Millimeter wave radar based vehicle trajectory reconstruction method and system

Abstract

This application relates to the field of intelligent transportation data processing technology, and in particular to a vehicle trajectory reconstruction method and system based on millimeter-wave radar. By fusing observation data from upstream and downstream millimeter-wave radars, the spatial blind spots between radars are considered as continuous missing trajectory regions. The missing parts are uniformly characterized in time to achieve standardization of the time dimension, thereby forming a vehicle trajectory reconstruction region. By comprehensively extracting the spatiotemporal interaction features of the target vehicle and surrounding vehicles within the vehicle trajectory reconstruction region, these features are used as input conditional feature sequences and fed into a model with group interaction modeling capabilities to generate the target vehicle's trajectory within the vehicle trajectory reconstruction region, achieving complete vehicle trajectory reconstruction. This aims to solve the problem of how to reconstruct vehicle trajectories in road segments with detection blind spots.

Description

Technical Field

[0001] This application relates to the field of intelligent transportation data processing technology, and in particular to a vehicle trajectory reconstruction method and system based on millimeter-wave radar. Background Technology

[0002] With the continuous development of traffic detection technology, roadside cameras, ultrasonic radar, millimeter-wave radar, and radar-video fusion integrated detectors have gradually overcome the shortcomings of traditional trajectory acquisition methods in terms of accuracy and real-time performance. They can provide high-precision, real-time trajectory information and have become an important means of trajectory acquisition.

[0003] Among the relevant technical solutions, millimeter-wave radar is widely used in traffic detection scenarios due to its strong anti-interference performance and ability to work stably under various weather conditions.

[0004] However, in actual deployment, due to limitations in installation conditions and costs, the actual coverage of millimeter-wave radar is low, and the distance between adjacent radars often exceeds 500 meters. This low coverage characteristic results in blind spots on the detection road section, causing millimeter-wave radar to only acquire fragmented vehicle speed data, leading to insufficient accuracy of millimeter-wave radar in continuous acquisition of road trajectory data.

[0005] In view of this, this application proposes a vehicle trajectory reconstruction method based on millimeter-wave radar, which aims to achieve continuous prediction of vehicle trajectories in road sections with sparse radar coverage. Summary of the Invention

[0006] The main purpose of this application is to provide a vehicle trajectory reconstruction method based on millimeter-wave radar, which aims to solve the problem of how to reconstruct vehicle trajectories in road sections with detection blind spots.

[0007] To achieve the above objectives, this application provides a vehicle trajectory reconstruction method based on millimeter-wave radar, which includes the following steps:

[0008] The detection blind zone between two adjacent millimeter-wave radars is defined according to the preset vehicle trajectory reconstruction rules to form the vehicle trajectory reconstruction area;

[0009] In the vehicle trajectory reconstruction area, determine the speed difference, distance difference, and lane number between the target vehicle and adjacent vehicles, and integrate the speed difference, distance difference, and lane number into a simulated feature vector of the target vehicle in the vehicle trajectory reconstruction area;

[0010] The simulated feature vector is concatenated with the historical feature sequence collected when the target vehicle enters the detection blind zone and the future feature sequence collected when it leaves the detection blind zone to obtain a conditional feature sequence, which is then input into a preset model for prediction. The vehicle trajectory of the target vehicle in the vehicle trajectory reconstruction area is obtained from the output of the preset model.

[0011] Optionally, the preset vehicle trajectory reconstruction rules include at least one of neighbor vehicle selection rules and virtual vehicle supplementation rules;

[0012] The neighbor vehicle selection rule is as follows: the target vehicle only interacts with vehicles within the interaction domain, and the interaction domain is the nearest neighbor vehicle in each lane that is in front of or behind the target vehicle.

[0013] The virtual vehicle supplementary rule is as follows: if there are no neighboring vehicles within the interaction domain of the target vehicle, a virtual vehicle is set at the boundary of the interaction domain, wherein the virtual vehicle and the target vehicle have the same speed.

[0014] Optionally, the mathematical expression for the neighbor vehicle selection rule is:

[0015]

[0016] in, This indicates the rules for selecting adjacent vehicles. lane At any moment The collection of vehicles, Indicates the longitudinal position of the target vehicle. lane Upper The car at any time The vertical position.

[0017] The mathematical expression for the virtual vehicle supplementation rule is:

[0018]

[0019]

[0020]

[0021]

[0022] in, lane The group of vehicles positioned in front of the target vehicle. lane The group of vehicles located behind the target vehicle. An empty set indicates that there are no vehicles in that lane in the corresponding direction. This represents the longitudinal position of the virtual car. For the speed of the virtual car, This indicates the set longitudinal distance between the virtual preceding vehicle and the target vehicle. This indicates the set longitudinal distance between the virtual following vehicle and the target vehicle.

[0023] Optionally, the mathematical expression for the simulated feature vector is:

[0024]

[0025] in,

[0026] In the formula, For the target vehicle at time The vertical position, For the target vehicle at time speed, For the target vehicle at time Lane number, For neighboring cars At any moment speed, For neighboring cars At any moment The vertical position, For neighboring cars At any moment Lane number, It represents an 18-dimensional real vector space consisting of the speed difference, distance difference, and lane number of 6 adjacent vehicles.

[0027] Optionally, the mathematical expression for the historical feature sequence is:

[0028]

[0029] The mathematical expression for the future feature sequence is:

[0030]

[0031] In the formula, Represents a historical feature sequence. This represents the future feature sequence after the blind zone. For vehicles in Location at any given moment For vehicles in The speed of time, Indicates that the vehicle is in Momentary interaction characteristics To detect the start time of the blind spot, The end time for detecting the blind spot, This indicates a fixed upstream and downstream length.

[0032] Optionally, the preset model includes a generator, and during the prediction process, the generator's execution steps include:

[0033] Obtain the concatenated conditional feature sequence:

[0034]

[0035] in, For conditional feature sequences, Indicates the target vehicle at time The simulated feature vector, Historical feature sequence and future feature sequences The concatenated upstream and downstream interaction feature vectors This represents the feature vector space formed by concatenating the target vehicle's simulated feature vector with the upstream and downstream interactive feature vectors;

[0036] The conditional feature sequence is subjected to a nonlinear transformation to obtain a deep semantic representation:

[0037]

[0038] in, This is the deep semantic representation of conditional features after nonlinear transformation by a fully connected layer. This represents the weights of the conditional feature fully connected layer. The bias of the conditional feature fully connected layer. For activation function, The deep semantic feature vector space represents the conditional features after nonlinear transformation;

[0039] Random noise vector sampled from a normal distribution It is mapped through another fully connected layer and connected to the conditional feature sequence to form a joint feature sequence. :

[0040]

[0041] in, This represents the joint feature vector space formed by concatenating the deep semantic representation of conditional features with random noise features;

[0042] The joint feature sequence is input into the bidirectional GRU layer to obtain the bidirectional GRU at time step [time]. Hidden state :

[0043]

[0044] in, Indicates from time 1 to time 2. The joint feature sequence, Indicates the bidirectional GRU at time [time]. The output hidden state vector space;

[0045] The missing trajectory fragments are reconstructed by a decoder consisting of fully connected layers with LeakyReLU activation.

[0046]

[0047] in, For at any time The predicted trajectory segment, This is the weight matrix of the fully connected layer of the decoder. The bias vector of the fully connected layer of the decoder. This is the LeakyReLU activation function.

[0048] Optionally, the loss function for the generator to generate trajectory segments is expressed as:

[0049]

[0050] in, The input vector represents the conditional data, which includes historical trajectories, information about neighboring vehicles, and other relevant features. The parameters are... The parameter is used to control the degree to which the generator's output is aligned with the interpolation rate. Used to adjust the degree of matching between the generator output and the actual speed, parameters Ensure the smoothness of the generated velocity sequence; This represents the mathematical expectation of the distribution of trajectory samples generated by the generator. , and These represent the mean square error loss between the generated trajectory and the true trajectory, the interpolation consistency loss of the generated trajectory at the boundary of the detection blind zone, and the smoothness constraint loss of the generated velocity sequence, respectively.

[0051] Optionally, the preset model includes a discriminator, and the execution steps of the discriminator during the prediction process include:

[0052] After mapping the conditional feature sequence and the actual collected trajectory sequence through a fully connected layer, their respective high-dimensional representations are obtained:

[0053]

[0054]

[0055] in, This is a high-dimensional representation of the conditional feature sequence after mapping through a fully connected layer. For conditional feature sequences, This is a high-dimensional representation of the trajectory sequence after mapping through a fully connected layer. For trajectory sequence, The weights of the fully connected layer are embedded into the conditional features. The bias of embedding conditional features into the fully connected layer. The weights of the fully connected layer are embedded into the trajectory features. The bias of the fully connected layer is used to embed trajectory features;

[0056] The high-dimensional representation is concatenated and passed to a bidirectional GRU, which models the time dependencies in both directions and captures the dynamic relationships across time steps.

[0057]

[0058]

[0059] in, The concatenated feature vectors The hidden state sequence of a bidirectional GRU;

[0060] The final hidden state of the hidden state sequence of the bidirectional GRU is fed into a multilayer perceptron with a nonlinear transformation and a Leaky ReLU activation function to produce a scalar score, which is used as the output score of the discriminator.

[0061]

[0062] In the formula, Represented as a bidirectional GRU at time... The final hidden state;

[0063] in:

[0064]

[0065]

[0066] In the formula, Here is the weight matrix of the multilayer perceptron. The bias vector of the multilayer perceptron The LeakyReLU activation function is used. The negative slope coefficient of LeakyReLU. This is an intermediate representation of the output of the multilayer perceptron.

[0067] Optionally, the loss function for the discriminator to determine the authenticity of the generated trajectory segments is expressed as:

[0068]

[0069] in, This represents maximizing the discriminator's score on the true trajectory. This represents the score for minimizing the generated trajectory. This represents the gradient penalty term, which promotes smoothness by penalizing deviations in the gradient norm.

[0070] In addition, to achieve the above objectives, this application also provides a computer system, the computer system comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, it implements the steps of the vehicle trajectory reconstruction method based on millimeter-wave radar as described in any of the preceding claims.

[0071] This application has at least the following beneficial effects:

[0072] 1. By integrating observation data from upstream and downstream millimeter-wave radars, the spatial blind spots between radars are regarded as areas with continuous missing trajectories. The missing parts are uniformly characterized in time to achieve standardization of the time dimension, thereby forming a vehicle trajectory reconstruction area.

[0073] 2. By comprehensively extracting the spatiotemporal interaction features of the target vehicle and surrounding vehicles within the vehicle trajectory reconstruction area, and using them as input conditional feature sequences, the system generates the vehicle trajectory of the target vehicle within the vehicle trajectory reconstruction area by inputting these features into a model capable of group interaction modeling, thus achieving complete reconstruction of the vehicle trajectory.

[0074] 3. Introduce conditions with group interaction modeling capabilities into the preset model to further improve the accuracy of trajectory reconstruction;

[0075] 4. An adversarial training process is adopted to train the generator and discriminator, which further enhances the effect of all-time and all-space vehicle trajectory reconstruction and improves the robustness and accuracy of the method involved in this application. Attached Figure Description

[0076] Figure 1 This is a schematic flowchart of the vehicle trajectory reconstruction method based on millimeter-wave radar involved in the embodiments of this application;

[0077] Figure 2 This is a reconstruction of the target image in a sparse detector environment as described in the embodiments of this application;

[0078] Figure 3 This is an illustration of the vehicle interaction domain involved in the embodiments of this application;

[0079] Figure 4 This is a diagram of the preset model architecture involved in the embodiments of this application;

[0080] Figures 5-8These are reconstruction result diagrams for different blind zone ranges involved in the embodiments of this application;

[0081] Figures 9-16 This is a comparison diagram of velocity contour lines under different blind zone ranges involved in the embodiments of this application;

[0082] Figure 17 This is a schematic diagram of the hardware operating environment of the computer system involved in the embodiments of this application.

[0083] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0084] To better understand the above technical solutions, exemplary embodiments of this disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of this disclosure to those skilled in the art.

[0085] First Embodiment

[0086] Reference Figure 1 This embodiment provides a vehicle trajectory reconstruction method based on millimeter-wave radar, which includes the following steps:

[0087] Step S10: Define the detection blind zone between two adjacent millimeter-wave radars according to the preset vehicle trajectory reconstruction rules to form a vehicle trajectory reconstruction area.

[0088] In this embodiment, the observation data generated by two adjacent millimeter-wave radars are unified into a millimeter-wave radar data environment, and the spatial blind zone between the two radars is used as the continuous missing area of ​​the vehicle trajectory. By characterizing the missing parts of the trajectory of all vehicles according to a uniform time interval, standardization in the time dimension is achieved. The data environment and the spatial range of the blind zone together constitute the vehicle trajectory reconstruction area.

[0089] In some alternative implementations, the time unit in the observation data collected by the upstream and downstream millimeter-wave radars is converted to seconds, and the position is converted to meters, as shown in the following formula:

[0090]

[0091]

[0092] in, Indicates the original frame number. This represents the corresponding timestamp, converted to seconds. This is a time conversion factor; This indicates the actual detection range of the millimeter-wave radar. This is the distance conversion factor. This is the converted distance, and the unit of the converted distance is meters.

[0093] In a length of upstream location of the road section and downstream location Two millimeter-wave radars were deployed to monitor the passage of... Vehicle data collection within a time interval Vehicle trajectory data passing through this section of road, such as Figure 2 As shown. The vehicle trajectory data set is... The distance between the upstream and downstream radars It is relatively large, appearing in the middle of each trajectory with a length of approximately The observation blind zone. The length of this blind zone is approximately equal to the distance between the two radars, resulting in a continuous missing region in the trajectory of each vehicle. The continuous missing segment formed by the spatial blind zone between the upstream and downstream radars constitutes the vehicle reconstruction region. The vehicle trajectory includes vehicle ID, timestamp, speed, and position. The raw data for each vehicle can be represented by a matrix:

[0094]

[0095] Further and optionally, the preset vehicle trajectory reconstruction rules include at least one of neighbor vehicle selection rules and virtual vehicle supplementation rules;

[0096] The neighbor vehicle selection rule is as follows: the target vehicle only interacts with vehicles within the interaction domain, and the interaction domain is the nearest neighbor vehicle in each lane that is in front of or behind the target vehicle.

[0097] Specifically, the mathematical expression for the neighbor vehicle selection rule is:

[0098]

[0099] in, This indicates the rules for selecting adjacent vehicles. lane At any moment The collection of vehicles, Indicates the longitudinal position of the target vehicle. lane Upper The car at any time The vertical position.

[0100] The virtual vehicle supplementary rule is as follows: if there are no neighboring vehicles within the interaction domain of the target vehicle, a virtual vehicle is set at the boundary of the interaction domain, wherein the virtual vehicle and the target vehicle have the same speed.

[0101] Specifically, the mathematical expression for the virtual vehicle supplementation rule is:

[0102]

[0103]

[0104]

[0105]

[0106] in, lane The group of vehicles positioned in front of the target vehicle. lane The group of vehicles located behind the target vehicle. An empty set indicates that there are no vehicles in that lane in the corresponding direction. This represents the longitudinal position of the virtual car. For the speed of the virtual car, This indicates the set longitudinal distance between the virtual preceding vehicle and the target vehicle. This indicates the set longitudinal distance between the virtual following vehicle and the target vehicle.

[0107] Step S20: Determine the speed difference, distance difference, and lane number between the target vehicle and adjacent vehicles in the vehicle trajectory reconstruction area, and integrate the speed difference, distance difference, and lane number into a simulated feature vector of the target vehicle in the vehicle trajectory reconstruction area;

[0108] In this embodiment, after defining the vehicle trajectory reconstruction region, the speed difference, distance difference and lane information between the target vehicle and each adjacent vehicle are characterized in the interaction domain. Combined with the target vehicle's own state, a simulated feature vector is constructed.

[0109] Specifically, with the target vehicle Centered on the central axis, extending longitudinally forward and backward. , Within the range, covering all lanes (assuming three lanes). This constitutes an interaction domain, with the target vehicle being... At any moment The vertical position is The lane is Each vehicle can act as the target vehicle (master vehicle). It is assumed that the target vehicle only interacts with the nearest vehicles in front and behind it in each lane within the area. When the target vehicle occupies a different lane, its interaction with adjacent vehicles remains unchanged. In each lane... Select the target vehicle. The nearest vehicles in front and behind; in this example, to obtain a fixed set of 6 adjacent vehicles, the three lanes traveling in the same direction as the target vehicle (left lane / current lane / right lane) are typically selected. and order Six neighboring vehicle samples were obtained. When a certain lane... If there is no vehicle in front or behind, place a virtual vehicle. It travels at the same speed as the main vehicle. For example... Figure 3 As shown, the calculation is performed for each selected neighboring vehicle. The system calculates three types of correlation parameters with the target vehicle: position difference, speed difference, and the lane the target vehicle is in (i.e., lane information). The target vehicle's current position, speed, and lane, along with three parameters for each of the other six vehicles, are combined to form a vector. , which is used as the feature vector input for the model.

[0110] Further, and optionally, the mathematical expression for the simulated feature vector is:

[0111]

[0112] in,

[0113] In the formula, For the target vehicle at time The vertical position, For the target vehicle at time speed, For the target vehicle at time Lane number, For neighboring cars At any moment speed, For neighboring cars At any moment The vertical position, For neighboring cars At any moment Lane number, It represents an 18-dimensional real vector space consisting of the speed difference, distance difference, and lane number of 6 adjacent vehicles.

[0114] Step S30: The simulated feature vector is concatenated with the historical feature sequence collected when the target vehicle enters the detection blind zone and the future feature sequence collected when it leaves the detection blind zone to obtain a conditional feature sequence, which is then input into a preset model for prediction. The vehicle trajectory of the target vehicle in the vehicle trajectory reconstruction area is obtained from the preset model.

[0115] In this embodiment, after obtaining the simulated feature vector, a sample segmentation strategy is constructed, which divides the blind zone into historical segments and future upstream and downstream segments, and normalizes the three as the conditional input of the model.

[0116] The sample segmentation strategy refers to a blind-zone-centric segmentation and sample construction strategy. For each vehicle, all missing points within the blind zone are identified, and fixed-length historical and future upstream and downstream segments (including position, speed, and interaction features) are extracted from the observable region. After normalization, these segments are used as conditional inputs, while the missing parts are used as outputs for training and evaluation. Unlike global segmentation, this method uses a sliding window to dynamically adapt to blind zones of different lengths and locations.

[0117] Further, and optionally, the mathematical expression for the historical feature sequence is:

[0118]

[0119] The mathematical expression for the future feature sequence is:

[0120]

[0121] In the formula, Represents a historical feature sequence. This represents the future feature sequence after the blind zone. For vehicles in Location at any given moment For vehicles in The speed of time, Indicates that the vehicle is in Momentary interaction characteristics To detect the start time of the blind spot, The end time for detecting the blind spot, This indicates a fixed upstream and downstream length.

[0122] Furthermore, the mathematical expression for the sliding window used to extract the feature sequence is:

[0123]

[0124] in, For the first The time range of a sliding window For the first The starting time of each blind spot For the first The end of the blind spot This represents the number of samples generated through the sliding window.

[0125] Finally, the vehicle trajectory of the target vehicle output by the preset model in the vehicle trajectory reconstruction area is obtained, and the reconstruction of the vehicle trajectory in the detection blind zone is completed.

[0126] In the technical solution provided in this embodiment, by fusing observation data from upstream and downstream millimeter-wave radars, the spatial blind zone between radars is regarded as a region with continuous missing trajectories. The missing parts are uniformly characterized in time to achieve standardization of the time dimension, thereby forming a vehicle trajectory reconstruction region. Then, the spatiotemporal interaction features of the target vehicle and surrounding vehicles are comprehensively extracted in this region and used as input as a conditional feature sequence. This sequence is then input into a model with group interaction modeling capabilities to generate the vehicle trajectory of the target vehicle in the vehicle trajectory reconstruction region, thus achieving complete reconstruction of the vehicle trajectory.

[0127] Second Embodiment

[0128] Based on the first embodiment, this embodiment provides a design scheme for the architecture of the generator and discriminator in a preset model, see [link to relevant documentation]. Figure 4 The following diagram illustrates the pre-defined model architecture. The design steps for the generator and discriminator are explained below:

[0129] For the generator, firstly, for each time step of the target vehicle... The model collects a fixed length Simulated feature vectors And connect it with the upstream and downstream interaction characteristics of historical and future time windows. These are concatenated to form a series of conditional feature vectors. Then, these conditional feature vectors are passed through a fully connected layer. and nonlinear activation functions It is then converted into a deep semantic representation. Simultaneously, a random noise vector sampled from a normal distribution is passed through another fully connected layer. and nonlinear functions The mapping is performed and concatenated with conditional features to form a joint feature representation. Then, this joint feature sequence... The hidden states are fed into a bidirectional GRU layer, which captures temporal dependencies from historical and future contexts. The hidden states at each time step encode global temporal relationships and underlying dynamics. Finally, the encoded sequence of hidden states... By weight and leakyReLU activation function The decoder, composed of these components, maps the high-dimensional representation back to the trajectory space, reconstructing the missing trajectory segments, as shown in the following equation:

[0130]

[0131] in, Indicates the target vehicle at time Historical trajectory fragment vectors, For upstream and downstream interaction feature vectors, Conditional eigenvectors:

[0132]

[0133] in, This is the deep semantic representation of conditional features after nonlinear transformation by a fully connected layer. This represents the weights of the conditional feature fully connected layer. The bias of the conditional feature fully connected layer. This is the activation function.

[0134]

[0135]

[0136] in, It is represented as a random noise vector sampled from a standard normal distribution. This represents the vector after the noise has been mapped through the fully connected layer. To map the weights of the fully connected layer to noise, The bias of the fully connected layer is used to map noise. It is a non-linear activation function.

[0137]

[0138] in, This is the deep semantic representation of conditional features after nonlinear transformation by a fully connected layer. This is the vector of noise after being mapped through a fully connected layer.

[0139]

[0140] in, Indicates the bidirectional GRU at time [time]. The hidden state.

[0141]

[0142] in, This is the weight matrix of the fully connected layer of the decoder. The bias vector of the fully connected layer of the decoder. The LeakyReLU activation function is used. For at any time The predicted trajectory segment.

[0143] The following steps are summarized:

[0144] Step S100: Obtain the concatenated conditional feature sequence.

[0145]

[0146] in, For conditional feature sequences, Indicates the target vehicle at time The simulated feature vector, Historical feature sequence and future feature sequences The concatenated upstream and downstream interaction feature vectors This represents the feature vector space formed by concatenating the target vehicle's simulated feature vector with the upstream and downstream interactive feature vectors;

[0147] It should be noted here that the historical feature sequence represents the state feature sequence of the target vehicle and its neighboring vehicles at several past moments. It describes the vehicle's motion behavior within a historical time window and is used to capture dynamic trends.

[0148] The future feature sequence represents the expected or generated feature sequence of the target vehicle and its neighboring vehicles within the reconstruction time period. It provides future time series or generated targets for evaluating or generating the future trajectory distribution of the target vehicle.

[0149] Since the operating state of a vehicle is influenced by the themes of neighboring vehicles and vehicles in adjacent lanes, historical feature sequences can describe the propagation of upstream traffic conditions, such as the influence of the preceding vehicle on the target vehicle, while future feature sequences can describe the propagation of downstream traffic conditions, that is, the influence of changes in the target vehicle on the following vehicle. Therefore, it is necessary to realize bidirectional information propagation in the feature space, which is more conducive to the model learning the temporal dynamics of vehicles and the potential interaction patterns between vehicles.

[0150] Step S200: Perform a nonlinear transformation on the conditional feature sequence to obtain a deep semantic representation:

[0151]

[0152] in, This is the deep semantic representation of conditional features after nonlinear transformation by a fully connected layer. This represents the weights of the conditional feature fully connected layer. The bias of the conditional feature fully connected layer. For activation function, The deep semantic feature vector space represents the conditional features after nonlinear transformation;

[0153] Step S300: Sample random noise vector from a normal distribution. It is mapped through another fully connected layer and connected to the conditional feature sequence to form a joint feature sequence. :

[0154]

[0155] in, This represents the joint feature vector space formed by concatenating the deep semantic representation of conditional features with random noise features;

[0156] Step S400: Input the joint feature sequence into the bidirectional GRU layer to obtain the bidirectional GRU at time step S400. Hidden state :

[0157]

[0158] in, Indicates from time 1 to time 2. The joint feature sequence, Indicates the bidirectional GRU at time [time]. The output hidden state vector space;

[0159] Step S500: The missing trajectory fragment is reconstructed by a decoder consisting of a fully connected layer with LeakyReLU activation.

[0160]

[0161] in, For at any time The predicted trajectory segment, This is the weight matrix of the fully connected layer of the decoder. The bias vector of the fully connected layer of the decoder. This is the LeakyReLU activation function.

[0162] For the discriminator, it receives two inputs: a conditional feature sequence. (Including the target vehicle's historical trajectory, interaction characteristics, etc.) and trajectory sequence (Real sequences or generated sequences). Each input is handled by a fully connected layer. and They are processed independently to extract depth representations and embed them into a unified high-dimensional space.

[0163] Then, the encoded conditions and trajectory features are concatenated and passed to a bidirectional GRU, which models the time dependencies in both directions and captures the dynamic relationships across time steps.

[0164] Finally, the final hidden state of the GRU is fed into a multilayer perceptron (MLP) with a nonlinear transformation and a LeakyReLU activation function, producing a scalar score. As the output score of the discriminator, this score reflects the authenticity of the trajectory under given conditions, as shown in the following formula:

[0165]

[0166]

[0167] in, This is a high-dimensional representation of the conditional features after mapping through a fully connected layer. For conditional feature sequences, This is a high-dimensional representation of the trajectory sequence after mapping through a fully connected layer. For trajectory sequence, The weights of the fully connected layer are embedded into the conditional features. The bias of embedding conditional features into the fully connected layer. The weights of the fully connected layer are embedded into the trajectory features. The bias of embedding trajectory features into the fully connected layer.

[0168]

[0169] in, This is the concatenated feature vector.

[0170]

[0171] in, This is the hidden state sequence of a bidirectional GRU.

[0172]

[0173] in, Here is the weight matrix of the multilayer perceptron. This is the bias vector of the multilayer perceptron.

[0174]

[0175] in, The LeakyReLU activation function is used. The negative slope coefficient of LeakyReLU. This is an intermediate representation of the output of the multilayer perceptron.

[0176]

[0177] in, Represented as a bidirectional GRU at time... The final hidden state.

[0178] The following steps are required for organization:

[0179] Step S1000: After mapping the conditional feature sequence and the actual collected trajectory sequence through a fully connected layer, their respective high-dimensional representations are obtained.

[0180]

[0181]

[0182] in, This is a high-dimensional representation of the conditional feature sequence after mapping through a fully connected layer. For conditional feature sequences, This is a high-dimensional representation of the trajectory sequence after mapping through a fully connected layer. For trajectory sequence, The weights of the fully connected layer are embedded into the conditional features. The bias of embedding conditional features into the fully connected layer. The weights of the fully connected layer are embedded into the trajectory features. The bias of the fully connected layer is used to embed trajectory features;

[0183] Step S2000: The high-dimensional representation is concatenated and passed to the bidirectional GRU, which models the time dependency in two directions and captures the dynamic relationship across time steps.

[0184]

[0185]

[0186] in, The concatenated feature vectors The hidden state sequence of a bidirectional GRU;

[0187] Step S3000: The final hidden state of the hidden state sequence of the bidirectional GRU is fed into a multilayer perceptron with a nonlinear transformation and a LeakyReLU activation function to generate a scalar score, which is used as the output score of the discriminator.

[0188]

[0189] In the formula, Represented as a bidirectional GRU at time... The final hidden state;

[0190] in:

[0191]

[0192]

[0193] In the formula, Here is the weight matrix of the multilayer perceptron. The bias vector of the multilayer perceptron The LeakyReLU activation function is used. The negative slope coefficient of LeakyReLU. This is an intermediate representation of the output of the multilayer perceptron.

[0194] Third Embodiment

[0195] Based on any of the above embodiments, in this embodiment, in order to improve the robustness and accuracy of the preset model proposed in this application, an adversarial training process is adopted to train the generator and discriminator, further enhancing the effect of all-time-space vehicle trajectory reconstruction, thereby completing the all-time-space non-connected vehicle trajectory reconstruction within the reconstruction area and obtaining the optimal all-time-space vehicle trajectory. The adversarial training process is specifically as follows:

[0196] Step S1: Initialize training parameters, including the number of training epochs. Batch size Loss weight The generator and discriminator are initialized. The raw data for each vehicle is preprocessed, including normalization, construction of interaction features, blind spot masking, and interpolation of missing segments.

[0197] Step S2: During training, the generator and discriminator are updated alternately: within each minimum training round, real trajectories and their interaction features are sampled from the dataset, and random noise is sampled from the normal distribution. The generator produces a virtual trajectory, the discriminator loss is calculated, and the discriminator is updated. Then, the virtual trajectory is generated again, the generator's overall loss is calculated, and the generator is updated. This process is repeated until... The training session is complete.

[0198] Furthermore, and optionally, the loss function for the generator to generate trajectory segments is as follows:

[0199]

[0200] in This represents the conditional input vector, which includes historical trajectories, information about neighboring vehicles, and other relevant features. Parameters The degree to which the generator's output aligns with the interpolation speed is controlled, thereby improving the accuracy of the interpolation and achieving a smoother, more physically consistent result. Parameters Adjust the degree of matching between the generator output and the actual speed; the higher the value, the stronger the consistency with the real speed. Parameter Ensure the smoothness of the generated velocity sequences, suppress unrealistic sudden changes, and maintain consistency with the physical laws governing real vehicle dynamics; This represents the mathematical expectation of the distribution of trajectory samples generated by the generator. , and These represent the mean square error loss between the generated trajectory and the true trajectory, the interpolation consistency loss of the generated trajectory at the boundary of the detection blind zone, and the smoothness constraint loss of the generated velocity sequence, respectively.

[0201] Furthermore, and optionally, the loss function for the discriminator to determine the authenticity of the generated trajectory segments is as follows:

[0202]

[0203] The loss function consists of three parts: It is about maximizing the discriminator's score on the true trajectory. Minimize the score of the generated trajectory—this together guides the discriminator to effectively distinguish between them. It is a gradient penalty term that promotes smoothness by penalizing the deviation of the gradient norm, preventing gradient vanishing and oversensitivity. This regularization ensures more stable training and improves the realism of the generated trajectories.

[0204] Verification of Examples

[0205] Based on any of the above embodiments, this embodiment verifies the effectiveness of the methods proposed in the above embodiments, as follows:

[0206] The following experiment uses a two-lane highway from the HighD dataset as the experimental subject, selecting a 400m long highway segment with high traffic density. Trajectory data for over 300 vehicles were recorded within a 10-minute observation period. This dataset, characterized by high vehicle speeds and clear free-flowing traffic, is highly suitable for thoroughly testing the applicability and versatility of the proposed trajectory completion model in typical highway scenarios.

[0207] First, the time unit in the dataset was converted from frames to seconds, and the location was converted from kilometers to meters. Some of the original data in the HighD dataset is shown in Table 1:

[0208] Table 1. Partial raw trajectory data from the HighD dataset.

[0209]

[0210] The conversion formulas for time and location units are as follows:

[0211] (27)

[0212] (28)

[0213] For each moment, the normalized speed features, position features, and lane number of the main vehicle are extracted.

[0214] Secondly, based on the actual road lengths in the experimental dataset, it is assumed that the maximum blind zone length on the road is 200 meters. To systematically evaluate the performance of the proposed method under different blind zone lengths, the blind zone length is set to... To evaluate the model's robustness under various missing data scenarios, the following additional assumptions were made in the experimental design: For the master vehicle at each time step, normalized speed features, position features, and lane number were extracted. Vehicle trajectory and speed in... Intra-range normalization is applied; there are available observation points before and after each blind spot, and vehicle interactions are only considered with adjacent vehicles traveling in the same direction within a 50-meter radius in the adjacent lane. The single-frame interaction vector is composed of the target vehicle features and the features of neighboring vehicles, and data processing and feature extraction are based on these physical and observational assumptions.

[0215] Next, the vehicle interaction features are input into the GI-WCGAN-GP model, and adversarial training is performed. In this embodiment, the hyperparameter values ​​during training are... , , , , , Through these assumptions and hyperparameter configurations, the proposed model can be comprehensively evaluated in terms of reconstruction capability and robustness under different blind zone lengths.

[0216] The analysis of the generated results obtained according to the steps of this embodiment includes multiple aspects to evaluate model performance. The accuracy and reliability of well completion results are evaluated using the reconstructed trajectory and evaluation metrics, such as... Figures 5-8 As shown in the figure. The results show that the experimental results of the proposed method were tested on real data with blind zone lengths of 50 meters, 100 meters, 150 meters and 200 meters. In the visualization, the orange part represents the blind zone area, while the black dashed line and the blue solid line represent the actual trajectory and the reconstructed trajectory of the undetected vehicle, respectively. Figures 5-8 The reconstruction results for 100 vehicles in a free-flow scenario are presented. It can be observed that, with different blind zone lengths, the blue and black lines are highly consistent within the orange area, indicating that regardless of the blind zone length, the proposed method can accurately reconstruct and recover the true trajectory in most cases.

[0217] On the other hand, by analyzing the velocity contour distribution to evaluate the model's ability to capture spatiotemporal dynamics, the results are as follows: Figures 9-16As shown, the reconstruction accuracy of the blind zone trajectory in this embodiment was quantified using mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results show that the model exhibits excellent trajectory reconstruction performance with shorter blind zones. When the blind zone length is 50m, the reconstructed trajectory is highly consistent with the true trajectory. The MAE is 0.28m, the MAPE is 0.12%, and the RMSE is 0.40m, indicating that the model can accurately recover missing trajectory segments and effectively complete blind zone data. As the blind zone length increases, the reconstruction error rises moderately. When the blind zone length reaches 200m, the MAE is 1.47m, the MAPE is 0.74%, and the RMSE is 1.96m.

[0218] In this embodiment, velocity contour maps visually compare the actual ground conditions and reconstructed velocities within blind zones, providing meaningful insights into model performance. Since trajectory generation incorporates velocity-based constraints and links position to time through velocity, these maps highlight the model's effectiveness in capturing spatiotemporal vehicle dynamics. The tight alignment of the contours indicates that the proposed model effectively captures the spatiotemporal evolution of vehicle speed even with missing portions of the trajectory. Although longer blind zones may introduce minor deviations, the overall pattern remains consistent, validating the benefits of explicit velocity constraints during training. The results show that regardless of blind zone length, the model accurately recovers the velocity distribution characteristics within the missing regions, with the overall trend closely matching the measured data. This demonstrates the model's strong generalization ability and adaptability to complex traffic scenarios. In small blind zones (e.g., 50m, 100m), the model accurately recovers well-structured and detailed velocity distributions, reflecting its sensitivity to spatiotemporal interactions. Even in larger blind zones (e.g., 150m, 200m), it can infer reasonable velocity fields from limited data, effectively reducing uncertainty. The model exhibits strong robustness in both boundary and missing regions, demonstrating reliable inference even with incomplete data. Due to the sparse observations in the blind zone, predictions may show slight smoothing or bias near the boundary, which is common in GAN-based methods that rely on neighboring data. While prediction uncertainty increases with blind zone length, the overall trend remains consistent with ground reality, confirming the model's robustness and applicability. Even in challenging scenarios, the generated trajectories maintain reliable accuracy with errors within acceptable limits.

[0219] As one implementation scheme, Figure 17 This is a schematic diagram of the hardware operating environment of the computer system involved in the embodiments of this application.

[0220] like Figure 17As shown, the computer system may include: a processor 1001, such as a CPU; a memory 1005; a user interface 1003; a network interface 1004; and a communication bus 1002. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be high-speed RAM or non-volatile memory, such as a disk drive. Optionally, the memory 1005 may also be a storage device independent of the aforementioned processor 1001.

[0221] Those skilled in the art will understand that Figure 17 The computer system architecture shown does not constitute a limitation on the computer system and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0222] like Figure 17 As shown, the memory 1005, as a storage medium, may include an operating system, a network communication module, a user interface module, and computer programs. The operating system is a program that manages and controls the hardware and software resources of the computer system, as well as the operation of the computer programs and other software or programs.

[0223] exist Figure 17 In the computer system shown, the user interface 1003 is mainly used to connect to the terminal and communicate with the terminal; the network interface 1004 is mainly used to communicate with the backend server; and the processor 1001 can be used to call the computer program stored in the memory 1005.

[0224] In this embodiment, the computer system includes: a memory 1005, a processor 1001, and a computer program stored in the memory and executable on the processor, wherein:

[0225] When processor 1001 calls a computer program stored in memory 1005, it performs the following operations:

[0226] The detection blind zone between two adjacent millimeter-wave radars is defined according to the preset vehicle trajectory reconstruction rules to form the vehicle trajectory reconstruction area;

[0227] In the vehicle trajectory reconstruction area, determine the speed difference, distance difference, and lane number between the target vehicle and adjacent vehicles, and integrate the speed difference, distance difference, and lane number into a simulated feature vector of the target vehicle in the vehicle trajectory reconstruction area;

[0228] The simulated feature vector is concatenated with the historical feature sequence collected when the target vehicle enters the detection blind zone and the future feature sequence collected when it leaves the detection blind zone to obtain a conditional feature sequence, which is then input into a preset model for prediction. The vehicle trajectory of the target vehicle in the vehicle trajectory reconstruction area is obtained from the output of the preset model.

[0229] Furthermore, those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program includes program instructions and can be stored in a storage medium, which is a computer-readable storage medium. The program instructions are executed by at least one processor in a computer system to implement the process steps of the embodiments of the above methods.

[0230] Therefore, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the various steps of the vehicle trajectory reconstruction method based on millimeter-wave radar as described in the above embodiments.

[0231] The computer-readable storage medium can be any computer-readable storage medium capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), magnetic disk, or optical disk.

[0232] It should be noted that, since the storage medium provided in the embodiments of this application is the storage medium used to implement the methods of the embodiments of this application, those skilled in the art can understand the specific structure and variations of the storage medium based on the methods described in the embodiments of this application, and therefore will not be repeated here. All storage media used in the methods of the embodiments of this application fall within the scope of protection of this application.

[0233] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0234] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0235] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0236] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0237] It should be noted that any reference signs placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. This application can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names.

[0238] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0239] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A vehicle trajectory reconstruction method based on millimeter-wave radar, characterized in that, The vehicle trajectory reconstruction method based on millimeter-wave radar includes the following steps: The detection blind zone between two adjacent millimeter-wave radars is defined according to the preset vehicle trajectory reconstruction rules to form the vehicle trajectory reconstruction area; In the vehicle trajectory reconstruction area, determine the speed difference, distance difference, and lane number between the target vehicle and adjacent vehicles, and integrate the speed difference, distance difference, and lane number into a simulated feature vector of the target vehicle in the vehicle trajectory reconstruction area; The simulated feature vector is concatenated with the historical feature sequence collected when the target vehicle enters the detection blind zone and the future feature sequence collected when it leaves the detection blind zone to obtain a conditional feature sequence, which is then input into a preset model for prediction. The vehicle trajectory of the target vehicle in the vehicle trajectory reconstruction area is obtained from the output of the preset model. The preset vehicle trajectory reconstruction rules include at least one of the neighbor vehicle selection rules and the virtual vehicle supplementation rules; The neighbor vehicle selection rule is as follows: the target vehicle only interacts with vehicles within the interaction domain, and the interaction domain is the nearest neighbor vehicle in each lane that is in front of or behind the target vehicle. The virtual vehicle supplementation rule is as follows: if there are no neighboring vehicles within the interaction domain of the target vehicle, then a virtual vehicle is set at the boundary of the interaction domain, wherein the virtual vehicle and the target vehicle have the same speed. The mathematical expression for the neighbor vehicle selection rule is: ； in, This indicates the rules for selecting adjacent vehicles. lane At any moment The collection of vehicles, For the target vehicle at time The vertical position, lane Upper The car at any time The longitudinal position; The mathematical expression for the virtual vehicle supplementation rule is: ； ； ； ； in, lane The group of vehicles positioned in front of the target vehicle. lane The group of vehicles located behind the target vehicle. An empty set indicates that there are no vehicles in that lane in the corresponding direction. This represents the longitudinal position of the virtual car. For the speed of the virtual car, This indicates the set longitudinal distance between the virtual preceding vehicle and the target vehicle. This indicates the set longitudinal distance between the virtual following vehicle and the target vehicle; The mathematical expression for the simulated feature vector is: ； in, ; In the formula, For the target vehicle at time The vertical position, For the target vehicle at time speed, For the target vehicle at time Lane number, Δ v i ( t (adjacent car) At any moment speed, Δ x i ( t (adjacent car) At any moment The vertical position, For neighboring cars At any moment Lane number, Represents an 18-dimensional real vector space consisting of the speed difference, distance difference, and lane number of 6 adjacent vehicles; The mathematical expression for the historical feature sequence is: ； The mathematical expression for the future feature sequence is: ； In the formula, Represents a historical feature sequence. This represents the future feature sequence after the blind zone. For vehicles in Location at any given moment For vehicles in The speed of time, Indicates that the vehicle is in Momentary interaction characteristics To detect the start time of the blind spot, The end time for detecting the blind spot, This indicates a fixed upstream and downstream length.

2. The vehicle trajectory reconstruction method based on millimeter-wave radar as described in claim 1, characterized in that, The preset model includes a generator, and the execution steps of the generator during the prediction process include: Obtain the concatenated conditional feature sequence: ； in, For conditional feature sequences, Indicates the target vehicle at time The simulated feature vector, Historical feature sequence and future feature sequences The concatenated upstream and downstream interaction feature vectors This represents the feature vector space formed by concatenating the target vehicle's simulated feature vector with the upstream and downstream interactive feature vectors; The conditional feature sequence is subjected to a nonlinear transformation to obtain a deep semantic representation: ； in, This is the deep semantic representation of conditional features after nonlinear transformation by a fully connected layer. This represents the weights of the conditional feature fully connected layer. The bias of the conditional feature fully connected layer. For activation function, The deep semantic feature vector space represents the conditional features after nonlinear transformation; Random noise vector sampled from a normal distribution It is mapped through another fully connected layer and connected to the conditional feature sequence to form a joint feature sequence. : ； in, This represents the joint feature vector space formed by concatenating the deep semantic representation of conditional features with random noise features; The joint feature sequence is input into the bidirectional GRU layer to obtain the bidirectional GRU at time step [time]. Hidden state : ； in, Indicates from time 1 to time 2. The joint feature sequence, Indicates the bidirectional GRU at time [time]. The output hidden state vector space; The missing trajectory fragments are reconstructed by a decoder consisting of fully connected layers with LeakyReLU activation. ； in, For at any time The predicted trajectory segment, This is the weight matrix of the fully connected layer of the decoder. The bias vector of the fully connected layer of the decoder. This is the LeakyReLU activation function.

3. The vehicle trajectory reconstruction method based on millimeter-wave radar as described in claim 2, characterized in that, The loss function for the generator to generate trajectory segments is expressed as: ； in, The input vector represents the conditional data, which includes historical trajectories, information about neighboring vehicles, and other relevant features. The parameters are... The parameter is used to control the degree to which the generator's output is aligned with the interpolation rate. The parameter is used to adjust the degree of matching between the generator output and the actual speed. Ensure the smoothness of the generated velocity sequence; This represents the mathematical expectation of the distribution of trajectory samples generated by the generator. , and These represent the mean square error loss between the generated trajectory and the true trajectory, the interpolation consistency loss of the generated trajectory at the boundary of the detection blind zone, and the smoothness constraint loss of the generated velocity sequence, respectively.

4. The vehicle trajectory reconstruction method based on millimeter-wave radar as described in claim 1, characterized in that, The preset model includes a discriminator, and the execution steps of the discriminator during the prediction process include: After mapping the conditional feature sequence and the actual collected trajectory sequence through a fully connected layer, their respective high-dimensional representations are obtained: ； ； in, This is a high-dimensional representation of the conditional feature sequence after mapping through a fully connected layer. For conditional feature sequences, This is a high-dimensional representation of the trajectory sequence after mapping through a fully connected layer. For trajectory sequence, The weights of the fully connected layer are embedded into the conditional features. The bias of embedding conditional features into the fully connected layer. The weights of the fully connected layer are embedded into the trajectory features. The bias of the fully connected layer is used to embed trajectory features; The high-dimensional representation is concatenated and passed to a bidirectional GRU, which models the time dependencies in both directions and captures the dynamic relationships across time steps. ； ； in, The concatenated feature vectors The hidden state sequence of a bidirectional GRU; The final hidden state of the hidden state sequence of the bidirectional GRU is fed into a multilayer perceptron with a nonlinear transformation and a Leaky ReLU activation function to produce a scalar score, which is used as the output score of the discriminator. ； In the formula, Represented as a bidirectional GRU at time... The final hidden state; in: ； ； In the formula, This is the weight matrix of the fully connected layer of the decoder. The bias vector of the fully connected layer of the decoder The LeakyReLU activation function is used. The negative slope coefficient of LeakyReLU. This is an intermediate representation of the output of the multilayer perceptron.

5. The vehicle trajectory reconstruction method based on millimeter-wave radar as described in claim 4, characterized in that, The loss function of the discriminator in determining the authenticity of generated trajectory segments is expressed as: ； in, This represents maximizing the discriminator's score on the true trajectory. This represents the score for minimizing the generated trajectory. This represents the gradient penalty term, which promotes smoothness by penalizing deviations in the gradient norm.

6. A computer system, characterized in that, The computer system includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, it implements the steps of the vehicle trajectory reconstruction method based on millimeter-wave radar as described in any one of claims 1 to 5.

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