic light countdown according to the following formula: , In the formula, Countdown to the red light, Countdown to the green light, Indicates The red light start time of each cycle.

[0060] In addition, when the timing is a fixed timing scenario, the fixed timing scenario can also be processed periodically in the following manner: If the signal timing is of fixed period type (i.e. the timing parameters of each period are consistent), the calculation can be simplified by modular operation: ,when When The remaining time of the green light will be calculated.

[0061] In addition, the boundary conditions and constraints are handled as follows: 1. Time out-of-bounds processing: like (out of the analysis period), default is from the first period Start the loop calculation, that is (M is the number of cycle repetitions, is the average cycle length).

[0062] 2. Discrete time matching: when If the model does not fall precisely within the discrete time interval (e.g. the model is in seconds, but the real time contains milliseconds), the nearest neighbor method or linear interpolation is used to determine the period to which it belongs, ensuring .

[0063] 3.Multi-phase support: For multi-phase signal control, the above steps are performed independently for each phase, and the cycle length Ln and red light length Rn of each phase are estimated through the probe data in the corresponding direction, and the remaining time of each phase is calculated respectively.

[0064] Next, a numerical experiment is carried out on the present invention, and the experiment mainly includes the following steps: Step 1: Experimental preparation.

[0065] (1) Data acquisition and processing: The simulated data generated by VISSIM software and the NGSIM real data set were selected as the experimental data sources. For the simulated data, the simulation was performed for intersection scenarios with fixed and adaptive signal timing. During the simulation process, the parameters such as saturation flow rate, road segment division, and time interval were carefully set. The saturation flow rate was set to 1800pcu / h / lane, the signalized road segment was divided into small segments of 6 meters, and the analysis period was discretized into intervals of 2 seconds to construct a spatiotemporal map with a specific resolution. At the same time, considering that there may be noise interference in the actual data, the simulated data was processed accordingly to simulate the real situation. For the real data, the signalized intersection data of Peachtree Street in Atlanta, Georgia in the NGSIM project was selected. The data was collected by eight video cameras and recorded from 12:45 to 13:00 on November 8, 2006. It contains rich content such as vehicle trajectories, signal timing, and geographic information. Since there are limited trajectory data for the east and west directions in the dataset, the experiment focuses on the north and south directions. The intersection uses fixed signal timing, and its cycle length is known to be 98 seconds, with a red light duration of 64 seconds and a green light duration of 34 seconds.

[0066] (2) Experimental environment construction: The experimental program was written in Python 3.9 programming language, and the integer programming model was solved with the help of Gurobi 11.0 optimizer. All experiments were run on a desktop computer equipped with an Intel 5.20 GHz CPU and 64 GB memory. Considering that the standard branch and bound algorithm may have the problem of long solution time when the model is dealing with large-scale problems, this paper proposes an efficient and easy-to-handle two-step algorithm to improve the model solution efficiency and ensure the feasibility and efficiency of the experiment.

[0067] Step 2: Simulate data experiment.

[0068] (1) Fixed-timing intersection test: Ten cycle data with two different signal timing schemes were selected for the experiment. Unlike traditional methods, the model involved in the present invention has the ability to automatically identify different cycle types without manual pre-distinction. In order to comprehensively evaluate the performance of the model under different data qualities, four combinations of detection vehicle penetration and sampling interval were set, namely [100%, 1s], [100%, 30s], [10%, 1s] and [10%, 30s]. These combinations cover different scenarios from high-quality data to sparse data. Mean absolute error (MAE) and mean absolute percentage error (MAPE) were used as evaluation indicators to measure the model's estimation accuracy of cycle length and red light duration. Experimental results show that the model can accurately identify different types of cycles and achieve good estimation results under various data conditions. Even in the [10%, 30s] scenario where the data is the most sparse, the model can still maintain a high degree of effectiveness, with an average MAE of 1.8 seconds and a MAPE of 1.5% for the cycle length; and an average MAE of 2 seconds and a MAPE of 2.67% for the red light duration.

[0069] (2) Adaptive timing intersection test: The model was validated using data from ten cycles with different signal timing schemes. In the adaptive signal timing intersection scenario, since the signal timing scheme for each cycle is considered to be a specific type, some constraints applicable to fixed timing intersections are no longer required here. The experimental results show that although the performance of the model at adaptive signal timing intersections is slightly lower than that at fixed timing intersections, satisfactory results can still be obtained in most cases. The average MAPE range of the estimated cycle length and red light duration is 3.77% - 11.65%, respectively, which fully verifies the applicability and effectiveness of this model in different signal timing scenarios.

[0070] (3) Analysis of the impact of erroneous data: Considering that random Gaussian errors are inevitable in the actual data collection process and will affect the accuracy of model estimation, an experiment on the impact of erroneous data is carried out. According to the conventional practice of existing similar studies, the amplitude of the measurement error is set to [1, 2, 3] ( is the standard deviation of the observed velocity), and the error percentage is set to [5%, 10%, 15%, 20%, 25%, 30%], thus forming 18 different error scenarios. Under the conditions of 10% penetration rate and 30s sampling interval, the experiment is repeated five times for each error scenario to conduct sensitivity analysis. Figure 4As shown in the figure, the observed and recovered cell states in one cycle are shown when the permeability is 10% and the sampling interval is 30 seconds. The experimental results show that when the error percentage is in the range of [0%, 25%], the estimation results of the model remain stable and accurate; when the error percentage exceeds 25% and the amplitude reaches 3 When , the estimated MAE and MAPE will increase significantly, resulting in unsatisfactory estimation results. But in general, this model is highly robust to erroneous data, and can resist the interference of data errors to a certain extent, thus ensuring the reliability of estimation results.

[0071] Step 3: Real data experiment.

[0072] The NGSIM real data set was used to further verify the performance of the patented model in actual scenarios. During the experiment, four combinations of detection vehicle penetration and sampling intervals were set, namely [100%, 1s], [100%, 30s], [10%, 1s], and [10%, 30s], and the experiment was repeated five times for each combination to reduce the impact of random factors on the experimental results. The experimental results show that under the combination of [10%, 30s] where the data is the sparsest, the model's estimated MAE for cycle length is 4.4 seconds and MAPE is 4.49%; the estimated MAE for red light duration is 3.6 seconds and MAPE is 5.63%. These results show that even in the presence of noise and sparsity in actual data, the patented model can still effectively restore the cell state and accurately estimate the signal timing information, fully verifying the effectiveness and practicality of the model in real scenarios.

[0073] It should be understood that the above embodiments and descriptions only describe the principles, main features and advantages of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, and these changes and improvements all fall within the scope of protection of the present invention.

Claims

1. A signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves, characterized in that: The steps include: (1) Divide the target road section into several road section units at equal intervals, discretize the time axis into several time periods, and thus divide the space-time into several space-time grids; (2) calculating a vehicle grid observation state value of each space-time grid according to the instantaneous speed of each detection vehicle on each space-time grid, wherein the vehicle grid observation state value is used to characterize the observed movement state of each detection vehicle on each space-time grid; (3) Establish a traffic light countdown estimation model that integrates the spatiotemporal propagation law of traffic waves. The traffic light countdown estimation model is specifically as follows: ， In the formula, K represents the number of detected vehicles, is the space-time grid ( ) of the vehicle grid recovery state, when the space-time grid ( ) is at rest =1, otherwise =0; is the variable indicating the actual state of the grid, Represents a space-time grid ( ) of the vehicle grid observation state value, They represent the road section unit number and time period number of the detection vehicle k respectively; is the red light start time indicator variable. When t is the red light start time of a cycle, ,otherwise , is the green light start time indicator variable. When t is the green light start time of a cycle, ,otherwise ; Pair indicator variables for traffic lights. When the red light and green light start time of the same cycle ,otherwise ; is a continuous red light indicator variable. When the red light starts for two consecutive cycles ,otherwise ; represents a period classification indicator variable, when The two periodic signals of the red light start at the same time ,otherwise ; is an arbitrary time period number, and , ; (4) Adding constraints to the traffic light countdown estimation model; (5) Solve the traffic light countdown estimation model and obtain the decision variables The optimal value of The optimal value of is calculated to get the traffic light countdown.

2. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 1 is characterized in that: Step (2) specifically includes: (2.1) Obtain the instantaneous speed of each detection vehicle on each space-time grid; (2.2) According to the instantaneous speed, the grid state value used to characterize the movement state of each detection vehicle on each space-time grid is calculated according to the following formula: , In the formula, when It is considered that the detection vehicle k is in the space-time grid ( ) is in a stationary state, at this time, , otherwise it is considered to be in a moving state. ,s k represents the instantaneous speed of the detection vehicle k, s th Indicates the speed threshold.

3. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 1 is characterized in that: The constraints include red light start time constraint, green light start time constraint, red and green light start time pairing constraint, continuous cycle identification constraint, shock wave spatiotemporal propagation constraint, vehicle waiting time reduction constraint, signal cycle classification constraint, cycle length range constraint and decision variable constraint.

4. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 3 is characterized in that: The red light start time constraint is specifically: ; ; ; The green light start time constraint is specifically: ; ; ; In the formula, , are the grid actual state indicator variables of the space-time grids (1, t) and (1, t-1), and T represents the number of time periods.

5. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 3 is characterized in that: The traffic light start time pairing constraint is specifically: , ; , ; , ； ， ； In the formula, T represents the number of time periods, for The value of t is the value when t1. for The value when t is t2.

6. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 3 is characterized in that: The continuous cycle identification constraint is specifically: , ; , ; , ; , ; In the formula, T represents the number of time periods, for The value of t is the value when t1. for The value when t is t3.

7. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 3 is characterized in that: The shock wave spatiotemporal propagation constraints are specifically: ; ; The vehicle waiting time decreasing constraint is specifically: , ; In the formula, , They are all indicator variables of the actual state of the grid, I represents the number of road section units, and T represents the number of time periods.

8. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 3 is characterized in that: The signal period classification constraints are specifically: ； ； ； ； ； ； ； ； ； ， ， , ; ; ; ; ; In the formula, , are the absolute value of the difference between the two cycles of the red light starting at time t1 and time t3, and the absolute value of the difference between the two cycles of the red light starting at time t1 and time t3, They are , Auxiliary variables used to assist in determining , The values ​​of are all binary decision variables, taking values ​​of 0 or 1. , , They represent the period length and duration of the red light when the red light starts at t1. , , , They represent the cycle length and duration of the red light when the red light starts at t3, t4 and t5 are the time period numbers. is the continuous red light indicator variable, is the traffic light pairing indicator variable, M is a positive number greater than the preset threshold, represents the signal period, and T represents the number of time periods.

9. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 3 is characterized in that: The cycle length range constraint is specifically: ， The decision variable constraints are specifically: ； ； ； ； ； ； ； ； ； ； In the formula, , They represent the minimum and maximum cycle lengths respectively, T represents the number of time periods, and I represents the number of road section units.

10. The signal light countdown estimation method integrating the spatiotemporal propagation law of traffic waves according to claim 1 is characterized in that: The basis The steps of calculating the optimal value of the signal light countdown specifically include: (5.1) According to The optimal value of extracts the following key signal timing parameters: Red light start time series: from The optimal value is 1. , set the value to 1 The time point corresponding to the time period serial number t is taken as the red light start time point of a cycle. The red light start time points of all cycles are arranged in chronological order as follows: , They represent the red light start time points of the 1st, kth, and Nth cycles after sorting, respectively, and N is the total number of cycles; Green light start time: from The optimal value is 1. , set the value to 1 The time point corresponding to the time period serial number t is taken as the green light start time of a cycle; Cycle length and red light duration: according to The optimal value of is calculated as follows: ， ， In the formula, They represent the period length and duration of the red light when the red light starts at t1. The two cycles are of the same type, that is, the cycle length is the same as the red light duration; (5.2) Locate the period to which the current time belongs according to the following formula , and obtain the cycle length of the cycle and red light duration : ； In the formula, represents the current time, m represents the time period number, Indicates the start time of the red light in the mth cycle; (5.3) Calculate the traffic light countdown according to the following formula: , In the formula, Countdown to the red light, Countdown to the green light, Indicates The red light start time of each cycle.

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