Information fusion optimization method based on fixed and mobile vehicle detection data

Abstract

This invention discloses an information fusion optimization method based on fixed and mobile vehicle detection data. The method includes decomposing the transportation system into several input and output subsystems and acquiring multi-source detection data from each subsystem; extracting traffic information from historical traffic datasets; establishing a combinatorial optimization model; using dynamic programming to solve the joint matching probability model of mobile and fixed detection data; directly matching upstream and downstream fixed detection data marked with the same mobile detection data through data fusion; and using the K-M algorithm to solve the joint matching probability model of upstream and downstream fixed detection data to achieve joint matching between unmarked upstream and downstream fixed detection data. This method can obtain globally optimal matching results in a very short time, and even if the mobile detection data has significant inaccuracies or the fixed detection data has some gaps, the data matching accuracy remains at a high level, enabling a more accurate reflection of the micro-level traffic flow state.

Description

Technical Field

[0001] This invention relates to the field of traffic engineering, and in particular to a data and information fusion optimization method based on fixed and mobile vehicle detection data. Background Technology

[0002] Vehicle traffic information is primarily acquired using fixed and mobile detectors. While fixed detectors can collect large-scale vehicle data, they can only record at fixed points, resulting in spatially discrete data with a degree of error (e.g., some vehicles pass by the detector but are not detected). Mobile detectors can continuously record more detailed vehicle information, but they only record data for vehicles equipped with the device, failing to reflect the overall traffic situation on a road segment. Furthermore, the data may involve user privacy, limiting its use. Therefore, both types of vehicle detector data have their own shortcomings.

[0003] In recent years, multi-source data fusion methods that consider both fixed and mobile detection data have been developed to complement each other, thereby improving the accuracy of information acquisition. However, most current multi-source data fusion methods acquire macroscopic, aggregated traffic parameters, such as average travel time and average speed. Only a few methods can obtain more microscopic traffic conditions, such as individual travel times. These latter methods often employ exhaustive methods or heuristic algorithms (such as tabu search) to fuse multi-source data, lack consideration for vehicle-specific characteristics during information integration, and require separate assumptions for long and short road segments regarding whether to add First-In-First-Out (FIFO) constraints.

[0004] First, while exhaustive methods for fusing moving and fixed data can achieve a globally optimal result, they are computationally too time-consuming. Heuristic algorithms, on the other hand, offer shorter computation times but only achieve locally optimal results. Second, because the unique characteristics of vehicles are not considered, the integrated traffic information is incomplete and fails to accurately reflect real traffic flow conditions. Therefore, using incomplete integrated traffic information increases the error in the results. Third, the practice of not considering the first-in-first-out (FIFO) condition for long road segments but considering it for short road segments is based on normal traffic flow. However, this approach is not applicable to abnormal traffic flows (e.g., excessive aggressive driving on short road segments leading to frequent lane changes). Artificially setting the FIFO condition in this way can actually increase the error in the results, leading to a more distorted description of traffic flow conditions.

[0005] The data and information fusion method based on fixed and mobile vehicle detection data given in patent CN107886192B still has some of the technical problems mentioned above.

[0006] Therefore, there is currently a lack of a data fusion and information integration method that can quickly fuse mobile and fixed data, consider the vehicle's own characteristic information, does not require the assumption of first-in-first-out (FIFO) conditions, and can be solved analytically to achieve the globally optimal result. Summary of the Invention

[0007] The purpose of this invention is to provide an information fusion optimization method based on fixed and mobile vehicle detection data. This method can fuse mobile and fixed detection data in a short time, and significantly improve the accuracy of data fusion and information integration results by integrating the vehicle's own detection length information and using an analytical method that can achieve global optimization. Using this method, the micro-level traffic flow state can be described more accurately.

[0008] The technical solution adopted by this invention to achieve its objective is: an information fusion optimization method based on fixed and mobile vehicle detection data, the method comprising the following steps:

[0009] S1. Decompose the transportation system (road network) into several input (road segments) and output (intersection) subsystems, and obtain multi-source detection data for each subsystem; the multi-source detection data includes fixed detection data and mobile detection data; the fixed detection data includes timestamps, lane information, and vehicle length information of vehicles passing through upstream and downstream fixed detectors of the subsystem; the mobile detection data includes vehicle ID, timestamps recorded at a fixed frequency, and vehicle location information, which are used to verify and calibrate the fixed detection data;

[0010] S2. Extract traffic information from historical traffic datasets, including the probability of each possible lane selection or merging selection, the probability distribution of travel time under each possible lane selection or merging selection, and the probability distribution of error in vehicle detection length.

[0011] S3. Establish a combined optimization model, including: a joint matching probability model of mobile detection data and fixed detection data, and a joint matching probability model of upstream and downstream fixed detection data; the objective function and constraints of the combined optimization model;

[0012] S4. Use dynamic programming to solve the joint matching probability model of mobile detection data and fixed detection data to achieve the fusion of upstream mobile detection data and upstream fixed detection data, as well as the fusion of downstream mobile detection data and downstream fixed detection data; through data fusion, upstream and downstream fixed detection data marked by the same mobile detection data can be directly matched.

[0013] S5. Use the KM algorithm (i.e., Kuhn-Munkres algorithm) to solve the joint matching probability model of upstream and downstream fixed detection data, realize the joint matching between upstream and downstream fixed detection data that are not marked by moving detection data, and find the matching result that maximizes the probability between upstream and downstream fixed detection data.

[0014] Furthermore, step S2 specifically includes extracting the following four probabilistic information items from the historical traffic dataset:

[0015] S2-1, Lane Selection Probability That is, the probability that a vehicle passing through downstream lane l also passes through upstream lane l′, where: uppercase symbols L and L′ represent random variables, and lowercase symbols l and l′ represent the values ​​of random variables; It is determined by the number of historical data samples for downstream lane l and upstream lane l′. It is the total number of historical data samples from the downstream lane l;

[0016] S2-2, Vehicle Merging Probability That is, the probability that a vehicle flowing downstream to u has an upstream flow direction of u′, where: uppercase symbols L and L′ represent random variables, and lowercase symbols u and u′ represent the values ​​of random variables; It is the number of historical data samples flowing downstream to u and upstream to u′; It is the total number of historical data samples flowing downstream to u;

[0017] The lane selection probability and vehicle merging probability mentioned above have the same mathematical expression; the former applies to the input subsystem (road segment), and the latter applies to the output subsystem (intersection). In the following description, both the lane selection probability and the vehicle merging probability are expressed as p. L L / L′ means that for the input subsystem, L / L′ represents a lane; for the output subsystem, L / L′ represents a lane group.

[0018] S2-3, Probability of travel time distribution That is, the probability that the travel time from the upstream lane or lane group l′ to the downstream lane or lane group l is τ, where: τ=tt′, t represents the timestamp of the vehicle passing the downstream fixed detector, and t′ represents the timestamp of the vehicle passing the upstream fixed detector; This represents the travel time of vehicles that sequentially pass through the upstream lane or lane group l′ and the downstream lane or lane group l in historical data; n is the number of historical data samples, and τ is the travel time record for each historical travel time. n h represents bandwidth; for a given pair of upstream and downstream fixed detection data, the corresponding probability density can be found at the travel time τ = tt′;

[0019] S2-4, Error Distribution Probability of Vehicle Detection Length That is, the probability that the vehicle length record c′ detected by the upstream fixed detector and the vehicle length record c detected by the downstream fixed detector originate from the same vehicle, where: σ s The standard deviation is the value of which can be determined based on historical data or by experts who study the accuracy of vehicle length detection.

[0020] Furthermore, step S3 specifically includes:

[0021] S3-1. Establish a joint matching probability model for mobile detection data and fixed detection data;

[0022] Let P(M=m) and P(M′=m′) represent the joint matching probabilities between the downstream and upstream fixed detection datasets and the mobile detection dataset, respectively. Their mathematical expressions are shown in Equation (4) and Equation (5), respectively:

[0023]

[0024]

[0025] In equations (4) and (5), the index of vehicle j in the downstream mobile detection dataset corresponding to its downstream fixed detection dataset is defined as {M j ∈M|j=1,2,...,N m}, where M j m is the ordinal variable. j The value of the ordinal variable; for a vehicle k in the upstream moving detection dataset, the corresponding ordinal number in its upstream fixed detection dataset is defined as {M′ k ∈M′|k=1,2,...,N m}, where M′ k Let m' be the ordinal variable. k The value of the sequence number variable; the amount of motion detection data in both the upstream and downstream is equal to N. m α M and α M ′ represents a term; for the same vehicle, considering the possibility of overtaking within a road segment or intersection, its position in the upstream and downstream motion detection datasets may differ. Therefore, different subscripts j and k are used to represent the vehicle's index in the downstream and upstream motion detection datasets. For j≠j′ and k≠k′, it must be ensured that m j ≠m j ′,m′ k ≠m′ k′ This ensures a one-to-one match between mobile detection data and fixed detection data; p M (m j ) and p M′ (m′ k) represent the discrete matching probabilities between the fixed detection record and the moving detection record at the downstream and upstream positions, respectively. These two probabilities are calculated according to equations (6) and (7):

[0026]

[0027]

[0028] Equation (6) represents the downstream j-th movement detection record and the downstream m-th movement detection record. j The matching probability of a fixed number of detection records, which is related to the timestamps of the two records. and The probability density function of the difference follows a normal distribution, where This represents the timestamp of the j-th vehicle in the downstream mobile detection dataset passing through the downstream fixed detection point. Represents the m-th element in the downstream fixed detection dataset. j The timestamp of the record; Equation (7) represents the k-th upstream motion detection record and the m′ upstream record. k The matching probability of a fixed number of detection records, which is related to the timestamps of the two records. and The probability density function of the difference follows a normal distribution, where This represents the timestamp of the k-th vehicle in the upstream mobile detection dataset passing through the upstream fixed detection point. Denotes the m′-th value in the upstream fixed detection dataset. k The timestamp of each record;

[0029] S3-2. Establish a joint matching probability model for upstream and downstream fixed detection data;

[0030] P(S=s) represents the joint matching probability between the downstream and upstream fixed detection data that are not labeled by the moving detection data, and its mathematical expression is shown in Equation (8):

[0031]

[0032] In equation (8), the random variable {S} i ∈S|i=1,2,...,N s} represents the index of the i-th vehicle in the downstream fixed detection dataset that is not labeled by the mobile detection data, within the upstream fixed detection dataset that is not labeled by the mobile detection data, where N s This represents the total number of samples in the downstream fixed detection dataset that are not labeled by the moving detection data; for any i≠i′, then si≠si′ to ensure a one-to-one match between each downstream fixed detection data and each upstream fixed detection data. Indicates downstream fixed detection data (l) i , ti c i ) and upstream fixed detection data The matching probability between them is expressed as shown in equation (9):

[0033]

[0034] Equation (9) is the lane selection probability or vehicle merging probability. Travel time distribution probability Error distribution probability of vehicle detection vehicle length The integration is represented by the product of the three, α S To be classified under one item;

[0035] S3-3. Establish the objective function and constraints of the combinatorial optimization model, expressed by equations (10.1) to (10.5):

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] Equation (10.1) is the objective function, and the optimization result requires maximizing the overall matching probability; Equations (10.2) and (10.3) are constraints, ensuring that the relative sequence numbers of two moving detection records in the moving detection dataset and the fixed detection dataset are consistent; Equation (10.4) is a constraint, ensuring that the matching between the upstream fixed detection data and the downstream fixed detection data is only performed on the fixed detection data that has not been marked by the moving detection data; Equation (10.5) is a constraint, ensuring a one-to-one matching between the fixed detection data.

[0042] Furthermore, step S4 specifically includes:

[0043] S4-1. Use dynamic programming to solve the joint matching probability model of upstream mobile detection data and upstream fixed detection data to achieve the fusion of upstream mobile detection data and upstream fixed detection data; the upstream dynamic programming solution formula is as follows:

[0044]

[0045]

[0046] m′ k+1 =x′ k (11.3)

[0047] k≤m′ k <x′ k ≤N s -N m +k+1 (11.4)

[0048] Equation (11.1) is the objective function, where V M′ (m′ k ) represents the upstream k-th to N-th m The product of the maximum probability of matching between the moving detection data and the fixed detection dataset, p M′ (m′ k ) indicates that the k-th upstream movement detection data is matched with the m′ upstream movement detection data. k The probability of a fixed number of detection data, V M′ (m′ k+1 ) represents the upstream k+1th to Nth m The product of the maximum probability of matching the moving detection data and the fixed detection dataset; Equation (11.2) is the constraint condition, i.e., the boundary condition of dynamic programming; Equation (11.3) is the constraint condition, where x′ k As the decision variable, it determines the relationship between the (k+1)th upstream movement detection data and the m′ upstream movement detection data. k+1 Matching of fixed detection data; Equation (11.4) is a constraint condition. For two upstream moving detection records, it is ensured that they are matched with the upstream fixed detection dataset according to the condition that the relative sequence numbers are consistent.

[0049] S4-2. Use dynamic programming to solve the joint matching probability model of downstream mobile detection data and downstream fixed detection data to achieve the fusion of downstream mobile detection data and downstream fixed detection data; the downstream dynamic programming solution formula is as follows:

[0050]

[0051]

[0052] m j+1 =x j (12.3)

[0053] j≤m j <x j ≤N s -N m +j+1 (12.4)

[0054] Equation (12.1) is the objective function, where V M (m j ) represents the downstream from the j-th to the N-th m The product of the maximum probability of matching between the moving detection data and the fixed detection dataset, pM (m j This indicates that the j-th downstream motion detection data is matched to the m-th data. j The probability of a fixed number of detection data, V M (m j+1 ) represents the downstream from the (j+1)th to the Nth m The product of the maximum probability of matching the moving detection data and the fixed detection dataset; Equation (12.2) is the constraint condition, i.e., the boundary condition of dynamic programming; Equation (12.3) is the constraint condition, where x j As a decision variable, it determines the relationship between the (j+1)th downstream motion detection data and the mth downstream data. j+1 Fixed data matching; Equation (12.4) is a constraint condition, which ensures that the two downstream moving detection records are matched with the downstream fixed detection dataset according to the condition that the relative sequence numbers are consistent.

[0055] Furthermore, step S5 specifically includes:

[0056] S5-1. Convert the joint matching probability model of upstream and downstream fixed detection data into a linear mathematical form so that it can be solved using the KM algorithm;

[0057] The joint matching probability model of upstream and downstream fixed detection data can be converted into a linear mathematical form as follows:

[0058]

[0059] stw i，s =ln p S (s i =s) (13.2)

[0060]

[0061] S i ={s|t(s;i)∈range(P T (t′ s ;l i ,l′ s , t i ))} (13.4)

[0062]

[0063]

[0064] Equation (13.1) is the summation form of the joint matching probability P(S=s) of the upstream and downstream fixed detection data, which is obtained by taking the logarithm of P(S=s), where w i，s Let p be the probability function S (s i=s) in logarithmic form, as shown in equation (13.2), where the lowercase letter s represents the sequence number of the i-th downstream fixed detection data in the upstream fixed detection dataset; x in equation (13.3) i，s As a decision variable, S is 1 when the i-th fixed detection data downstream is matched with the s-th fixed detection data upstream, and 0 otherwise; S in equation (13.4) i Let represent the set of sequence numbers of the i-th downstream fixed detection data in the upstream fixed detection dataset, i.e., the set of upstream fixed detection data that can be matched with the i-th downstream fixed detection data. This set is determined by the range of historical travel time; this range is represented by range(·) in equation (13.4). If the travel time between the i-th downstream fixed detection data and the s-th upstream fixed detection data exceeds this range, then the probability that these two fixed detection data originated from the same vehicle is very small and can be ignored. Therefore, for the i-th downstream fixed detection data, it can only be matched with S… i The upstream fixed detection data within the set are matched; Equation (13.5) is used to ensure that each downstream fixed detection data is matched only once with the upstream fixed detection data; Equation (13.6) is used to ensure that the matching of upstream and downstream fixed detection data is performed one-to-one.

[0065] S5-2. Solve the joint matching probability model of upstream and downstream fixed detection data using the KM algorithm, including:

[0066] S5-2-1. Label the downstream fixed detection data set that has not been labeled by the moving detection data as set X, and the records in it are called X records; label the upstream fixed detection data set that has not been labeled by the moving detection data as set Y, and the records in it are called Y records; assign a matching weight w between the records in set X and set Y. i，s Transform into an adjacency weight matrix W, and label each X and Y record according to the adjacency weight matrix W, where the label of the X record is represented as X. [i] The label of record Y is represented as Y [s] ;X [i] It equals the maximum matching weight of the i-th record X, which is the maximum value of the i-th row of the adjacency weight matrix W, while Y [s] All are 0; the sum of these labels equals the maximum possible matching weight between records in sets X and Y (i.e., downstream and upstream);

[0067] S5-2-2. To find the matching with the maximum weight, a set of feasible edges by label is generated based on the labels of all records; in the set of feasible edges by label LES, each edge e i，s All satisfy the condition that the matching weight between the i-th X record and the s-th Y record is equal to the sum of their labels, i.e., w. i，s =X [i] +Y [s]This condition is used to ensure that if the matching is completed in the set of feasible edges labeled LES, then the weight of this matching is equal to the sum of all labels, i.e., the maximum matching weight. Therefore, each X record is matched with the Y record one by one in the set of feasible edges labeled LES.

[0068] S5-2-3. In the set of feasible edges labeled LES, the edges used to match records X and Y are called active edges, and the remaining edges are called inactive edges. Based on the set of feasible edges labeled LES, select an unmatched record X, and starting from this record X, alternate between active and inactive edges to form an alternating tree.

[0069] S5-2-4. In the alternation tree, find a path that starts from the unmatched X record and ends at the unmatched Y record. This path is called a successful path. If there is at least one successful path in the alternation tree, go to step S5-2-5. If there is no successful path in the alternation tree, go to step S5-2-6.

[0070] S5-2-5. Turn inactive edges in the successful path into active edges, and vice versa, turn active edges in the successful path into inactive edges to decompose the successful path and form a new matching state. Determine whether all X records are matched in the new matching state. If yes, go to step S5-2-7; otherwise, return to step S5-2-3.

[0071] S5-2-6. Modify the labels of X and Y records in the alternating tree and add new feasible edges with new labels to expand the alternating tree. Specifically, this includes: First, finding the minimum cost to expand the alternating tree; Second, subtracting the minimum cost from the label of the X record in the alternating tree and adding the minimum cost to the label of the Y record in the alternating tree; Finally, generating a set of feasible edges with new labels LES based on the new labels, and returning to step S5-2-3.

[0072] S5-2-7, Output the match with the highest weight.

[0073] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] (1) The invention method takes into account the vehicle's own detection length information and integrates this information with lane selection / vehicle merging and travel time information, so that the extracted traffic information is more complete and can more accurately reflect the traffic status.

[0075] (2) The invention method does not need to consider the first-in-first-out (FIFO) condition, thus avoiding errors caused by human assumptions.

[0076] (3) The invention method integrates mobile detection data and fixed detection data through dynamic programming. It is an analytical solution model with a low-order polynomial computational complexity. It can match mobile detection data and fixed detection data one-to-one in a very short time, which greatly reduces the computation time of data fusion.

[0077] (4) The invention method matches upstream and downstream fixed detection data through the KM algorithm. It is an analytical solution model with a low-order polynomial computational complexity. It can achieve the global optimum, i.e. the highest accuracy, in a short time.

[0078] (5) The matching accuracy obtained by the method of this invention is minimally affected by inaccurate or missing data. Even if the mobile detection data has significant inaccuracies or the fixed detection data has some missing information, the matching accuracy remains at a high level. Since the number of vehicles equipped with mobile detection devices in traffic flow is still relatively small, i.e., the penetration rate of mobile detectors is not high, this invention is more advantageous when the penetration rate of mobile detectors is low, which has great practical significance.

[0079] (6) The method of this invention is used to pair vehicle data collected from upstream and downstream. The matching accuracy is significantly better than that of the existing technology (patent CN107886192B, a data and information fusion method based on fixed and mobile vehicle detection data, hereinafter the same). Numerical experiments show that, under low mobile detector penetration, the accuracy obtained by using this invention is improved by 2.42% to 5.35% at intersections and by 7.40% to 37.71% on road sections. At the same time, the method of this invention can better describe the travel conditions of a single vehicle on the main road (the trajectory and travel time of a single vehicle through the main road). Experiments show that the main road matching accuracy obtained by this method is improved by 3.60% to 9.63% compared with the main road matching accuracy using the existing technology.

[0080] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings, but this does not imply any limitation on the scope of protection of the present invention. Attached Figure Description

[0081] Figure 1 This is a flowchart of an embodiment of the information fusion optimization method based on fixed and mobile vehicle detection data according to the present invention.

[0082] Figure 2 This is a schematic diagram of a subsystem obtained by decomposing a large open traffic system in an embodiment of the present invention, with boxes indicating the positions of fixed traffic detectors; wherein, Figure 2 The subsystem in (A) describes the traffic flow within a road segment. Figure 2 The subsystem in (B) describes the traffic flow within the intersection.

[0083] Figure 3 This is a schematic diagram illustrating the use of dynamic programming to match moving and fixed detection data in an embodiment of the present invention.

[0084] Figure 4 This is a schematic diagram of the lane-based travel time probability distribution of the road segment subsystem in an embodiment of the present invention; wherein, Figure 4 (A) represents the probability distribution of travel time for vehicles traveling from upstream lane 1 to downstream lane 1; Figure 4 (B) represents the probability distribution of travel time for vehicles traveling from upstream lane 1 to downstream lane 2; Figure 4 (C) represents the probability distribution of travel time for vehicles traveling from upstream lane 1 to downstream lane 3; Figure 4 (D) represents the probability distribution of travel time for vehicles traveling from upstream lane 2 to downstream lane 1; Figure 4 (E) represents the probability distribution of travel time for vehicles traveling from upstream lane 2 to downstream lane 2; Figure 4 (F) represents the probability distribution of travel time for vehicles traveling from upstream lane 2 to downstream lane 3.

[0085] Figure 5 This is a schematic diagram illustrating the use of the KM algorithm to match upstream and downstream fixed detection data that have not been marked by moving detection data in an embodiment of the present invention; wherein, Figure 5 (A) is a schematic diagram of labeling downstream fixed detection data (X record) and upstream fixed detection data (Y record) using the adjacency weight matrix; Figure 5 (B) is the initial set of labeled feasible edges, LES; Figure 5 (C1) represents the matching process for the first downstream fixed detection data; Figure 5 (C2) is the matching process for the second downstream fixed detection data; Figure 5 (C3) is the matching process for the third downstream fixed detection data; Figure 5 (C4) is the matching process for the fourth downstream fixed detection data; Figure 5 (C5) is the matching process for the fifth downstream fixed detection data; Figure 5 (D1) is a schematic diagram of the set of feasible edges LES with new labels generated according to the new labels; Figure 5 (D2) is a schematic diagram of the process of matching the sixth downstream fixed detection data based on the set of feasible edges with new labels (LES).

[0086] Figure 6 To illustrate the ideal scenario where both mobile and fixed detection data are completely accurate, a comparison chart of the data matching accuracy of each subsystem obtained using the method of this invention (denoted as the DFII method) and existing technologies is presented; wherein, Figure 6(A), (C), and (E) represent the data matching accuracy at intersection 1, intersection 2, and intersection 3, respectively. The horizontal axis represents the penetration rate of the mobile detector, and the vertical axis represents the matching accuracy of the upstream and downstream fixed detection data. Figure 6 (B), (D), and (F) represent the data matching accuracy in road segment 1, road segment 2, and road segment 3, respectively. The horizontal axis represents the penetration rate of the mobile detector, and the vertical axis represents the matching accuracy of the upstream and downstream fixed detection data.

[0087] Figure 7 To compare the data matching accuracy of each subsystem obtained using the method of this embodiment (denoted as DFII) and the prior art under different degrees of data inaccuracy (denoted by σ), a comparison chart is provided. Figure 7 (A), (C), and (E) represent the data matching accuracy at intersection 1, intersection 2, and intersection 3, respectively. The horizontal axis represents the penetration rate of the mobile detector, and the vertical axis represents the matching accuracy of the upstream and downstream fixed detection data. Figure 7 (B), (D), and (F) represent the data matching accuracy in road segment 1, road segment 2, and road segment 3, respectively. The horizontal axis represents the penetration rate of the mobile detector, and the vertical axis represents the matching accuracy of the upstream and downstream fixed data.

[0088] Figure 8 To compare the trunk road matching accuracy obtained using the method of this embodiment (denoted as DFII) and the prior art under different degrees of data inaccuracy (σ represents the degree of data inaccuracy); where the horizontal axis represents the penetration rate of the moving detector and the vertical axis represents the matching accuracy of the data.

[0089] Figure 9 To compare the matching accuracy of the subsystem with missing data and the main road matching accuracy obtained using the method of this embodiment (denoted as DFII) and the prior art under different levels of data missing (0%, 5%, and 10%), the following charts are provided; Figure 9 (A) represents the data matching accuracy of the subsystem with missing data, the horizontal axis represents the penetration rate of the mobile detector, and the vertical axis represents the data matching accuracy. Figure 9 (B) represents the data matching accuracy of the main road, the horizontal axis represents the penetration rate of the mobile detector, and the vertical axis represents the data matching accuracy. Detailed Implementation

[0090] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0091] Example

[0092] This example demonstrates an information fusion optimization method based on fixed and mobile vehicle detection data, such as... Figure 1As shown, the method includes the following steps:

[0093] S1. Decompose the transportation system (road network) into several input (road segments) and output (intersection) subsystems, and obtain multi-source detection data for each subsystem. The multi-source detection data includes fixed detection data and mobile detection data. The fixed detection data includes the timestamps, lane information, and vehicle length information of vehicles passing through the upstream and downstream fixed detectors of the subsystem. The mobile detection data includes the vehicle ID and timestamps recorded at a fixed frequency (0.1s time interval) and vehicle location information, which are used to verify and calibrate the fixed detection data.

[0094] Figure 2 A schematic diagram of the subsystems obtained from the decomposition of a large open transportation system is given in this example, where the positions of fixed detectors are represented by boxes. Figure 2 The subsystem in (A) describes the traffic flow within a road segment. Figure 2 The subsystem in (B) describes the traffic flow within the intersection. Whenever a vehicle passes a fixed detector in a lane, its corresponding time, lane information, and vehicle length are recorded. Mobile detection data primarily records the vehicle's GPS trajectory (timestamped in 0.1s increments and corresponding vehicle location information) and its unique ID.

[0095] This example assumes that each subsystem has 5 moving detection data points and 11 stationary detection data points.

[0096] S2. Extract traffic information from historical traffic datasets, including the probability of each possible lane selection or merging selection, the probability distribution of the corresponding travel time under each possible lane selection or merging selection, and the probability distribution of the error in vehicle detection length.

[0097] Step S2 in this example specifically includes extracting the following four probability information items from the historical traffic dataset:

[0098] S2-1, Lane Selection Probability That is, the probability that a vehicle passing through downstream lane l also passes through upstream lane l′, where: uppercase symbols L and L′ represent random variables, and lowercase symbols l and l′ represent the values ​​of random variables; It is determined by the number of historical data samples for downstream lane l and upstream lane l′. It is the total number of historical data samples from the downstream lane l.

[0099] S2-2, Vehicle Merging Probability That is, the probability that a vehicle flowing downstream to u has an upstream flow direction of u′, where: uppercase symbols L and L′ represent random variables, and lowercase symbols u and u′ represent the values ​​of random variables; It is the number of historical data samples flowing downstream to u and upstream to u′; It is the total number of historical data samples that flow downstream to u.

[0100] The lane selection probability and vehicle merging probability mentioned above have the same mathematical expression; the former applies to the input subsystem (road segment), and the latter applies to the output subsystem (intersection). In the following description, both the lane selection probability and the vehicle merging probability are expressed as p. L L / L′ means that for the input subsystem, L / L′ represents a lane; for the output subsystem, L / L′ represents a lane group.

[0101] S2-3, Probability of travel time distribution That is, the probability that the travel time from the upstream lane or lane group l′ to the downstream lane or lane group l is τ; where: τ=tt′, t represents the timestamp of the vehicle passing the downstream fixed detector, and t′ represents the timestamp of the vehicle passing the upstream fixed detector; This represents the travel time of vehicles that sequentially pass through the upstream lane or lane group l′ and the downstream lane or lane group l in historical data; n is the number of historical data samples, and τ is the travel time record for each historical travel time. n h represents bandwidth; for a given pair of upstream and downstream fixed detection data, the corresponding probability density can be found at the travel time τ = tt′.

[0102] S2-4, Error Distribution Probability of Vehicle Detection Length That is, the probability that the vehicle length record c′ detected by the upstream fixed detector and the vehicle length record c detected by the downstream fixed detector originate from the same vehicle; where σ s The standard deviation is the value of which can be determined based on historical data or by experts who study the accuracy of vehicle length detection.

[0103] S3. Establish a combined optimization model, including: a joint matching probability model of mobile detection data and fixed detection data, a joint matching probability model of upstream and downstream fixed detection data; the objective function and constraints of the combined optimization model.

[0104] Step S3 in this example specifically includes:

[0105] S3-1. Establish a joint matching probability model for mobile detection data and fixed detection data.

[0106] Let P(M=m) and P(M′=m′) represent the joint matching probabilities between the downstream and upstream fixed detection datasets and the mobile detection dataset, respectively. Their mathematical expressions are shown in Equation (4) and Equation (5), respectively:

[0107]

[0108]

[0109] In equations (4) and (5), the index of vehicle j in the downstream mobile detection dataset corresponding to its downstream fixed detection dataset is defined as {M j ∈M|j=1,2,...,5}, where M j m is the ordinal variable. j The value of the ordinal variable; for a vehicle k in the upstream moving detection dataset, the corresponding ordinal number in its upstream fixed detection dataset is defined as {M′ k ∈M′|k=1,2,...,5}, where M′ k Let m' be the ordinal variable. k The value of the sequence number variable; the amount of motion detection data in both the upstream and downstream is equal to 5, α M and α M ′ represents a term; for the same vehicle, considering the possibility of overtaking within a road segment or intersection, its position in the upstream and downstream motion detection datasets may differ. Therefore, different subscripts j and k are used to represent the vehicle's index in the downstream and upstream motion detection datasets. For j≠j′ and k≠k′, it must be ensured that m j ≠m j ′,m′ k ≠m′ k′ This ensures a one-to-one match between mobile detection data and fixed detection data; p M (m j ) and p M ′(m′ k ) represent the discrete matching probabilities between the fixed detection record and the moving detection record at the downstream and upstream positions, respectively. These two probabilities are calculated according to equations (6) and (7):

[0110]

[0111]

[0112] Equation (6) represents the downstream j-th movement detection record and the downstream m-th movement detection record. j The matching probability of a fixed number of detection records, which is related to the timestamps of the two records. and The probability density function of the difference follows a normal distribution, where This represents the timestamp of the j-th vehicle in the downstream mobile detection dataset passing through the downstream fixed detection point. Represents the m-th element in the downstream fixed detection dataset. j The timestamp of each record. Equation (7) represents the timestamp of the k-th upstream motion detection record and the timestamp of the m′ upstream motion detection record. k The matching probability of a fixed number of detection records, which is related to the timestamps of the two records. and The probability density function of the difference follows a normal distribution, where This represents the timestamp of the k-th vehicle in the upstream mobile detection dataset passing through the upstream fixed detection point. Denotes the m′-th value in the upstream fixed detection dataset. k The timestamp of each record.

[0113] S3-2. Establish a joint matching probability model for upstream and downstream fixed detection data.

[0114] P(S=s) represents the joint matching probability between the downstream and upstream fixed detection data that are not labeled by the moving detection data, and its mathematical expression is shown in Equation (8):

[0115]

[0116] In equation (8), the random variable {S} i ∈S|i=1,2,...,N s} represents the index of the i-th vehicle in the downstream fixed detection dataset that is not labeled by the mobile detection data, within the upstream fixed detection dataset that is not labeled by the mobile detection data, where N s This represents the total number of samples in the downstream fixed detection dataset that were not labeled by the mobile detection data. In this example, since each subsystem has 5 mobile detection data points and 11 fixed detection data points, after data fusion, there are 6 fixed detection data points that were not labeled by the mobile detection data, i.e., N. S =6. For any i ≠ i′, then s i ≠s i This ensures a one-to-one match between each downstream fixed detection data point and each upstream fixed detection data point; Indicates downstream fixed detection data (l) i , t i c i ) and upstream fixed detection data The matching probability between them is expressed as shown in equation (9):

[0117]

[0118] Equation (9) is the lane selection probability or vehicle merging probability. Travel time distribution probability Error distribution probability of vehicle detection vehicle length The integration is represented by the product of the three, α S To be classified under one item;

[0119] S3-3. Establish the objective function and constraints of the combinatorial optimization model, expressed by equations (10.1) to (10.5):

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] Equation (10.1) is the objective function, and the optimization result requires maximizing the overall matching probability. Equations (10.2) and (10.3) are constraints, ensuring that for two moving detection records, their relative indices in the moving detection dataset and the fixed detection dataset are consistent. Equation (10.4) is a constraint, ensuring that the matching between upstream and downstream fixed detection data is performed only on fixed detection data that has not been labeled by the moving detection data. Equation (10.5) is a constraint, ensuring a one-to-one matching between fixed detection data.

[0126] S4. Use dynamic programming to solve the joint matching probability model of mobile detection data and fixed detection data to achieve the fusion of upstream mobile detection data and upstream fixed detection data, as well as the fusion of downstream mobile detection data and downstream fixed detection data. Through data fusion, upstream and downstream fixed detection data marked by the same mobile detection data can be directly matched.

[0127] Step S4 in this example specifically includes:

[0128] S4-1. Use dynamic programming to solve the joint matching probability model of upstream mobile detection data and upstream fixed detection data to achieve the fusion of upstream mobile detection data and upstream fixed detection data; define the stage of upstream dynamic programming as the index k of upstream mobile detection data, and define the state of upstream dynamic programming as its index m′ in the upstream fixed detection dataset. k The optimal state in the k-th stage is m′ k The meaning is to combine the k-th move data and the m′-th move data. k Matching fixed data. The upstream dynamic programming solution formula is as follows:

[0129]

[0130] stV M ′(m′6)=1 (11.2)

[0131] m′ k+1 =x′ k (11.3)

[0132] k≤m′ k <x′k ≤11-5+k+1 (11.4)

[0133] Equation (11.1) is the objective function, where V M ′(m′ k ) represents the product of the maximum probability of matching between the k-th to 5th moving detection data items and the fixed detection dataset; p M′ (m′ k ) indicates that the k-th upstream movement detection data is matched with the m′ upstream movement detection data. k The probability of a fixed set of detection data; V M ′(m′ k+1 ) represents the product of the maximum probability of matching between the (k+1)th to the 5th upstream moving detection data and the fixed detection dataset; when k=1, V M The value of (m′1) is equal to the joint matching probability P(M′=m′), which is the joint matching probability of matching the 5 upstream moving detection data with the 11 upstream fixed detection data, maximizing V. M ′(m′1), that is, maximizing P(M′=m′). Equation (11.2) is the constraint condition, that is, the boundary condition of the upstream dynamic programming. Starting from the 6th virtual point (virtual movement detection data), the backward dynamic programming continues until the first movement detection data (k=1), as follows. Figure 3 As shown. Equation (11.3) represents the constraint conditions, where x′ k As the decision variable, it determines the relationship between the (k+1)th upstream movement detection data and the m′ upstream movement detection data. k+1 Matching of fixed detection data, its corresponding Figure 3 The arrows in the equation. Equation (11.4) represents the constraint condition: for two upstream moving detection records, it ensures that they are matched with the upstream fixed detection dataset according to the condition that their relative sequence numbers are consistent. Figure 3 The arrows in the text all point to the lower right. From Figure 3 Starting with the first piece of mobile data (Phase 1), a "optimal path" is dynamically planned to the 6th virtual point (Phase 6). The matching on this "optimal path" is the matching that maximizes the joint matching probability of the upstream mobile detection data and the upstream fixed detection data.

[0134] S4-2. Use dynamic programming to solve the joint matching probability model of downstream mobile detection data and downstream fixed detection data to achieve the fusion of downstream mobile detection data and downstream fixed detection data; define the stage of downstream dynamic programming as the index j of downstream mobile detection data, and define the state of downstream dynamic programming as its index m in the downstream fixed detection dataset. j The optimal state in stage j is m j The meaning is to combine the j-th move data and the m-th move data. j Matching of fixed data. The downstream dynamic programming solution formula is as follows:

[0135]

[0136] stV M (m6)=1 (12.2)

[0137] m j+1 =x j (12.3)

[0138] j≤m j <x j ≤11-5+j+1 (12.4)

[0139] Equation (12.1) is the objective function, where V M (m j ) represents the product of the maximum probability of matching between the downstream moving detection data from the jth to the 5th data point and the fixed detection dataset; p M (m j This indicates that the j-th downstream motion detection data is matched to the m-th data. j The probability of a fixed set of detection data; V M (m j+1 ) represents the product of the maximum probability of matching between the (j+1)th to the 5th downstream moving detection data and the fixed detection dataset; when j=1, V M The value of (m1) is equal to the joint matching probability P(M=m), which is the joint matching probability of matching the 5 downstream moving detection data with the 11 downstream fixed detection data, maximizing V. M (m1), that is, maximizing P(M′=m′). Equation (12.2) is the constraint condition, that is, the boundary condition of the downstream dynamic programming. Starting from the 6th virtual point (virtual movement data), the reverse dynamic programming continues until the first movement data (j=1), as follows. Figure 3 As shown. Equation (12.3) represents the constraints, where x j As a decision variable, it determines the relationship between the (j+1)th downstream motion detection data and the mth downstream data. j+1 Matching of fixed detection data, its corresponding Figure 3 The arrows in the equation. Equation (12.4) represents the constraint condition: for two downstream moving detection records, it ensures that they are matched with the downstream fixed detection dataset according to the condition that their relative sequence numbers are consistent. Figure 3 The arrows in the text all point to the lower right. From Figure 3 Starting with the first piece of mobile detection data (Phase 1), a "optimal path" is dynamically planned to the 6th virtual point (Phase 6). The matching on this "optimal path" is the matching that maximizes the joint matching probability of downstream mobile detection data and downstream fixed detection data.

[0140] S5. Use the KM algorithm to solve the joint matching probability model of upstream and downstream fixed detection data, realize the joint matching between upstream and downstream fixed detection data that are not marked by moving detection data, and find the matching result that maximizes the probability between upstream and downstream fixed detection data.

[0141] Step S5 in this example specifically includes:

[0142] S5-1. Convert the joint matching probability model of upstream and downstream fixed detection data into a linear mathematical form so that it can be solved using the KM algorithm;

[0143] The joint matching probability model of upstream and downstream fixed detection data can be converted into a linear mathematical form as follows:

[0144]

[0145] stw i，s =ln p S (s i =s) (13.2)

[0146]

[0147] S i ={s|t(s;i)∈range(P T (t′ s ;l i ,l′ s , t i ))} (13.4)

[0148]

[0149]

[0150] Equation (13.1) is the summation form of the joint matching probability P(S=s) of the upstream and downstream fixed detection data, which is obtained by taking the logarithm of P(S=s), where w i，s Let p be the probability function S (s i =s) in logarithmic form, as shown in equation (13.2), where the lowercase letter s represents the sequence number of the i-th downstream fixed detection data in the upstream fixed detection dataset; x in equation (13.3) i，s As a decision variable, S is 1 when the i-th fixed detection data downstream is matched with the s-th fixed detection data upstream, and 0 otherwise; S in equation (13.4) iThis represents the set of sequence numbers of the i-th downstream fixed detection data in the upstream fixed detection dataset, i.e., the set of upstream fixed detection data that can be matched with the i-th downstream fixed detection data. It is determined by the range of historical travel time; that is, the travel time distribution probability based on the lane, i.e., P in step S2-3. T (t′;l,l′,t) usually has a range (see Figure 4 In equation (13.4), this range is represented by range(·). If the travel time between the downstream i-th fixed detection data and the upstream s-th fixed detection data exceeds this range, then the probability that these two fixed detection data originate from the same vehicle is very small and can be ignored. Therefore, for the downstream i-th fixed detection data, it can only be generated by the s-th fixed detection data. i The upstream fixed detection data within the set are matched; Equation (13.5) is used to ensure that each downstream fixed detection data is matched only once with the upstream fixed detection data; Equation (13.6) is used to ensure that the matching of upstream and downstream fixed detection data is one-to-one.

[0151] S5-2. Solve the joint matching probability model of upstream and downstream fixed detection data using the KM algorithm. After fusing 5 mobile detection data in step S4, there are 5 fixed detection data that can be directly matched between upstream and downstream. There are 6 remaining fixed detection data that were not marked by the mobile detection data. Match these 6 upstream and downstream fixed detection data using the KM algorithm. The steps include:

[0152] S5-2-1. Label the downstream fixed detection data set that has not been labeled by the moving detection data as set X, and the records in it are called X records; label the upstream fixed detection data set that has not been labeled by the moving detection data as set Y, and the records in it are called Y records; assign a matching weight w between the records in set X and set Y. i，s Transform it into an adjacency weight matrix W, such as Figure 5 As shown in (A), in this adjacency weight matrix W, each row has one or more maximum values, marked with gray boxes; the weights w in the gray boxes are... i，s This represents the maximum weight of the matching of the i-th X record. Based on these maximum weight values, each X record and Y record is labeled, where the label of the X record is denoted as X. [i] The label of record Y is represented as Y [s] ;X [i] It equals the maximum matching weight of the i-th record X, which is the maximum value of the i-th row of the adjacency weight matrix W, while Y [s] All are 0; the sum of these labels equals the maximum possible matching weight between records in sets X and Y (i.e., downstream and upstream).

[0153] S5-2-2. To find the matching with the maximum weight, based on the labels of all records, generate a set of feasible edges by label, LES, such as... Figure 5 As shown in (B); in the set of feasible edges LES labeled with labels, each edge e i，s All satisfy the condition that the matching weight between the i-th X record and the s-th Y record is equal to the sum of their labels, i.e., w. i，s =X [i] +Y [s] This condition is used to ensure that if the matching is completed in the set of feasible edges labeled LES, then the weight of this matching is equal to the sum of all labels, i.e., the maximum matching weight. Therefore, each X record is matched with the Y record one by one in the set of feasible edges labeled LES.

[0154] S5-2-3. In the set of feasible edges labeled LES, the edge used to match the X record and the Y record is called an active edge (in...). Figure 5 (C1) to Figure 5 In (D2), the edges marked as thick connecting lines are called inactive edges (in...). Figure 5 (C1) to Figure 5 In (D2), the line is marked as a thin line; based on the set of feasible edges labeled LES, select an unmatched record X, and start from this record X, alternately pass through active and inactive edges to form an alternating tree.

[0155] For example, Figure 5 In (C1), the alternation tree of the first X record is formed by starting from the first X record, ① passing through the inactive edge e 1，1 To the first Y record, and ② through the inactive edge e 1，2 It is formed by the second Y record; Figure 5 In (C2), the alternation tree of the second X record is formed by starting from the second X record and alternately traversing the inactive edge e. 2，1 Active side e 1，1 and inactive edge e 1，2 Finally, it reaches the second Y record and is formed; Figure 5 In (C3), the alternation tree of the third X record is formed by starting from the third X record and passing through the inactive edge e. 3，3 It is formed by the third Y record; Figure 5 In (C4), the alternation tree of the fourth X record is formed by starting from the fourth X record, ① passing through the inactive edge e 4，3 and active side e 3，3 up to the third record X, and ② through the inactive edge e 4，4 Up to the fourth Y record, and ③ through the inactive edge e 4，5 It is formed by the fifth Y record; Figure 5In (C5), the alternation tree of the fifth X record is formed by starting from the fifth X record, ① passing through the inactive edge e 5，4 Active side e 4，4 and inactive edge e 4，5 Up to the fifth Y record, and ② through the inactive edge e 5，4 Active side e 4，4 Inactive side e 4，3 and active side e 3，3 It is formed by the third X record; Figure 5 In (D1), the alternation tree of the sixth X record is formed by starting from the sixth X record, ① passing through the inactive edge e 6，5 Active side e 5，4 Inactive side e 4，3 and active side e 3，3 up to the third record X, and ② through the inactive edge e 6，5 Active side e 5，4 Inactive side e 4，4 and active side e 4，5 It was formed by the fifth X record.

[0156] S5-2-4. In the alternation tree, find a path that starts from the unmatched X record and ends at the unmatched Y record. This path is called a successful path. If there is at least one successful path in the alternation tree, go to step S5-2-5. If there is no successful path in the alternation tree, go to step S5-2-6.

[0157] For example, Figure 5 In (C1), the alternation tree of the first X record contains two paths. Since both paths end at unmatched Y records, namely the first and second Y records, both paths are successful paths. Proceed to step S5-2-5. Figure 5 In (C2), the alternation tree of the second X record contains a path, which is a successful path because it ends at the second Y record that was not matched. Proceed to step S5-2-5. Figure 5 In (C3), the alternation tree of the third X record contains a path, which is a successful path because it ends at the third unmatched Y record. Proceed to step S5-2-5. Figure 5 In (C4), the alternation tree of the fourth X record contains three paths, the latter two of which end at unmatched Y records, namely the fourth and fifth Y records. Therefore, the latter two paths are successful paths, and we proceed to step S5-2-5. Figure 5 In (C5), the alternation tree of the fifth X record contains two paths, the former of which ends at the unmatched fifth Y record, and is therefore a successful path. Proceed to step S5-2-5. Figure 5In (D1), the alternation tree of the sixth X record contains two paths, but both paths end at X records, namely the third X record and the fifth X record. Therefore, there is no successful path. Proceed to step S5-2-6.

[0158] S5-2-5. Change the inactive edges in the successful path to active edges, and vice versa, change the active edges in the successful path to inactive edges, so as to decompose the successful path and form a new matching state. Determine whether all X records are matched in the new matching state. If yes, go to step S5-2-7; if not, return to step S5-2-3.

[0159] For example, Figure 5 In (C1), select the first successful path and remove the inactive edge e. 1，1 Once it becomes an active edge, the first X record is matched. Since there are still unmatched X records, we return to step S5-2-3. Figure 5 In (C2), by using the inactive edges e on the successful path 2，1 and e 1，2 Become an active edge, or conversely, make active edge e 1，1 The edge becomes inactive, and the successful path is decomposed, forming a new matching state (the matching of the first X record is adjusted, and the second X record is matched). Since there are still unmatched X records, we return to step S5-2-3. Figure 5 In (C3), the inactive edge e on the only successful path is... 3，3 The edge becomes active, so the third X record is matched. Since there are still unmatched X records, we return to step S5-2-3. Figure 5 In (C4), select the first successful path and remove the inactive edge e. 4，4 The edge becomes active, so that the fourth X record is matched. Since there are still unmatched X records, we return to step S5-2-3. Figure 5 In (C5), the inactive edges e on the successful path will be... 5，4 and e 4，5 Become an active edge, or conversely, make active edge e 4，4 The edge becomes inactive. The successful path is decomposed so that the matching of the fourth X record is adjusted and the fifth X record is matched. Since there is still a sixth X record that is not matched in this new matching state, we return to step S5-2-3.

[0160] S5-2-6. Modify the labels of X and Y records in the alternating tree and add new feasible edges with new labels to expand the alternating tree. Specifically, this includes: First, finding the minimum cost to expand the alternating tree; Second, subtracting the minimum cost from the label of the X record in the alternating tree and adding the minimum cost to the label of the Y record in the alternating tree; Finally, generating a new set of feasible edges with new labels LES based on the new labels, and returning to step S5-2-3.

[0161] For example, Figure 5 In (D1), the X and Y records on the alternation tree are respectively packed into sets. and From The i-th record X in the array is extended to The s-th record Y in the set needs to have a new feasible edge e labeled. i，s The reason why an edge is not a labeled feasible edge is X [i] +Y [s] >w i，s Therefore, to transform it into a labeled feasible edge, we need to start from the corresponding X. [i] Subtract a value g from the middle i，s This g i，s =X [i] +Y [s] -w i，s This is called expansion cost, where the minimum expansion cost corresponds to the optimal expansion direction, such as... Figure 5 In (D1), g 5，6 Assuming minimum expansion cost, the index of all X records in the alternating tree minus g 5，6 Add g to the label of all Y records in the alternation tree. 5，6 Then, based on the new label values, the set of feasible edges with labels LES will be updated, and after the update, the set of feasible edges with labels LES will have one more feasible edge with label e. 5，6 At this point, the alternation tree of the sixth X record has been expanded. Returning to step S5-2-3, a successful path ending at the sixth unmatched Y record can be found, such as... Figure 5 As shown in (D2), the path was successfully decomposed in step S5-2-5, and the sixth X record was matched. At this point, all X records were matched, so we proceed to step S5-2-7.

[0162] S5-2-7, Output the match with the highest weight.

[0163] This study uses open-source NGSIM data to verify the effectiveness and superiority of the proposed method compared to existing technologies. The existing technology referred to here is patent CN107886192B, which describes a data and information fusion method based on fixed and mobile vehicle detection data. The experimental data includes three intersection subsystems and three road segment subsystems, with each subsystem containing data from 100 to 200 vehicles. Mobile detection data was sampled at 10% intervals from 0% to 100%. Experiments were conducted under ideal conditions (completely accurate and without missing mobile and fixed detection data), inaccurate data conditions, and missing data conditions. The results are as follows:

[0164] Figure 6 This paper presents a comparison of the data matching accuracy of each subsystem obtained using the proposed method (denoted as the DFII method) and existing technologies under the ideal condition where both mobile and fixed detection data are completely accurate. Clearly, the proposed method is significantly superior to existing technologies. It can correctly match over 60% of the fixed detection data upstream and downstream of the road segment subsystem, and over 90% of the fixed detection data upstream and downstream of the intersection subsystem. Compared to results obtained using existing technologies, at low mobile detector penetration rates, the proposed method can improve data matching accuracy at intersections by 2.42%–5.35%, and at road segments by 7.40%–37.71%. Since the number of vehicles equipped with mobile detection devices in traffic flow is currently relatively small, i.e., the mobile detector penetration rate is still low, this invention is even more advantageous at low mobile detector penetration rates, which has significant practical implications.

[0165] Figure 7 The paper presents a comparison of the data matching accuracy of each subsystem obtained using the method described in this example (denoted as DFII) and existing techniques under different degrees of data inaccuracy (denoted by σ). Figure 7 As can be seen, using the method described in this example, even with high inaccuracies in the motion detection data, the matching results are still better than those obtained using existing technologies when the motion detection data is completely accurate, especially in the road segment subsystem. Furthermore, the results obtained using this method are less affected by inaccuracies in the motion detection data; even with significant interference, the matching accuracy still increases with the increase in motion detector penetration. In contrast, existing technologies, after incorporating highly inaccurate motion detection data, show a decreasing trend in matching accuracy.

[0166] Figure 8The paper presents a comparison of the arterial road matching accuracy obtained using the proposed method (denoted as DFII) and existing techniques under different levels of data inaccuracy (σ represents the degree of data inaccuracy). The results show that, compared to existing techniques, the arterial road matching accuracy obtained using the proposed method is less affected by the inaccuracy of motion detection data.

[0167] Figure 9 This paper presents a comparison of the matching accuracy of subsystems with missing data and trunk line matching accuracy obtained using the proposed method (denoted as DFII) and existing technologies under different levels of data missing (0%, 5%, and 10%). Regarding the matching accuracy of subsystems with missing data, the analysis shows that the proposed method is not highly sensitive to data missing; even with 10% data missing, fusing only 20% of the motion detection data can achieve a matching accuracy of over 60%. In contrast, existing technologies are significantly affected by data missing; even a 5% data missing result in a substantial drop in matching accuracy. The same trend is observed for trunk line matching accuracy. The proposed method is minimally affected by data missing; a 10% data missing only causes a slight decrease in trunk line matching accuracy. Existing technologies, however, are significantly affected by data missing; even a 5% data missing results in a substantial drop in trunk line matching accuracy.

[0168] The present invention has been described above by way of example in conjunction with the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the embodiments shown herein.

Claims

1. A method for information fusion and optimization based on fixed and mobile vehicle detection data, characterized in that, The method includes the following steps: S1. Decompose the transportation system into several input and output subsystems, and obtain multi-source detection data for each subsystem; the multi-source detection data includes fixed detection data and mobile detection data; the fixed detection data includes timestamps, lane information and vehicle length information of vehicles passing through upstream and downstream fixed detectors of the subsystem; the mobile detection data includes vehicle ID and timestamps recorded at a fixed frequency and vehicle location information, which are used to verify and calibrate the fixed detection data. S2. Extract traffic information from historical traffic datasets, including the probability of each possible lane selection or merging selection, the probability distribution of travel time under each possible lane selection or merging selection, and the probability distribution of error in vehicle detection length. S3. Establish a combined optimization model, including: a joint matching probability model of mobile detection data and fixed detection data, and a joint matching probability model of upstream and downstream fixed detection data; the objective function and constraints of the combined optimization model; S4. Use dynamic programming to solve the joint matching probability model of mobile detection data and fixed detection data to achieve the fusion of upstream mobile detection data and upstream fixed detection data, as well as the fusion of downstream mobile detection data and downstream fixed detection data; through data fusion, upstream and downstream fixed detection data marked by the same mobile detection data can be directly matched. S5. Use the KM algorithm to solve the joint matching probability model of upstream and downstream fixed detection data, realize the joint matching between upstream and downstream fixed detection data that are not marked by mobile detection data, and find the matching result that maximizes the probability between upstream and downstream fixed detection data. Step S5 specifically includes: S5-1. Convert the joint matching probability model of upstream and downstream fixed detection data into a linear mathematical form so that it can be solved using the KM algorithm; The joint matching probability model of upstream and downstream fixed detection data can be converted into a linear mathematical form as follows: Equation (13.1) represents the joint matching probability of upstream and downstream fixed detection data. The summation form, which is obtained by... Taking the logarithm, we get, where For probability functions The logarithmic form of is shown in equation (13.2), with lowercase letters. Indicates the downstream first The sequence number of each fixed detection data point in the upstream fixed detection dataset; Equation (13.3) As a decision variable, when the downstream first Fixed detection data and upstream When a fixed set of detection data matches, the value is 1; otherwise, it is 0. Equation (13.4) Indicates the downstream first The set of sequence numbers of each fixed detection data point in the upstream fixed detection dataset can be used as the downstream... The set of upstream fixed detection data that matches the fixed detection data is determined by the range of historical travel time; this range is represented in equation (13.4) by... This indicates that if the downstream... Fixed detection data and upstream If the travel time between two fixed detection data points exceeds this range, the probability that these two fixed detection data points originated from the same vehicle is very small and can be ignored. Therefore, for the downstream... For a fixed set of test data, it can only be compared with... The upstream fixed detection data within the set are matched; Equation (13.5) is used to ensure that each downstream fixed detection data is matched only once with the upstream fixed detection data; Equation (13.6) is used to ensure that the matching of upstream and downstream fixed detection data is performed one-to-one. S5-2. Solve the joint matching probability model of upstream and downstream fixed detection data using the KM algorithm, including: S5-2-1, Mark the downstream fixed detection data set that has not been marked by the moving detection data as... A set, in which records are called Record; mark the set of fixed detection data upstream that has not been marked by the moving detection data as A set, in which records are called Record; will Sets and Matching weights between records in a set Convert to adjacency weight matrix According to the adjacency weight matrix For each Records and Record label, among which The record number is represented as , The record number is represented as ; equal to the strip The maximum matching weight recorded, i.e., the adjacency weight matrix. No. The maximum value of the row, and All zeros; the sum of these labels equals Sets and The maximum possible matching weight between records in a set; S5-2-2. To find the matching with the maximum weight, a set of feasible edges by label is generated based on the labels of all records; in the set of feasible edges by label LES, each edge... All satisfy the first strip Records and the strip The matching weight between records is equal to the sum of their labels, i.e. This condition guarantees that if a match is completed within the set of feasible edges labeled LES, then the weight of this match is equal to the sum of all labels, i.e., the maximum matching weight. Therefore, for each feasible edge in the set of feasible edges labeled LES... Record one by one Records are matched; S5-2-3, In the set LES of labeled feasible edges, used for matching Records and The edges that are recorded are called active edges, and the rest are called inactive edges; based on the set of feasible edges (LES) with labels, one unmatched edge is selected. Record, from this Record the starting point, and alternate between active and inactive edges to form an alternating tree; S5-2-4. In an alternating tree, find a path that starts from the unmatched node. The record ends with a single unmatched record. The recorded path is called a successful path; if there is at least one successful path in the alternation tree, proceed to step S5-2-5; if there is no successful path in the alternation tree, proceed to step S5-2-6. S5-2-5. Transform inactive edges in the successful path into active edges, and vice versa, transform active edges in the successful path into inactive edges to decompose the successful path and form a new matching state. Determine whether all edges in the new matching state are active. All records are matched; if so, proceed to step S5-2-7; otherwise, return to step S5-2-3. S5-2-6, Modify the alternation tree Records and The recorded labels are used to add feasible edges with new labels to expand the alternating tree. Specifically, this involves: first, finding the minimum cost to expand the alternating tree; second, adding feasible edges with new labels to the alternating tree. Subtract the minimum cost from the record's label, and then add the alternating tree. Add the minimum cost to the recorded label; finally, generate the set of feasible edges LES with the new label based on the new label, and return to step S5-2-3; S5-2-7, Output the match with the highest weight.

2. The information fusion optimization method based on fixed and mobile vehicle detection data according to claim 1, characterized in that, Step S2 specifically includes extracting the following four probability information items from the historical traffic dataset: S2-1, Lane Selection Probability That is, through the downstream lane Vehicles also passed through the upstream lane The probability, where: uppercase sign and To represent a random variable, use lowercase signs. and Represents the value of a random variable; via the downstream lane and upstream lane The number of historical data samples; via the downstream lane The total number of historical data samples; S2-2, Vehicle Merging Probability That is, flowing downstream to The vehicles' upstream flow direction is The probability, where: uppercase sign and To represent a random variable, use lowercase signs. and Represents the value of a random variable; Through downstream flow and upstream flow direction The number of historical data samples; Through downstream flow The total number of historical data samples; The lane selection probability and vehicle merging probability mentioned above have the same mathematical expression; the former is applied to the input subsystem, and the latter to the output subsystem. In the following description, both the lane selection probability and the vehicle merging probability will be expressed using... This indicates that, for the input subsystem, / Indicates the lane; for the output subsystem, / Indicates lane group; S2-3, Probability of travel time distribution That is, the upstream lane or lane group To the downstream lane or lane group The travel time is The probability of , where: , This indicates the timestamp when the vehicle passes the downstream fixed detector. This indicates the timestamp of the vehicle passing the upstream fixed detector; This indicates that the historical data shows the sequential passage through the upstream lane or lane group. and downstream lanes or lane groups The vehicle's travel time; The number of historical data samples is [number], and the time record for each historical trip is [number]. ; Indicates bandwidth; for a given pair of upstream and downstream fixed detection data, it can be expressed in the travel time. Find the corresponding probability density at the location; S2-4, Error Distribution Probability of Vehicle Detection Length That is, the upstream fixed detector detects the vehicle length record. and downstream fixed detectors detect vehicle length records The probability of originating from the same vehicle, where: The standard deviation is the value of which can be determined based on historical data or by experts who study the accuracy of vehicle length detection.

3. The information fusion optimization method based on fixed and mobile vehicle detection data according to claim 1, characterized in that, Step S3 specifically includes: S3-1. Establish a joint matching probability model for mobile detection data and fixed detection data; use and Let represent the joint matching probability between the upstream and downstream fixed detection datasets and the mobile detection dataset, respectively, and their mathematical expressions are shown in equations (4) and (5), respectively: In equations (4) and (5), for vehicles in the downstream motion detection dataset The corresponding sequence number in its downstream fixed detection dataset is defined as ,in For the ordinal variable, The value of the sequence number variable; for vehicles in the upstream motion detection dataset. The corresponding sequence number in its upstream fixed detection dataset is defined as ,in For the ordinal variable, The value of the sequence number variable is equal to the amount of motion detection data in both the upstream and downstream regions. , and To group a single item; for the same vehicle, considering the possibility of overtaking within a road segment or intersection, its position in the upstream and downstream motion detection datasets may differ, so different indices are used. and To represent the vehicle sequence number in the downstream and upstream motion detection datasets, for and It is necessary to ensure , This ensures a one-to-one match between mobile detection data and fixed detection data; and Let represent the discrete matching probabilities between the fixed detection record and the moving detection record at the downstream and upstream positions, respectively. These two probabilities are calculated according to equations (6) and (7): Equation (6) represents the downstream first The first mobile detection record and downstream The matching probability of a fixed number of detection records, which is related to the timestamps of the two records. and The probability density function of the difference follows a normal distribution, where Indicates the first in the downstream motion detection dataset The timestamp of the vehicle passing through the downstream fixed inspection point. Represents the first in the downstream fixed detection dataset The timestamp of the record; Equation (7) represents the upstream record's timestamp. The first movement detection record and the upstream The matching probability of a fixed number of detection records, which is related to the timestamps of the two records. and The probability density function of the difference follows a normal distribution, where Indicates the first in the upstream motion detection dataset The timestamp of the vehicle passing through the upstream fixed checkpoint. Represents the first in the upstream fixed detection dataset The timestamp of each record; S3-2. Establish a joint matching probability model for upstream and downstream fixed detection data; use The mathematical expression for the joint matching probability between the downstream and upstream fixed detection data that are not labeled by the mobile detection data is shown in Equation (8): In equation (8), the random variable This indicates the first [item] in the fixed detection dataset that was not labeled by the downstream mobile detection data. The vehicle's sequence number in the fixed detection dataset upstream that was not labeled by the moving detection data, where This represents the total number of samples in the fixed detection dataset that were not labeled by the moving detection data downstream; for any Then there is This ensures a one-to-one match between each piece of downstream fixed detection data and each piece of upstream fixed detection data; Indicates downstream fixed detection data and upstream fixed detection data The matching probability between them is expressed as shown in equation (9): Equation (9) is the lane selection probability or vehicle merging probability. Probability of travel time distribution Error distribution probability of vehicle detection vehicle length The integration is represented by the product of the three. To be classified under one item; S3-3. Establish the objective function and constraints of the combinatorial optimization model, expressed by equations (10.1) to (10.5): Equation (10.1) is the objective function, and the optimization result requires maximizing the overall matching probability; Equations (10.2) and (10.3) are constraints, ensuring that the relative sequence numbers of two moving detection records in the moving detection dataset and the fixed detection dataset are consistent; Equation (10.4) is a constraint, ensuring that the matching between the upstream fixed detection data and the downstream fixed detection data is only performed on the fixed detection data that has not been marked by the moving detection data; Equation (10.5) is a constraint, ensuring a one-to-one matching between the fixed detection data.

4. The information fusion optimization method based on fixed and mobile vehicle detection data according to claim 1, characterized in that, Step S4 specifically includes: S4-1. Use dynamic programming to solve the joint matching probability model of upstream mobile detection data and upstream fixed detection data to achieve the fusion of upstream mobile detection data and upstream fixed detection data; the upstream dynamic programming solution formula is as follows: Equation (11.1) is the objective function, where Indicates the upstream number Article to No. The product of the maximum probability of matching between the moving detection data and the fixed detection dataset. This indicates that the upstream first The movement detection data is matched to the upstream first The probability of a fixed set of detection data. Indicates the upstream number Article to No. The product of the maximum probability of matching the moving detection data and the fixed detection dataset; Equation (11.2) is the constraint condition, i.e., the boundary condition of dynamic programming; Equation (11.3) is the constraint condition, where As a decision variable, it determines the upstream first The mobile detection data and the upstream Matching of fixed detection data; Equation (11.4) is a constraint condition. For two upstream moving detection records, it is ensured that they are matched with the upstream fixed detection dataset according to the condition that the relative sequence numbers are consistent. S4-2. Use dynamic programming to solve the joint matching probability model of downstream mobile detection data and downstream fixed detection data to achieve the fusion of downstream mobile detection data and downstream fixed detection data; the downstream dynamic programming solution formula is as follows: Equation (12.1) is the objective function, where Indicates the downstream first Article to No. The product of the maximum probability of matching between the moving detection data and the fixed detection dataset. This indicates that the downstream first Matching the movement detection data to the first The probability of a fixed set of detection data. Indicates the downstream first Article to No. The product of the maximum probability of matching the moving detection data and the fixed detection dataset; Equation (12.2) is the constraint condition, i.e., the boundary condition of dynamic programming; Equation (12.3) is the constraint condition, where As a decision variable, it determines the downstream first The mobile detection data and the downstream Fixed data matching; Equation (12.4) is a constraint condition, which ensures that the two downstream moving detection records are matched with the downstream fixed detection dataset according to the condition that the relative sequence numbers are consistent.

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