A markov vehicle trajectory prediction method fusing lense data

Abstract

The application belongs to the technical field of vehicle management, and discloses a Markov vehicle trajectory prediction method fusing loop data; a passing event record is obtained when a vehicle passes through a detection line; all passing event records of the same license plate identifier are extracted to obtain a plurality of continuous trajectory sequences; a unique direction label is generated for each passing event record in each trajectory sequence, and a passing time is mapped into a time period code; the trajectory sequence is converted into a state sequence; based on a road network topology, a global reachability mask and a direction compatibility mask are pre-constructed; a current state of the vehicle is obtained, a transition probability tensor is inquired, a state matched with the current state and having the maximum transition probability is selected as a next loop for prediction, and when multi-step prediction is needed, the predicted next loop is taken as a new current state until a preset step number is reached to stop, thereby realizing Markov vehicle trajectory prediction fusing loop data.

Description

Technical Field

[0001] This invention relates to the field of vehicle management technology, and more specifically, to a Markov vehicle trajectory prediction method that integrates checkpoint data. Background Technology

[0002] When using checkpoint data to predict vehicle trajectories, two key issues are often encountered, leading to inaccurate prediction results.

[0003] The first problem is the "unclear checkpoint direction." In road networks, lanes in opposite directions at the same physical location, or ramps and main roads with merging or diverging relationships, often share a single checkpoint number, and data records only include the checkpoint ID. However, on actual roads, the same checkpoint number may correspond to lanes in different directions, such as a two-way detector on a road, or a checkpoint on a main road where multiple ramps merge. When recording data, only the checkpoint number is recorded, without distinguishing whether the vehicle is "entering" or "leaving." As a result, when analyzing vehicle movement patterns, records from different directions are mixed together, failing to accurately reflect the vehicle's turning intentions.

[0004] The second problem is the "lack of time reasonableness checks." Due to occasional equipment failures, detection blind spots, equipment malfunctions, or communication packet loss, the vehicle passage times recorded by checkpoints may be discontinuous and the time intervals may be irregular. If the data is not filtered based on the actual distance of the road and the reasonable vehicle speed at different times, some "impossible" journeys may appear in the statistical results—for example, a vehicle may appear at two checkpoints that are far apart in a very short period of time, or skip checkpoints that it should have passed along the way.

[0005] Both of these problems stem from insufficiently refined raw data, which means that a single checkpoint number actually corresponds to multiple possible driving directions and paths. This leads to deviations in the statistical analysis of vehicle movement patterns, ultimately affecting the accuracy of predictions.

[0006] Based on the above problem description, a Markov vehicle trajectory prediction method that integrates checkpoint data is designed. Summary of the Invention

[0007] To overcome the aforementioned deficiencies of the prior art and to achieve the above objectives, the present invention provides the following technical solution: a Markov vehicle trajectory prediction method integrating checkpoint data, comprising:

[0008] Step S1: When a vehicle passes through the detection line, the front-end device at the checkpoint acquires and generates a vehicle passage event record in real time.

[0009] Step S2: Extract all vehicle passing event records with the same license plate identifier and arrange them in ascending order of passing time to form an overall sequence. If the time difference between two adjacent vehicle passing event records exceeds the trajectory segmentation threshold, then segment at that point to obtain multiple continuous trajectory sequences.

[0010] Step S3: Generate a unique direction label for each vehicle passing event record in each trajectory sequence, and map it to a time period code; then convert each vehicle passing event record into a state represented by a triple, thereby converting the trajectory sequence into a state sequence;

[0011] Step S4: Based on the road network topology, preconstruct a global reachability mask and a direction compatibility mask; count only adjacent state pairs that simultaneously satisfy the reachability mask and the direction compatibility mask to obtain a transition count tensor; otherwise, generate an interpolation sequence and include it in the transition count tensor; output the summarized transition count tensor.

[0012] Step S5: Based on the summarized transition count tensor, the initial scale vector is obtained through the Dirichlet prior distribution, and the final transition probability tensor is obtained by using mask constraints and probability constraints.

[0013] Step S6: Obtain the current state of the vehicle, query the transfer probability tensor, and select the state that matches it and has the highest transfer probability as the predicted next checkpoint.

[0014] Preferably, each vehicle passing event record in each trajectory sequence generates a unique direction label, the method comprising:

[0015] Each vehicle passage event record includes the license plate number, checkpoint number, passage time, and checkpoint location;

[0016] For the first and last records of the trajectory sequence, the azimuth angle is obtained from the checkpoint geographical location of the record and its adjacent vehicle passing event records, quantized into a direction label, and written into the record;

[0017] For each vehicle passage event record that is not the first or last record in the trajectory sequence, the azimuth angle is obtained from the checkpoint geographical location of the previous and next records, quantified into a direction label, and then written into the corresponding vehicle passage event record.

[0018] When there is a missing vehicle passage event record or the azimuth angle is uncertain, all possible passage directions of the current checkpoint are located based on the road network topology to form a direction candidate set. Then, a unique direction label is matched and determined from the candidate set according to the actual preceding or succeeding checkpoint number of the record.

[0019] Preferably, the method of encoding time-to-segment mapping includes:

[0020] Divide a day and night into several fixed and non-overlapping time periods, and assign a unique time period code to each time period;

[0021] For vehicle passage events that span multiple days, time period codes are assigned according to the modal cyclical rule;

[0022] When performing state transition statistics, the time period code of the starting state in the state sequence is used as the time period label for the entire transition process; each state in the state sequence includes a tuple, including the checkpoint number, direction label, and time period code;

[0023] For each independent time period code, maintain its corresponding velocity quantile estimate, which includes the lower velocity quantile and the upper velocity quantile.

[0024] Preferably, the road network topology includes a basic road network topology and a checkpoint projection topology. The basic road network topology uses road intersections as nodes, establishes directed edges of road segments according to the direction of travel, and configures attributes for the directed edges under each time period encoding. The attributes include length, heading angle, speed quantile, passage and turning restriction attributes. The checkpoint projection topology defines the set of incoming edges or outgoing edges of the checkpoints by anchoring the checkpoints to the nodes or edges of the basic road network topology, and establishes the connection relationship between checkpoints when there is a path that satisfies the reachability criterion.

[0025] Preferably, the method for pre-constructing a global reachability mask and a direction-compatible mask includes:

[0026] Initialize two global mask matrices, one for reachability and the other for orientation compatibility. By default, all mask values ​​between state pairs are marked as infeasible.

[0027] Calculate the shortest path distance between any two checkpoints in the road network topology.

[0028] For each time period encoding, based on its corresponding lower and upper velocity quantiles and combined with the shortest path distance, the initial lower and upper bounds of the feasible travel time window are calculated, and a preset time tolerance is superimposed on the feasible travel time window to output the final feasible travel time window.

[0029] For all possible state pairs, i.e., any combination of a starting state and an ending state, calculate the theoretical time difference of the corresponding vehicle passing event record. Then, compare the theoretical time difference with its corresponding feasible travel time window. If it is within the window, set the mask value corresponding to the state pair in the reachability mask matrix as feasible; otherwise, set it as infeasible.

[0030] Check whether the direction label corresponding to the starting state is consistent with the allowed entry direction of the checkpoint corresponding to the ending state in the road network topology; if they are consistent, set the mask value corresponding to the state pair in the direction compatibility mask matrix to feasible, otherwise set it to infeasible.

[0031] Preferably, the method for outputting the summarized transition count tensor includes:

[0032] Iterate through all adjacent state pairs in the state sequence; for each adjacent state pair, query its value in the pre-constructed global reachability mask and orientation compatibility mask;

[0033] If the values ​​of the state pair are feasible in both masks, and the actual time difference of the state pair in the trajectory sequence is within its corresponding feasible travel time window, then the transitions of the state pair are counted, and the count results are accumulated in the transition count tensor.

[0034] If the actual time difference of the state pair in the trajectory sequence does not meet the feasible travel time window, but does not exceed the preset interpolation upper bound, then trajectory interpolation is initiated, an interpolation sequence is generated, and it is decomposed into several state transition segments; these are included in the transition count tensor, and finally the summarized transition count tensor is obtained.

[0035] Preferably, the method for initiating trajectory interpolation and generating an interpolation sequence includes:

[0036] In the road network topology, K shortest paths connecting the adjacent states are found to obtain a sequence of candidate intermediate nodes. Then, the paths that simultaneously satisfy the reachability mask and direction compatibility mask constraints are selected from them, and an optimal path is solved based on the criterion of maximizing the path probability product, thereby generating an interpolation sequence consisting of several intermediate checkpoints.

[0037] Preferably, the method for obtaining the final transition probability tensor includes:

[0038] For each starting state and its corresponding time period code, read the corresponding transition count vector in the transition count tensor and add it to the preset Dirichlet prior parameter vector to obtain the smoothed initial scale vector.

[0039] Query the global reachability mask and direction compatibility mask related to the starting state. For the ending state marked as infeasible in any mask, force the corresponding component value in the initial scaling vector to zero to obtain a scaling vector after mask constraint.

[0040] Subsequently, the proportional vector constrained by the mask is normalized to obtain an initial transition probability vector;

[0041] Starting from the initial transition probability vector, an iterative scaling algorithm is used to perform iterative projection correction under the constraint of the mask until it converges to a stable probability distribution, which is the final transition probability vector.

[0042] The final transition probability vectors of all starting states together constitute the final transition probability tensor.

[0043] Preferably, the final transition probability tensor performs online learning, including: after new vehicle passing event records are continuously generated and new state sequences are generated, using a preset forgetting factor to exponentially update the historical velocity quantiles; and simultaneously, using the forgetting factor to exponentially decay the historical transition count tensor.

[0044] Based on the new state sequence, repeat step S5 to update the transition probability tensor.

[0045] Preferably, the checkpoint update method includes: when a checkpoint number or direction label not seen in historical data appears, locating its adjacent known nodes in the road network topology;

[0046] In the set of outgoing or incoming edges of its adjacent known nodes, establish a set of candidate endpoint states that are compatible with it.

[0047] Assign preset Dirichlet prior parameters to the states in the candidate endpoint state set, set the components corresponding to incompatible endpoint states to zero, initialize their corresponding transition probability vectors, and incorporate them into the final transition probability tensor.

[0048] The technical effects and advantages of the Markov vehicle trajectory prediction method that integrates checkpoint data in this invention are as follows:

[0049] By eliminating ambiguity in checkpoint directions through directional labels, capturing the temporal characteristics of traffic flow through time-period coding, and eliminating physically unreachable paths through a masking mechanism, the accuracy of state definition is improved from multiple dimensions, fundamentally enhancing prediction quality.

[0050] A rigorous data cleaning and verification mechanism was established. Through reachability verification, direction compatibility checks, and intelligent trajectory interpolation, errors and omissions in the data were effectively identified and corrected, improving the reliability of the input data.

[0051] By systematically integrating prior knowledge such as road network topology, traffic rules, and physical laws into the machine learning model, and using mask constraints and projection algorithms, the system ensures that all predictions conform to the physical laws of the real world. A robust online learning and new element initialization mechanism enables the system to automatically adapt to changes in traffic patterns and promptly incorporate new road infrastructure, guaranteeing its long-term effectiveness and practicality.

[0052] Based on the traditional Markov model, this paper innovatively introduces the directional dimension, time dimension, physical constraints, and online learning, forming a more complete theoretical framework and constructing an accurate, reliable, and highly adaptive vehicle trajectory prediction system, which effectively solves the core problems existing in the current trajectory prediction based on checkpoint data. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the Markov vehicle trajectory prediction method that integrates checkpoint data according to the present invention.

[0054] Figure 2 This is a schematic diagram of the method for outputting the summarized transfer count tensor in this invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figure 1 and Figure 2 In this embodiment of the invention, a Markov vehicle trajectory prediction method that integrates checkpoint data includes:

[0057] In vehicle trajectory prediction based on checkpoint data, ambiguity in checkpoint direction and lack of time accessibility constraints lead to confusion in state definitions and distortion in transition statistics. Specifically, bidirectional checkpoints or multi-ramp merging points at the same physical location on the road are often recorded with the same number, failing to distinguish the entry and exit directions of vehicles under that number. Subsequent transition frequency statistics based on checkpoint number will mix transitions from different directions. Simultaneously, trajectory records contain detection gaps and irregular time intervals, and transition statistics include records inconsistent with road distance and feasible travel time. Accessibility filtering based on road network distance and time-of-day speed is not performed, resulting in physical inaccessibility or skipped transitions into the state transition matrix. These shared problems of undisambiguated directions and unfiltered accessibility cause a single checkpoint node in the Markov state space to simultaneously carry multiple transition edges from opposite directions and different road topologies, resulting in mixed counting and affecting transition probability estimation and subsequent prediction. Therefore, a design is proposed based on these problems, as detailed below:

[0058] Step S1: When a vehicle passes through the detection line, the front-end device at the checkpoint acquires and generates a vehicle passage event record in real time. Each record includes the license plate identifier, checkpoint number, passage time (which refers to the event timestamp entered by the device's local clock when the vehicle passes through the checkpoint acquisition device), and checkpoint geographical location (the checkpoint geographical location is obtained by associating the checkpoint number or device number with the checkpoint basic information table).

[0059] Step S2: Extract all vehicle passing event records with the same license plate identifier and arrange them in ascending order of passing time to form an overall sequence. A preset trajectory segmentation threshold is set, and the entire overall sequence is traversed. If the time difference between two adjacent vehicle passing event records exceeds the trajectory segmentation threshold, the sequence is segmented at that point to obtain multiple continuous trajectory sequences.

[0060] Step S3: Generate a unique direction label for each vehicle passing event record in each trajectory sequence to represent the vehicle's direction of travel at that location. This is then mapped to a time period encoding; subsequently, each vehicle passing event record is converted into a state represented by a triple, thus transforming the trajectory sequence into a state sequence; and state definitions are then performed.

[0061] Each state in the state sequence includes a tuple (checkpoint number, direction label, time period code);

[0062] To address the issue of indistinguishable vehicle travel directions using the same checkpoint number, a method combining dynamic calculation and static inference is employed to assign precise direction labels to each checkpoint record, thus eliminating directional ambiguity. Details are as follows:

[0063] For each trajectory sequence, a direction label is generated for each vehicle passing event record. The methods include:

[0064] For the first record (the vehicle passing event record at the beginning of the trajectory sequence) and the last record (the vehicle passing event record at the end of the trajectory sequence), the azimuth angle is obtained from the checkpoint geographical location of the record (first record or last record) and its adjacent vehicle passing event records, and quantized into a direction label and written into the record;

[0065] For each vehicle passage event record that is not the first or last record in the trajectory sequence, the azimuth angle is obtained from the checkpoint geographical location of the previous and next records, quantified into a direction label, and then written into the corresponding vehicle passage event record.

[0066] When there is a missing vehicle passage event record or the azimuth angle is uncertain, all possible passage directions of the current checkpoint are located based on the road network topology to form a direction candidate set. Then, a unique direction label is matched and determined from the candidate set according to the actual preceding or succeeding checkpoint number of the record.

[0067] When obtaining the azimuth angle based on the geographical location of adjacent vehicle passing event records, the geographical location of the checkpoint includes the latitude and longitude coordinates (or other planar coordinates) of the checkpoint. For any vehicle passing event record, the position vector is calculated, which represents the instantaneous travel direction of the vehicle when passing through the Re_i checkpoint.

[0068] If it is located in the middle, then calculate the vector V = (Lon_{i+1} - Lon_{i-1}, Lat_{i+1} - Lat_{i-1}).

[0069] For the first record, the vector V = (Lon_{i+1}-Lon_i, Lat_{i+1}-Lat_i),

[0070] For the tail record, the vector V = (Lon_i - Lon_{i-1}, Lat_i - Lat_{i-1}).

[0071] Lon represents longitude, Lat represents latitude, i represents the vehicle passage event record generated for checkpoint Re_i, i.e., the current record; i-1 represents the previous vehicle passage event record before the current record; i+1 represents the next vehicle passage event record after the current record.

[0072] The azimuth angle of vector V is calculated using the two-parameter arctangent function atan2. It is then quantized into direction labels according to preset angle partitions. For example, 360 degrees is divided into 8 45-degree intervals or 16 22.5-degree intervals. Each interval corresponds to a direction label. The azimuth angle of vector V is mapped to the interval, the corresponding direction label is obtained, and it is written to the corresponding vehicle passing event record.

[0073] Azimuth uncertainty refers to situations where adjacent checkpoints are extremely close, or where GPS errors result in nearly identical coordinates, causing the two-parameter arctangent function atan2 to calculate invalid values. The solution is to find the node corresponding to the current checkpoint number in the checkpoint projection topology. Starting from this node, retrieve all directly connected and permitted road edges (directed edges) in the road network, forming an outgoing edge set. For each outgoing edge, calculate its approximate direction. Discretize these outgoing edge directions using the same rules for quantizing direction labels, ultimately obtaining the set of all theoretically possible travel directions for the current checkpoint, i.e., the direction candidate set. Check the direction candidate set to determine which direction candidate can legally and directly reach the preceding or succeeding checkpoint from which the current checkpoint originates. The direction candidate that connects these two checkpoints is determined as the unique direction label for that record.

[0074] To address the issue of insufficient utilization of time-dimensional features, a fine-grained time segmentation system was established, creating independent velocity models for different time periods, thereby improving the efficiency of utilizing time-dimensional features. Specifically:

[0075] Methods that map time to time-segment encoding include:

[0076] A 24-hour period is divided into several fixed and non-overlapping time periods, and each time period is assigned a unique time period code; the purpose is to ensure that any time period can be mapped to the corresponding time period code.

[0077] For vehicle passage events that cross day limits (i.e., midnight), time period codes are assigned according to a modal cyclical rule. The modal cyclical rule means that when the time period code sequence increases beyond the maximum value, it doesn't stop but automatically cycles back to the minimum value to start again, forming a recurring cycle. Specifically, assuming a day and night are divided into N time periods, the time period codes are 0, 1, 2, ..., N-1. For a given passage timestamp, the time period code within a calendar day is first determined. If it's N_cu, then when the vehicle trajectory crosses midnight, for records in the new day, the time period code N_cu will be renumbered starting from 0, logically continuing from the last code N-1 of the previous day. Therefore, when processing data, according to the modal cyclical rule, records belonging to the same trip but located before and after midnight are correctly associated with the same trajectory sequence, ensuring continuity in the time dimension and seamlessly handling vehicle trajectories crossing midnight, avoiding trajectory breaks caused by date changes.

[0078] When performing state transition statistics, the time period code of the starting state in the state sequence is used as the time period label for the entire transition process.

[0079] For each independent time period code, maintain its corresponding velocity quantile estimate, which includes the lower velocity quantile and the upper velocity quantile.

[0080] To address the disconnect between road network topology information and checkpoint data, a two-layer topology structure was constructed to accurately map physical checkpoints into the road network model, providing a foundation for subsequent physical rule verification. The details are as follows:

[0081] Step S4: Preconstruct the road network topology, global reachability mask, and direction compatibility mask; count only adjacent state pairs that simultaneously satisfy the reachability mask and direction compatibility mask to obtain the transition count tensor; otherwise, generate an interpolation sequence and include it in the transition count tensor; output the summarized transition count tensor; form a transition count tensor organized by time period encoding.

[0082] The road network topology includes the basic road network topology and the checkpoint projection topology. The basic road network topology uses road intersections as nodes, establishes directed edges for road segments according to the direction of travel, and configures attributes for directed edges under each time period code. The attributes include length (referring to the actual drivable distance from the start to the end of the road segment corresponding to the directed edge), heading angle (referring to the average azimuth angle of the vehicle in the direction of travel on the directed edge), speed quantile (referring to the statistical quantile value of the historical vehicle speed on the road segment under a specific time period code, used to estimate the reasonable time range required to travel on the road segment), and traffic and turning restrictions (used to describe traffic law constraints). The checkpoint projection topology defines the set of incoming edges or outgoing edges of the checkpoint by anchoring the checkpoint to the nodes or edges of the basic road network topology, and establishes the connection relationship between checkpoints when there is a path that satisfies the reachability criterion.

[0083] The inbound set of a checkpoint refers to the set of all directed roads in the road network that can directly lead to the checkpoint, indicating which directed roads a vehicle can come from and reach the checkpoint. The outbound set refers to the set of all directed roads that can be directly accessed from the checkpoint, mainly indicating which directions a vehicle can go from the checkpoint.

[0084] The reachability criterion is used to filter physically feasible connections within the checkpoint projection topology. It is determined based on the travel time window calculated using the shortest path distance and time-period speed quantiles, along with directional compatibility conditions. Specifically, a path must satisfy all of the following criteria to be considered reachable: 1. In the basic road network topology, there must exist a connected path consisting of continuous directed edges connecting the starting and ending checkpoints. 2. The travel direction of the entire path must conform to the road's directional traffic rules (e.g., no reverse travel). 3. The path must comply with all traffic control rules, including but not limited to prohibitions on entry and turns (e.g., no left turns). 4. The path length and expected speed can support a reasonable travel time, providing a spatial basis for subsequent feasible travel time windows. This ensures that the connections established in the checkpoint projection topology are real, legal, and accessible, filtering out invalid connections that are impassable or violate traffic regulations.

[0085] To address the issue of physically unreachable paths being included in state transition statistics, a global masking mechanism based on road network physical rules was established. This fundamentally eliminates unreasonable transitions and improves statistical quality, as detailed below:

[0086] Methods for constructing reachability masks and orientation-compatible masks include:

[0087] Initialize two global mask matrices, one for reachability and the other for orientation compatibility. By default, all mask values ​​between state pairs are marked as infeasible.

[0088] In the road network topology, Dijkstra's algorithm is used to calculate the shortest path distance between any two checkpoints;

[0089] For each time period encoding, based on its corresponding lower and upper velocity quantiles and combined with the shortest path distance, the initial lower and upper bounds of the feasible travel time window are calculated, and a preset time tolerance is superimposed on the feasible travel time window to output the final feasible travel time window.

[0090] For all possible state pairs, i.e., any combination of a starting state and any ending state, perform the following operation:

[0091] For the starting state and the ending state, calculate the theoretical time difference of the corresponding vehicle passing event record. Then, compare the theoretical time difference with its corresponding feasible travel time window. If it is within the window, set the mask value of the state pair in the reachability mask matrix as feasible; otherwise, set it as infeasible.

[0092] Check whether the direction label corresponding to the starting state is consistent with the allowed entry direction of the checkpoint corresponding to the ending state in the road network topology; if they are consistent, set the mask value corresponding to the state pair in the direction compatibility mask matrix to feasible, otherwise set it to infeasible.

[0093] For example, suppose a miniature road network has only three checkpoints, A, B, and C; the basic information is as follows:

[0094] Directional labels include East (E) and West (W), and all checkpoints are bidirectional. There is only one fixed time period T for the time slot coding; the road network topology is as follows: A to B is 1000 meters apart, A(E) direction is compatible with B(W) direction; B to C is 800 meters apart, B(E) direction is compatible with C(W) direction; there is no direct connection between A and C; the shortest path is A→B→C, with a total distance of 1800 meters; → indicates a directed edge.

[0095] The velocity percentile is set at 5 m / s for the lower percentile and 20 m / s for the upper percentile in time interval T; the time tolerance is set to 120 seconds.

[0096] Taking the journey from A to C as an example, the feasible travel time window is calculated. The shortest path distance is 1800 meters.

[0097] Initial lower bound: 1800m ÷ 20m / s = 90s.

[0098] Initial upper bound: 1800m ÷ 5m / s = 360s.

[0099] The final feasible travel time window after adding tolerances is: [90s-120s, 360s+120s]=[0s, 480s], and the lower bound is 0 if it is less than 0.

[0100] The theoretical time difference is used for judgment when constructing the reachability mask, which is calculated based on the shortest path distance and velocity quantile.

[0101] Check the following possible state pairs:

[0102] Starting state End point state Theoretical time difference Accessibility judgment reachability mask Direction compatibility judgment Direction-compatible mask (A, E, T) (B, W, T) 1000m ÷ 20m / s = 50s yes feasible A(E) and B(W) are compatible = Yes feasible (A, E, T) (C, W, T) 1800m ÷ 20m / s = 90s yes feasible A(E) and C(W) are compatible = Yes feasible (A, W, T) (B, E, T) 1000m ÷ 20m / s = 50s yes feasible AW and B(E) are incompatible = No Not feasible (B, E, T) (A, W, T) 1000m ÷ 20m / s = 50s yes feasible B(E) and A(W) are incompatible = No Not feasible

[0103] This generates a reliable global mask lookup table.

[0104] To address the issue of incomplete trajectory statistics due to missing data, statistical counting is performed under strict quality control, and missing trajectories are repaired through intelligent interpolation, thereby improving data utilization and statistical completeness. Specifically, this includes:

[0105] Methods for outputting the summarized transition count tensor include:

[0106] Traverse all adjacent state pairs in the state sequence; for each pair of adjacent states, query its value in the pre-constructed global reachability mask and orientation compatibility mask; in the pre-constructed global mask matrix, each state pair (starting state, ending state) has a value in the reachability mask and orientation compatibility mask (indicating feasibility or infeasibility). When making a judgment, simply use the current state pair (i.e., the two adjacent states) as the key to query the value at the corresponding position in these two mask matrices. If both values ​​are "feasible", then the condition is satisfied.

[0107] If the values ​​of the state pair are feasible in both masks, and the actual time difference of the state pair in the trajectory sequence falls within its corresponding feasible travel time window, then the transitions of the state pair are counted, and the count results are accumulated in the transition count tensor. Here, the actual time difference refers to the passage time of the later record minus the passage time of the earlier record in the vehicle passage event records corresponding to these two adjacent states. For example, if the vehicle passage record time corresponding to state AQ is t1 and the vehicle passage record time corresponding to state BQ is t2, then the actual time difference is t2 - t1.

[0108] The transfer count tensor is a multidimensional array with dimensions including the starting checkpoint number, the starting direction label, the starting time period code, the ending checkpoint number, the ending direction label, and the ending time period code. In actual storage, a sparse structure or a dimensionality reduction method may be used.

[0109] Adding the counting results to the transition count tensor means that when the mask and actual time difference conditions are met, and the state transitions from state D1 to state D2, 1 is added to the corresponding positions D1 and D2 in the transition count tensor. If it is a continuous transition segment interpolated, then each transition segment is accumulated separately.

[0110] If the actual time difference of the state pair in the trajectory sequence does not meet the feasible travel time window, but does not exceed the preset interpolation upper bound, then trajectory interpolation is initiated, an interpolation sequence is generated, and it is decomposed into several continuous, physically feasible state transition segments; these are included in the transition count tensor, and finally the summarized transition count tensor is obtained.

[0111] Specifically, the interpolation sequence consists of one or more intermediate checkpoint states. For example, if the interpolation sequence from state D1 to state D2 is D1→M1→M2→D2, then the decomposed transition segments are three segments: D1→M1, M1→M2, and M2→D2. Each segment must be feasible within the pre-constructed mask, and the theoretical time of each segment should also be within the feasible time window.

[0112] Methods for initiating trajectory interpolation and generating interpolation sequences include:

[0113] In the road network topology, K shortest paths connecting adjacent states are found to obtain a sequence of candidate intermediate nodes. Then, paths that simultaneously satisfy reachability and orientation compatibility mask constraints are selected, and an optimal path is calculated based on maximizing the path probability product. This generates an interpolation sequence consisting of several intermediate checkpoints; these checkpoints can be one or more, resulting in multiple candidate paths (K paths) during trajectory interpolation. Each path consists of a series of states (checkpoints). The maximization of the path probability product criterion means that for each candidate path, the product of the transition probabilities between adjacent states on that path (the transition probabilities are derived from an existing transition probability tensor) is calculated, and the path with the largest product is selected as the optimal interpolation path.

[0114] To address the issue that traditional statistical methods cannot simultaneously accommodate data-driven approaches and physical constraints, this paper employs prior smoothing, masking constraints, and iterative optimization to obtain transition probabilities that conform to both historical patterns and physical rules. Specifically, this includes:

[0115] Step S5: Based on the summarized transition count tensor, an initial scaling vector is obtained by introducing a pre-defined Dirichlet prior distribution. Then, masking and probability constraints are used to obtain the final transition probability tensor. Specifically, based on the transition count tensor output in step S4, a Dirichlet prior distribution is introduced for smoothing, and the reachability mask and orientation compatibility mask constructed in step S4 are strictly applied for constraints. The final transition probability tensor is calculated using masked normalization and iterative projection algorithms. This tensor is the core prediction model, defining the Markov probability of transitioning from one state to another within a specific time period.

[0116] Step S6: Obtain the current state of the vehicle, query the transition probability tensor, and select the state with the highest transition probability that matches it as the next checkpoint to be predicted. When multiple prediction steps are required, the predicted next checkpoint is used as the new current state, the time period code is updated, and the process is iterated until the preset number of steps is reached. Specifically, when trajectory prediction of the target vehicle is required, the following operations are performed:

[0117] Starting from its latest vehicle passage event record, generate its current state according to the method in step S3;

[0118] The query step S5 outputs the final transition probability tensor, finds all possible next states that match the current state, and takes the state with the highest transition probability as the next state prediction result.

[0119] When performing multi-step prediction, the predicted next state is taken as the new current state, and the time period code is updated according to the road network distance and time period speed. The query and selection process is repeated until the preset number of prediction steps is reached.

[0120] The method for obtaining the final transition probability includes: for each starting state and its corresponding time period code, reading the transition count vector corresponding to it in the transition count tensor, and adding it with the preset Dirichlet prior parameter vector to obtain the smoothed initial scale vector;

[0121] Query the global reachability mask and direction compatibility mask related to the starting state. For the ending state marked as infeasible in any mask, force the corresponding component value in the initial scaling vector to zero to obtain a scaling vector after mask constraint.

[0122] Subsequently, the proportional vector constrained by the mask is normalized to obtain an initial transition probability vector;

[0123] Starting from the initial transition probability vector, an iterative scaling algorithm is used to perform iterative projection correction under the constraints of the mask until it converges to a stable probability distribution, which is the final transition probability vector that satisfies all physical and probabilistic constraints.

[0124] The final transition probability vectors of all starting states together constitute the final transition probability tensor.

[0125] To address the issue of static models failing to adapt to dynamic changes in traffic flow, online learning and adaptive updates of the model ensure continuous optimization of predictive performance. Specifically, this includes:

[0126] The final transition probability tensor undergoes online learning, including: as the system continuously generates new vehicle passage event records and produces new state sequences, the following update process is executed:

[0127] Use a preset forgetting factor to exponentially weight the historical velocity quantiles;

[0128] Simultaneously, the forgetting factor is used to exponentially decay the historical transition count tensor;

[0129] Based on the new state sequence, according to the process of "outputting the summarized transfer count tensor" and "starting trajectory interpolation and generating the interpolation sequence", the newly added transfer count tensor is verified and statistically obtained. It is added to the decayed historical transfer count tensor to complete the data update and obtain the updated transfer count tensor. Based on the updated transfer count tensor and the velocity quantile, the process described in "the method of obtaining the final transfer probability" is re-executed (that is, step S5 is re-executed) to dynamically update the historical final transfer probability tensor, so that the prediction model can adapt to the changes in traffic flow patterns over time.

[0130] To address the issue of newly emerging checkpoints or directions not being promptly incorporated into the prediction system, a robust new element initialization mechanism is provided, ensuring the system's scalability and continued effectiveness. Specifically, this includes:

[0131] The checkpoint update method includes: when a checkpoint number or direction label not seen in historical data appears, locating the adjacent known nodes of the new checkpoint in the road network topology;

[0132] In the set of outgoing or incoming edges of the adjacent known nodes, establish a set of candidate endpoint states that are compatible with the new checkpoint or new direction label;

[0133] Assign preset Dirichlet prior parameters to the states in the candidate endpoint state set, and set the components corresponding to incompatible endpoint states to zero, thereby initializing the count of the corresponding row in the transition count tensor for that state.

[0134] Based on this initial count, the corresponding transition probability vector is initialized through the process described in step S5, and incorporated into the final transition probability tensor to participate in subsequent online updates and predictions.

[0135] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0136] It should be noted that all formulas in this manual are calculated by removing dimensions and taking their numerical values. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0137] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A Markov vehicle trajectory prediction method integrating checkpoint data, characterized in that, include: Step S1: When a vehicle passes through the detection line, the front-end device at the checkpoint acquires and generates a vehicle passage event record in real time. Step S2: Extract all vehicle passing event records with the same license plate identifier and arrange them in ascending order of passing time to form an overall sequence. If the time difference between two adjacent vehicle passing event records exceeds the trajectory segmentation threshold, then segment at that point to obtain multiple continuous trajectory sequences. Step S3: Generate a unique direction label for each vehicle passing event record in each trajectory sequence, and map it to a time period code; then convert each vehicle passing event record into a state represented by a triple, thereby converting the trajectory sequence into a state sequence; Step S4: Based on the road network topology, pre-construct a global reachability mask and a direction compatibility mask; count only adjacent state pairs that simultaneously satisfy the reachability mask and the direction compatibility mask to obtain a transition count tensor; otherwise, generate an interpolation sequence for adjacent states and include it in the transition count tensor. Output the summed transition count tensor; The method for preconstructing a global reachability mask and a direction-compatible mask includes: Initialize two global mask matrices, one for reachability and the other for orientation compatibility. By default, all mask values ​​between state pairs are marked as infeasible. Calculate the shortest path distance between any two checkpoints in the road network topology. For each time period encoding, based on its corresponding lower and upper velocity quantiles and combined with the shortest path distance, the initial lower and upper bounds of the feasible travel time window are calculated, and a preset time tolerance is superimposed on the feasible travel time window to output the final feasible travel time window. For all possible state pairs, i.e., any combination of a starting state and an ending state, calculate the theoretical time difference of the corresponding vehicle passing event record. Then, compare the theoretical time difference with its corresponding feasible travel time window. If it is within the window, set the mask value corresponding to the state pair in the reachability mask matrix as feasible; otherwise, set it as infeasible. Check whether the direction label corresponding to the starting state is consistent with the allowed entry direction of the checkpoint corresponding to the ending state in the road network topology; if they are consistent, set the mask value corresponding to the state pair in the direction compatibility mask matrix to feasible; otherwise, set it to infeasible. Step S5: Based on the summarized transition count tensor, the initial scale vector is obtained through the Dirichlet prior distribution, and the final transition probability tensor is obtained by using mask constraints and probability constraints. Step S6: Obtain the current state of the vehicle, query the transfer probability tensor, and select the state that matches it and has the highest transfer probability as the predicted next checkpoint.

2. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 1, characterized in that, Each vehicle passage event record in each trajectory sequence generates a unique direction label, the method of which includes: Each vehicle passage event record includes the license plate number, checkpoint number, passage time, and checkpoint location; For the first and last records of the trajectory sequence, the azimuth angle is obtained from the checkpoint geographical location of the record and its adjacent vehicle passing event records, quantized into a direction label, and written into the record; For each vehicle passage event record that is not the first or last record in the trajectory sequence, the azimuth angle is obtained from the checkpoint geographical location of the previous and next records, quantified into a direction label, and then written into the corresponding vehicle passage event record. When there is a missing vehicle passage event record or the azimuth angle is uncertain, all possible passage directions of the current checkpoint are located based on the road network topology to form a direction candidate set. Then, a unique direction label is matched and determined from the candidate set according to the actual preceding or succeeding checkpoint number of the record.

3. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 2, characterized in that, The method of mapping time to time segment encoding includes: Divide a day and night into several fixed and non-overlapping time periods, and assign a unique time period code to each time period; For vehicle passage events that span multiple days, time period codes are assigned according to the modal cyclical rule; When performing state transition statistics, the time period code of the starting state in the state sequence is used as the time period label for the entire transition process; each state in the state sequence includes a tuple, including the checkpoint number, direction label, and time period code; For each independent time period code, maintain its corresponding velocity quantile estimate, which includes the lower velocity quantile and the upper velocity quantile.

4. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 3, characterized in that, The road network topology includes a basic road network topology and a checkpoint projection topology. The basic road network topology uses road intersections as nodes, establishes directed edges for road segments according to the direction of travel, and configures attributes for the directed edges under each time period encoding. The attributes include length, heading angle, speed percentile, passage and turning restriction attributes. The checkpoint projection topology defines the set of incoming edges or outgoing edges of the checkpoints by anchoring the checkpoints to the nodes or edges of the basic road network topology, and establishes the connection relationship between checkpoints when there is a path that satisfies the reachability criterion.

5. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 4, characterized in that, The method for outputting a summary transition count tensor includes: Iterate through all adjacent state pairs in the state sequence; for each adjacent state pair, query its value in the pre-constructed global reachability mask and orientation compatibility mask; If the values ​​of the state pair are feasible in both masks, and the actual time difference of the state pair in the trajectory sequence is within its corresponding feasible travel time window, then the transitions of the state pair are counted, and the count results are accumulated in the transition count tensor. If the actual time difference of the state pair in the trajectory sequence does not meet the feasible travel time window, but does not exceed the preset interpolation upper bound, then trajectory interpolation is initiated, an interpolation sequence is generated, and it is decomposed into several state transition segments; these are included in the transition count tensor, and finally the summarized transition count tensor is obtained.

6. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 5, characterized in that, The method for initiating trajectory interpolation and generating the interpolation sequence includes: In the road network topology, K shortest paths connecting the adjacent states are found to obtain a sequence of candidate intermediate nodes. Then, the path that satisfies both the reachability mask and the direction compatibility mask constraints for any adjacent nodes is selected. The optimal path is solved by maximizing the product of path probabilities, thereby generating an interpolation sequence consisting of several intermediate checkpoints.

7. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 6, characterized in that, The method for obtaining the final transition probability tensor includes: For each starting state and its corresponding time period code, read the corresponding transition count vector in the transition count tensor and add it to the preset Dirichlet prior parameter vector to obtain the smoothed initial scale vector. Query the global reachability mask and direction compatibility mask related to the starting state. For the ending state marked as infeasible in any mask, force the corresponding component value in the initial scaling vector to zero to obtain a scaling vector after mask constraint. Subsequently, the proportional vector constrained by the mask is normalized to obtain an initial transition probability vector; Starting from the initial transition probability vector, an iterative scaling algorithm is used to perform iterative projection correction under the constraint of the mask until it converges to a stable probability distribution, which is the final transition probability vector. The final transition probability vectors of all starting states together constitute the final transition probability tensor.

8. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 7, characterized in that, The final transition probability tensor undergoes online learning, including: after new vehicle passing event records are continuously generated and new state sequences are generated, using a preset forgetting factor to exponentially update the historical velocity quantiles; simultaneously, using the forgetting factor to exponentially decay the historical transition count tensor. Based on the new state sequence, repeat step S5 to update the transition probability tensor.

9. The Markov vehicle trajectory prediction method based on fused checkpoint data according to claim 8, characterized in that, The checkpoint update method includes: when a checkpoint number or direction label not seen in historical data appears, locating its adjacent known nodes in the road network topology; In the set of outgoing or incoming edges of its adjacent known nodes, establish a set of candidate endpoint states that are compatible with it. Assign preset Dirichlet prior parameters to the states in the candidate endpoint state set, set the components corresponding to incompatible endpoint states to zero, initialize their corresponding transition probability vectors, and incorporate them into the final transition probability tensor.

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