A vehicle trajectory reconstruction method based on parameter residual field calibration and physical constraint fusion

Abstract

The present application relates to a kind of vehicle trajectory reconstruction method based on parameter residual field calibration and physical constraint fusion, belong to vehicle trajectory reconstruction technical field.The method includes: based on fixed detection section, networked vehicle trajectory and vehicle front-back relationship Construction ordered vehicle chain and reference vehicle pair, estimate basic parameters, construct reference parameter residual field by dynamic time warping, by calibration vehicle correct system deviation, basic parameters and calibrated parameter residual are superimposed to form time-varying reaction time and time-varying spatial interval, drive to generate initial physical reconstruction trajectory with the Newell follow model characterized by reaction time and spatial interval Delayed following relationship;Again, complete vehicle trajectory reconstruction is obtained by calibration and repair operation, and parameter domain fusion is carried out to forward and reverse candidates.The present application aims to solve the technical problems of incomplete trajectory in low penetration rate network environment in the prior art.

Description

Technical Field

[0001] This invention relates to a vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints, belonging to the field of vehicle trajectory reconstruction technology. Background Technology

[0002] Vehicle trajectories are crucial foundational data for traffic state estimation, congestion propagation analysis, queue length identification, micro-traffic simulation calibration, and traffic control evaluation. In real-world roads, the penetration rate of connected vehicles is typically limited, and ordinary vehicles can only generate locally reliable observations near fixed detection sections, resulting in significant gaps in complete trajectories.

[0003] Existing interpolation or extrapolation methods mainly directly complete the position sequence, which is difficult to reflect the interaction mechanism between vehicles; fixed parameter car-following models have physical meaning, but cannot describe the changes in reaction time and spatial distance with individual vehicles, traffic conditions and congestion propagation process; pure data-driven methods can fit trajectories, but usually cannot synchronously output time-varying parameters with clear traffic meaning.

[0004] The Newell car-following model uses reaction time and spatial spacing to describe the spatiotemporal relationship between vehicles. When the trajectory of the driving vehicle, along with the reaction time and spatial spacing, is known, the trajectory of the target vehicle can be generated. However, reaction time and spatial spacing are not constant values ​​in different time periods, such as free flow, congestion formation, congestion core, and queue release. If a single parameter is still used, the model error will accumulate vehicle-by-vehicle in the chain reconstruction.

[0005] Reference vehicle pairs can provide statistical information on parameter changes as road progress or traffic phases change, but there may be phase differences and system biases between the reference vehicle pairs and the target vehicle. If the reference trajectory or reference residual is directly fed into the target vehicle, it can easily lead to problems such as overall elevation, overall depression, congestion phase misalignment, or congestion residual contamination of the free flow segment.

[0006] The observation trajectory within a fixed detection section and its adjacent segments typically has high reliability. Directly replacing the observation segment into the reconstructed trajectory can ensure local positional accuracy, but when the absolute reference of the trajectory outside the segment is incorrect, steps, repetitive spatial positions, or plateaus may appear at the boundaries. If such anomalies are used by subsequent vehicles as driving vehicle speed patterns, they will further amplify the chain error.

[0007] Therefore, a vehicle trajectory reconstruction method is needed that does not use the actual trajectory of a normal vehicle as the selection criterion during operation, can convert trajectory errors into car-following parameter residuals, can identify reference residual field system deviations by using calibrated vehicles, and can perform hierarchical calibration and repair of the initial physical trajectory. Summary of the Invention

[0008] The purpose of this invention is to provide a vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints, aiming to solve the technical problem of incomplete trajectory in existing technologies under low-penetration connected environments. Specifically:

[0009] Given that ordinary vehicles only have local high-confidence observations and the complete real trajectory cannot be used for online reconstruction, how can we utilize a limited number of connected vehicles and the physical relationships between vehicles to reconstruct the complete position trajectory of ordinary vehicles, and simultaneously obtain interpretable time-varying reaction time and time-varying spatial spacing; while suppressing the propagation of reference residual field error and driving vehicle error along the vehicle chain?

[0010] To achieve the above objectives, the technical solution of this invention is: a vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints. This method does not directly use the external reference trajectory as the absolute trajectory of the target vehicle. Instead, it first estimates the basic parameters, then constructs and calibrates the parametric residual field. The basic parameters and the residual calibration quantity together form time-varying parameters. Subsequently, an initial physical reconstruction trajectory is generated through a physical car-following model. The subsequent processing of the initial physical reconstruction trajectory is uniformly organized into a hierarchical calibration and repair chain, including the following steps:

[0011] S1: Obtain the trajectory of connected vehicles within the target road section, fixed detection sections, and the target vehicle observation trajectory, vehicle front-to-back relationship, and road spatial boundary within the preset observation range of the fixed detection sections; construct an ordered vehicle chain using the vehicle front-to-back relationship and the order in which vehicles pass through the fixed detection sections, and determine the driving vehicle of the target vehicle from the ordered vehicle chain; identify connected vehicles that have uploaded their own trajectories, and obtain the front and rear vehicle trajectories collected by the connected vehicles within the preset perception range, and then form a reference vehicle pair with each connected vehicle and its adjacent front and rear vehicles within the common observable time interval;

[0012] S2: Based on the ordered vehicle chain, the target vehicle's observed trajectory, and the driving vehicle's trajectory, estimate the target vehicle's basic parameters; and using the reference vehicle to invert the observed parameters, align and aggregate the differences between the observed parameters and the corresponding basic parameters according to road progress to obtain a reference parameter residual field. Based on the reference parameter residual field, make the following judgments:

[0013] When a calibration vehicle exists in the ordered vehicle chain and its trajectory is observable, the system bias of the reference parameter residual field is identified using the observable trajectory of the calibration vehicle to obtain the calibrated parameter residual field; when no calibration vehicle exists in the ordered vehicle chain or the calibration vehicle is unobservable or its observation is discontinuous, the reference parameter residual field is used as the calibrated parameter residual field, and the system correction term is set to zero.

[0014] The basic parameters include basic reaction time and basic spatial spacing, the observation parameters include observation reaction time and observation spatial spacing, and the calibration vehicle is a connected vehicle that has uploaded its own trajectory and whose trajectory covers the target road section.

[0015] S3: Based on the basic parameters and the calibrated parameter residual field, the time-varying reaction time and time-varying spatial spacing of the target vehicle are obtained;

[0016] S4: Generate the initial physical reconstruction trajectory of the target vehicle based on the trajectory of the driving vehicle, the time-varying reaction time, and the time-varying spatial spacing;

[0017] S5: Use the target vehicle's observed trajectory to perform reference calibration on the initial physical reconstruction trajectory, and perform repair operations on the reference-calibrated trajectory in sequence according to the traffic state of the target vehicle to obtain the complete position trajectory and velocity sequence of the target vehicle, and combine the time-varying reaction time and time-varying spatial spacing as the vehicle trajectory reconstruction result.

[0018] Optionally, the step of using the reference vehicle to retrieve the inversion observation parameters specifically involves:

[0019]

[0020] In the formula, and The inverted observation response time and observation spatial spacing are the values ​​obtained from the inversion. These represent the candidate reaction time and candidate spatial spacing during the parameter search process, respectively. For the common observable time interval of the reference vehicle pairs, For a moment The observation weights, For the observation position of the rear vehicle, Delay for the vehicle in front The subsequent observation position, and These are the smoothing or physically feasible regularization terms for reaction time and spatial spacing, respectively. and This represents the weight of the regularization term.

[0021] Optionally, the obtained reference parameter residual field specifically refers to:

[0022] Within the common observable time interval of each reference vehicle pair, based on the observation trajectory of the preceding vehicle, the observation trajectory of the following vehicle, and the Newell car-following relationship, search for the observation reaction time and observation spatial distance that minimize the weighted position error between the delayed position of the preceding vehicle and the observation position of the following vehicle.

[0023] The difference between the observed reaction time and the baseline reaction time, as well as the difference between the observed spatial spacing and the baseline spatial spacing, are calculated separately to obtain the parameter residual samples;

[0024] The speed difference, vehicle spacing difference, and traffic state change time difference between different reference vehicle pairs constitute the matching cost of dynamic time warping, and the traffic phase correspondence between the parameter residual samples is established.

[0025] Based on the traffic phase correspondence, the parameter residual samples are mapped to a unified road progress, and the median aggregation is performed on the parameter residual samples corresponding to the same road progress to obtain the reference reaction time residual function and the reference spatial spacing residual function, which together constitute the reference parameter residual field; wherein, the road progress is the position variable of the vehicle in the unified road coordinate system.

[0026] Optionally, the matching cost is specifically:

[0027]

[0028]

[0029] In the formula, For the cost of local matching, To accumulate matching costs, and These are the discrete-time indices of the two reference vehicle pairs. and Let the speeds of the two reference vehicle pairs be at the corresponding indices. and For the corresponding vehicle spacing, Penalties for inconsistent phases in traffic incidents , and The weights are non-negative.

[0030] Optionally, when a calibration vehicle exists in the ordered vehicle chain and its trajectory is observable, the systematic bias of the reference parameter residual field is identified using the observable trajectory of the calibration vehicle to obtain the calibrated parameter residual field. Specifically, this involves:

[0031] The driving vehicle of the calibration vehicle is determined based on the ordered vehicle chain and the front-to-back relationship of the vehicles. Based on the observable trajectory of the calibration vehicle and the trajectory of the driving vehicle of the calibration vehicle, the basic reaction time and basic spatial distance of the calibration vehicle are estimated.

[0032] The observation response time and observation spatial spacing are retrieved by inverting the observable trajectory of the calibration vehicle and the trajectory of the driving vehicle of the calibration vehicle.

[0033] The difference between the observed reaction time and the baseline reaction time, and the difference between the observed spatial spacing and the baseline spatial spacing are calculated respectively to obtain the self-reaction time residual function and the self-spatial spacing residual function of the calibrated vehicle.

[0034] The differences between the self-reaction time residual function, the self-spatial spacing residual function and the corresponding residual function in the reference parameter residual field are calculated respectively. Adjacent road progress sampling points with the same sign are merged into continuous segments, and the differences within the continuous segments are determined as reaction time system correction terms and spatial spacing system correction terms respectively.

[0035] The reaction time system correction term and the spatial spacing system correction term are respectively superimposed onto the corresponding residual functions in the reference parameter residual field to obtain the calibrated parameter residual field.

[0036] Optionally, obtaining the time-varying reaction time and time-varying spatial spacing of the target vehicle specifically involves:

[0037]

[0038]

[0039] In the formula, and These are the time-varying reaction time and the time-varying spatial spacing, respectively. Number the target vehicle. and These are the basic reaction time and the basic spatial spacing, respectively. For the target vehicle at time Corresponding road progress, and These are the reaction time residual function and the spatial spacing residual function defined in the road progress domain, respectively.

[0040] Optionally, the initial physical reconstruction trajectory of the target vehicle is generated using a Newell car-following model, specifically:

[0041] When the Newell car-following model performs forward car-following reconstruction along the vehicle's direction of travel, the expression for the initial physical reconstruction trajectory is:

[0042]

[0043] When the Newell car-following model performs a reverse car-following reconstruction along the opposite vehicle chain order, the expression for the initial physical reconstruction trajectory is:

[0044]

[0045] in, For the target vehicle at time Location, The vehicle number is assigned to the target vehicle. To drive the vehicle's trajectory, and These represent the time-varying reaction time and the time-varying spatial spacing, respectively.

[0046] Optionally, the specific steps of performing the repair operation are:

[0047] Based on the dual congestion state, dual free state, congestion-free state, or free-congestion state combination, and the congestion side, free side, or transition side where the target vehicle is located, macroscopic structure repair or free flow structure maintenance is selected.

[0048] Based on geometric diagnosis, local morphological residual repair is performed, and the repair operation is completed by reviewing factors such as vehicle spacing, road space boundary, speed, acceleration, jerk, trajectory monotonicity, and endpoint uniqueness.

[0049] The beneficial effects of this invention are:

[0050] First, this invention expresses the reaction time and spatial spacing of the Newell car-following model as the sum of the basic parameters and the parameter residual calibration, so that trajectory correction is implemented on time-varying parameters with physical meaning, rather than simply performing unconstrained fitting on the position points.

[0051] Second, the reference parameter residual field constructed by this invention achieves cross-vehicle traffic phase alignment through physically constrained dynamic time warping, calibrating vehicles to further identify transferable system biases and suppressing the propagation of reference residual field errors along the vehicle chain.

[0052] Third, the local high-confidence observation reference calibration of the present invention adopts benchmark extrapolation, which can correct the absolute position benchmark while retaining the velocity change pattern expressed by the input trajectory or time-varying parameters, and reduce the steps and plateaus caused by hard bonding.

[0053] Fourth, this invention ensures that the macroscopic residual of congestion does not contaminate the free flow trajectory by using combinations of dual congestion, dual freedom, congestion-free and free-congestion states, as well as explicit distinctions between the congestion side, the free side and the transition side.

[0054] Fifth, this invention uses vehicle spacing, road space boundaries, and motion continuity as the basis for online write-back through a layered calibration and repair chain, without relying on the actual trajectory of ordinary vehicles throughout the entire process, making it suitable for deployment in actual low-penetration scenarios. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0056] Figure 2This is a schematic diagram showing the compositional relationship between the basic parameters, reference parameter residuals, calibration system correction terms, and time-varying parameters of this invention.

[0057] Figure 3 This is a schematic diagram illustrating the reference vehicle parameter inversion, physically constrained dynamic time warping, and reference parameter residual field construction of the present invention.

[0058] Figure 4 This is a schematic diagram illustrating the vehicle self-parameter residual inversion, system correction term extraction, and calibration propagation packet generation of the present invention.

[0059] Figure 5 This is a schematic diagram of the fixed detection section local high confidence observation maintenance and bidirectional reference extrapolation of the present invention;

[0060] Figure 6 This is a schematic diagram of the dual congestion, dual freedom, congestion-free and freedom-congestion state combinations, as well as the scheduling of the congestion side, free side and transition side of the present invention;

[0061] Figure 7 This is a schematic diagram of the congestion macroscopic structural residual, congestion support interval, core moment, release moment, and allowable deviation band of the present invention.

[0062] Figure 8 This is a schematic diagram of the local geometric baseline, morphological residual, and continuous low-frequency morphological correction amount of the present invention;

[0063] Figure 9 This is a schematic diagram of the forward car-following reconstruction candidates, reverse car-following reconstruction candidates, and parameter domain fusion of the present invention;

[0064] Figure 10 This is a schematic diagram illustrating the review of source evidence for trajectory steps, stagnant platforms, repetitive spatial locations, and endpoint anomalies in this invention. Detailed Implementation

[0065] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0066] Example 1: As Figure 1 As shown, a vehicle trajectory reconstruction method based on the fusion of parameter residual field calibration and physical constraints is presented. This method outputs an ordered vehicle chain, driving vehicle relationships, and reference vehicle pairs via S1; basic parameters, reference parameter residual fields, and calibrated parameter residual fields via S2, and outputs a calibration propagation packet when the calibration reliability meets the requirements; time-varying reaction time and time-varying spatial spacing via S3; initial physically reconstructed trajectory via S4; and complete trajectory after layered calibration and repair, along with audit information via S5. The method includes the following steps:

[0067] S1: Obtain the trajectory of connected vehicles within the target road section, fixed detection sections, and the target vehicle observation trajectory, vehicle front-to-back relationship, and road spatial boundary within the preset observation range of the fixed detection sections; construct an ordered vehicle chain using the vehicle front-to-back relationship and the order in which vehicles pass through the fixed detection sections, and determine the driving vehicle of the target vehicle from the ordered vehicle chain; identify connected vehicles that have uploaded their own trajectories, and obtain the front and rear vehicle trajectories collected by the connected vehicles within the preset perception range, and then form a reference vehicle pair with each connected vehicle and its adjacent front and rear vehicles within the common observable time interval;

[0068] Optionally, in this embodiment, a target road section is selected and the road coordinates are standardized so that the position increases monotonically along the vehicle's direction of travel.

[0069] S2: Based on the ordered vehicle chain, the target vehicle's observed trajectory, and the driving vehicle's trajectory, estimate the target vehicle's basic parameters; and using the reference vehicle to invert the observed parameters, align and aggregate the differences between the observed parameters and the corresponding basic parameters according to road progress to obtain a reference parameter residual field. Based on the reference parameter residual field, make the following judgments:

[0070] When a calibration vehicle exists in the ordered vehicle chain and its trajectory is observable, the system bias of the reference parameter residual field is identified using the observable trajectory of the calibration vehicle to obtain the calibrated parameter residual field; when no calibration vehicle exists in the ordered vehicle chain or the calibration vehicle is unobservable or its observation is discontinuous, the reference parameter residual field is used as the calibrated parameter residual field, and the system correction term is set to zero.

[0071] The basic parameters include basic reaction time and basic spatial spacing, the observation parameters include observation reaction time and observation spatial spacing, and the calibration vehicle is a connected vehicle that has uploaded its own trajectory and whose trajectory covers the target road section.

[0072] Optionally, for any reference vehicle pair, the reaction time and spatial spacing that minimize the Newell car-following error are searched within a local time interval, and the inverted observation parameters are retrieved using the reference vehicle pair as follows:

[0073]

[0074] In the formula, and The inverted observation response time and observation spatial spacing are the values ​​obtained from the inversion. These represent the candidate reaction time and candidate spatial spacing during the parameter search process, respectively. For the common observable time interval of the reference vehicle pairs, For a moment The observation weights, For the observation position of the rear vehicle, Delay for the vehicle in front The subsequent observation position, and These are the smoothing or physically feasible regularization terms for reaction time and spatial spacing, respectively. and This represents the weight of the regularization term.

[0075] Optionally, in this embodiment, the basic parameter estimation can be performed within a locally high-confidence observation segment. A physically feasible interval search is performed on candidate reaction times and spatial spacing, and parameters that minimize the error between the local observations of the target vehicle and the Newell car-following relationship and do not cause vehicle spacing conflicts are selected as the basic parameters. When local observations are insufficient, the distribution of basic parameters of adjacent vehicles can be used as a weak prior, but the full-length true trajectory of the target ordinary vehicle is not used.

[0076] Optionally, such as Figure 2 As shown, the basic parameters are not the final parameters. The reference vehicle constructed by S1 provides road progress-related parameter residuals, and the calibration vehicle provides system correction terms for the reference residual field. The basic parameters, reference parameter residuals, and system correction terms together form time-varying parameters. These time-varying parameters change with the road progress of the target vehicle and can describe the car-following behavior in the free flow, congestion response, and release phases, respectively. Specifically, the reference parameter residual field is obtained as follows:

[0077] Within the common observable time interval of each reference vehicle pair, based on the observation trajectory of the preceding vehicle, the observation trajectory of the following vehicle, and the Newell car-following relationship, search for the observation reaction time and observation spatial distance that minimize the weighted position error between the delayed position of the preceding vehicle and the observation position of the following vehicle.

[0078] The difference between the observed reaction time and the baseline reaction time, as well as the difference between the observed spatial spacing and the baseline spatial spacing, are calculated separately to obtain the parameter residual samples;

[0079] The speed difference, vehicle spacing difference, and traffic state change time difference between different reference vehicle pairs constitute the matching cost of dynamic time warping, and the traffic phase correspondence between the parameter residual samples is established.

[0080] Based on the traffic phase correspondence, the parameter residual samples are mapped to a unified road progress, and the median aggregation is performed on the parameter residual samples corresponding to the same road progress to obtain the reference reaction time residual function and the reference spatial spacing residual function, which together constitute the reference parameter residual field; wherein, the road progress is the position variable of the vehicle in the unified road coordinate system.

[0081] Optionally, since different reference vehicles respond differently to the same traffic event, this embodiment uses physically constrained Dynamic Time Warping (DTW) to establish the phase correspondence between parameter residuals. The matching cost is specifically as follows:

[0082]

[0083]

[0084] In the formula, For the cost of local matching, To accumulate matching costs, and These are the discrete-time indices of the two reference vehicle pairs. and Let the speeds of the two reference vehicle pairs be at the corresponding indices. and For the corresponding vehicle spacing, Penalties for inconsistent phases in traffic incidents , and The weights are non-negative.

[0085] It is understood that the dynamic time warping introduced in this embodiment is only used for phase alignment and does not directly change the trajectory of any target vehicle. After phase alignment, the difference between the observed parameters and the basic parameters is mapped to a unified road progress, forming reaction time residual samples and spatial spacing residual samples respectively. Aggregation and low-frequency smoothing are performed on each road progress neighborhood, and the number of support samples, phase coverage, and residual direction consistency are recorded simultaneously to obtain the reference parameter residual field and its reliability.

[0086] Furthermore, such as Figure 3 As shown, the parameter inversion of the constructed reference vehicle pairs is first performed within a common observable interval, and then the velocity changes, vehicle spacing changes, and traffic event phases are aligned using physically constrained dynamic time warping. The aligned path is not directly used as the trajectory output, but is used to map the parameter residuals of different reference vehicle pairs to a unified road progress. The median or weighted robust mean is aggregated for each road progress neighborhood, and the number of supporting samples and directional consistency are preserved as confidence.

[0087] Optionally, when a calibration vehicle exists in the ordered vehicle chain and its trajectory is observable, the systematic bias of the reference parameter residual field is identified using the observable trajectory of the calibration vehicle to obtain the calibrated parameter residual field. Specifically, this involves:

[0088] The driving vehicle of the calibration vehicle is determined based on the ordered vehicle chain and the front-to-back relationship of the vehicles. Based on the observable trajectory of the calibration vehicle and the trajectory of the driving vehicle of the calibration vehicle, the basic reaction time and basic spatial distance of the calibration vehicle are estimated.

[0089] The observation response time and observation spatial spacing are retrieved by inverting the observable trajectory of the calibration vehicle and the trajectory of the driving vehicle of the calibration vehicle.

[0090] The difference between the observed reaction time and the baseline reaction time, and the difference between the observed spatial spacing and the baseline spatial spacing are calculated respectively to obtain the self-reaction time residual function and the self-spatial spacing residual function of the calibrated vehicle.

[0091] The differences between the self-reaction time residual function, the self-spatial spacing residual function and the corresponding residual function in the reference parameter residual field are calculated respectively. Adjacent road progress sampling points with the same sign are merged into continuous segments, and the differences within the continuous segments are determined as reaction time system correction terms and spatial spacing system correction terms respectively.

[0092] The reaction time system correction term and the spatial spacing system correction term are respectively superimposed onto the corresponding residual functions in the reference parameter residual field to obtain the calibrated parameter residual field.

[0093] It is important to understand that in this embodiment, the role of the calibrated vehicle is not to propagate its own absolute trajectory to ordinary vehicles, but rather to examine where the reference parameter residual field produces systematic biases. Specifically:

[0094]

[0095] In the formula, To obtain the self-parameter residual field from the continuous high-confidence trajectory inversion of the calibration vehicle, For reference parameters, residual field, This represents the difference between the self-parameter residual field and the reference parameter residual field. For system correction terms that are stable and transferable within the continuous road progress range, The remaining items are only relevant to the individual calibrated vehicles.

[0096] Furthermore, the reliability of the system correction term is jointly determined by the coverage of the calibration vehicle observations, the actual activity of the reference parameter residual field at that road progress, the consistency of the correction direction in continuous segments, the consistency between the traffic state of the calibration vehicle and the traffic state of the target vehicle, and the physical feasibility after correction. The system correction term, reliability, effective road progress interval, and overshoot protection information together constitute the calibration propagation package.

[0097] It is important to understand that the target vehicle only reads the calibration propagation packet when it actually reads the same or compatible reference parameter residual field as the calibration vehicle. Therefore, bad segments of the reference residual field detected by the calibration vehicle can be propagated to subsequent vehicles, but the calibration vehicle's own individual errors will not be unconditionally propagated.

[0098] Furthermore, such as Figure 4 As shown, when a calibration vehicle appears in an ordered vehicle chain, a reference parameter residual field and a Newell car-following model are first used to generate a calibration vehicle reference trajectory. Then, the self-parameter residual is inverted using the continuous high-confidence trajectory of the calibration vehicle. Differences with consistent direction within continuous segments are retained as system correction terms; isolated abrupt changes, differences that are only effective for a single vehicle, or differences that lead to a deterioration of physical constraints are retained as individual residual terms and do not enter the calibration propagation packet.

[0099] S3: Based on the basic parameters and the calibrated parameter residual field, the time-varying reaction time and time-varying spatial spacing of the target vehicle are obtained;

[0100] Optionally, in this embodiment, for each discrete moment of the target vehicle, the reference parameter residual field and calibration propagation packet are queried based on the current road progress of the target vehicle, and the time-varying reaction time and time-varying spatial interval are calculated. If the supporting samples for the corresponding road progress are insufficient, the parameter residual amplitude is reduced; if there is no calibration propagation packet, or the calibration propagation packet is incompatible with the reference parameter residual field actually read by the target vehicle, the propagation coefficient and system correction term are both set to zero, and only the reference parameter residual constrained by confidence is retained.

[0101] Optionally, obtaining the time-varying reaction time and time-varying spatial spacing of the target vehicle specifically involves:

[0102]

[0103]

[0104] In the formula, and These are the time-varying reaction time and the time-varying spatial spacing, respectively. Number the target vehicle. and These are the basic reaction time and the basic spatial spacing, respectively. For the target vehicle at time Corresponding road progress, and These are the reaction time residual function and the spatial spacing residual function defined in the road progress domain, respectively.

[0105] Optionally, in this embodiment, to distinguish between the original residuals provided by the reference vehicle and the system corrections provided by the calibration vehicle, the reaction time residual function and the spatial spacing residual function can be further defined as follows: and The expression is:

[0106]

[0107]

[0108] In the formula, For road progress, and For the reaction time residual and spatial spacing residual in the reference parameter residual field, To calibrate vehicle numbers, and To calibrate the system correction items identified by the vehicle, To calibrate credibility, The adaptive propagation coefficient when reading the calibration propagation packet for the target vehicle.

[0109] S4: Generate the initial physical reconstruction trajectory of the target vehicle based on the trajectory of the driving vehicle, the time-varying reaction time, and the time-varying spatial spacing;

[0110] Optionally, in this embodiment, forward car-following reconstruction uses the preceding vehicle in the vehicle's driving direction as the driving vehicle, and reverse car-following reconstruction reads the trajectory in the opposite chain order. The initial physical reconstruction trajectory of the target vehicle is generated by the Newell car-following model, specifically:

[0111] When the Newell car-following model performs forward car-following reconstruction along the vehicle's direction of travel, the expression for the initial physical reconstruction trajectory is:

[0112]

[0113] When the Newell car-following model performs a reverse car-following reconstruction along the opposite vehicle chain order, the expression for the initial physical reconstruction trajectory is:

[0114]

[0115] in, For the target vehicle at time Location, The vehicle number is assigned to the target vehicle. To drive the vehicle's trajectory, and These represent the time-varying reaction time and the time-varying spatial spacing, respectively.

[0116] Optionally, in this embodiment, for segments that exceed the time coverage of the driving vehicle, the endpoint position of the driving vehicle is not constantly extended, but extrapolated based on the effective speed pattern of the target vehicle or visible boundary conditions to avoid generating a zero-speed platform.

[0117] S5: Use the target vehicle's observed trajectory to perform reference calibration on the initial physical reconstruction trajectory, and perform repair operations on the reference-calibrated trajectory in sequence according to the traffic state of the target vehicle to obtain the complete position trajectory and velocity sequence of the target vehicle, and combine the time-varying reaction time and time-varying spatial spacing as the vehicle trajectory reconstruction result.

[0118] Optionally, such as Figure 5 As shown, a local high-confidence observation reference calibration is first performed. The observation trajectory is maintained within the observation section; when completing the path towards the road's starting point, the boundary point on that side is used as the starting point; when completing the path towards the road's ending point, the boundary point on the other side is used. Thus, the boundary of the observation section provides a positional reference without masking the system offset of the input trajectory through smoothing across the entire section. Specifically, the local high-confidence observation reference calibration is as follows:

[0119] The local high-confidence observation section near the fixed detection section is used as the absolute position benchmark, and the observation trajectory within the section remains unchanged. Outside the section, instead of using long-distance smoothing to mask benchmark misalignment, the corresponding boundary point of the observation section is selected as the new starting point based on the extrapolation direction. The expression is:

[0120]

[0121] In the formula, To change the baseline extrapolation candidate, For the boundary time of the local high-confidence observation section, The high-confidence observation position at the boundary time. To reconstruct the trajectory at time 0 The velocity change pattern. When pushing outwards towards the starting point of the road, use the boundary point closest to the starting point; when pushing outwards towards the ending point of the road, use another boundary point.

[0122] Understandably, the essence of benchmark extrapolation is to preserve the velocity change pattern expressed by the initial physical trajectory or time-varying parameters, while correcting the absolute position benchmark with reliable observations. If a candidate exhibits a new velocity jump, vehicle spacing exceeding the limit, or road boundary exceeding the limit at the boundary of the observation section, the correction intensity is reduced or the initial physical trajectory is maintained.

[0123] Furthermore, such as Figure 6As shown, traffic state classification and macro-structure repair are performed. Based on the traffic state of vehicles at both ends of the target road section during the study period, the section is explicitly divided into four combinations: dual-congestion state, dual-free state, congestion-free state, or free-congestion state. In the dual-congestion state, congestion structure information is allowed at both ends; in the dual-free state, the free-flow structure is maintained throughout the entire section; in the two mixed states, depending on whether the target vehicle is located on the congestion boundary side, the free boundary side, or in between, it is marked as the congested side, the free side, or the transition side, and different processing strategies are adopted for the congested side, the free side, and the transition side. The obtained scheduling results are directly used as input for macro-structure repair and local morphological repair, rather than just for result interpretation.

[0124] Furthermore, before entering the macroscopic structural repair phase, vehicles on the congested side have already formed a complete initial physical reconstruction trajectory based on time-varying parameters and the Newell car-following model. Macroscopic structural repair does not regenerate the absolute trajectory; instead, it examines whether the overall trajectory exhibits discontinuities in the connection of support intervals, distortion of congestion depth, misalignment of release timing, or anomalies at the release tail. The expression is:

[0125]

[0126] In the formula, The congestion macrostructure residuals for the target vehicle. This is a congestion-free reference baseline constructed based on the free-flow velocity trends before and after congestion. This is the trajectory for entering the macroscopic structure repair process. The macroscopic structure repair output includes the congestion support interval, core time, release time, congestion intensity, and allowable deviation band. Limited write-back is only performed when the input trajectory significantly deviates from this structure and the correction does not disrupt the observation section, vehicle spacing, or motion continuity.

[0127] Furthermore, vehicles on the free side do not read the macroscopic structural residuals of congestion; the focus is on maintaining free-flow velocity trends, local high-confidence observation benchmarks, and road boundary integrity. Vehicles on the transition side are not forcibly classified as congested or free; only connectivity continuity and physical feasibility protections are implemented.

[0128] Furthermore, such as Figure 7 As shown, the macroscopic structure repair on the congestion side reads the congestion support interval, core time, release time, congestion intensity, and allowable deviation zone, and checks the overall connectivity, congestion depth, and release tail. If the input trajectory is already within the allowable deviation zone, the macroscopic structure repair remains unchanged; if the input trajectory clearly exceeds the boundary and there are continuous repairable sections, a restricted low-frequency candidate is generated and written back after the vehicle spacing and motion continuity are approved.

[0129] Furthermore, such as Figure 8As shown, local morphological repair is performed after macroscopic structural review. Local morphological repair does not handle instantaneous velocity, acceleration, or jerk anomalies already identified by the peak detection layer; instead, it addresses connectivity, slope, curvature, release tails, and low-frequency morphological deviations across the entire trajectory scale. The morphological correction is zero at the boundary of the local high-confidence observation segment and expands continuously away from the boundary. The local morphological repair is performed using geometric diagnostics and the residual domain, specifically:

[0130] Based on the low-frequency trend of the input trajectory, the boundary of the observation section, and the traffic conditions, a local geometric baseline is constructed. Then, the morphological residual of the input trajectory relative to the local geometric baseline is calculated, expressed as:

[0131]

[0132]

[0133] In the formula, For morphological residuals, For local geometric baselines, This is a continuous low-frequency morphological correction amount generated based on the abnormal location and duration. Candidate for morphological repair.

[0134] Optionally, in this embodiment, the congestion side focuses on repairing the overall connection and releasing the tail; the free side focuses on repairing the slope, curvature, and velocity trends outside the observation section; and the transition side only performs minor continuity repairs.

[0135] Furthermore, morphological restoration candidates must pass through a non-truth value safety gate. The decision to write back is based solely on local high-confidence observation consistency, vehicle spacing, road spatial boundaries, speed jumps, acceleration, jerkiness, and trajectory monotonicity, without utilizing the actual trajectory error of ordinary vehicles throughout the entire journey to select candidates.

[0136] Furthermore, such as Figure 9 As shown, both forward and reverse candidates can be generated simultaneously for vehicles in transition areas or intermediate zones. The two candidates are first reviewed based on their respective local observations, vehicle spacing, and motion continuity. Then, a common traffic phase is established using dynamic time warping. Finally, time-varying parameters are fused, and the fused parameters are re-substituted into the Newell car-following model to obtain the trajectory, specifically:

[0137] When a target vehicle has both forward car-following reconstruction candidates and reverse car-following reconstruction candidates, a common traffic phase for both is first established using dynamic time warping, and then fused preferentially in the parameter domain. The expression is:

[0138]

[0139]

[0140] In the formula, and For forward-selective time-varying parameters, and For time-varying parameters that are reverse candidates, and These are the time-varying parameters after fusion. The time-varying fusion weights take values ​​between 0 and 1.

[0141] Optionally, the time-varying fusion weights are jointly determined by the consistency of local high-confidence observations, the confidence level of the reference parameter residual field, the confidence level of calibration propagation, the vehicle spacing margin, the road spatial boundary margin, and the relative position of the target vehicle to the reliable boundaries on both sides. If parameter domain fusion does not satisfy the physical feasibility of the Newell car-following model, it degenerates into position residual fusion relative to a common base trajectory.

[0142] Furthermore, such as Figure 10 As shown, the final review reads the source evidence written in the previous steps. For steps caused by maintaining local high-confidence observations, extrapolation is performed again based on the boundary of the observation section; for steps caused by vehicle spacing constraints, the side that was not forcibly pulled back and still meets the safe spacing is used as the reference; for repeated positions at the end or beginning of the road, only one legal boundary point is retained; for platforms caused by insufficient time coverage of the preceding vehicle, extrapolation is performed using the effective speed trend of the target vehicle.

[0143] After the repair candidates are completed, the velocity, acceleration, and jerk of adjacent points are calculated in chronological order, and one-to-many time mapping, boundary violations, and rollbacks are checked in chronological order of road progress. If a repair candidate increases vehicle spacing violations, road boundary violations, or kinematic anomalies, the candidate is rejected and the trajectory before entering the final review is retained.

[0144] Furthermore, the final review scans the complete trajectory along both the time and road progress directions. The time direction scan is used to detect speed jumps, acceleration anomalies, jerk anomalies, plateaus, and speed lag; the road progress direction scan is used to detect multiple time points corresponding to the same spatial location, repeated points at road boundaries, clipping and rollback, and endpoint jumps.

[0145] Furthermore, each anomaly retains source evidence, including the preservation of local high-confidence observations, vehicle spacing corridor pullback, road spatial boundary clipping, insufficient driving vehicle time coverage, and preceding module splicing markers. If the anomaly is caused by vehicle spacing constraints, the side that was not forcibly pulled back and still meets the safety spacing requirement is selected as the baseline; if the anomaly is caused by the preservation of local high-confidence observation segments, the boundary point of the observation segment is selected as the baseline; if the anomaly is caused by insufficient driving vehicle time coverage, extrapolation is performed using the target vehicle's own effective speed trend to avoid filling the missing coverage with a zero-speed platform. After the anomaly segment is repaired, vehicle spacing, road spatial boundaries, speed, acceleration, jerkiness, trajectory monotonicity, and endpoint uniqueness are checked again. Only if the repair candidate does not increase safety constraint violations and reduces identified anomalies is the data written back; otherwise, it reverts to the trajectory before entering the final review.

[0146] Furthermore, the final output includes the complete location trajectory, velocity sequence, time-varying reaction time, time-varying spatial spacing, source of reference parameter residuals, source of calibration propagation, traffic conditions, module window, reasons for candidate acceptance or rejection, and physical constraint review results for each target vehicle.

[0147] In summary, this invention, in a low-penetration connected vehicle environment, takes the calibration of car-following model parameter residuals as the main line, superimposes the basic parameters with the calibrated parameter residual field to form time-varying parameters, and combines local high-confidence observation reference calibration, calibrated vehicle reliable propagation, traffic state classification, macroscopic structure repair, local morphological repair and final physical verification to reconstruct the complete trajectory of ordinary vehicles and their time-varying parameters.

[0148] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints, characterized in that, The method includes the following steps: S1: Obtain the trajectory of connected vehicles within the target road section, fixed detection sections, and the target vehicle observation trajectory, vehicle front-to-back relationship, and road spatial boundary within the preset observation range of the fixed detection sections; construct an ordered vehicle chain using the vehicle front-to-back relationship and the order in which vehicles pass through the fixed detection sections, and determine the driving vehicle of the target vehicle from the ordered vehicle chain; identify connected vehicles that have uploaded their own trajectories, and obtain the front and rear vehicle trajectories collected by the connected vehicles within the preset perception range, and then form a reference vehicle pair with each connected vehicle and its adjacent front and rear vehicles within the common observable time interval; S2: Based on the ordered vehicle chain, the target vehicle's observed trajectory, and the driving vehicle's trajectory, estimate the target vehicle's basic parameters; and using the reference vehicle to invert the observed parameters, align and aggregate the differences between the observed parameters and the corresponding basic parameters according to road progress to obtain a reference parameter residual field. Based on the reference parameter residual field, make the following judgments: When a calibration vehicle exists in the ordered vehicle chain and its trajectory is observable, the system bias of the reference parameter residual field is identified using the observable trajectory of the calibration vehicle to obtain the calibrated parameter residual field; when no calibration vehicle exists in the ordered vehicle chain or the calibration vehicle is unobservable or its observation is discontinuous, the reference parameter residual field is used as the calibrated parameter residual field, and the system correction term is set to zero. The basic parameters include basic reaction time and basic spatial spacing, the observation parameters include observation reaction time and observation spatial spacing, and the calibration vehicle is a connected vehicle that has uploaded its own trajectory and whose trajectory covers the target road section. S3: Based on the basic parameters and the calibrated parameter residual field, the time-varying reaction time and time-varying spatial spacing of the target vehicle are obtained; S4: Generate the initial physical reconstruction trajectory of the target vehicle based on the trajectory of the driving vehicle, the time-varying reaction time, and the time-varying spatial spacing; S5: Use the target vehicle's observed trajectory to perform reference calibration on the initial physical reconstruction trajectory, and perform repair operations on the reference-calibrated trajectory in sequence according to the traffic state of the target vehicle to obtain the complete position trajectory and velocity sequence of the target vehicle, and combine the time-varying reaction time and time-varying spatial spacing as the vehicle trajectory reconstruction result.

2. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 1, characterized in that, The specific steps for retrieving inversion observation parameters using the reference vehicle are as follows: ； In the formula, and The inverted observation response time and observation spatial spacing are the values ​​obtained from the inversion. These represent the candidate reaction time and candidate spatial spacing during the parameter search process, respectively. For the common observable time interval of the reference vehicle pairs, For a moment The observation weights, For the observation position of the rear vehicle, Delay for the vehicle in front The subsequent observation position, and These are the smoothing or physically feasible regularization terms for reaction time and spatial spacing, respectively. and This represents the weight of the regularization term.

3. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 1, characterized in that, The obtained reference parameter residual field is specifically as follows: Within the common observable time interval of each reference vehicle pair, based on the observation trajectory of the preceding vehicle, the observation trajectory of the following vehicle, and the Newell car-following relationship, search for the observation reaction time and observation spatial distance that minimize the weighted position error between the delayed position of the preceding vehicle and the observation position of the following vehicle. The difference between the observed reaction time and the baseline reaction time, as well as the difference between the observed spatial spacing and the baseline spatial spacing, are calculated separately to obtain the parameter residual samples; The speed difference, vehicle spacing difference, and traffic state change time difference between different reference vehicle pairs constitute the matching cost of dynamic time warping, and the traffic phase correspondence between the parameter residual samples is established. Based on the traffic phase correspondence, the parameter residual samples are mapped to a unified road progress, and the median aggregation is performed on the parameter residual samples corresponding to the same road progress to obtain the reference reaction time residual function and the reference spatial spacing residual function, which together constitute the reference parameter residual field; wherein, the road progress is the position variable of the vehicle in the unified road coordinate system.

4. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 3, characterized in that, The matching cost is specifically as follows: ； ； In the formula, For the cost of local matching, To accumulate matching costs, and These are the discrete-time indices of the two reference vehicle pairs. and Let the speeds of the two reference vehicle pairs be at the corresponding indices. and For the corresponding vehicle spacing, Penalties for inconsistent phases in traffic incidents , and The weights are non-negative.

5. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 1, characterized in that, When a calibration vehicle exists in the ordered vehicle chain and its trajectory is observable, the systematic bias of the reference parameter residual field is identified using the observable trajectory of the calibration vehicle to obtain the calibrated parameter residual field. Specifically, this is as follows: The driving vehicle of the calibration vehicle is determined based on the ordered vehicle chain and the front-to-back relationship of the vehicles. Based on the observable trajectory of the calibration vehicle and the trajectory of the driving vehicle of the calibration vehicle, the basic reaction time and basic spatial distance of the calibration vehicle are estimated. The observation response time and observation spatial spacing are retrieved by inverting the observable trajectory of the calibration vehicle and the trajectory of the driving vehicle of the calibration vehicle. The difference between the observed reaction time and the baseline reaction time, and the difference between the observed spatial spacing and the baseline spatial spacing are calculated respectively to obtain the self-reaction time residual function and the self-spatial spacing residual function of the calibrated vehicle. The differences between the self-reaction time residual function, the self-spatial spacing residual function and the corresponding residual function in the reference parameter residual field are calculated respectively. Adjacent road progress sampling points with the same sign are merged into continuous segments, and the differences within the continuous segments are determined as reaction time system correction terms and spatial spacing system correction terms respectively. The reaction time system correction term and the spatial spacing system correction term are respectively superimposed onto the corresponding residual functions in the reference parameter residual field to obtain the calibrated parameter residual field.

6. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 1, characterized in that, The specific details of obtaining the time-varying reaction time and time-varying spatial distance of the target vehicle are as follows: ； ； In the formula, and These are the time-varying reaction time and the time-varying spatial spacing, respectively. Number the target vehicle. and These are the basic reaction time and the basic spatial spacing, respectively. For the target vehicle at time Corresponding road progress, and These are the reaction time residual function and the spatial spacing residual function defined in the road progress domain, respectively.

7. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 1, characterized in that, The initial physical reconstruction trajectory of the target vehicle is generated using the Newell car-following model, specifically: When the Newell car-following model performs forward car-following reconstruction along the vehicle's direction of travel, the expression for the initial physical reconstruction trajectory is: ； When the Newell car-following model performs a reverse car-following reconstruction along the opposite vehicle chain order, the expression for the initial physical reconstruction trajectory is: ； in, For the target vehicle at time Location, The vehicle number is assigned to the target vehicle. To drive the vehicle's trajectory, and These represent the time-varying reaction time and the time-varying spatial spacing, respectively.

8. The vehicle trajectory reconstruction method based on the fusion of parametric residual field calibration and physical constraints according to claim 1, characterized in that, The specific steps for performing the repair operation are as follows: Based on the dual congestion state, dual free state, congestion-free state, or free-congestion state combination, and the congestion side, free side, or transition side where the target vehicle is located, macroscopic structure repair or free flow structure maintenance is selected. Based on geometric diagnosis, local morphological residual repair is performed, and the repair operation is completed by reviewing factors such as vehicle spacing, road space boundary, speed, acceleration, jerk, trajectory monotonicity, and endpoint uniqueness.

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