Double-lane outer side geomagnetic vehicle track continuous reconstruction method and system for multiple leak detection

Abstract

The invention discloses a double-lane outer side geomagnetic vehicle track continuous reconstruction method and system for multiple leak detection, and is suitable for a scene in which geomagnetic sensors are arranged on outer side lane lines of two sides of a one-way double lane and are not arranged in the middle. And taking the event-level geomagnetic detection result as input, establishing a time index cache sorted according to measurement timestamps in a data center, and processing out-of-order events in a fixed lag sliding window. Self-calibrating the omission ratio of each sensor group on line based on the output stable track segment and obtaining the reliability; constructing an event transfer graph allowing to cross a plurality of sensor groups, accumulating detection-lacking punishment according to the reliability of the intermediate sensor group, and forming connection cost by combining time-space and feature consistency; and solving the minimum total cost connection under one-to-one constraint to obtain a trajectory path. And connecting the cross-missing section to generate a virtual track point and outputting a stable track section in a fixed lag manner. According to the invention, waveform level processing or additional hardware is not needed, and track continuity and online output stability can be improved.

Description

Technical Field

[0001] This invention belongs to the fields of intelligent transportation systems (ITS), Internet of Things traffic perception, and multi-target tracking technology, specifically relating to a method and system for continuous reconstruction of the outer geomagnetic vehicle trajectory of a two-lane road with multiple missed detections. Background Technology

[0002] Geomagnetic sensors, with their advantages of low cost, easy installation and maintenance, and minimal susceptibility to light and weather conditions, have been widely used for lane-level vehicle detection, speed estimation, and traffic flow monitoring. In some engineering deployments, to reduce construction damage and maintenance costs, geomagnetic sensors are often deployed only along the outer lane lines on both sides of the road, rather than in the middle lane lines. The sensors typically upload vehicle detection events to roadside base stations or data centers via wireless networks.

[0003] In existing vehicle trajectory tracking solutions, some methods rely on the fusion of radar and cameras to achieve target tracking. For example, the patent document "Vehicle Trajectory Tracking Method and System Based on Radar and Video Fusion" (Application No.: 202210867558.4, Publication (Announcement) No.: CN115327527A) proposes to achieve trajectory tracking by synchronizing timestamps from multiple sensor sources and associating the data. However, such solutions typically depend on installation conditions such as gantry cranes, resulting in high equipment costs and the detection performance being easily affected by environmental factors such as rain and fog.

[0004] Another approach relies on multiple geomagnetic sensors to achieve vehicle trajectory tracking and correlation. For example, the patent document "A Method for Vehicle Trajectory Tracking and False Trajectory Judgment Based on Multiple Geomagnetic Sensors" (Application No.: CN202410215061.3, Publication (Announcement) No.: CN118197070A) proposes correlation and tracking based on geomagnetic detection results. However, in scenarios where sensors are deployed on the outer side of a two-lane road, geomagnetic detection event data often exhibits "sparse, missing, and out-of-order" input characteristics in engineering applications. Among these, multiple missed detections and continuous missing detections are significant bottlenecks affecting trajectory continuity.

[0005] Furthermore, packet loss, congestion, and retransmission in wireless links can lead to discrepancies between the arrival order of events and the measurement timestamps, resulting in out-of-order input. Simply employing a "wait for all events to arrive" or simple discarding strategy can easily introduce significant delays or cause missing trajectory information, making it difficult to simultaneously ensure real-time performance and global consistency. Therefore, there is an urgent need for a new method and system that can maintain trajectory continuity under multiple missed detection conditions, reduce false associations and ID switching, and ensure project feasibility. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a method and system for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a dual-lane roadway with multiple missed detections. The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, the present invention provides a method for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a two-lane roadway with multiple missed detections, comprising: Acquire vehicle detection event reporting data from a network of multiple geomagnetic sensors deployed on the outer lane lines of both sides of a one-way dual-lane road. The vehicle detection event reporting data includes at least the measurement timestamp, sensor group identifier, lane identifier, and event-level geomagnetic characteristics. The time index cache window is maintained in the data center, and the time index cache window overrides the preset cache time window; For vehicle detection events that arrive out of order and whose measurement timestamps fall within the window of the time index cache, perform insertion and ordered maintenance by measurement timestamp sorting, and discard or bypass outdated events whose measurement timestamps are earlier than the start of the window of the time index cache. Vehicle detection events within the time index cache window are grouped into scan sequences according to measurement timestamps, and a fixed-hysteresis sliding window covering multiple consecutive scans is maintained. Based on the output stable trajectory segments, the expected number of times the vehicle passes through each sensor group is inferred and the actual number of detections for the corresponding sensor group is counted. Based on the expected number of passes and the actual number of detections, the missed detection rate estimate for each sensor group is updated online, and the missed detection rate estimate is updated only using the output stable segments outside the window boundary. An event transition graph is constructed within a fixed-hysteresis sliding window. The nodes of the event transition graph represent vehicle detection events, and the edges of the event transition graph represent candidate connections between vehicle detection events. The candidate connections are established when the longitudinal position increment and equivalent speed constraints are satisfied, and are allowed to cross one or more intermediate sensor groups to characterize multiple missed detections. The missed detection penalty is calculated based on the estimated false negative rate for candidate connectivity relationships. The missed detection penalty, along with the spatiotemporal consistency cost and the event feature consistency cost, constitutes the connectivity cost. The missed detection penalty is calculated by summing the reliability of the intermediate sensor groups traversed and multiplying by a coefficient. , The penalty coefficient is denoted as , and the more reliable the intermediate sensor group is, the greater the penalty for missing detection. The penalty for missing detection makes the connection edge of missing event at the reliable sensor group more costly, thereby suppressing erroneous reconnection, and also allows for lower penalties at the unreliable sensor group to improve reconnectivity across missing detection segments. Under one-to-one constraints, solve the minimum total cost connection relationship of the event transition graph so that each vehicle detection event is connected to at most one predecessor event and one successor event, and generate a set of vehicle trajectory paths based on the minimum total cost connection relationship. When the minimum total cost connection relationship spans one or more sensor groups or multiple scanning intervals, virtual trajectory points are generated based on the measurement timestamps and longitudinal positions of the events at both ends of the connection relationship and written into the trajectory point sequence of the corresponding vehicle trajectory to form the missing segment interpolation result. A fixed lag output mechanism is used to output stable trajectory segments that are earlier than the fixed lag sliding window boundary, resulting in a continuously reconstructed set of vehicle trajectories. The set of vehicle trajectories includes a timestamp sequence, a longitudinal position sequence, and a longitudinal velocity sequence.

[0007] Secondly, the present invention also provides a continuous reconstruction system for the geomagnetic vehicle trajectory on the outer side of a two-lane road with multiple missed detections, comprising: The data access module is used to access vehicle detection events reported by the geomagnetic sensor; The time index cache module is used to perform in-window insertion sorting on out-of-order vehicle detection events and to discard or bypass outdated events. The scan construction and sliding window module is used to merge vehicle detection events into a scan sequence and maintain a fixed-hysteresis sliding window. The missed detection rate self-calibration module is used to update the missed detection rate estimate of each sensor group online based on stable trajectory segments. The event transition graph construction module is used to build candidate connections that can span multiple sensor groups and calculate connection costs. The global connectivity solver module is used to solve for the minimum total cost connectivity under one-to-one constraints and generate a set of vehicle trajectory paths; The interpolation and output module is used to generate virtual trajectory points at missing locations and output stable trajectory segments using a fixed lag output mechanism.

[0008] The beneficial effects of this invention are: This invention provides a method and system for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a two-lane road with multiple missed detections. First, by allowing candidate connections across multiple sensor groups and explicitly introducing a missed detection penalty into the connection cost, trajectory continuity can be maintained under continuous missed detection conditions, significantly reducing trajectory fragmentation. Second, by estimating the missed detection rate of each sensor group online, the system can distinguish between reliable sensor failures and sensor stage failures, thereby reducing the probability of erroneous reconnection across missed detection segments. Furthermore, the combination of time index caching and a fixed-hysteresis sliding window can absorb out-of-order events and perform controllable corrections to the results within the window, thereby reducing trajectory label jitter. Moreover, the method relies only on event-level geomagnetic detection results, requiring no waveform-level processing or additional hardware modifications, and can be used for online upgrades and deployments of existing geomagnetic sensor networks.

[0009] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0010] Figure 1 This is a flowchart of a method for continuous reconstruction of the outer geomagnetic vehicle trajectory of a two-lane road with multiple missed detections, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of the deployment location of the geomagnetic sensor in a two-lane scenario provided in an embodiment of the present invention; Figure 3 This is another flowchart of the method for continuous reconstruction of the outer geomagnetic vehicle trajectory of a two-lane road with multiple missed detections provided in the embodiments of the present invention; Figure 4 This is a schematic diagram illustrating the access and sorting of out-of-order events within a fixed lag window, as provided in an embodiment of the present invention. Detailed Implementation

[0011] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0012] This invention provides a method and system for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a two-lane road with multiple missed detections, in order to solve the problems of trajectory breakage, fragmentation, erroneous reconnection, and frequent switching of trajectory identifiers that are prone to occur in existing solutions under conditions of continuous missing detections and out-of-order uploading.

[0013] To achieve the above objectives, the present invention adopts the following technical solution.

[0014] First, a time index cache with measurement timestamps as the primary order is established, coupled with a fixed-lag sliding window, to achieve online access and stable output of out-of-order events. The data center inserts and sorts vehicle detection events falling within the cache time window by measurement timestamp, and discards or bypasses outdated events that exceed the cache time window. At the same time, events in the cache are merged into scan sequences, and subsequent connection solving and trajectory reconstruction updates are completed uniformly within the fixed-lag sliding window.

[0015] Second, an online self-calibration mechanism for the false negative rate is proposed for multiple false negatives. The system uses the monotonic longitudinal passage pattern of the vehicle corresponding to the output stable trajectory segment to deduce the expected number of times the vehicle passes through each sensor group, and updates the false negative rate estimate of each sensor group online by combining it with the actual number of events detected, thereby obtaining the sensor reliability over time.

[0016] Third, a reconnection mechanism for the event transition graph driven by missed detection penalties is proposed, explicitly incorporating multiple missed detections into the global association. Within a fixed-hysteresis sliding window, an event transition graph is constructed using vehicle detection events as nodes. Candidate connections are established between event pairs that satisfy both vertical position increment and reasonable equivalent speed. These candidate connections are allowed to span one or more intermediate sensor groups to characterize consecutive missed detections. Simultaneously, the missed detection rate is estimated as the cumulative missed detection penalty for the intermediate sensor groups spanned, ensuring that the more reliable the sensor group, the greater the missed detection penalty, thereby suppressing unreasonable reconnections at reliable sensors where no events occur.

[0017] Fourth, under one-to-one constraints, the global minimum total cost of event connections is solved to generate a set of vehicle trajectory paths. The one-to-one constraints are used to ensure that each vehicle detection event belongs to at most one vehicle trajectory, and each vehicle detection event is connected to at most one predecessor event and one successor event, thereby obtaining globally consistent association results within the window and reducing trajectory identifier switching.

[0018] Fifth, for connections that cross missing positions, virtual trajectory points are generated at the missing positions and the interpolation results of the missing segments are output; and a fixed lag output mechanism is used to output only stable trajectory segments that are earlier than the sliding window boundary, so as to ensure real-time performance while taking into account global consistency and output stability.

[0019] Please see Figure 1 , Figure 1 This is a flowchart of a method for continuous reconstruction of the outer geomagnetic vehicle trajectory of a two-lane roadway with multiple missed detections, provided by an embodiment of the present invention. The method includes: S101. Obtain vehicle detection event reporting data from multiple sets of geomagnetic sensor networks deployed on the outer lane lines on both sides of a one-way dual-lane road. The vehicle detection event reporting data shall include at least the measurement timestamp, sensor group identifier, lane identifier, and event-level geomagnetic characteristics. S102. Maintain a time index cache window in the data center. The time index cache window overrides the preset cache time window. S103. Perform insertion and ordered maintenance by measurement timestamp for vehicle detection events that arrive out of order and whose measurement timestamps fall into the time index cache window, and discard or bypass outdated events whose measurement timestamps are earlier than the start of the time index cache window. S104. Group the vehicle detection events in the time index cache window into a scan sequence according to the measurement timestamp, and maintain a fixed hysteresis sliding window that covers multiple consecutive scans. S105. Based on the output stable trajectory segments, infer the expected number of times the vehicle will pass through each sensor group and count the actual number of detections for the corresponding sensor group; based on the expected number of passes and the actual number of detections, update the missed detection rate estimate for each sensor group online, and the missed detection rate estimate is updated only using the output stable segments outside the window boundary. S106. Construct an event transition graph within a fixed hysteresis sliding window. The nodes of the event transition graph represent vehicle detection events, and the edges of the event transition graph represent candidate connection relationships between vehicle detection events. The candidate connection relationships are established when the longitudinal position increment and equivalent speed constraints are satisfied, and are allowed to cross one or more intermediate sensor groups to characterize multiple missed detections. S107. Calculate the missing detection penalty based on the estimated false negative rate for candidate connectivity relationships, and combine the missing detection penalty with the spatiotemporal consistency cost and the event feature consistency cost to form the connectivity cost; wherein, the missing detection penalty is calculated by summing and multiplying the reliability of the intermediate sensor groups traversed by a coefficient. , The penalty coefficient is denoted as , and the more reliable the intermediate sensor group is, the greater the penalty for missing detection. The penalty for missing detection makes the connection edge of missing event at the reliable sensor group more costly, thereby suppressing erroneous reconnection, and also allows for lower penalties at the unreliable sensor group to improve reconnectivity across missing detection segments. S108. Solve the minimum total cost connection relationship of the event transition graph under one-to-one constraints, so that each vehicle detection event can establish a connection with at most one predecessor event and one successor event, and generate a set of vehicle trajectory paths based on the minimum total cost connection relationship. S109. When the minimum total cost connection relationship spans one or more sensor groups or multiple scanning intervals, virtual trajectory points are generated based on the measurement timestamps and longitudinal positions of the events at both ends of the connection relationship and written into the trajectory point sequence of the corresponding vehicle trajectory to form the missing segment interpolation result. S110. A stable trajectory segment earlier than the fixed lag sliding window boundary is output using a fixed lag output mechanism to obtain a continuously reconstructed vehicle trajectory set, which includes a timestamp sequence, a longitudinal position sequence, and a longitudinal velocity sequence.

[0020] In an optional embodiment of the invention, the vehicle detection event includes sensor identification and mass indication, and the event-level geomagnetic feature includes at least one or more of peak intensity, event energy, and event duration.

[0021] In an optional embodiment of the present invention, the window maintenance rules for the time index cache include: The default cache time window length is The current processing time of the data center is ; When the measurement timestamp of a newly arriving vehicle detection event satisfy At that time, vehicle detection events are inserted into the time index cache and sorted by measurement timestamp; When measuring timestamps Less than When a vehicle detection event is identified as an outdated event, it will be discarded or bypassed for offline statistical processing.

[0022] In an optional embodiment of the present invention, vehicle detection events within a time index cache window are grouped into a scan sequence according to measurement timestamps, including: Set scan interval Divide the time axis into continuous scan intervals ; Will fall into the same scanning range Vehicle inspection events within the premises constitute the first Measurement set of the second scan The fixed-hysteresis sliding window is formed by a series of consecutive scans of the index.

[0023] In an optional embodiment of the present invention, updating the missed detection rate estimate for each sensor group online includes: Beta-Bernoulli conjugate update of false negative rate estimation is used; The reliability of each sensor group is estimated based on the false negative rate, where the reliability is a monotonic function of the false negative rate estimate.

[0024] In an optional embodiment of the present invention, the constraints for establishing candidate connection relationships include: Candidate connection relationships satisfy the condition that the vertical position of the successor event is greater than the vertical position of the predecessor event, and the equivalent velocity of the successor event and the predecessor event are equal. satisfy .

[0025] In an optional embodiment of the present invention, the calculation process for the missing test penalty includes: The penalty for missing detection is the set of intermediate sensor groups traversed by the candidate connectivity. The calculation of the missing measurement penalty, obtained by summing, is based on the principle that the greater the reliability of the intermediate sensor group, the greater the penalty.

[0026] In an optional embodiment of the present invention, solving for the minimum total cost connection relationship of the event transition graph under one-to-one constraints includes: The event transition graph is transformed into a bipartite graph consisting of the set of predecessor events and the set of successor events. The minimum cost matching is obtained under one-to-one constraints to obtain the minimum total cost connection relationship, or the minimum cost flow algorithm is used to obtain the set of vehicle trajectory paths.

[0027] In an optional embodiment of the present invention, the data center uses the event-level detection results generated by the geomagnetic sensor when a vehicle passes as input. First, a time index cache with the measurement timestamp as the main sequence is established in the data center to absorb out-of-order arrivals caused by network jitter. Then, the events in the cache are grouped into discrete scan sequences according to time and uniformly inferred within a fixed lag sliding window. This allows for controllable correction of the results caused by late events within the window range, while ensuring stable output of results outside the window.

[0028] To address the trajectory breakage problem caused by continuous missing data, this embodiment does not rely on waveform-level matching, nor does it employ a strategy of thresholding only for single missed detections. Instead, it first performs online self-calibration of the missed detection rate of each sensor group based on the output stable trajectory segments, obtaining the reliability of each sensor group. Then, it constructs an event transition graph within a window that allows crossing multiple sensor groups, and transforms "crossing missing data" into a measurable missing data penalty, ensuring that "the more reliable the sensor group, the less likely it is to be crossed without events," thereby avoiding erroneous reconnection during global connectivity solving. Finally, it solves the minimum total cost connectivity relationship under one-to-one constraints to obtain the event path, and generates virtual trajectory points only for path segments that "cross missing positions," forming missing segment interpolation results to output a temporally continuous trajectory sequence that can be used for speed estimation and subsequent traffic analysis.

[0029] Please see Figure 2 and Figure 3 , Figure 2 This is a schematic diagram illustrating the deployment location of a geomagnetic sensor in a two-lane scenario, as provided in an embodiment of the present invention. Figure 3 This is another flowchart of the method for continuous reconstruction of the outer geomagnetic vehicle trajectory of a two-lane road with multiple missed detections provided by the embodiments of the present invention, and further describes the implementation steps of the embodiments of the present invention.

[0030] Step 1, Sensor deployment and location mapping.

[0031] Geomagnetic sensors are deployed at intervals along the outer lane lines on both sides of a one-way two-lane road, according to the direction of travel. Two geomagnetic sensors at the same longitudinal position are defined as the same sensor group, and the sensor group is identified as follows: The data center pre-stores the fixed longitudinal position corresponding to each sensor group. And assign a unique sensor identifier to each geomagnetic sensor. Lane markings The location is determined by the outer lane line to which the sensor belongs; the above position mapping is used for subsequent longitudinal monotonicity constraints, equivalent speed calculations, and missed detection rate statistics.

[0032] Step 2: Vehicle detection and event-level feature reporting.

[0033] Step 2.1: The magnetic sensors in each location continuously collect triaxial magnetic field strength sequences at a preset sampling period, and run a vehicle detection algorithm at the sensor end to determine whether a vehicle enters or leaves the detection range.

[0034] Step 2.2, taking first-order differential detection as an example, let the magnetic field strength sequence be... The first-order difference signal is When no vehicles are passing by, the magnetic field sequence changes gradually. The amplitude stabilizes near zero; when a vehicle passes by, the magnetic field disturbance caused by the vehicle causes... Significant fluctuations occur, triggering vehicle entry and departure events. Based on the boundaries between entry and departure events, the continuous sampling sequence can be segmented into event segments corresponding to a single vehicle passage.

[0035] Step 2.3: Extract event-level geomagnetic feature vectors from event segments at the sensor end. An event-level geomagnetic feature vector may include at least one or more of the following: peak intensity, event energy, and event duration. The event energy characterizes the cumulative disturbance intensity of an event segment above a detection threshold and can be expressed as the event segment's... The results are obtained by summing or squaring. To facilitate engineering implementation, the data center-side core inference of this invention is completed using only event-level data and does not rely on waveform-level alignment or waveform morphological matching.

[0036] Step 2.4: The sensor reports vehicle detection events via wireless link. Vehicle detection events must include at least a measurement timestamp. Sensor group identification Lane markings and event-level geomagnetic features Optionally includes sensor identifier With quality indication quantity Quality indicators are used to characterize the quality of event data. Quality indicators can be set as signal-to-noise ratio, confidence level, or anomaly flag.

[0037] Step 3: Establish a time index cache to access out-of-order data.

[0038] Step 3.1, due to network jitter in wireless transmission, the event... The order of arrival may be related to its measurement timestamp. Inconsistent, please refer to Figure 4 , Figure 4 This is a schematic diagram illustrating the out-of-order event access and window sorting processing provided by an embodiment of the present invention. To balance real-time performance and consistency, the data center maintains a time index cache with measurement timestamps as the primary order, and the cache covers the most recent... Event data with varying durations. Among them, The duration can be 3 to 10 seconds.

[0039] Step 3.2, Data center maintains the current processing time. , The maximum measured timestamp from the currently received events can be retrieved. When a new event arrives, the following processing is performed: (1) If Falling into the range Then the event will be inserted into the cache. And according to the measurement timestamp Sort; (2) If Less than If the event is deemed too old, it is either discarded or bypassed and written to the offline statistics queue. (3) When cached When the set of internal events changes, steps 4 to 8 are triggered to perform reconstruction inference and trajectory update within a fixed-hysteresis sliding window.

[0040] Step 4: Construct the scan sequence and maintain a fixed hysteresis sliding window.

[0041] Step 4.1: To convert the continuous-time event stream into a discrete sequence that is easy to window-process, set the scan interval. The time axis is divided into continuous scanning intervals. The time interval can range from 50 milliseconds to 200 milliseconds and can be adjusted according to the vehicle speed range and the distance between sensors.

[0042] Step 4.2, the The time interval corresponding to each scan is defined as: ; Step 4.3, measure the timestamp fall into The events were merged into the first Measurement set of the second scan : ; in, For scanning Number of internal events, per measurement Includes at least a measurement timestamp Sensor group identification Lane markings Corresponding to the fixed longitudinal position and event-level geomagnetic features .

[0043] Step 4.4, System maintenance covers continuous A fixed-hysteresis sliding window for each scan Window length The allowable fixed hysteresis and network out-of-order range can be set, for example, from 20 to 60.

[0044] Step 4.5, Window The unified execution event transfer graph is constructed and the global connectivity is solved; the trajectory segments outside the window boundary are considered to be stable and can be output and used for false negative rate self-calibration.

[0045] Step 5: Online self-calibration of the missed detection rate.

[0046] To ensure quantifiable reliability for reconnection across missing measurement segments, this embodiment establishes an online estimate of the false negative rate for each sensor group. The false negative rate characterizes the probability that a vehicle passes through the sensor group without generating a detection event. This step only uses the output stable trajectory segments for statistical analysis to avoid contaminating the false negative rate estimate with trajectory results that have not yet converged within the window.

[0047] Step 5.1, in one embodiment, employs a Beta-Bernoulli conjugate update. For each sensor group... Maintaining the Beta prior distribution ,in, , These are prior parameters and can be initialized to... , To represent unbiased a priori.

[0048] Step 5.2: Model the vehicle's "whether it detects an event" in this sensor group as a Bernoulli random variable. ,in, This indicates that an event has been detected. This indicates a missed detection.

[0049] For a stable trajectory segment that has already been output, let the sequence of sensor groups it covers in the longitudinal direction be . arrive And the vertical position satisfies Based on the physical constraint that the vehicle moves monotonically along the longitudinal direction, it can be inferred that the vehicle should pass through the following locations sequentially within this trajectory segment. and For each sensor group between them, let the expected set be denoted as . For each If the stable trajectory segment is within the sensor array If a corresponding detection event exists at that location, then let Otherwise, .

[0050] Step 5.3: Obtain the posterior parameters using conjugate update: ; This yields the sensor group. Estimate the false negative rate: ; Furthermore, the reliability of the sensor array can be defined. Reliability is used for subsequent calculation of missing test penalties.

[0051] Step 6: Construct an event transition graph with missing test penalties.

[0052] Step 6.1, in the fixed hysteresis sliding window Within the window, vehicle detection events are used as the set of nodes. Construct an event transition graph . Figure 4 Each directed edge represents a candidate connection, with the connection direction aligned with the vehicle's travel direction. To avoid unreasonable connections and reduce computational complexity, candidate edges are only established between event pairs that satisfy the criteria of increasing vertical position, increasing time, and reasonable equivalent speed.

[0053] Step 6.2, let the predecessor event be... The subsequent event was The corresponding longitudinal fixed positions of the two are respectively , The measurement timestamps are respectively , When satisfied and Then, calculate the equivalent speeds of the two: ; When the equivalent speed satisfies At that time, and Candidate connection edges are established between them. , The speed boundary is configurable and can be set according to road speed limits and traffic conditions. In one embodiment, to limit the crossing range, the number of intermediate sensor groups crossed by the candidate connecting edge can be further limited to no more than [a certain number]. or time difference not exceeding .

[0054] Step 6.3: For candidate connection edges that are allowed to cross intermediate sensor groups, denote the set of intermediate sensor groups they cross as . To characterize multiple missed detections, this invention allows... Calculate the connection cost for each candidate connection edge. The connection cost includes at least the following three parts: (1) Cost of spatiotemporal consistency It is used to characterize the rationality and smoothness of the equivalent velocity; (2) Cost of consistency of event characteristics This is used to characterize the similarity of event-level features between events; (3) Penalty for missing the test This is used to characterize the irrationality of crossing intermediate sensor groups without any events.

[0055] In one embodiment, the connection cost can be expressed as: ; in, , These are the weighting coefficients. The equivalent velocity can be deviated from the prior velocity. The normalized squared error, for example: ; in, , It can be obtained from historical statistics or online estimation. You can use the normalized distance of the event-level feature vectors, for example: .

[0056] Step 6.4: The penalty for missing data is obtained by summing the reliability of the intermediate sensor groups, satisfying the condition that "the more reliable the intermediate sensor group, the greater the penalty." In one embodiment: ; in, is the penalty coefficient. This missing detection penalty makes the connection edge of the missing event more expensive at reliable sensor groups, thus suppressing erroneous reconnection; at unreliable sensor groups, a lower penalty is allowed to improve reconnectivity across missing detection segments.

[0057] Step 7: Global connectivity solution and trajectory generation.

[0058] To avoid false associations and ID switching caused by single-step greedy connections in scenarios with missed detections, this embodiment uses a window... The internal algorithm performs a global minimum total cost connection solution on the event transition graph. The goal is to select a number of connection edges under one-to-one constraints such that the total connection cost is minimized, and each event is connected to at most one predecessor event and one successor event.

[0059] Step 7.1, in one embodiment, event connectivity can be modeled as a bipartite graph matching problem. The event set... Copy them separately as a predecessor set With successor set Candidate connection edges Corresponding to the edge of the bipartite graph The cost is Virtual start and virtual end points are introduced to allow trajectory initiation and termination. The minimum total cost connection relationship can be obtained by solving the minimum cost matching under one-to-one constraints.

[0060] In another embodiment, event connectivity can be modeled as a minimum cost flow problem. For each event node, input and output edges with a capacity of 1 are constrained, and several unit flows are sought between the source and sink nodes, each unit flow corresponding to a vehicle trajectory path. Solving this problem using the minimum cost flow algorithm yields a globally consistent set of trajectory paths.

[0061] Step 7.2: Based on the minimum total cost connection relationship obtained from the solution, the events are connected in series according to the direction of the connecting edges to form a set of vehicle trajectory paths. When an event does not have a preceding connecting edge, it is taken as the starting point of the new trajectory; when an event does not have a succeeding connecting edge, it is taken as the ending point of the trajectory.

[0062] Step 8: Repeatedly check for missed breaks in bridging and missing segments for interpolation.

[0063] The global connection solution yields an "event-to-event" trajectory path. When two adjacent events cross one or more sensor groups or multiple scanning intervals, it indicates that the vehicle has continuous missed detections within that interval, and the trajectory lacks observable event points at these locations. To output a continuous trajectory and provide a complete sequence of trajectory points for subsequent statistics and applications, this embodiment generates virtual trajectory points at the missing locations as interpolation results.

[0064] For connecting edges If the set of intermediate sensor groups it traverses is For each A virtual trajectory point is inserted into the trajectory. In one embodiment, the longitudinal position of the virtual trajectory point is taken as a fixed position corresponding to the sensor group. The measurement timestamps of virtual trajectory points can be linearly interpolated based on the equivalent velocity. ; The longitudinal velocity of the virtual trajectory point can be taken as follows Alternatively, linear interpolation can be performed based on the velocities at both ends of the missing segment when necessary. Virtual trajectory points can be marked with flags to distinguish between "measured points" and "interpolated points".

[0065] Step 9, fixed lag output.

[0066] To accommodate out-of-order events and in-window reconstruction corrections, this embodiment employs a fixed-latency output strategy. Let the current scan index be... Fixed lag is The data center only outputs stable trajectory segments earlier than the window boundary, such as those that satisfy the timestamp. The trajectory points; located in the window The trajectory segment within the underscore is temporarily stored and allowed to be corrected by subsequent late events. By using fixed-hysteresis output, frequent trajectory marker jumps and false reconnections can be significantly reduced while maintaining linearity.

[0067] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0068] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0069] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a two-lane road with multiple missed detections, characterized in that, include: The vehicle detection event reporting data is obtained from a network of multiple geomagnetic sensors deployed on the outer lane lines of both sides of a one-way dual-lane road. The vehicle detection event reporting data includes at least a measurement timestamp, sensor group identifier, lane identifier, and event-level geomagnetic characteristics. A window for maintaining a time index cache in the data center is provided, which covers a preset cache time window; For vehicle detection events that arrive out of order and whose measurement timestamps fall within the window of the time index cache, perform insertion and ordered maintenance by measurement timestamp sorting, and discard or bypass outdated events whose measurement timestamps are earlier than the start of the window of the time index cache. The vehicle detection events within the time index cache window are grouped into a scan sequence according to the measurement timestamp, and a fixed-hysteresis sliding window covering multiple consecutive scans is maintained. Based on the output stable trajectory segments, infer the expected number of times the vehicle will pass through each sensor group and count the actual number of detections for the corresponding sensor group. Based on the expected number of passes and the actual number of detections, the missed detection rate estimate of each sensor group is updated online, and the missed detection rate estimate is updated only using the statistics of the stable segment already output outside the window boundary; An event transition graph is constructed within the fixed hysteresis sliding window. The nodes of the event transition graph represent vehicle detection events, and the edges of the event transition graph represent candidate connection relationships between vehicle detection events. The candidate connection relationships are established when the longitudinal position increment and equivalent speed constraints are satisfied, and are allowed to cross one or more intermediate sensor groups to characterize multiple missed detections. The missed detection penalty is calculated based on the estimated false negative rate for the candidate connectivity, and the missed detection penalty, along with the spatiotemporal consistency cost and the event feature consistency cost, constitutes the connectivity cost; wherein, the missed detection penalty is summed and multiplied by a coefficient based on the reliability of the intermediate sensor groups traversed. , The penalty coefficient is denoted as , and the more reliable the intermediate sensor group is, the greater the penalty for missing detection. The penalty for missing detection makes the connection edge of missing event at the reliable sensor group more costly, thereby suppressing erroneous reconnection, and also allows for lower penalties at the unreliable sensor group to improve reconnectivity across missing detection segments. The minimum total cost connection relationship of the event transition graph is solved under one-to-one constraints, so that each vehicle detection event is connected to at most one predecessor event and one successor event, and a set of vehicle trajectory paths is generated based on the minimum total cost connection relationship. When the minimum total cost connection relationship spans one or more sensor groups or multiple scanning intervals, virtual trajectory points are generated based on the measurement timestamps and longitudinal positions of the events at both ends of the connection relationship and written into the trajectory point sequence of the corresponding vehicle trajectory to form the missing segment interpolation result. A stable trajectory segment earlier than the boundary of the fixed lag sliding window is output using a fixed lag output mechanism to obtain a continuously reconstructed set of vehicle trajectories. The set of vehicle trajectories includes a timestamp sequence, a longitudinal position sequence, and a longitudinal velocity sequence.

2. The method for continuous reconstruction of dual-lane outer geomagnetic vehicle trajectories for multiple missed detections as described in claim 1, characterized in that, The vehicle detection event includes sensor identification and mass indication, and the event-level geomagnetic feature includes at least one or more of peak intensity, event energy, and event duration.

3. The method for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a dual-lane road with multiple missed detections, as described in claim 1, is characterized in that... The window maintenance rules for the time index cache include: The default cache time window length is The current processing time of the data center is ; When the measurement timestamp of a newly arriving vehicle detection event satisfy When the vehicle detection event is detected, it is inserted into the time index cache and sorted by measurement timestamp; When measuring timestamps Less than When the vehicle detection event is deemed to be an outdated event, it will be discarded or bypassed for offline statistical processing.

4. The method for continuous reconstruction of geomagnetic vehicle trajectories on the outer side of a dual-lane road with multiple missed detections as described in claim 1, characterized in that, The vehicle detection events within the time index cache window are grouped into scan sequences according to the measurement timestamp, including: Set scan interval Divide the time axis into continuous scan intervals ; Will fall into the same scanning range Vehicle inspection events within the premises constitute the first Measurement set of the second scan The fixed-hysteresis sliding window is formed by a series of consecutive scans of the index.

5. The method for continuous reconstruction of dual-lane outer geomagnetic vehicle trajectories for multiple missed detections as described in claim 1, characterized in that, Online updates of the missed detection rate estimates for each sensor group, including: Beta-Bernoulli conjugate update of false negative rate estimation is used; The reliability of each sensor group is estimated based on the false negative rate, wherein the reliability is a monotonic function of the false negative rate estimate.

6. The method for continuous reconstruction of dual-lane outer geomagnetic vehicle trajectories for multiple missed detections as described in claim 1, characterized in that, The constraints for establishing the candidate connection relationships include: Candidate connection relationships satisfy the condition that the vertical position of the successor event is greater than the vertical position of the predecessor event, and the equivalent velocity of the successor event and the predecessor event are equal. satisfy .

7. The method for continuous reconstruction of dual-lane outer geomagnetic vehicle trajectories for multiple missed detections as described in claim 1, characterized in that, The calculation process for the missing test penalty includes: The penalty for missing data is the set of intermediate sensor groups traversed by the candidate connectivity. The calculation of the missing measurement penalty, when accumulated, satisfies the condition that the greater the reliability of the intermediate sensor group, the greater the penalty.

8. The method for continuous reconstruction of dual-lane outer geomagnetic vehicle trajectories for multiple missed detections as described in claim 1, characterized in that, Solving for the minimum total cost connectivity in the event transition graph under one-to-one constraints includes: The event transition graph is transformed into a bipartite graph consisting of a set of predecessor events and a set of successor events. The minimum cost matching is solved under one-to-one constraints to obtain the minimum total cost connection relationship, or the minimum cost flow algorithm is used to solve for the set of vehicle trajectory paths.

9. A continuous reconstruction system for the geomagnetic vehicle trajectory on the outer side of a dual-lane road with multiple missed detections, characterized in that, include: The data access module is used to access vehicle detection events reported by the geomagnetic sensor; The time index cache module is used to perform in-window insertion sorting on out-of-order vehicle detection events and to discard or bypass outdated events. The scan construction and sliding window module is used to merge vehicle detection events into a scan sequence and maintain a fixed-hysteresis sliding window. The missed detection rate self-calibration module is used to update the missed detection rate estimate of each sensor group online based on stable trajectory segments. The event transition graph construction module is used to build candidate connections that can span multiple sensor groups and calculate connection costs. The global connectivity solver module is used to solve for the minimum total cost connectivity under one-to-one constraints and generate a set of vehicle trajectory paths; The interpolation and output module is used to generate virtual trajectory points at missing locations and output stable trajectory segments using a fixed lag output mechanism.

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