Method for accurately estimating target geometric features under laser radar point cloud integration

Abstract

The invention provides a method for accurately estimating target geometric features under laser radar point cloud integration. The method is divided into a modeling stage and an operation stage. In the modeling stage, a system state equation and a measurement equation are established according to the relation between the real geometrical characteristics and motion characteristics of a target during point cloud integration, the relation between the geometrical characteristics detected by a sensor and a sampling period and the relation between point cloud integration times. In the operation stage, firstly, original point cloud is preprocessed, a non-ground point cloud set is segmented, and then point cloud integration and clustering are performed to realize target detection, so that a target measurement set is obtained; secondly, carrying out one-step prediction, calculating target similarity, and carrying out target and trajectory association by utilizing the similarity; and finally, the optimal estimation of the geometric features and the motion features of the target is obtained by using Kalman filtering. According to the method, the precision of target geometric feature estimation under the point cloud integration method can be improved, the small target detection performance of the low-line-number laser radar is enhanced, and the cost of a target detection system based on the laser radar is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous unmanned system environment perception, and specifically relates to a method for accurately estimating target geometric features under laser radar point cloud integration. Background Art

[0002] Environmental perception is a key technology for autonomous unmanned systems (including driverless vehicles and intelligent robots), and forms the foundation for decision-making, planning, and control. LiDAR, a primary environmental perception sensor, and its target detection methods play a crucial role in autonomous unmanned systems. However, due to cost constraints, high-line-count LiDAR cannot be deployed on a large scale, while low-line-count LiDAR is less effective at detecting distant and small objects.

[0003] The Chinese patent application, "LiDAR Point Cloud Target Detection Method, System, and Apparatus" (Application Number: CN202011060317.6), discloses a LiDAR point cloud target detection method. This method constructs a front view grid from point cloud information, extracts features from the front view grid separately, and extracts point features from the nearest point within each front view grid, combining these features. This method then uses a three-dimensional object detector to detect obstacles. This method only utilizes current LiDAR data and cannot address the issue of missed detection of sparse point clouds with low-line-count LiDARs at long distances or for small targets. A Chinese patent application, "A LiDAR Point Cloud Integration Target Detection Method, Medium, and System" (Application Number: CN202111191668.5), discloses a LiDAR point cloud integration target detection method. This method constructs a point cloud time integration model for non-ground point clouds, performs different time integration operations based on point cloud distance, clusters the integrated point cloud, and tracks and filters the clustered targets to obtain the target's motion state. However, this method does not address the smearing problem of the target object point cloud generated after point cloud integration, resulting in the inability to obtain the true size characteristics of the detected target. A Chinese patent application, "A Road Litter Detection Method" (Application Number: CN202410033344.6), discloses a road litter detection method based on LiDAR point clouds. This method first increases the density of the original point cloud through point cloud integration, then clusters the point cloud and tracks the target to complete target detection. However, this method ignores the object point cloud smearing problem caused by point cloud integration. When the target is moving too fast or the number of integrations is high, the size characteristics of the detected target differ significantly from the actual target, resulting in poor target detection.

[0004] Aiming at the problem of target size feature error caused by laser radar point cloud integration in the environment perception of autonomous unmanned systems, the present invention proposes a method for accurately estimating target geometric features under laser radar point cloud integration. Summary of the Invention

[0005] This invention aims to address the problem of inaccurate target geometric feature detection caused by point cloud integration, improve the accuracy of target geometric feature estimation using point cloud integration methods, enhance the performance of low-line-count laser radar for small target detection, and reduce the cost of laser radar-based target detection systems. A method for accurately estimating target geometric features using laser radar point cloud integration is proposed. The technical solution of this invention is as follows:

[0006] A method for accurately estimating target geometric features based on laser radar point cloud integration, comprising the following steps:

[0007] Modeling stage: Based on the relationship between the target's true geometric and motion characteristics during point cloud integration, the geometric characteristics detected by the sensor and the sampling period, and the number of point cloud integration times, the system state equation and measurement equation are established;

[0008] Operation phase: First, the original point cloud is preprocessed to segment the non-ground point cloud set, and then point cloud integration and clustering are performed to achieve target detection, thereby obtaining a target measurement set; secondly, a one-step prediction is performed to calculate the target similarity, and the similarity is used to associate the target with the trajectory; finally, the Kalman filter is used to obtain the optimal estimate of the target's geometric and motion features.

[0009] Furthermore, the system model includes the system state equation and measurement equation:

[0010] The state equation is:

[0011] Assume the state model of the target is:

[0012]

[0013] Where x is the target x position, y is the target y position, is the target x speed, is the target y speed, L is the target length, W is the target width, H is the target height, θ is the target heading angle, is the target angular velocity;

[0014] Establish a state transition model for the target:

[0015] X k =F k-1 X k-1 +w k-1 #(2)

[0016] Among them, X k is the target state vector at time k; F k-1 is the state transfer matrix, specifically:

[0017] T is the sampling period; X k-1 is the target state vector at time k-1; wk-1 is the process noise;

[0018] The measurement equation is:

[0019] Establish a measurement model for the target:

[0020] Z k =H k X k +v k #(3)

[0021] where Z k = [xy LWH θ], which represents the x and y position measurements, and the length, width, and height measurements of the target at time k, respectively; H k is the measurement matrix, specifically:

[0022] Where α is the influence factor of target speed on the measured size, N is the number of integration times, and T is the sampling period; X k is the target state vector at time k; v k To measure noise.

[0023] Furthermore, the steps of the operation phase include:

[0024] 3.1 First, PC the point cloud data collected by the lidar k Perform preprocessing to obtain the non-ground point cloud set PC′ k , then perform point cloud integration to obtain enhanced point cloud set After clustering and target detection, the target measurement value set is obtained

[0025] 3.2 One-step prediction: Using the optimal estimate of the target at the previous moment and the system state transition equation, the predicted state of each target in the target set at time k is obtained. Specifically, at the current time k, for target i in the target set, one-step prediction is performed based on the target motion state estimate at the previous moment, and the target motion state prediction at time k can be obtained. and the covariance matrix P of the one-step forecast error k|k-1 :

[0026]

[0027] in is the optimal state estimate of the target at time k-1, is the state prediction value of the target at time k, Q k-1 is the process noise covariance matrix, F k-1 is the state transfer matrix, P k-1|k-1 represents the posterior estimated covariance at time k-1;

[0028] 3.3 Data Association: Data association is performed by introducing target position features and shape features. This mainly includes two steps: similarity calculation and target-observation pairing based on similarity.

[0029] 3.4 Tracking Filtering: After completing data association, the successfully associated targets are tracked and filtered;

[0030] For each step prediction target and measurement targets Calculate the Kalman gain K k , and then combine the prior estimate and measurement data to obtain the optimal state estimate of the target And update the optimal estimated covariance P k|k :

[0031]

[0032] P k|k =(IK k H k )P k|k-1 #(14)

[0033] Where I is the identity matrix, R k is the measurement noise covariance matrix. Through the above steps, the target optimal state estimation at time k can be obtained and the updated estimated covariance P k|k , and and P k|k The state estimation at the next moment is achieved by time shifting.

[0034] Furthermore, the step 3.3 data association: introducing target position features and shape features for data association, specifically includes two steps:

[0035] 3.3.1 Similarity calculation: Calculate the position similarity and shape similarity between the target measurement and the target one-step prediction respectively;

[0036] Position similarity S p (i,j) is measured using the Euclidean distance, and the positions of the target one-step prediction i and the target measurement j at time k are respectively Position similarity describes the positional relationship between target one-step prediction i and target measurement j;

[0037] Shape similarity S f (i, j) is also measured using Euclidean distance. Suppose the shape feature of target one-step prediction i and target measurement j at time k is Shape similarity describes the shape relationship between the target one-step prediction i and the target measurement j;

[0038] Normalize the above two similarities and then calculate the comprehensive similarity S(i,j);

[0039] 3.3.2 Similarity-based target-observation pairing: Based on the calculated comprehensive similarity, the cost matrix C is constructed, where each element C ij Represents the matching cost between target i and observation j. Finally, the Hungarian algorithm is used to optimally match the cost matrix C to find the target-observation pairing with the minimum total cost, thereby completing data association.

[0040] Furthermore, the similarity normalization step is also included:

[0041] The position similarity S p (i, j), shape similarity S f (i, j) is normalized, and the maximum values ​​of position and shape similarity are set to be and The normalized position and shape similarity is:

[0042]

[0043] Calculate the comprehensive similarity based on the normalized similarity:

[0044]

[0045] where n regulates the influence of position and shape similarity on the comprehensive similarity.

[0046] Furthermore, the method also includes the following steps:

[0047] Based on the calculated comprehensive similarity, a cost matrix C is constructed. Suppose there are m target predictions i and n measurements j, where the elements of the matrix are comprehensive similarities S(i, j). The cost matrix C is in the following form:

[0048]

[0049] Matching is accomplished using the Hungarian algorithm: First, each row in the cost matrix is ​​zeroed. This involves finding the minimum value in each row and subtracting it from all elements in that row, ensuring that each row has at least one zero value. A similar zeroing operation is then performed on each column, finding the minimum value in each column and subtracting it from all elements in that column, ensuring that each column has at least one zero value. Next, an attempt is made to find independent zero elements in the matrix that are not covered by other zero elements, performing a preliminary match. If the number of independent zero elements found equals the number of rows in the matrix, the match is complete. Otherwise, the matrix is ​​adjusted by finding the smallest uncovered element and further operations are performed until sufficient independent zero elements are found. Once sufficient independent zero elements are found, the row and column indices corresponding to each zero element represent the optimal match. For cases where the number of targets and measurements is unequal, the matrix is ​​balanced by adding dummy rows or columns. The costs of these dummy rows and columns are set to a large value, representing the penalty for mismatches and ensuring a successful matching process. The target-observation pair with the lowest total cost is found, completing the data association.

[0050] The advantages and beneficial effects of the present invention are as follows:

[0051] In order to solve the problem that the target size characteristics are difficult to estimate correctly under the current laser radar point cloud integration, the present invention proposes a method for accurately estimating the target geometric characteristics under the laser radar point cloud integration. The method is divided into a modeling stage and an operation stage. In the modeling stage, the system state equation and measurement equation are established based on the relationship between the real geometric characteristics and motion characteristics of the target during point cloud integration, the geometric characteristics detected by the sensor and the sampling period, and the number of point cloud integration times. In the operation stage, the original point cloud is first preprocessed to segment the non-ground point cloud set, and then point cloud integration and clustering are performed to achieve target detection, thereby obtaining a target measurement set; secondly, a one-step prediction is performed to calculate the target similarity, and the similarity is used to associate the target with the trajectory; finally, the Kalman filter is used to obtain the optimal estimate of the target geometric characteristics and motion characteristics. In claim 2.2, the present invention innovatively introduces the relationship between target speed, point cloud integration times, sensor sampling period and target size characteristics, and establishes a measurement model that can represent this relationship, so that the Kalman filter can obtain the optimal estimation of the target geometric characteristics and motion characteristics under point cloud integration; in step 3.3 of the claim, the present invention innovatively considers the comprehensive similarity of the target shape and position relationship, so that the data association is more accurate, the accuracy of state estimation is improved, and thus the filtering effect and system performance are enhanced.

[0052] This method can improve the accuracy of target geometric feature estimation under the point cloud integration method, enhance the performance of low-line-count lidar for small target detection, and reduce the cost of lidar-based target detection systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is an overall flow chart of a method for accurately estimating target geometric features under laser radar point cloud integration according to a preferred embodiment of the present invention;

[0054] Figure 2 Shown is a schematic diagram of the system state model according to the present invention;

[0055] Figure 3 Shown is a schematic diagram of the effect of the present invention. DETAILED DESCRIPTION

[0056] The following will describe the technical solutions in the embodiments of the present invention in detail with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention.

[0057] The technical solution of the present invention to solve the above technical problems is:

[0058] like Figure 1 The figure shows the overall flow chart of the present invention, which includes the following steps:

[0059] 1 First, PC the point cloud data collected by the laser radar k Perform preprocessing to obtain the non-ground point cloud set PC′ k , then perform point cloud integration to obtain enhanced point cloud set After clustering and target detection, the target measurement value set is obtained

[0060] 2 One-step prediction: Using the optimal estimate of the target at the previous moment and the system state transfer equation to obtain the predicted state of each target in the target set at time k, specifically including: at the current moment k, for target i in the target set, one-step prediction is performed based on the target motion state estimate at the previous moment, and the target motion state prediction at time k can be obtained and the covariance matrix P of the one-step forecast error k|k-1 ,

[0061]

[0062] in is the optimal state estimate of the target at time k-1, is the state prediction value of the target at time k, Q k-1 is the process noise covariance matrix, F k-1 is the state transfer matrix, P k-1|k-1 represents the posterior estimated covariance at time k-1.

[0063] 3. Data association: Introducing target location features and shape features for data association, which mainly includes two steps:

[0064] 3.1 Similarity calculation: Calculate the position similarity and shape similarity between the target measurement and the target one-step prediction respectively.

[0065] Position similarity S p (i,j) is measured using the Euclidean distance, and the positions of the target one-step prediction i and the target measurement j at time k are respectively The position similarity is:

[0066]

[0067] Position similarity describes the positional relationship between the target one-step prediction i and the target measurement j.

[0068] Shape similarity S f (i, j) is also measured using Euclidean distance. Suppose the shape feature of target one-step prediction i and target measurement j at time k is The shape similarity is:

[0069]

[0070] Shape similarity describes the shape relationship between the target one-step prediction i and the target measurement j.

[0071] The position similarity S p (i, j), shape similarity S f (i, j) is normalized, and the maximum values ​​of position and shape similarity are set to be and The normalized position and shape similarity is:

[0072]

[0073] Calculate the comprehensive similarity based on the normalized similarity:

[0074]

[0075] Where n is the effect of adjusting position and shape similarity on the overall similarity.

[0076] 3.2 Similarity-based target-observation pairing: Based on the calculated comprehensive similarity, a cost matrix C is constructed. Suppose there are m target predictions i and n measurements j, where the elements of the matrix are comprehensive similarities S(i, j). The cost matrix C is in the following form:

[0077]

[0078] Matching is accomplished using the Hungarian algorithm: First, each row in the cost matrix is ​​zeroed. This involves finding the minimum value in each row and subtracting it from all elements in that row, ensuring that each row has at least one zero value. Next, a similar zeroing operation is performed on each column, finding the minimum value in each column and subtracting it from all elements in that column, ensuring that each column has at least one zero value. Next, an attempt is made to find independent zero elements in the matrix that are not overlapped by other zero elements, performing a preliminary match. If the number of independent zero elements found equals the number of rows in the matrix, the match is complete. Otherwise, the matrix is ​​adjusted by finding the smallest uncovered element and further operations are performed on the matrix until sufficient independent zero elements are found. Once sufficient independent zero elements are found, the row and column indices corresponding to each zero element represent the optimal match. If the number of targets and measurements is unequal, the matrix is ​​balanced by adding dummy rows or columns. The cost of these dummy rows and columns is set to a larger value, representing the penalty for mismatches and ensuring a successful matching process. The target-observation pair with the lowest total cost is found, completing the data association.

[0079] 4 Tracking filtering: After completing data association, the successfully associated targets are tracked and filtered.

[0080] For each step prediction target and measurement targets Calculate the Kalman gain K k , and then combine the prior estimate and measurement data to obtain the optimal state estimate of the target And update the optimal estimated covariance P k|k :

[0081]

[0082] P k|k =(IK k H k )P k|k-1 #(14)

[0083] Where I is the identity matrix, R k is the measurement noise covariance matrix. Through the above steps, the target optimal state estimation at time k can be obtained and the updated estimated covariance P k|k , and and P k|k The state estimation at the next moment is achieved by time shifting.

[0084] like Figure 2The figure shows a schematic diagram of the system state model for a method of accurately estimating the geometric features of a target under the integration of a lidar point cloud. The target moves in the X-axis and Y-axis planes and does not move in the Z direction. The geometric features of the target include length (L), width (W), and height (H), and its direction of motion is represented by the heading angle θ, that is, the orientation of the object relative to the X-axis. In the modeling stage, the system state equation and measurement equation are established based on the relationship between the target's true geometric features and motion features during point cloud integration, the geometric features detected by the sensor and the sampling period, and the number of point cloud integrations:

[0085] Assume the state model of the target is:

[0086]

[0087] Where x is the target x position, y is the target y position, is the target x speed, is the target y speed, L is the target length, W is the target width, H is the target height, θ is the target heading angle, is the target angular velocity.

[0088] Establish a state transition model for the target:

[0089] X k =F k-1 X k-1 +w k-1 #(2)

[0090] Among them, X k is the target state vector at time k; F k-1 is the state transfer matrix, specifically:

[0091] T is the sampling period; X k-1 is the target state vector at time k-1; w k-1 is the process noise.

[0092] Establish a measurement model for the target:

[0093] Z k =H k x k +v k #(3)

[0094] where Z k =[xyLWHθ], which represent the x and y position measurements, and the length, width, and height measurements of the target at time k, respectively; H k is the measurement matrix, specifically:

[0095] Where α is the influence factor of target speed on the measured size, N is the number of integration times, and T is the sampling period; X k is the target state vector at time k; v k To measure noise.

[0096] Figure 3 Shown is a schematic diagram of the effect of the present invention. Figure 3 As shown in (a), under normal circumstances, at time T1, if the target is at position A, the point cloud is dense due to the short distance, and the target can be detected normally. If the target is at position B, the point cloud is sparse due to the long distance, and the target is difficult to detect. Figure 3 As shown in (b), at time T2, under the point cloud integration condition, point cloud accumulation is performed at this time, that is, the point cloud of the previous time T1 is accumulated with the point cloud of the current time T2, which increases the point cloud density. When the target is at position A, it can be detected normally. When the target is at position B, it can also be detected under the action of point cloud integration, but point cloud integration makes it difficult to correctly detect the target size features; Figure 3 As shown in (c), at time T2, in the case of point cloud integration, point cloud accumulation is performed at this time, that is, the point cloud of the previous time T1 is accumulated with the point cloud of the current time T2, which improves the point cloud density. The target is detected normally when it is at position A. After this method, it can also be detected at position B and the target geometric size characteristics can be correctly estimated.

[0097] The systems, devices, modules, or units described in the above embodiments may be implemented by computer chips or entities, or by products having certain functions. A typical implementation device is a computer. Specifically, the computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0098] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0099] The above embodiments should be understood as merely illustrating the present invention and not as limiting the scope of protection of the present invention. After reading the contents of the present invention, technicians may make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for accurately estimating target geometric features under laser radar point cloud integration, characterized in that: The following steps are involved: Modeling stage: According to the relationship between the real geometric features and motion features of the target during point cloud integration, the geometric features detected by the sensor and the sampling period, and the number of point cloud integration times, the system state equation and measurement equation are established; Operation phase: First, the original point cloud is preprocessed to segment the non-ground point cloud set, and then point cloud integration and clustering are performed to achieve target detection, thereby obtaining a target measurement set; secondly, a one-step prediction is performed to calculate the target similarity, and the similarity is used to associate the target with the trajectory; finally, the Kalman filter is used to obtain the optimal estimate of the target's geometric and motion features.

2. The method for accurately estimating target geometric features by laser radar point cloud integration according to claim 1, characterized in that: The system model includes system state equations and measurement equations: The state equation is: Assume the state model of the target is: Where x is the target x position, y is the target y position, is the target x speed, is the target y speed, L is the target length, W is the target width, H is the target height, θ is the target heading angle, is the target angular velocity; Establish the state transition model of the target: X k =F k-1 X k-1 +w k-1 #(2) Among them, X k is the target state vector at time k; F k-1 is the state transfer matrix, specifically: T is the sampling period; X k-1 is the target state vector at time k-1; w k-1 is the process noise; The measurement equation is: Establish a measurement model for the target: Z k =H k X k +v k #(3) Where Z k =[xy LWH θ], which respectively represent the x and y position measurement values, and the length, width, and height measurement values ​​of the target at time k; H k is the measurement matrix, specifically: Where α is the influence factor of the target speed on the measured size, N is the number of integration times, and T is the sampling period; X k is the target state vector at time k; v k To measure noise.

3. The method for accurately estimating target geometric features under laser radar point cloud integration according to claim 1, characterized in that: The steps of the operation phase include: 3.1 First, PC the point cloud data collected by the laser radar k Preprocessing is performed to obtain the non-ground point cloud set PC′ k , then perform point cloud integration to obtain the enhanced point cloud set After clustering and target detection, we get a set of target measurement values 3.2 One-step prediction: The predicted state of each target in the target set at time k is obtained by using the optimal estimate of the target at the previous moment and the system state transfer equation. Specifically, at the current moment k, one-step prediction is performed on target i in the target set based on the target motion state estimate at the previous moment, and the target motion state prediction at time k can be obtained. and the covariance matrix P of the one-step forecast error k|k-1 : in is the optimal state estimate of the target at time k-1, is the state prediction value of the target at time k, Q k-1 is the process noise covariance matrix, F k-1 is the state transfer matrix, P k-1|k-1 represents the posterior estimated covariance at time k-1; 3.3 Data Association: Introducing target position features and shape features for data association, which mainly includes two steps: similarity calculation and target-observation pairing based on similarity: 3.4 Tracking filtering: After completing data association, the successfully associated targets are tracked and filtered; For each step prediction target And measurement target Calculate the Kalman gain K k , and then combine the prior estimate and the measurement data to obtain the optimal state estimate of the target And update the optimal estimated covariance P k|k : P k|k =(I-K k H k )P k|k-1 #(14) Where I is the identity matrix, R k is the measurement noise covariance matrix. Through the above steps, the target optimal state estimation at time k can be obtained and the updated estimated covariance P k|k , and and P k|k The state estimation at the next moment is achieved by time shifting.

4. The method for accurately estimating target geometric features by laser radar point cloud integration according to claim 3, characterized in that: The step 3.3 data association: introducing the target position feature and the shape feature for data association, specifically includes two steps: 3.3.1 Similarity calculation: Calculate the position similarity and shape similarity between the target measurement and the target one-step prediction respectively; Position similarity S p (i,j) is measured using the Euclidean distance. Suppose the positions of the target one-step prediction i and the target measurement j at time k are respectively Position similarity describes the positional relationship between target one-step prediction i and target measurement j; Shape similarity S f (i, j) is also measured using the Euclidean distance. Suppose the shape features of the target one-step prediction i and the target measurement j at time k are Shape similarity describes the shape relationship between target one-step prediction i and target measurement j; Normalize the above two similarities, and then calculate the comprehensive similarity S(i,j); 3.3.2 Similarity-based target-observation pairing: Based on the calculated comprehensive similarity, the cost matrix C is constructed, where each element C ij Represents the matching cost of target i and observation j. Finally, the Hungarian algorithm is used to optimally match the cost matrix C to find the target-observation pairing with the minimum total cost, thereby completing the data association.

5. The method for accurately estimating target geometric features by laser radar point cloud integration according to claim 4, characterized in that: It also includes the similarity normalization step: The position similarity S p (i, j), shape similarity S f (i, j) is normalized, and the maximum values ​​of position and shape similarity are set to be and The normalized position and shape similarity is: Calculate the comprehensive similarity based on the normalized similarity: where n regulates the influence of position and shape similarity on the comprehensive similarity.

6. The method for accurately estimating target geometric features by laser radar point cloud integration according to claim 5, characterized in that: Also included are the steps of the associated method: Based on the calculated comprehensive similarity, the cost matrix C is constructed. There are m target predictions i and n measurements j. The elements of the matrix are the comprehensive similarities S(i, j). The cost matrix C is in the following form: Use the Hungarian algorithm to complete the matching: First, zero each row in the cost matrix, that is, find the minimum value in each row and subtract the value from all elements in the row so that each row has at least one zero value; then, perform a similar zeroing operation on each column, find the minimum value in each column and subtract all elements in the column to ensure that each column has at least one zero value; then, try to find independent zero elements in the matrix that are not covered by other zero elements for preliminary matching. If the number of independent zero elements found is equal to the number of rows in the matrix, the matching is complete; Otherwise, adjust the matrix by finding the smallest uncovered element and further operating on the matrix until enough independent zero elements can be found; After finally finding enough independent zero elements, the row and column index corresponding to each zero element represents the best match. In the case where the number of targets and measurements is not equal, it is necessary to balance the matrix by adding virtual rows or columns. The cost of the virtual rows and columns is set to a larger value, representing the penalty for mismatching, to ensure that the matching process is completed smoothly; find the target-observation pairing with the minimum total cost to complete the data association.

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