A Method for Estimating Signal Light Countdown by Integrating the Spatiotemporal Propagation Law of Traffic Waves

Abstract

The present invention discloses a method for estimating the signal light countdown by integrating the spatio-temporal propagation law of traffic waves, which comprises the following steps: (1) equally dividing a target road section into a plurality of road section units, discretizing the time axis into a plurality of time periods, so as to divide the spatio-temporal into a plurality of spatio-temporal grids; (2) calculating a grid state value for characterizing the moving state of each detection vehicle on each spatio-temporal grid according to the instantaneous speed of each detection vehicle on each spatio-temporal grid; (3) establishing a signal light countdown estimation model by integrating the spatio-temporal propagation law of traffic waves; (4) adding constraint conditions to the signal light countdown estimation model; (5) solving the signal light countdown estimation model to obtain the optimal value of the decision variable, and calculating the signal light countdown according to the optimal value of the decision variable. The present invention has a wider applicable scenario.

Description

Technical Field

[0001] The present invention relates to traffic technologies, and in particular, to a method for estimating signal countdown by integrating the spatio-temporal propagation law of traffic waves. Background Art

[0002] Traffic signal timing information, including cycle length, red light and green light durations, etc., plays a key role in the efficient operation of urban traffic. It can help drivers adjust their vehicle speeds, reduce unnecessary stops and starts, and thus reduce fuel consumption and gas emissions by 10% - 20%. In the context of autonomous driving and vehicle-to-everything (V2X), this information is also an important basis for achieving safe and efficient driving, and helps navigation systems more accurately estimate travel times and develop better route plans. However, there are many obstacles to directly obtaining this information from traffic signal systems. For safety reasons, access to traffic signal system interfaces is strictly restricted to prevent hackers from manipulating traffic signals through the interfaces, 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 among management organizations. Although some map service providers have obtained and displayed signal timing information for some regions, the coverage is limited and mainly concentrated on central signalized intersections.

[0003] Currently, traffic signal timing information estimation methods are mainly divided into two categories. Methods based on trajectory reconstruction use vehicle trajectory data for estimation. For example, by tracking the time when a vehicle passes the stop line to determine signal timing information, this method requires a high sampling frequency and penetration rate of data. With the development of sensing technologies, some studies use data collected by probe vehicles or other sensors for estimation, such as using bus data to reconstruct trajectories to infer signal timing, but these methods generally have assumptions, such as vehicles traveling at a constant speed, constant acceleration and deceleration, etc., which overly simplify the actual traffic dynamics and driving behaviors, and are greatly limited in practical applications. Methods based on shock waves estimate signal timing information according to the formation and dissipation processes of traffic shock waves. For example, using a triangle to approximate the boundary of a congestion event, or determining the timing by fitting the shock wave with a piecewise linear function. However, these methods have limitations. On the one hand, they can only use specific geometric shapes to approximate the shock wave boundary, with a narrow scope of application; on the other hand, they mainly target signal timings with fixed cycle lengths and are difficult to apply to intersections with different timing plans. In addition, there are also some studies using statistical or machine learning techniques, which can predict the remaining waiting time using past observation data, but they also have limitations and cannot handle complex and changing traffic scenarios well. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide a method for estimating signal countdown by integrating the spatio-temporal propagation law of traffic waves with a wider range of practical application scenarios.

[0005] To achieve the above-mentioned invention object, the present invention provides the following technical solutions:

[0006] A method for estimating the signal light countdown by integrating the spatio-temporal propagation law of traffic waves, comprising the following steps:

[0007] (1) Divide the target road section into several road section units at equal intervals, and discretize the time axis into several time periods, so as to divide the spatio-temporal into several spatio-temporal grids;

[0008] (2) Calculate the vehicle grid observation state value of each spatio-temporal grid according to the instantaneous speed of each detection vehicle on each spatio-temporal grid, and the vehicle grid observation state value is used to characterize the moving state of each detected vehicle on each spatio-temporal grid;

[0009] (3) Establish a signal light countdown estimation model that integrates the spatio-temporal propagation law of traffic waves. The signal light countdown estimation model is specifically:

[0010] ,

[0011] In the formula, K represents the number of detection vehicles, is the vehicle grid recovery state of the spatio-temporal grid ( ). When the spatio-temporal grid ( ) restored by the model is in a stationary state = 1, otherwise = 0; is the grid actual state indicator variable, represents the vehicle grid observation state value of the spatio-temporal grid ( ), respectively represent the road section unit serial number and the time period serial number of the detection vehicle k; is the red light start time indicator variable. When t is the start time of the red light in a cycle , otherwise , is the green light start time indicator variable. When t is the start time of the green light in a cycle , otherwise ; is the red and green light pairing indicator variable. When are the start times of the red light and the green light in the same cycle , otherwise ; is the continuous red light indicator variable. When are the start times of the red lights in two consecutive cycles , otherwise ; represents the cycle classification indicator variable. When the signal timings of two cycles starting with a red light at the moment are the same , otherwise ; is the serial number of any time period, and , ;

[0012] (4) Add constraint conditions to the traffic signal countdown estimation model;

[0013] (5) Solve the traffic signal countdown estimation model to obtain the optimal value of the decision variable , and calculate the traffic signal countdown according to the optimal value of .

[0014] Further, step (2) specifically includes:

[0015] (2.1) Obtain the instantaneous speed of each detection vehicle on each spatio-temporal grid;

[0016] (2.2) Calculate the grid state value used to characterize the moving state of each detection vehicle on each spatio-temporal grid according to the instantaneous speed by the following formula:

[0017] ,

[0018] In the formula, when , it is considered that the detection vehicle k is in a stationary state in the spatio-temporal grid ( ), at this time, , otherwise it is considered to be in a moving state, at this time , s k represents the instantaneous speed of the detection vehicle k, and s th represents the speed threshold.

[0019] Further, the constraint conditions include red light start time constraint, green light start time constraint, red and green light start time pairing constraint, continuous cycle recognition constraint, shock wave spatio-temporal propagation constraint, vehicle waiting time decreasing constraint, signal cycle classification constraint, cycle length range constraint and decision variable constraint.

[0020] Further, the red light start time constraint is specifically:

[0021] ;

[0022] ;

[0023] ;

[0024] The green light start time constraint is specifically:

[0025] ;

[0026] ;

[0027] ;

[0028] Wherein, and are the grid actual state indication variables when the value of i is 1 at the time points of the spatio-temporal grids (1, t) and (1, t - 1) respectively, and T represents the number of time periods.

[0029] Furthermore, the specific traffic light start time pairing constraint is:

[0030] , ;

[0031] , ;

[0032] , ;

[0033] , ;

[0034] Wherein, T represents the number of time periods, is the value of when t takes the value of t1, and is the value of when t takes the value of t2.

[0035] Furthermore, the specific continuous cycle recognition constraint is:

[0036] , ;

[0037] , ;

[0038] , ;

[0039] , ;

[0040] Wherein, T represents the number of time periods, is the value of when t takes the value of t1, and is the value of when t takes the value of t3.

[0041] Furthermore, the specific shock wave spatio-temporal propagation constraint is:

[0042] ;

[0043] ;

[0044] The vehicle waiting time decreasing constraint is specifically as follows:

[0045] , ;

[0046] In the formula, 、 are both grid actual state indication variables, I represents the number of road section units, and T represents the number of time periods.

[0047] Furthermore, the signal cycle classification constraint is specifically as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] , , , ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] In the formula, 、 are respectively the absolute value of the difference in cycle lengths of two cycles starting with red lights at times t1 and t3, and the absolute value of the difference in red light durations of two cycles starting with red lights at times t1 and t3, are respectively 、 Auxiliary variables are used to assist in determining and The values of are all binary decision variables, taking values of 0 or 1. , , respectively represent the cycle length and red light duration of the cycle with the starting time of the red light being t1. , , and respectively represent the cycle length and red light duration of the cycle with the starting time of the red light being t3. t4 and t5 are time period numbers. is a continuous red light indication variable. is a traffic light pairing indication variable. M is a positive number greater than a preset threshold. represents the signal cycle, and T represents the number of time periods.

[0063] Furthermore, the specific constraint of the cycle length range is as follows:

[0064] ,

[0065] The specific constraint of the decision variable is as follows:

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] In the formula, and respectively represent the minimum and maximum cycle lengths. T represents the number of time periods, and I represents the number of road section units.

[0077] Furthermore, the steps for calculating the traffic light countdown based on the optimal value of specifically include:

[0078] (5.1) Extract the following key signal timing parameters according to the optimal value:

[0079] Red light start time sequence: Select the with a value of 1 from the optimal value of . Take the time point corresponding to the time period serial number t of the with a value of 1 as the red light start time point of a cycle. Arrange the red light start time points of all cycles in chronological order as , respectively represent the red light start time points of the 1st, …, kth, Nth cycles after sorting, and N is the total number of cycles;

[0080] Green light start time: Select the with a value of 1 from the optimal value of . Take the time point corresponding to the time period serial number t of the with a value of 1 as the green light start time of a cycle;

[0081] Cycle length and red light duration: Calculate according to the optimal value of as follows:

[0082] ,

[0083] ,

[0084] In the formula, respectively represent the cycle length and red light duration of the cycle with the red light start time of t1. When

[0085] (5.2) Locate the cycle to which the current time belongs according to the following formula , and obtain the cycle length and red light duration of this cycle:

[0086] ;

[0087] In the formula, represents the current time, m represents the time period serial number, represents the red light start time of the mth cycle;

[0088] (5.3) Calculate the signal light countdown according to the following formula:

[0089] ,

[0090] In the formula, is the red light countdown, This is the green light countdown indicating the start time of the red light in the th cycle.

[0091] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention can estimate the most likely traffic signal timing information from noise interference and sparse data. By integrating the spatio-temporal propagation law of traffic waves, the model takes the positions and speeds of probe vehicles on the signal-controlled section as inputs and outputs signal timing information including signal cycle length, red light and green light durations, etc. Compared with existing methods, the present invention does not need to preset the specific shape of the queue profile in the spatio-temporal diagram of the signal intersection and can distinguish different types of signal cycles, where the same type of cycles has the same signal timing scheme, so as to estimate the signal timing information more accurately. Under appropriate assumptions, the present invention can achieve unbiased estimation, and solving this 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 under low penetration rate 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 lengths, has a wider application range, and can well handle complex and changeable traffic scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 FIG. is a schematic flow chart of a signal light countdown estimation method that integrates the spatio-temporal propagation law of traffic waves provided by an embodiment of the present invention;

[0093] Figure 2 FIG. is a schematic diagram of traffic signal timing at a signal intersection and a corresponding queue profile diagram in a spatio-temporal diagram;

[0094] Figure 3 FIG. is a schematic diagram showing the gradually decreasing waiting time of vehicles from downstream to upstream in a single cycle;

[0095] Figure 4 FIG. is a schematic diagram of estimating signal timing of the NGSIM dataset under 10% penetration rate and 30-second sampling interval. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0096] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0097] Before introducing the present invention, the related terms used in the present invention are explained as follows:

[0098] Traffic signal timing information: Refers to parameters such as the cycle length, red light duration, and green light duration of traffic signals. It is crucial for intelligent transportation systems, which can help drivers optimize their driving behavior, reduce fuel consumption and emissions, and also improve the performance of autonomous driving and navigation systems. Traffic signal timing information is difficult to obtain directly from traffic signal systems.

[0099] Probe 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 problems of data sparsity and noise. In this paper, by discriminating the state of the data points of the probe vehicle (divided into stationary and moving states according to the comparison of speed with a threshold), it is used as the input of the model to estimate the signal timing.

[0100] Traffic wave propagation: Traffic wave propagation refers to a phenomenon in which traffic flow propagates on a road, similar to waves in a fluid. By establishing a mathematical programming model, the spatio-temporal impact range of traffic accidents can be estimated, and the output results of the model can satisfy the propagation law of traffic waves.

[0101] An embodiment of the present invention provides a method for estimating the countdown of traffic lights by integrating the spatio-temporal propagation law of traffic waves, as Figure 1 shown, specifically including:

[0102] (1) Divide the target road section into several road section units at equal intervals, and discretize the time axis into several time periods, so as to divide the spatio-temporal into several spatio-temporal grids.

[0103] Specifically, divide the target road section into I road section units at equal intervals, and discretize the time axis into T time periods, so as to divide the spatio-temporal into I×T spatio-temporal grids.

[0104] (2) Calculate the vehicle grid observation state value of each spatio-temporal grid according to the instantaneous speed of each probe vehicle on each spatio-temporal grid, and the vehicle grid observation state value is used to characterize the moving state of each observed probe vehicle on each spatio-temporal grid.

[0105] This step specifically includes:

[0106] (2.1) Obtain the instantaneous speed of each probe vehicle on each spatio-temporal grid;

[0107] (2.2) Calculate the grid state value used to characterize the moving state of each probe vehicle on each spatio-temporal grid according to the instantaneous speed according to the following formula:

[0108] ,

[0109] In the formula, when it is considered that the probe vehicle k is in a stationary state in the spatio-temporal grid ( ), at this time, , otherwise it is considered to be in a moving state, and at this time , s k represents the instantaneous speed of the detection vehicle k, s th represents the speed threshold, which is set to 2 km / h in this embodiment.

[0110] In addition, a fault-tolerant mapping relationship between the observed state and the true state can be established by introducing an error compensation term to effectively eliminate sensor noise interference; at the same time, a coverage matrix is constructed to identify the data sparse area, and a constraint-driven state inference mechanism is adopted for data completion of the uncovered grid cells. Taking as the input variable to construct the method realizes the multi-dimensional feature analysis and anti-noise characterization of the traffic flow state, provides a structured input with both spatio-temporal correlation and robustness for the subsequent optimization model, and the technical effect is significantly better than the traditional continuous variable processing method. as the input variable to construct the method realizes the multi-dimensional feature analysis and anti-noise characterization of the traffic flow state, provides a structured input with both spatio-temporal correlation and robustness for the subsequent optimization model, and the technical effect is significantly better than the traditional continuous variable processing method.

[0111] (3) Establish a signal light countdown estimation model that integrates the spatio-temporal propagation law of traffic waves.

[0112] When constructing the objective function of the signal light countdown estimation model, the core purpose is to accurately estimate the traffic signal timing information by means of the detection vehicle data, and at the same time fully consider 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 observed data, and the specific construction process is as follows:

[0113] 1. Establish the construction purpose: The aim is to accurately infer the traffic signal timing information from the noisy and sparse detection vehicle data, covering key elements such as cycle length, red light and green light duration. Given the characteristics of the detection vehicle speed data s k , it is difficult to directly deduce the signal timing plan P accurately based on these data. Therefore, the construction of the objective function focuses on how to efficiently use the existing data to improve the accuracy of the estimation.

[0114] 2. Define the key elements: Based on the detection vehicle data, divide the data point state according to the speed threshold s th into stationary and moving states, and define a discriminant binary index to represent the observed cell state.

[0115] The finally established signal light countdown estimation model is specifically:

[0116] ,

[0117] In the formula, K represents the number of detection vehicles, is the vehicle grid recovery state of the spatio-temporal grid ( ), when the spatio-temporal grid ([[]] When in a stationary state = 1, otherwise = 0; is the actual state indication variable of the grid, indicating the observed state value of the vehicle grid of the spatio-temporal grid ( ), respectively representing the section unit number and time period number of the detection vehicle k; is the red light start time indication variable. When t is the start time of the red light in a cycle , otherwise , is the green light start time indication variable. When t is the start time of the green light in a cycle , otherwise ; is the traffic light pairing indication variable. When are the start times of the red light and the green light in the same cycle , otherwise ; is the consecutive red light indication variable. When are the start times of the red light in two consecutive cycles , otherwise ; represents the cycle classification indication variable. When the signal timings of two cycles starting with a red light at the moment are the same , otherwise ; is any time period number, and , .

[0118] In this objective function, when , that is, when it is observed that the cell is in a stationary state, the expected decision variable is also 1 to ensure that the state restored by the model is consistent with the actual observed state; conversely, when , ideally should be 0. By minimizing the difference between the two, it can be ensured that the cell state restored by the model is in the best agreement with the actual observed data. This enables the model to analyze the cell state more accurately when estimating traffic signal timing information, thereby improving the reliability and accuracy of the estimation results. The objective function optimizes the decision variables, comprehensively covering multiple key aspects such as the identification and pairing of the start times of red and green lights in a traffic signal cycle, the classification of cycle types, and the restoration of cell states, fully reflecting the comprehensive requirements of the model for estimating traffic signal timing information. Among the decision variables, and cooperate with each other to accurately depict the start time points of red and green lights in the signal cycle; in the complex time series of multiple cycles, through It can effectively identify the pairing relationship between the start times of red and green lights in the same cycle, providing necessary conditions for determining the cycle length and red light duration; clarifies the continuity of the start times of different cycles, combined with it can accurately calculate the cycle length and red light duration, thus completely describing the time characteristics of the signal cycle; It is used to restore the actual state of grid cells in the spatio-temporal diagram. In the analysis based on the spatio-temporal diagram, due to sparse data points and noise interference, it is difficult to judge the state of grid cells; The introduction of variables can accurately identify the state of grid cells according to the actual traffic state, providing a reliable basis for estimating traffic signal timing information based on the cell state. Considering that the data of a single cycle is limited and the timing of adjacent time periods has a certain stability, through classifying signal cycles, it can effectively integrate the data of multiple cycles, improve the estimation accuracy of the model for signal timing information, especially in the scenario of adaptive signal timing intersections, and can better adapt to the dynamic changes of traffic conditions.

[0119] In summary, the objective function closely focuses on the core task of accurately estimating traffic signal timing information by using probe vehicle data. By minimizing the difference between the 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.

[0120] (4) Add constraint conditions to the signal light countdown estimation model.

[0121] Among them, the constraint conditions 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 spatio-temporal propagation constraint, vehicle waiting time decreasing constraint, signal cycle classification constraint, cycle length range constraint and decision variable constraint.

[0122] The specific red light start time constraint is:

[0123] ;(1)

[0124] ;(2)

[0125] ;(3)

[0126] Among them, constraint (1) means that when time t corresponds to the start time of the red light in a certain cycle, that is, when, the first cell <1, t> at the stop line must be in a stationary state, so it is required that , 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 this cell in a stationary state.

[0127] Constraint (2) means that, also at time t corresponding to the start time of the red light 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 before the red light comes on, the vehicle can pass normally, which conforms to the actual traffic scenario.

[0128] Constraint (3) is used to verify in reverse whether time t is the start time of the red light. When and when, according to the actual traffic logic, at this time t should be the start time of the red light, that is , this constraint guarantees this logical judgment.

[0129] The specific green light start time constraint is as follows:

[0130] ;(4)

[0131] ;(5)

[0132] ;(6)

[0133] In the formula, is the value of when i takes the value of 1, and T represents the number of time periods.

[0134] Constraint (4) means that when time t corresponds to the start time of a certain cycle of the green light, the vehicle in the cell <1, t> at the stop line should be in a moving state of starting to drive, so there is .

[0135] Constraint (5) means that at time t when it is the start time of the green light the vehicle 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 the vehicle waits in front of the stop line before the green light comes on.

[0136] Constraint (6) is used to determine in reverse whether time t is the start time of the green light. When and when, according to traffic common sense, t should be the start time of the green light, that is , this constraint guarantees the judgment of this logical relationship.

[0137] The specific red and green light start time pairing constraint is as follows:

[0138] , ; (7)

[0139] , ; (8)

[0140] , ; (9)

[0141] , ; (10)

[0142] In the formula, T represents the number of time periods, is the value when t takes the value of t1 in is the value when t takes the value of t2 in

[0143] Constraint (7) means that when t1 is the starting time of the red light ( ), t2 is the starting time of the green light ( ) and there are no other starting times of red lights and green lights between t1 and t2 ( ), according to the definition of the traffic signal cycle, it can be inferred that t1 and t2 correspond to the starting times of the red light and the green light in the same cycle, that is .

[0144] Constraints (8), (9), and (10) together mean that if the conditions of Constraint (7) are not met, that is , or , or , it can be determined that t1 and t2 do not correspond to the starting times of the red light and the green light in the same cycle, that is .

[0145] The specific continuous cycle recognition constraint is as follows:

[0146] , ; (11)

[0147] , ; (12)

[0148] , ; (13)

[0149] , ; (14)

[0150] In the formula, T represents the number of time periods, is The value of t when t takes the value of t1, is the value of t when t takes the value of t3.

[0151] Constraint (11) indicates that when t1 and t3 are respectively the starting times of red lights in two cycles ( ), and there is no other starting time of red lights 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 .

[0152] Constraints (12), (13), and (14) together indicate that if the conditions of Constraint (11) are not met, that is , or , or , we can know that t1 and t3 do not correspond to consecutive cycles, that is .

[0153] The specific constraints on the spatio-temporal propagation of the shock wave are as follows:

[0154] ; (15)

[0155] ; (16)

[0156] The specific constraints on the decreasing waiting time of vehicles are as follows:

[0157] , ; (17)

[0158] In the formula, , are both grid actual state indicator variables, I represents the number of road section units, and T represents the number of time periods. As Figure 2 shown, it shows a signalized intersection with multiple cycle types and the queue profile in the corresponding spatio-temporal diagram. The horizontal axis represents time, and the vertical axis represents the distance to the stop line.

[0159] Constraint (15) indicates that in the spatio-temporal diagram, the propagation of the traffic shock wave has a specific law. When the cell <i, t> is in a stationary state, according to the continuity and directionality of the shock wave propagation, it is required that its adjacent cell <i - 1, t> or <i, t - 1>, or both must be in a stationary state ( , or , or both are 1).

[0160] Constraint (16) indicates that, also based on the shock wave propagation law, when both cells <i - 1, t> and <i, t - 1> are in a stationary state ( ), according to the propagation characteristics of the shock wave, the cell <i,t> must also be in a stationary state ( ).

[0161] Constraint (17) indicates that within a signal cycle, starting from when the red light comes on, vehicles closer to the downstream of the stop line will wait longer than those upstream.

[0162] The specific signal cycle classification constraints are as follows:

[0163] ; (18)

[0164] ; (19)

[0165] ; (20)

[0166] ; (21)

[0167] ; (22)

[0168] ; (23)

[0169] ; (24)

[0170] ; (25)

[0171] ; (26)

[0172] , , , ; (27)

[0173] ; (28)

[0174] ; (29)

[0175] ; (30)

[0176] ; (31)

[0177] In the formula, , are respectively the absolute value of the difference in cycle lengths between two cycles starting with a red light at times t1 and t3, and the absolute value of the difference in red light durations between two cycles starting with a red light at times t1 and t3, are respectively , auxiliary variables used to assist in determining , The values of are all binary decision variables, taking values of 0 or 1. , , respectively represent the cycle length and the red - light duration of the cycle with the red - light start time at t1. , , , respectively represent the cycle length and the red - light duration of the cycle with the red - light start time at t3. t4 and t5 are time - period serial numbers. is the continuous red - light indication variable. is the traffic - light pairing indication variable. M is a positive number greater than a preset threshold. represents the signal cycle, and T represents the number of time periods.

[0178] Constraints (18) to (27) together represent that when t1 and t3 correspond to the red - light start times of two consecutive cycles ( = 1), and their signal timing plans are the same ( , = ), according to the signal - cycle classification rule, these two cycles belong to the same type ( = 1), which is achieved by a series of constraints constructed by and the introduced variables , , .

[0179] Constraints (28) to (30) together represent that if the conditions of , and and = are not met, that is, , or , or , then these two cycles will not be classified as the same type, that is, = 0.

[0180] Constraint (31) represents that the type number of the signal cycle can be determined according to and . This constraint helps to further analyze the distribution of different cycle types and provides an important basis for the optimization of traffic - signal timing.

[0181] The specific cycle - length range constraint is as follows:

[0182] , (32)

[0183] The specific decision - variable constraint is as follows:

[0184] ; (33)

[0185] ; (34)

[0186] ; (35)

[0187] ; (36)

[0188] ; (37)

[0189] ; (38)

[0190] ; (39)

[0191] ; (40)

[0192] ; (41)

[0193] ; (42)

[0194] In the formula, respectively represent the minimum and maximum cycle lengths, T represents the number of time periods, and I represents the number of road section units.

[0195] Constraints (33) to (37) together represent that, to ensure the consistency and solvability of the model calculation, the decision variables are restricted to be binary.

[0196] Constraints (38) to (42) together represent that, for a given spatio-temporal boundary condition, when the subscripts of the decision variables exceed the normal range, to ensure the rationality and stability of the model, these decision variables are assigned a value of 0.

[0197] (5) Solve the signal light countdown estimation model to obtain the optimal values of the decision variables According to the optimal values of calculate the signal light countdown.

[0198] This step specifically includes:[[]]

[0199] (5.1) Extract the following key signal timing parameters according to the optimal values of :

[0200] Red light start time sequence: Select the with a value of 1 from the optimal values of and the The time point corresponding to the time period serial number t is used as the starting time point of the red light for one cycle. The starting time points of the red lights for all cycles are arranged in chronological order as , indicating the starting time points of the red lights for the 1st, kth, and Nth cycles after sorting, where N is the total number of cycles;

[0201] Starting time of the green light: Select the value of 1 from the optimal values of , and use the time point corresponding to the time period serial number t of the value of 1 as the starting time of the green light for one cycle; , The time point corresponding to the time period serial number t of the value of 1 is used as the starting time of the green light for one cycle.

[0202] Cycle length and red light duration: Calculate according to the optimal values of using the following formula:

[0203] ,

[0204] ,

[0205] In the formula, respectively represent the cycle length and red light duration of the cycle with the starting time of the red light being t1. When

[0206] (5.2) Locate the cycle to which the current time belongs using the following formula , and obtain the cycle length and the red light duration :

[0207] ;

[0208] In the formula, represents the current time, m represents the time period serial number, represents the starting time of the red light for the mth cycle;

[0209] (5.3) Calculate the signal light countdown using the following formula:

[0210] ,

[0211] In the formula, is the red light countdown, is the green light countdown, represents the th starting time of the red light for the cycle.

[0212] In addition, in the scenario of fixed timing, the cycle cycle processing for the fixed timing scenario can also be performed in the following manner:

[0213] If the signal timing is of the fixed - cycle type (i.e., the timing parameters of each cycle are the same), the calculation can be simplified through modulo operation: , when , calculate according to the remaining red - light time; when , calculate according to the remaining green - light time.

[0214] In addition, the boundary conditions and constraint processing are as follows:

[0215] 1. Time - out processing:

[0216] If (exceeding the analysis period), by default, start cyclic calculation from the first cycle , that is (M is the number of cycle repetitions, is the average cycle length).

[0217] 2. Discrete - time matching:

[0218] When does not exactly fall within the discrete - time interval of the model (for example, the model is in seconds while the real - time contains milliseconds), use the nearest - neighbor method or linear interpolation to determine the belonging cycle to ensure .

[0219] 3. Multi - phase support:

[0220] For multi - phase signal control, perform the above steps independently for each phase. Estimate the cycle length Ln and red - light length Rn of each phase through the probe data in the corresponding direction, and calculate the remaining time of each phase respectively.

[0221] Next, perform numerical experiments on the present invention. The experiments mainly include the following steps:

[0222] Step 1: Experiment preparation.

[0223] (1) Data acquisition and processing: The simulated data generated by VISSIM software and the NGSIM real dataset were selected as the sources of experimental data. For the simulated data, intersection scenarios with fixed and adaptive signal timings were simulated. During the simulation, parameters such as saturation flow rate, section division, and time interval were carefully set. The saturation flow rate was set to 1800 pcu / h / lane, the signalized sections were divided into small segments of 6 meters, and the analysis period was discretized into intervals of 2 seconds to construct a spatio-temporal map with a specific resolution. At the same time, considering the possible noise interference in the actual data, the simulated data was processed accordingly to simulate the real situation. For the real data, the signal intersection data located at Peachtree Street in Atlanta, Georgia in the NGSIM project was selected. This data was collected by eight video cameras and recorded from 12:45 - 13:00 on November 8, 2006, and contains rich content such as vehicle trajectories, signal timings, and geographical information. Since the trajectory data in the eastward and westward directions in the dataset is limited, the experiment focused on the northward and southward directions, and the intersection uses fixed signal timing. The cycle length is known to be 98 seconds, the red light duration is 64 seconds, and the green light duration is 34 seconds.

[0224] (2) Experimental environment construction: An experimental program was written using the Python 3.9 programming language, and the Gurobi 11.0 optimizer was used to solve the integer programming model. All experiments were run on a desktop computer equipped with an Intel 5.20 GHz CPU and 64 GB of memory. Considering that the standard branch-and-bound algorithm may have a problem of too long solution time when dealing with large-scale problems, the present invention 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.

[0225] Step two: Simulated data experiment.

[0226] (1)Fixed-time intersection test: Ten cycles of data with two different signal timing schemes were selected for the experiment. Different from traditional methods, the model involved in the present invention has the ability to automatically identify different cycle types without prior manual distinction. To comprehensively evaluate the performance of the model under different data qualities, four combinations of probe vehicle penetration rate and sampling interval were set, namely [100%, 1s], [100%, 30s], [10%, 1s] and [10%, 30s], which cover different scenarios from high-quality data to sparse data. The mean absolute error (MAE) and mean absolute percentage error (MAPE) were used as evaluation metrics to measure the estimation accuracy of the model for cycle length and red light duration. The experimental results show that the present model can accurately identify different types of cycles and achieve good estimation results under various data conditions. Even in the [10%, 30s] scenario with the sparsest data, the model can still maintain high effectiveness, with an average MAE of 1.8 seconds and MAPE of 1.5% for cycle length; the average MAE is 2 seconds and MAPE is 2.67% for red light duration.

[0227] (2)Adaptive signal timing intersection test: The model was verified using ten cycles of data with different signal timing schemes. In the scenario of adaptive signal timing intersections, since the signal timing scheme of each cycle is regarded as a specific type, some constraint conditions applicable to fixed-time 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-time intersections, satisfactory results can still be obtained in most cases. The average MAPE ranges for estimating cycle length and red light duration are 3.77% - 11.65% respectively, which fully verifies the applicability and effectiveness of the present model under different signal timing scenarios.

[0228] (3)Analysis of the impact of incorrect data: Considering that random Gaussian errors are inevitable in the actual data collection process and will affect the model estimation accuracy, an experiment on the impact of incorrect data was carried out. According to the common practice of existing similar studies, the magnitude of the measurement error was set to [1, 2, 3] ( (standard deviation of the observed speed), and the error percentage was 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 was repeated five times for each error scenario for sensitivity analysis. As Figure 4As shown, it presents the observed and recovered cell states within one cycle when the permeability is 10% and the sampling interval is 30 seconds. The experimental results show that when the percentage error is in the range of [0%, 25%], the estimation results of the model remain stable and accurate; when the percentage error exceeds 25% and reaches 3 , there will be a significant increase in the estimated MAE and MAPE, resulting in the estimation results no longer being satisfactory. However, generally speaking, this model has strong robustness to incorrect data and can, to a certain extent, resist the interference of data errors and ensure the reliability of the estimation results.

[0229] Step 3: Real data experiment.

[0230] The NGSIM real dataset is used to further verify the performance of the patent model in an actual scenario. During the experiment, four combinations of probe vehicle permeability and sampling interval, namely [100%, 1s], [100%, 30s], [10%, 1s], and [10%, 30s], are also set, and each combination is repeated five times to reduce the influence of random factors on the experimental results. The experimental results show that in the [10%, 30s] combination where the data is the sparest, the estimated MAE of the model for the cycle length is 4.4 seconds, and the MAPE is 4.49%; the estimated MAE for the red light duration is 3.6 seconds, and the MAPE is 5.63%. These results indicate that even in the case of noise and sparsity in the actual data, the patent model can still effectively recover the cell states, accurately estimate the signal timing information, fully verifying the effectiveness and practicality of the model in a real scenario.

[0231] It should be understood that the above embodiments and the descriptions in the specification only illustrate the principles, main features, and advantages of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the protection scope of the present invention.

Claims

1. A method for estimating the signal light countdown by integrating the spatio-temporal propagation law of traffic waves, characterized in that, It includes the following steps: (1) Divide the target road section into a number of road section units at equal intervals, and discretize the time axis into a number of time periods, so as to divide the space-time into a number of space-time grids; (2) Calculate the vehicle grid observation state value of each space-time grid according to the instantaneous speed of each detection vehicle on each space-time grid, and the vehicle grid observation state value is used to characterize the moving state of each detected vehicle on each space-time grid; (3) Establish a signal light countdown estimation model that integrates the space-time propagation law of traffic waves. The signal light countdown estimation model is specifically: ， where K represents the number of detection vehicles, is the vehicle grid recovery status of the spatio-temporal grid ( ). When the spatio-temporal grid ( ) restored by the model is in a stationary state = 1, otherwise = 0; is the actual status indicator variable of the grid, represents the observed status value of the vehicle grid of the spatio-temporal grid ( ). respectively represent the section unit number and time period number of the detection vehicle k; is the red light start time indicator variable. When t is the start time of the red light in a cycle , otherwise . is the green light start time indicator variable. When t is the start time of the green light in a cycle , otherwise ; is the traffic light pairing indicator variable. When are the start times of the red light and the green light in the same cycle , otherwise ; is the continuous red light indicator variable. When are the start times of the red light in two consecutive cycles , otherwise ; represents the cycle classification indicator variable. When the signal timings of two cycles starting with a red light at the moment are the same , otherwise ; is any time period number, and , ; (4) Add constraint conditions to the signal light countdown estimation model; (5) Solve the traffic signal countdown estimation model to obtain the optimal value of the decision variable , and calculate the traffic signal countdown based on the optimal value of , specifically including: Extract the following key signal timing parameters according to the optimal value: Red light start time sequence: Select the value of 1 from the optimal values of , and use the time point corresponding to the time period number t of with the value of 1 as the red light start time point of one cycle. Arrange the red light start time points of all cycles in chronological order as , , respectively represent the red light start time points of the 1st, kth, and Nth cycles after sorting, where N is the total number of cycles; Green light start time: Select from the optimal values of the one with a value of 1, and use the time point corresponding to the time period serial number t of the one with a value of 1 as the green light start time for one cycle; Cycle length and red light duration: According to The optimal value is calculated according to the following formula: ， ， Wherein, respectively represent the cycle length and the red light duration of the cycle with the starting time of the red light being t1, the two cycle types are the same when, that is, the cycle length and the red light duration are the same; (5.2) Locate the period to which the current time belongs according to the following formula and obtain the period length of this period and the red light duration : ； wherein, represents the current time, m represents the period serial number, represents the starting time of the red light in the m-th cycle; (5.3) Calculate the signal light countdown according to the following formula: , Wherein, is the red light countdown, is the green light countdown, represents the starting time of the red light in the 2. The signal light countdown estimation method integrating the spatio-temporal propagation law of traffic waves according to claim 1, characterized in that Step (2) specifically includes: (2.1) Obtain the instantaneous speed of each detection vehicle on each space-time grid; (2.2) Calculate the grid state value used to characterize the moving state of each detection vehicle on each space-time grid according to the instantaneous speed according to the following formula: , In the formula, when , it is considered that the detection vehicle k is in a stationary state in the spatio-temporal grid ( ). At this time, . Otherwise, it is considered to be in a moving state. At this time , s k represents the instantaneous speed of the detection vehicle k, and s th represents the speed threshold.

3. The signal light countdown estimation method that integrates the spatio-temporal propagation law of traffic waves according to claim 1, characterized in that The constraint conditions 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 space-time propagation constraint, vehicle waiting time decreasing constraint, signal cycle classification constraint, cycle length range constraint and decision variable constraint.

4. The signal light countdown estimation method that integrates the spatio-temporal propagation law of traffic waves according to claim 3, characterized in that The red light start time constraint is specifically: ; ; ; The green light start time constraint is specifically: ; ; ; Wherein, and are respectively the grid actual state indication variables of the spatio-temporal grids (1, t) and (1, t-1), and T represents the number of time periods.

5. The signal light countdown estimation method for fusing the spatio-temporal propagation law of traffic waves according to claim 3, characterized in that, The red and green light start time pairing constraint is specifically: , ; , ; , ； ， ； Where T represents the number of time periods, is the value when t takes the value of t1 in is the value when t takes the value of t2 in.

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

7. The method for estimating the signal light countdown by integrating the spatio-temporal propagation law of traffic waves according to claim 3, wherein The shock wave space-time propagation constraint is specifically: ; ; The vehicle waiting time decreasing constraint is specifically: , ; Wherein, and are both grid actual status indication variables, I represents the number of road section units, and T represents the number of time periods.

8. The signal light countdown estimation method for fusing the spatio-temporal propagation law of traffic waves according to claim 3, characterized in that, The signal cycle classification constraint is specifically: ； ； ； ； ； ； ； ； ； ， ， , ; ; ; ; ; In the formula, and are respectively the absolute value of the difference in cycle lengths of two cycles starting with red lights at times t1 and t3, and the absolute value of the difference in red light durations of two cycles starting with red lights at times t1 and t3. are respectively and auxiliary variables used to assist in determining the values of and . Both are binary decision variables with values of 0 or 1. , , respectively represent the cycle length and red light duration of the cycle with the red light starting time at t1. , , and respectively represent the cycle length and red light duration of the cycle with the red light starting time at t3. t4 and t5 are time period serial numbers. is a continuous red light indication variable. is a traffic light pairing indication variable. M is a positive number greater than the preset threshold. represents the signal cycle, and T represents the number of time periods.

9. The method for estimating the signal light countdown by fusing the spatio-temporal propagation law of traffic waves according to claim 3, wherein The cycle length range constraint is specifically: ， The decision variable constraint is specifically: ； ； ； ； ； ； ； ； ； ； wherein and represent the minimum and maximum cycle lengths respectively, T represents the number of time periods, and I represents the number of road section units.

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