An anomaly identification method based on dynamic trajectory prediction

Abstract

An anomaly identification method based on dynamic trajectory prediction, belonging to the field of intelligent transportation and autonomous driving technology, is proposed to address the problems of existing trajectory prediction methods, such as high requirements for data quality and continuity and weak resistance to anomaly interference. This invention acquires trajectory points in real time and divides a continuous trajectory point sequence based on a dynamic threshold T; it calculates the probability density of each point using a multivariate Gaussian distribution, identifies and removes anomalies, and stores them in a candidate pool; it predicts trajectory points by weighting the spatiotemporal dimensions using a multi-head attention neural network; and it calculates the Mahalanobis distance between the historical trajectory center and the predicted and real-time points to further detect anomalies and update the sequence. In summary, dynamic grouping thresholds adapt to signal interruptions, ensuring data continuity; a multi-head attention mechanism is introduced to reduce dependence on high-precision data; and the combination of anomaly candidate pool and backtracking verification achieves pre-emptive removal and post-emptive repair, effectively distinguishing between misjudgments and genuine anomalies, thus improving the accuracy and anti-interference capability of trajectory prediction.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation and autonomous driving technology, and in particular to an anomaly point identification method based on dynamic trajectory prediction. Background Technology

[0002] In the era of explosive growth in intelligent driving, the prediction of vehicle trajectories and the identification of anomalies are becoming increasingly important. During the driving process, vehicles generally rely on GPS or BeiDou positioning. However, both GPS and BeiDou positioning are susceptible to signal weakness or interruption due to equipment failure, complex terrain (tunnels, tall buildings, etc.), and severe weather, which can lead to location offset or loss. This affects the operation and management platform's monitoring of vehicles, thereby impacting the overall platform's regulatory capabilities and increasing operational pressure.

[0003] Traditional methods typically employ neural networks and spatiotemporal distance algorithms. However, existing neural network-based trajectory prediction algorithms require high-quality data to ensure the accuracy and stability of both training and real-world data; otherwise, the overall prediction performance cannot be guaranteed. Furthermore, neural network models require a large amount of high-quality data during the initial training phase to ensure effective training. In real-world scenarios, data exhibits significant inconsistencies, and GPS and BeiDou systems frequently experience abnormal drift points or intermittent data uploads during vehicle movement. This manifests primarily in the following ways: The quality of prediction results is poor when continuous and large amounts of data are continuously input. Neural network models require a large amount of continuous data input when making predictions. When there is a lack of a large amount of continuous training data, the model suffers from overfitting, resulting in noisy prediction results. The neural network model has a weak ability to resist interference from trajectory anomalies. When training, the neural network model needs trajectory data that is regular and continuous. When there are anomalies or irregular discontinuities in the trajectory data, the neural network model cannot make effective judgments, resulting in a large error. Summary of the Invention

[0004] Based on the above analysis, the present invention aims to provide an anomaly identification method based on dynamic trajectory prediction, in order to solve the technical problems of existing trajectory prediction methods having high requirements for data quality and continuity and weak resistance to anomaly interference, reduce data accuracy requirements, and achieve intermittent short data prediction and accurate anomaly identification.

[0005] This invention provides an anomaly point identification method based on dynamic trajectory prediction, the method comprising the following steps: Step S1: Acquire device trajectory points in real time, calculate grouping threshold T in real time, and take the sequence of trajectory points with an interval of less than T between adjacent trajectory points as the current trajectory point sequence. Step S2: Based on the multivariate Gaussian distribution, calculate the probability density of each trajectory point in the current trajectory point sequence, identify the outliers in the current trajectory point sequence according to the probability density, store the outliers in the outlier candidate pool, and delete the outliers from the current trajectory point sequence. Step S3: For the current trajectory point sequence, a neural network algorithm with a multi-head attention mechanism is used to perform attention weighting calculations on the time dimension and the spatial dimension respectively to obtain the predicted trajectory points corresponding to each trajectory point in the current trajectory point sequence; Step S4: Calculate the Mahalanobis distance between the historical trajectory center and the predicted trajectory point and the corresponding real-time trajectory point, respectively, and determine whether the real-time trajectory point is an anomaly. If it is an anomaly, store it in the anomaly candidate pool and delete the anomaly from the current trajectory point sequence.

[0006] Based on the above solution, the present invention also makes the following improvements: Furthermore, the predicted trajectory points corresponding to each trajectory point are obtained through the neural network algorithm of the multi-head attention mechanism. This includes: The hidden state of the trajectory point at time step 1 in the current trajectory point sequence is calculated using an LSTM network. Based on the spatial attention mechanism, the spatial dimension of the hidden state at the i-th time step is weighted to obtain the spatial hidden state at the i-th time step. Based on the time attention mechanism, the hidden state at the first time step is weighted by time dimension to obtain the time hidden state at the first time step. By fusing the spatial hidden state and the temporal hidden state, a comprehensive hidden state at time step 1 is obtained. Based on the comprehensive hidden state, the predicted trajectory point corresponding to the trajectory point at time step 1 in the current trajectory point sequence is obtained.

[0007] Furthermore, the first The spatial hiding state at a given time is calculated using the following formula:

[0008] In the formula, For spatial attention scoring vectors, Train a weight matrix for the spatial dimension. For the first The hidden state of the time trajectory point After removing the time dimension, the first Spatial feature vectors of time trajectory points This is the spatial dimension bias term.

[0009] Furthermore, the first The time-hidden state at a given moment is calculated using the following formula:

[0010] In the formula, For time attention scoring vectors, Train the weight matrix for the time dimension. After removing the spatial dimension, the first The temporal characteristics of the trajectory points at any given time. This is the time dimension bias term.

[0011] Furthermore, the first The overall hidden state at time t is calculated using the following formula:

[0012] In the formula, Here is the forget gate weight matrix. For the forget gate bias term, No. The spatial hidden state at any given moment. No. The hidden state of time at any given moment.

[0013] Furthermore, the predicted trajectory points are obtained by calculating a predicted trajectory point vector, which is calculated using the following formula:

[0014] In the formula, For the current trajectory point sequence, the th The predicted trajectory point vector at time step, This is a preset prediction bias term; The first predicted trajectory point in the predicted trajectory point vector As the first The predicted trajectory point corresponding to the trajectory point at each time point.

[0015] Furthermore, the method also includes: if K consecutive real-time trajectory points are all judged as normal points, determining whether the trajectory point of the previous time of the K real-time trajectory points is in the abnormal point candidate pool; if it exists, triggering a backtracking verification mechanism to verify whether the trajectory point of the previous time of the K real-time trajectory points is a true abnormal point.

[0016] Furthermore, the backtracking verification mechanism includes: The trajectory point from the previous moment is taken out of the anomaly candidate pool and placed together with K real-time trajectory points in reverse chronological order to form a new current trajectory point sequence. Repeat steps 3 and 4; If the verification result is a true anomaly, then the predicted trajectory point is used instead; If the verification result is a normal point, then the trajectory point of the previous time step is removed from the abnormal point candidate pool.

[0017] Furthermore, the anomalies identified based on the probability density are not used for trajectory point prediction, but are only stored in the anomaly candidate pool, to be processed after the backtracking verification mechanism is triggered.

[0018] Furthermore, the Mahalanobis distance between the historical trajectory center and the predicted trajectory point is calculated using the following formula:

[0019] In the formula, As the center of historical trajectory, For the first The predicted trajectory point corresponding to the trajectory point at each time point.

[0020] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. Reduce the requirements for data accuracy By introducing a multi-head attention mechanism (RZ-LSTM), the model can dynamically adjust the prediction weights according to different data distributions, reducing the dependence on high accuracy and uniform distribution of input data.

[0021] 2. Provide data that adapts to intermittent nature. By using a grouping threshold, trajectory points with time intervals less than the grouping threshold are included in the current trajectory point sequence, thereby enabling the prediction of each trajectory point in the current trajectory point sequence. This solves the problem of data discontinuity caused by signal interruption affecting the prediction effect.

[0022] 3. Improve the accuracy and anti-interference capability of anomaly identification and trajectory prediction. By constructing a candidate pool through an anomaly identification algorithm and combining it with a backtracking verification mechanism, pre-emptive elimination and post-secondary verification are achieved, effectively distinguishing between real anomalies and misjudged points. Predicted points are then used to replace and repair these anomalies, thereby significantly improving the accuracy and anti-interference capability of trajectory prediction.

[0023] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0024] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0025] Figure 1 The flowchart illustrates the anomaly point identification method based on dynamic trajectory prediction provided in this embodiment of the invention. Detailed Implementation

[0026] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0027] A specific embodiment of the present invention discloses an anomaly point identification method based on dynamic trajectory prediction, the method flow is as follows: Figure 1 As shown, the specific steps include: Step S1: Acquire device trajectory points in real time, calculate the grouping threshold T in real time, and take the sequence of trajectory points with an interval of less than T between adjacent trajectory points as the current trajectory point sequence.

[0028] In the specific implementation process, based on the vehicle-mounted BeiDou or GPS positioning terminal, the device's latitude and longitude, timestamp, speed, and driving direction angle are collected in real time to obtain trajectory points containing the above positioning information. Each trajectory point contains multi-dimensional information and is represented by a feature vector. . Preferably, the multi-dimensional d is set to 5 dimensions, corresponding to the equipment's latitude and longitude, time, speed, and driving direction angle. This indicates the specific values ​​corresponding to longitude, latitude, time, speed, and direction of travel, respectively.

[0029] Specifically, adjacent trajectory points are defined according to their time intervals. The grouping threshold T is defined as three times the average time interval of all trajectory points acquired in real time. The grouping threshold T is calculated in real time, and the sequence of trajectory points with an adjacent time interval less than T is taken as the current trajectory point sequence. The grouping threshold is calculated for each trajectory point acquired in real time. It is then determined whether the time interval between the current trajectory point and the previous trajectory point is less than the grouping threshold. If it is less, all trajectory points, including the current trajectory point and all those before it, are included in the current trajectory point sequence. If it is greater, all trajectory points, excluding the current trajectory point, are included in the current trajectory point sequence.

[0030] Furthermore, the grouping threshold T is calculated using the following formula:

[0031] In the formula, This indicates the number of all trajectory points acquired in real time. This indicates the time of the first trajectory point acquired in real time. Indicates the number of times the data is obtained in real time. The time for each trajectory point.

[0032] For example, the current trajectory point sequence is represented as The current trajectory point sequence contains There are trajectory points, and The number is greater than or equal to 2 and less than or equal to 2 indivual.

[0033] Step S2: Based on the multivariate Gaussian distribution, calculate the probability density of each trajectory point in the current trajectory point sequence, identify the outliers in the current trajectory point sequence according to the probability density, store the outliers in the outlier candidate pool, and delete the outliers from the current trajectory point sequence.

[0034] Specifically, based on the probability density function of the multivariate Gaussian distribution, the probability density of each trajectory point in the current trajectory point sequence is calculated. It can be calculated using the following formula:

[0035] In the formula The mean is the average value of each dimension of the features of each trajectory point in the current trajectory point sequence. The covariance is the covariance of each dimension of the features of each trajectory point in the current trajectory point sequence.

[0036] Furthermore, The smaller the value, the higher the probability that the trajectory point is an anomaly. If the value is less than a preset threshold, the trajectory point is determined to be an anomaly, and the anomaly point is added to the anomaly point candidate pool for management. At the same time, the anomaly point is deleted from the current trajectory point sequence. Specifically, the preset threshold is set based on experience.

[0037] Step S3: For the current trajectory point sequence, a neural network algorithm with a multi-head attention mechanism is used to perform attention weighting calculations on the time dimension and the spatial dimension respectively to obtain the predicted trajectory points corresponding to each trajectory point in the current trajectory point sequence.

[0038] Step S31: Calculate the number of points in the current trajectory point sequence using an LSTM network. The hidden state of the time trajectory points.

[0039] In practice, the LSTM neural network processes each trajectory point in the current trajectory point sequence sequentially in chronological order. For the... Time trajectory points Combined with the first Hide state at all times The cell state is updated through forget gate, input gate, and output gate. and generate the first Hidden state of time trajectory points This allows for the extraction of temporal features of the trajectory. from Traversing to , arrive Arranged in chronological order.

[0040] Specifically, obtaining the forget gate result through the forget gate. It can be expressed by the following formula:

[0041] In the formula, For the input of the first Feature vectors of trajectory points at time points Here is the forget gate weight matrix.

[0042] For the forget gate bias term, For the first The status is always hidden.

[0043] It should be noted that the first Hide state at all times and the Cellular state at any moment The initial value is the zero vector, that is... hour .

[0044] Furthermore, the input gate result is obtained through the input gate. It can be expressed by the following formula:

[0045] In the formula, Here is the forget gate weight matrix. This is the input gate bias term.

[0046] Furthermore, the subsequent cell state is calculated. It can be expressed by the following formula:

[0047] In the formula, This is the subsequent cell state weight matrix. This is the subsequent cell state bias term.

[0048] Update the number of bytes using the forget gate, input gate, and output gate. Cellular state at any moment It can be expressed by the following formula:

[0049] In the formula, For the first Cell state at any given moment.

[0050] Furthermore, the output gate result is obtained through the output gate. and obtained the first Hidden state of time It can be expressed by the following formula: ;

[0051] In the formula, Here is the forget gate weight matrix. This is the input gate bias term.

[0052] It should be noted that when the trajectory point from Traversing to This allows us to obtain the hidden state of each trajectory point in the current trajectory point sequence.

[0053] Step S32: Based on the spatial attention mechanism, perform the following steps on the first... The hidden states at time step 1 are weighted according to spatial dimensions to obtain the 1st time step 2. The spatial hidden state at any given moment.

[0054] In specific implementation, a multi-head attention mechanism algorithm is adopted, based on the spatial attention mechanism for the first... The hidden states at time step 1 are used for weighted spatial attention calculations to obtain the 1st time step 2. Space Hidden State at Moment It can be calculated using the following formula:

[0055] In the formula, For spatial attention scoring vectors, Train a weight matrix for the spatial dimension. After removing the time dimension, the first Spatial feature vectors of time trajectory points This is the spatial dimension bias term. It should be noted that the first Spatial feature vector of trajectory point at time moment This refers to the data after removing the time dimension, i.e. .in This indicates the specific values ​​corresponding to longitude, latitude, time, speed, and direction of travel, respectively. Step S33: Based on the time attention mechanism, perform the following steps on the first... The hidden states at time step are weighted according to the time dimension to obtain the nth time step. The hidden state of time at any given moment.

[0056] In the specific implementation process, a multi-head attention mechanism algorithm is adopted, based on the time attention mechanism for the first... The hidden states at time step 1 are weighted by temporal attention to obtain the result. Time-hidden state of a moment It can be calculated using the following formula:

[0057] In the formula, For time attention scoring vectors, Train the weight matrix for the time dimension. After removing the spatial dimension, the first The temporal characteristics of the trajectory points at any given time. This is the time dimension bias term.

[0058] It should be noted that the first Temporal characteristics of trajectory points at time points This represents the data after removing the spatial dimension, i.e. .

[0059] Step S34: Merge the spatial hidden state and the temporal hidden state to obtain the first... The comprehensive hidden state at time step, and the th position in the current trajectory point sequence obtained based on the comprehensive hidden state. The predicted trajectory point corresponding to the trajectory point at each time point.

[0060] In specific implementation, a neural network algorithm with a multi-head attention mechanism is used to integrate the first... The hidden state of time at a given moment, the first The spatial hidden state at time t, yielding the t... The overall hidden state at any given moment and according to Get the current trajectory point sequence number The predicted trajectory point vector corresponding to the trajectory point at each time point It can be calculated using the following formula: ;

[0061] In the formula, This is the preset prediction bias term.

[0062] It should be noted that, include A predicted trajectory point, generally the predicted trajectory point vector. The first predicted trajectory point As the first in the current trajectory sequence The predicted trajectory point corresponding to the trajectory point at each time point.

[0063] Preferably, A predicted trajectory typically consists of 5 points.

[0064] It should be noted that when the trajectory point from Traversing to ,for At that time, the predicted trajectory point corresponding to the trajectory point. For its trajectory point itself .

[0065] Step S4: Calculate the Mahalanobis distance between the historical trajectory center and the predicted trajectory point and the corresponding real-time trajectory point, respectively. Determine whether the real-time trajectory point is an anomaly. If it is an anomaly, store it in the anomaly candidate pool and delete the anomaly from the current trajectory point sequence.

[0066] In the specific implementation process, the corresponding real-time trajectory point is the real-time trajectory point corresponding to the predicted trajectory point of each trajectory point in the current trajectory point sequence, and the historical trajectory center is defined by the average value of the corresponding dimension features of each historical trajectory point. The Mahalanobis distance between the historical trajectory center and the predicted trajectory point is calculated. Calculate the Mahalanobis distance between the historical trajectory center and the corresponding real-time trajectory point. Center of historical trajectory , as well as Calculated using the following formula: ; ;

[0067] In the formula, Indicates the first A historical trajectory point, This represents the number of all historical trajectory points. Indicates the current trajectory point sequence number. The real-time trajectory point corresponding to the predicted trajectory point at the given time trajectory point.

[0068] Furthermore, if If the corresponding real-time trajectory point is an anomaly, it is stored in the anomaly candidate pool; if... When the time is right, it indicates that the corresponding real-time trajectory point is a normal point, and the corresponding real-time trajectory point is retained in the current trajectory point sequence.

[0069] Step S5: If K consecutive real-time trajectory points are all judged as normal points, determine whether the trajectory point of the previous moment of the K real-time trajectory points is in the abnormal point candidate pool. If it exists, trigger the backtracking verification mechanism and repeat steps S3 and S4 to verify whether the trajectory point of the previous moment of the K real-time trajectory points is a true abnormal point.

[0070] In the specific implementation process, if K consecutive real-time trajectory points are all judged as normal points, it is determined whether the trajectory point of the previous time step of the K real-time trajectory points is in the anomaly candidate pool. If it exists, a backtracking verification mechanism is triggered, the point is taken out of the anomaly candidate pool, and placed together with the K real-time trajectory points, rearranged in reverse chronological order as a new current trajectory point sequence, and steps S3 and S4 are re-executed. By re-executing step S3, the predicted trajectory point of the taken anomaly point is obtained, and by re-executing step S4, it is determined whether the taken anomaly point is a true anomaly point. If the taken anomaly point is a true anomaly point, it is replaced by the predicted trajectory point obtained in step S3; if the taken anomaly point is a false anomaly point, the trajectory point of the previous time step is restored, removed from the anomaly candidate pool, and written into the current trajectory point sequence.

[0071] Specifically, the previous moment trajectory point of the K real-time trajectory points refers to the previous moment trajectory point of the first real-time trajectory point among the K real-time trajectory points. If the previous moment trajectory point of the first real-time trajectory point among the K real-time trajectory points is in the outlier candidate pool, then this point is also a selected outlier. This point is placed together with the K real-time trajectory points and rearranged in reverse chronological order to form the current trajectory point sequence when step S3 is re-executed. The predicted trajectory point of this point is obtained by re-executing step S3. The Mahalanobis distance between the historical trajectory center and the predicted trajectory point of this point is calculated by re-executing step S4, and the Mahalanobis distance between the historical trajectory center and the corresponding real-time trajectory point is calculated to determine whether this point is a true outlier. If the latter is greater than the former, the selected outlier is determined to be a true outlier; if the latter is less than or equal to the former, the selected outlier is determined to be a false outlier.

[0072] Preferably, There are typically 3 real-time trajectory points.

[0073] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0074] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An anomaly identification method based on dynamic trajectory prediction, characterized in that, Includes the following steps: Step S1: Acquire device trajectory points in real time, calculate grouping threshold T in real time, and take the sequence of trajectory points with an interval of less than T between adjacent trajectory points as the current trajectory point sequence; wherein, the value of the grouping threshold T is 3 times the average time interval of all trajectory points acquired in real time. Step S2: Based on the multivariate Gaussian distribution, calculate the probability density of each trajectory point in the current trajectory point sequence, identify the outliers in the current trajectory point sequence according to the probability density, store the outliers in the outlier candidate pool, and delete the outliers from the current trajectory point sequence. Step S3: For the current trajectory point sequence, a neural network algorithm with a multi-head attention mechanism is used to perform attention weighting calculations on the time dimension and the spatial dimension respectively to obtain the predicted trajectory points corresponding to each trajectory point in the current trajectory point sequence; Step S4: Calculate the Mahalanobis distance between the historical trajectory center and the predicted trajectory point and the corresponding real-time trajectory point, respectively, and determine whether the real-time trajectory point is an anomaly. If it is an anomaly, store it in the anomaly candidate pool and delete the anomaly from the current trajectory point sequence. The method further includes: if K consecutive real-time trajectory points are all judged as normal points, determine whether the trajectory point of the previous moment of the K real-time trajectory points is in the abnormal point candidate pool. If it exists, trigger the backtracking verification mechanism to verify whether the trajectory point of the previous moment of the K real-time trajectory points is a true abnormal point. The backtracking verification mechanism includes: The trajectory point from the previous moment is taken out of the anomaly candidate pool and placed together with K real-time trajectory points in reverse chronological order to form a new current trajectory point sequence. Repeat steps 3 and 4; If the verification result is a true anomaly, then the predicted trajectory point is used instead; If the verification result is a normal point, then the trajectory point of the previous time step is removed from the abnormal point candidate pool.

2. The method according to claim 1, characterized in that, The neural network algorithm using the multi-head attention mechanism obtains the predicted trajectory points corresponding to each trajectory point, including: The LSTM network is used to calculate the first [number]th [item] in the current trajectory point sequence. The hidden state of the time trajectory points; Based on the spatial attention mechanism, the first The hidden states at time step 1 are weighted according to spatial dimensions to obtain the 1st time step 2. The spatial hidden state at any given moment; Based on the time attention mechanism, the first The hidden states at time step are weighted according to the time dimension to obtain the nth time step. The hidden state of time at any given moment; By fusing the spatial hidden state and the temporal hidden state, the first... The comprehensive hidden state at time step, and the th position in the current trajectory point sequence obtained based on the comprehensive hidden state. The predicted trajectory point corresponding to the trajectory point at each time point.

3. The method according to claim 2, characterized in that, The first The spatial hiding state at a given time is calculated using the following formula: In the formula, For spatial attention scoring vectors, Train a weight matrix for the spatial dimension. For the first The hidden state of the time trajectory point After removing the time dimension, the first Spatial feature vectors of time trajectory points This is the spatial dimension bias term.

4. The method according to claim 2, characterized in that, The first The time-hidden state at a given moment is calculated using the following formula: In the formula, For time attention scoring vectors, Train the weight matrix for the time dimension. After removing the spatial dimension, the first The temporal characteristics of the trajectory points at any given time. This is the time dimension bias term.

5. The method according to claim 2, characterized in that, The first The overall hidden state at time t is calculated using the following formula: In the formula, Here is the forget gate weight matrix. For the forget gate bias term, No. The spatial hidden state at any given moment. No. The hidden state of time at any given moment.

6. The method according to claim 2, characterized in that, The predicted trajectory points are obtained by calculating a predicted trajectory point vector, which is calculated using the following formula: In the formula, For the current trajectory point sequence, the th The predicted trajectory point vector at time step, This is a preset prediction bias term; The first predicted trajectory point in the predicted trajectory point vector As the first The predicted trajectory point corresponding to the trajectory point at each time point.

7. The method according to claim 1, characterized in that, Anomalies identified based on the probability density are not used for trajectory point prediction, but are stored in the anomaly candidate pool and will be processed after the backtracking verification mechanism is triggered.

8. The method according to claim 1, characterized in that, The Mahalanobis distance between the center of the historical trajectory and the predicted trajectory point is calculated using the following formula: In the formula, As the center of historical trajectory, For the first The predicted trajectory point corresponding to the trajectory point at each time point.

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