Automatic camera-radar position offset calibration method and system based on calibration board

By introducing a scalable calibration board and a real-time sensor feedback system, and combining EPnP and LM algorithms to optimize the pose matrix, the problem of traditional calibration methods relying on manual operation in dynamic environments is solved, achieving high-precision and high-real-time automatic calibration, which is suitable for autonomous driving and robotic systems.

CN121784710APending Publication Date: 2026-04-03LIAOYANG VOCATIONAL & TECH COLLEGE
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-31
Publication Date
2026-04-03

AI Technical Summary

Technical Problem

Traditional calibration methods rely on manual operation in dynamic environments, making it difficult to quickly adapt to changes in sensor position. They lack flexibility and adaptability. Furthermore, deep learning methods consume high computational resources in real-time scenarios and have insufficient robustness and real-time performance.

Method used

An automatic calibration scheme combining a scalable calibration board and a real-time sensor feedback system is designed. The position of the calibration board is automatically adjusted through real-time data feedback from the camera and radar. The pose matrix is ​​optimized using EPnP and LM algorithms to achieve high-precision automatic calibration.

Benefits of technology

It enables high-precision and real-time automatic calibration in dynamic environments, reduces human intervention errors, improves the overall integration and reliability of the system, and is suitable for autonomous driving and robotic systems.

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Abstract

The invention discloses an automatic camera-radar position offset calibration method and system based on a calibration board, and relates to the technical field of position calibration. A calibration plate with a topological structure, a camera and a laser radar are placed on a carrier, the camera carries out image corner detection, the radar carries out point cloud corner extraction, the topological structure of the calibration plate and a detection and extraction result are subjected to corner corresponding matching, and a point pair set is established; the point pair set uses an EPnP algorithm to solve an initial pose matrix of a camera pose under an RANSAC random sampling consistency framework, a re-projection error is calculated through a projection equation according to the initial pose matrix, an LM algorithm is adopted under the RANSAC framework to carry out optimization, and an optimized pose matrix is output; according to the automatic camera-radar position offset calibration method and system based on the calibration plate, high-precision and stable camera-laser radar pose calibration is realized.
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Description

Technical Field

[0001] This invention relates to the field of position calibration technology, and in particular to an automatic camera-radar position offset calibration method and system based on a calibration board. Background Technology

[0002] Traditional calibration methods, such as those based on calibration boards, require manual placement and precise positioning of the calibration board. When the positions of the camera and radar shift, the calibration board must be reset. This makes the calibration process highly dependent on manual operation. In dynamic environments, such as when the sensor position shifts due to vehicle movement, the calibration process cannot quickly adapt to changes in sensor position and requires frequent manual adjustments. This lack of flexibility and adaptability makes it difficult to meet automation requirements.

[0003] While deep learning methods can learn features from large amounts of data and improve automation, they often require high computational resources during the inference phase and struggle to maintain high pose estimation accuracy in real-time scenarios. In dynamic environments, they are difficult to guarantee robustness and real-time performance. Furthermore, different scenarios or location settings may require retraining. Summary of the Invention

[0004] The purpose of this invention is to provide an automatic camera-radar position offset calibration method and system based on a calibration board, which aims to improve the problems of excessive manual intervention, unstable calibration accuracy, poor real-time performance and poor system integration in existing calibration technologies. By designing an automatic calibration scheme that combines a scalable calibration board and a real-time sensor feedback system, high-precision automatic calibration can be achieved in dynamic environments, and it is particularly suitable for multi-sensor fusion systems such as autonomous driving and robotics.

[0005] To achieve the above objectives, the present invention provides an automatic camera-radar position offset calibration method based on a calibration board, comprising the following steps: S1. Place a calibration board, camera, and lidar with a topological structure on the carrier; S2, Image corner detection is performed using the camera in S1 and point cloud corner extraction is performed using radar; S3. Using the topology of the calibration board in S1 and the results detected and extracted in S2, perform corner point correspondence matching to establish a 3D–2D point pair set. ; S4. Using the EPnP algorithm on the set of point pairs obtained in S3, solve for the initial pose matrix of the camera pose within the RANSAC random sampling consensus framework. ; S5. Calculate the reprojection error using the projection equation based on the initial pose matrix of S4. S6. Based on the reprojection error obtained in S5, the LM algorithm is used to optimize the position matrix within the RANSAC framework, and the optimized pose matrix is ​​output. .

[0006] Preferably, the calibration board of S1 is set within the common field of view of the camera and the lidar. The camera acquires a sequence of color images of the calibration board, and the lidar simultaneously acquires the three-dimensional point cloud data of the calibration board.

[0007] Preferably, the specific process of S2 is as follows: S21. Use the Shi-Tomasi corner detection algorithm to extract an initial set of corner points from the acquired camera images, and perform the sub-pixel refinement cornerSubPix algorithm on the detected corner points to improve pixel-level positioning accuracy, thus obtaining the set of corner points in the image coordinate system: ; in, The set of corner points of the image coordinate system includes The two-dimensional coordinates of each corner point in the image coordinate system It can be any positive integer; S22. Using the 3D Harris corner detection algorithm on the LiDAR point cloud, output the corner features at the intersection of the calibration board edge and the structure to obtain the corner set in the three-dimensional space of the LiDAR: in, The set of three-dimensional corner points in the lidar coordinate system includes The coordinates of a three-dimensional corner point in the lidar coordinate system.

[0008] Preferably, the specific process of S4 is as follows: S41. Solve for the pose matrix between the camera and the LiDAR to realize 3D points in the LiDAR coordinate system. To the camera coordinate system Conversion: ; in, Let them be rotation vectors and translation vectors. For 3D points in the lidar coordinate system, These are the points in the transformed camera coordinate system; S42, then through the camera intrinsic parameter matrix Projecting onto the pixel coordinate system yields ; ; in , These are the two-dimensional projected coordinates of a point in the pixel coordinate system. The horizontal axis coordinates of the pixel coordinate system is the vertical axis coordinate in the pixel coordinate system. The focal length of the camera in the horizontal direction. The focal length of the camera in the vertical direction. This represents the horizontal offset of the camera's principal optical center in the pixel coordinate system. This represents the horizontal offset of the camera's principal optical center in the pixel coordinate system.

[0009] Preferably, the specific process of S5 is as follows: S51. Substitute the initial pose matrix into the projection equation, the specific formula is as follows: ; in, The scale factor is a non-zero scalar in homogeneous coordinate projection, corresponding to a spatial point. Depth to the optical center of the camera; S52. Calculate the reprojection error based on the projection equation. Reprojection error The calculation formula is as follows: ; in, For the first A spatial feature point in 3D coordinates in a coordinate system This represents the reference coordinate system.

[0010] Preferably, the specific process of S6 is as follows: S61, Initial pose matrix based on camera pose Starting with S4, the initial solution is obtained by selecting the set of interiors with the largest number of interiors or the smallest cost through multiple samplings using RANSAC. Nonlinear least-squares refinement of the pose matrix under Lie algebra parameterization; S62. Define the reprojection residual for each interior point. for ; in, It is a Lie algebra vector representing the pose increment. , Indicates by Pose update obtained through exponential mapping; S63, Counterprojection error The reprojection error is minimized by weighting the sum of the L2 norms: ; in, To suppress outliers, Let be the set of all interior points; S64. Linearize the residuals and solve for the increment using the LM algorithm. : ; in, The approximate Hessian matrix constructed for the LM algorithm, The gradient vector, The damping factor, It is a diagonal matrix; S65, Each iteration passes Update the pose on the manifold until the termination criterion is met, and finally output the optimized pose matrix. ,in, This indicates the increment of the Lie algebra. Transformed via exponential mapping The pose increment in the equation is used to update the current pose on the manifold space formed by rotation and translation.

[0011] Preferably, the termination criterion for S65 is set as follows: ,in The termination threshold set for the LM algorithm.

[0012] Preferably, during the S6 iteration process, the rule for each pose update is as follows: ; in, For the first k The pose matrix of the next iteration, starting from the initial pose. Beginning, then N After the second iteration, we obtain: ; Among them, the number of iterations The calculation formula is as follows: ; in, For the expected confidence level, To estimate the out-of-point rate, The minimum number of samples; when the iteration converges, That is, the final pose matrix , The iterative solution process is the same as .

[0013] To achieve the above objectives, the present invention also provides an automatic camera-radar position offset calibration system based on a calibration board, including a retractable calibration board, a camera-radar sensor feedback module, a controller module, and a calibration algorithm module. The camera-radar sensor feedback module is mounted on the retractable calibration board, and the retractable calibration board can automatically adjust its position when the position of the camera-radar sensor feedback module shifts. The retractable calibration board, the camera-radar sensor feedback module, and the calibration algorithm module are all connected to the controller module. The controller module is responsible for receiving data from the camera-radar sensor feedback module in real time and processing it through the calibration algorithm module. By accurately calculating the relative position changes of the camera and radar, the control module drives the electric mechanism to adjust the position of the retractable calibration plate, ensuring that the relative position and attitude between the camera and radar are always kept in the optimal state.

[0014] Preferably, the telescopic calibration plate includes a fixed base, a rotating platform is provided above the fixed base, a camera-radar sensor is provided above the rotating platform, and a number of fixed ends of telescopic rods are connected around the rotating platform, with calibration plates provided on the movable ends of the telescopic rods.

[0015] Therefore, the automatic camera-radar position offset calibration method and system based on a calibration board, as described above, has the following advantages compared with the prior art: 1. This invention introduces a retractable calibration plate, which can automatically adjust the position of the calibration plate when the camera and radar shift, thereby eliminating the need for manual intervention. By utilizing the retractable calibration plate and a real-time sensor feedback system, combined with a dynamic judgment mechanism based on minimum reprojection error, the system achieves automated, real-time adjustment and intelligent calibration. By dynamically monitoring the position changes of the camera and radar, the calibration process is automatically initiated, effectively improving the calibration accuracy and real-time performance of the system under different working environments. It significantly reduces the errors caused by human intervention in traditional methods, and improves the overall integration and reliability of the system. This design enables the system to adapt to dynamic changes in sensor position and achieve automated calibration, making it particularly suitable for applications in dynamic environments, such as autonomous driving and robotic systems. 2. This invention has the function of automatically starting the calibration device. When the system detects that the calibration accuracy does not meet the requirements, it can automatically start the calibration device and optimize the pose relationship between the camera and the radar through intelligent adjustment algorithms. This function can maintain the calibration accuracy without human intervention. In addition, this invention can achieve high-precision and high-real-time automatic calibration in dynamic environments, and the calibration process does not rely on human intervention, reducing the impact of human factors on the calibration accuracy. This efficient automatic calibration method is particularly suitable for autonomous driving and robot application scenarios that require real-time updates of calibration information.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is an overall framework diagram of an automatic camera-radar position offset calibration method based on a calibration board according to the present invention; Figure 2 This is an overall structural diagram of an automatic camera-radar position offset calibration system based on a calibration board according to the present invention; Figure 3 This is a structural diagram of a scalable calibration plate for an automatic camera-radar position offset calibration system based on a calibration plate, according to the present invention.

[0018] Figure Labels 1. Fixed base; 2. Rotating platform; 3. Camera-radar sensor; 4. Telescopic rod; 5. Calibration plate. Detailed Implementation

[0019] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed when in use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0020] Example like Figure 1 As shown, the present invention provides an automatic camera-radar position offset calibration method based on a calibration board, comprising the following steps: S1. Place a calibration board, camera, and lidar with a topological structure on the carrier; The calibration board is set within the shared field of view of the camera and the lidar. The camera acquires a sequence of color images of the calibration board, while the lidar simultaneously acquires the three-dimensional point cloud data of the calibration board. S2, Image corner detection is performed using the camera in S1 and point cloud corner extraction is performed using radar; S21. Use the Shi-Tomasi corner detection algorithm to extract an initial set of corner points from the acquired camera images, and perform the sub-pixel refinement cornerSubPix algorithm on the detected corner points to improve pixel-level positioning accuracy, thus obtaining the set of corner points in the image coordinate system: ; in, The set of corner points of the image coordinate system includes The two-dimensional coordinates of each corner point in the image coordinate system It can be any positive integer; S22. Using the 3D Harris corner detection algorithm on the LiDAR point cloud, output the corner features at the intersection of the calibration board edge and the structure to obtain the corner set in the three-dimensional space of the LiDAR: in, The set of three-dimensional corner points in the lidar coordinate system includes The coordinates of a 3D corner point in the lidar coordinate system; S3. Using the topology of the calibration board in S1 and the results detected and extracted in S2, perform corner point correspondence matching to establish a 3D–2D point pair set. ,in For the first The two-dimensional coordinates of each corner point in the image coordinate system For the first The coordinates of each three-dimensional corner point in the lidar coordinate system The index number of the spatial feature points and ; S4. Using the point pair set obtained in S3, solve for the initial pose matrix of the camera pose within the RANSAC random sampling consensus framework using the Efficient Perspective-n-Point (EPnP) algorithm. ; S41. Solve for the pose matrix between the camera and the LiDAR to realize 3D points in the LiDAR coordinate system. To the camera coordinate system Conversion: ; in, Let them be rotation vectors and translation vectors. For 3D points in the lidar coordinate system, These are the points in the transformed camera coordinate system; S42, then through the camera intrinsic parameter matrix Projecting onto the pixel coordinate system yields ; ; in , These are the two-dimensional projected coordinates of a point in the pixel coordinate system. The horizontal axis coordinates of the pixel coordinate system These are the vertical axis coordinates in the pixel coordinate system. The focal length of the camera in the horizontal direction. The focal length of the camera in the vertical direction. This represents the horizontal offset of the camera's principal optical center in the pixel coordinate system. This represents the horizontal offset of the camera's principal optical center in the pixel coordinate system. S5. Calculate the reprojection error using the projection equation based on the initial pose matrix of S4. S51. Substitute the initial pose matrix into the projection equation, the specific formula is as follows: ; in, The scale factor is a non-zero scalar in homogeneous coordinate projection, corresponding to a spatial point. Depth to the camera's optical center; S52. Calculate the reprojection error based on the projection equation. Reprojection error The calculation formula is as follows: ; in, For the first A spatial feature point in 3D coordinates in a coordinate system The representative reference coordinate system; S6. Based on the reprojection error obtained in S5, optimize it using the LM (Levenberg-Marquardt algorithm) within the RANSAC framework and output the optimized pose matrix. ; S61, Initial pose matrix based on camera pose Starting with S4, the initial solution is obtained by selecting the set of interiors with the largest number of interiors or the smallest cost through multiple samplings using RANSAC. Nonlinear least-squares refinement of the pose matrix under Lie algebra parameterization; S62. Define the reprojection residual for each interior point. for ; in, It is a Lie algebra vector representing the pose increment. , Indicates by Pose update obtained through exponential mapping; S63, Counterprojection error The reprojection error is minimized by weighting the sum of the L2 norms: ; in, To suppress outliers, Let be the set of all interior points; S64. Linearize the residuals and solve for the increment using the LM algorithm. : ; in, The approximate Hessian matrix constructed for the LM algorithm, The gradient vector, The damping factor, It is a diagonal matrix; S65, Each iteration passes Update the pose on the manifold until the termination criterion is met, and finally output the optimized pose matrix. ,in, This indicates the increment of the Lie algebra. Transformed via exponential mapping The pose increment in the equation is used to update the current pose on the manifold space formed by rotation and translation. The termination criteria are set as follows: ,in The termination threshold set for the LM algorithm; During the iteration process, the rules for each pose update are as follows: ; in, For the first k The pose matrix of the next iteration, starting from the initial pose. Beginning, then N After the second iteration, we obtain: ; Among them, the number of iterations The calculation formula is as follows: ; in, For the expected confidence level, To estimate the out-of-point rate, The minimum number of samples; when the iteration converges, That is, the final pose matrix , The iterative solution process is the same as .

[0021] like Figures 2-3 As shown, the present invention also provides an automatic camera-radar position offset calibration system based on a calibration board. The system includes a retractable calibration board, a camera-radar sensor feedback module, a controller module, and a calibration algorithm module. The camera-radar sensor feedback module is installed on the retractable calibration board. The retractable calibration board can automatically adjust its position when the position of the camera-radar sensor feedback module shifts. The retractable calibration board, the camera-radar sensor feedback module, and the calibration algorithm module are all connected to the controller module. The controller module is responsible for receiving data from the camera-radar sensor feedback module in real time and processing it through the calibration algorithm module. By accurately calculating the relative position changes of the camera and radar, the control module drives the electric mechanism to adjust the position of the retractable calibration plate, ensuring that the relative position and attitude between the camera and radar are always kept in the optimal state.

[0022] Camera-radar sensor feedback module: The sensor feedback system is used to monitor the relative position of the camera and radar in real time. This system combines the camera and radar sensors and uses the minimum reprojection error between the camera and radar as the basis for whether recalibration is needed. The real-time data provided by the sensor feedback system will serve as the basis for the control system to adjust the position of the calibration board.

[0023] Control Module: The control system is responsible for receiving and processing sensor feedback data in real time. By accurately calculating the relative position changes of the camera and radar, the control system drives the electric mechanism to adjust the position of the calibration plate, ensuring that the external parameters (relative position and attitude) between the camera and radar are always kept in the optimal state. The control system also needs to optimize the real-time data to improve calibration accuracy.

[0024] Calibration algorithm module: The calibration algorithm module is used to calculate the extrinsic parameter matrix between the camera and the radar based on the real-time data of the sensor and the position adjustment information of the calibration board. This module adopts a specific mathematical model and improves the calibration accuracy through optimization algorithm. Through multiple feedback and iteration, the calibration accuracy is gradually improved, ensuring the stability of the system in complex environments.

[0025] The telescopic calibration plate includes a fixed base, a rotating platform is provided above the fixed base, a camera-radar sensor is provided above the rotating platform, and a number of fixed ends of telescopic rods are connected around the rotating platform. The movable ends of the telescopic rods are provided with calibration plates.

[0026] Scalable calibration plate: The calibration plate is the core component of this invention. It features an adjustable telescopic mechanism that automatically adjusts its position when the sensor (such as a camera or radar) shifts, ensuring calibration accuracy. The position change of the calibration plate is controlled by an electric drive system, which flexibly adjusts the relative position of the calibration plate according to the real-time position changes of the sensor. This design can automatically compensate for the offset between the camera and radar, eliminating the need for manual intervention.

[0027] In practical implementation, taking autonomous driving as an example, when the vehicle is stationary, the sensor feedback system acquires the initial pose data of the camera, radar, and lidar. The retractable calibration board is precisely adjusted by the control system to ensure that the relative position of the calibration board to the camera and radar is known. When the vehicle begins to move, the sensor feedback system continuously monitors the real-time pose changes of the camera, radar, and lidar. Due to factors such as vehicle movement, vibration, and temperature changes, the relative positions of the camera and radar may shift. The control system automatically adjusts the position of the calibration board by receiving feedback data in real time to compensate for the shift between the camera and radar, ensuring that the extrinsic parameter calibration is always accurate. During vehicle operation, the calibration algorithm module performs real-time optimization based on sensor data. Through incremental calibration and least-squares optimization, the system continuously adjusts the extrinsic parameter matrix to improve calibration accuracy. When the vehicle enters different road conditions or complex environments, the control system adjusts the position of the calibration board in real time to ensure that the calibration process maintains accuracy under any circumstances.

[0028] Therefore, the present invention adopts an automatic camera-radar position offset calibration method and system based on a calibration board, which utilizes a scalable calibration board and a real-time sensor feedback module, combined with a dynamic judgment mechanism based on minimum reprojection error, to realize the system's automation, real-time adjustment and intelligent calibration. By dynamically monitoring the position changes of the camera and radar, the calibration process is automatically started, effectively improving the calibration accuracy and real-time performance of the system under different working environments, significantly reducing the errors caused by human intervention in traditional methods, and improving the overall integration and reliability of the system.

[0029] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for automatic camera-radar position offset calibration based on a calibration board, characterized in that: Includes the following steps: S1. Place a calibration board, camera, and lidar with a topological structure on the carrier; S2, Image corner detection is performed using the camera in S1 and point cloud corner extraction is performed using radar; S3. Using the topology of the calibration board in S1 and the results detected and extracted in S2, perform corner point correspondence matching to establish a 3D–2D point pair set. ; S4. Using the EPnP algorithm on the set of point pairs obtained in S3, solve for the initial pose matrix of the camera pose within the RANSAC random sampling consensus framework. ; S5. Calculate the reprojection error using the projection equation based on the initial pose matrix of S4. S6. Based on the reprojection error obtained in S5, the LM algorithm is used to optimize the position matrix within the RANSAC framework, and the optimized pose matrix is ​​output. .

2. The automatic camera-radar position offset calibration method based on a calibration board according to claim 1, characterized in that: The S1 calibration board is positioned within the shared field of view of the camera and the LiDAR. The camera acquires a sequence of color images of the calibration board, while the LiDAR simultaneously acquires the 3D point cloud data of the calibration board.

3. The automatic camera-radar position offset calibration method based on a calibration board according to claim 2, characterized in that: The specific process of S2 is as follows: S21. Use the Shi-Tomasi corner detection algorithm to extract an initial set of corner points from the acquired camera images, and perform the sub-pixel refinement cornerSubPix algorithm on the detected corner points to improve pixel-level positioning accuracy, thus obtaining the set of corner points in the image coordinate system: ; in, The set of corner points of the image coordinate system includes The two-dimensional coordinates of each corner point in the image coordinate system It can be any positive integer; S22. Using the 3D Harris corner detection algorithm on the LiDAR point cloud, output the corner features at the intersection of the calibration board edge and the structure to obtain the corner set in the three-dimensional space of the LiDAR: in, The set of three-dimensional corner points in the lidar coordinate system includes The coordinates of a three-dimensional corner point in the lidar coordinate system.

4. The automatic camera-radar position offset calibration method based on a calibration board according to claim 3, characterized in that: The specific process of S4 is as follows: S41. Solve for the pose matrix between the camera and the LiDAR to realize 3D points in the LiDAR coordinate system. To the camera coordinate system Conversion: ; in, Let them be rotation vectors and translation vectors. For 3D points in the lidar coordinate system, These are the points in the transformed camera coordinate system; S42, then through the camera intrinsic parameter matrix Projecting onto the pixel coordinate system yields ; ; in , These are the two-dimensional projected coordinates of a point in the pixel coordinate system. The horizontal axis coordinates of the pixel coordinate system These are the vertical axis coordinates in the pixel coordinate system. The focal length of the camera in the horizontal direction. The focal length of the camera in the vertical direction. This represents the horizontal offset of the camera's principal optical center in the pixel coordinate system. This represents the horizontal offset of the camera's principal optical center in the pixel coordinate system.

5. The automatic camera-radar position offset calibration method based on a calibration board according to claim 4, characterized in that: The specific process of S5 is as follows: S51. Substitute the initial pose matrix into the projection equation, the specific formula is as follows: ; in, The scale factor is a non-zero scalar in homogeneous coordinate projection, corresponding to a spatial point. Depth to the camera's optical center; S52. Calculate the reprojection error based on the projection equation. Reprojection error The calculation formula is as follows: ; in, For the first A spatial feature point in 3D coordinates in a coordinate system This represents the reference coordinate system.

6. The automatic camera-radar position offset calibration method based on a calibration board according to claim 5, characterized in that: The specific process of S6 is as follows: S61, Initial pose matrix based on camera pose Starting with S4, the initial solution is obtained by selecting the set of interiors with the largest number of interiors or the smallest cost through multiple samplings using RANSAC. Nonlinear least-squares refinement of the pose matrix under Lie algebra parameterization; S62. Define the reprojection residual for each interior point. for ; in, It is a Lie algebra vector representing the pose increment. , Indicates by Pose update obtained through exponential mapping; S63, Counterprojection error The reprojection error is minimized by weighting the sum of the L2 norms: ; in, To suppress outliers, Let be the set of all interior points; S64. Linearize the residuals and solve for the increment using the LM algorithm. : ; in, The approximate Hessian matrix constructed for the LM algorithm, The gradient vector, The damping factor, It is a diagonal matrix; S65, Each iteration passes Update the pose on the manifold until the termination criterion is met, and finally output the optimized pose matrix. ,in, This represents the increment of the Lie algebra. Transformed via exponential mapping The pose increment in the equation is used to update the current pose on the manifold space formed by rotation and translation.

7. The automatic camera-radar position offset calibration method based on a calibration board according to claim 6, characterized in that: The termination criteria for S65 are set as follows: ,in The termination threshold set for the LM algorithm.

8. The automatic camera-radar position offset calibration method based on a calibration board according to claim 7, characterized in that: During the S6 iteration, the rules for each pose update are as follows: ; in, For the first k The pose matrix of the next iteration, starting from the initial pose. Beginning, then N After the second iteration, we obtain: ; Among them, the number of iterations The calculation formula is as follows: ; in, For the expected confidence level, To estimate the out-of-point rate, The minimum number of samples; when the iteration converges, That is, the final pose matrix , The iterative solution process is the same as .

9. An automatic camera-radar position offset calibration system based on a calibration board, characterized in that: An automatic camera-radar position offset calibration method based on a calibration board, as described in any one of claims 1-8, is provided. The system includes a retractable calibration board, a camera-radar sensor feedback module, a controller module, and a calibration algorithm module. The camera-radar sensor feedback module is mounted on the retractable calibration board. The retractable calibration board can automatically adjust its position when the position of the camera-radar sensor feedback module shifts. The retractable calibration board, the camera-radar sensor feedback module, and the calibration algorithm module are all connected to the controller module. The controller module is responsible for receiving data from the camera-radar sensor feedback module in real time and processing it through the calibration algorithm module. By accurately calculating the relative position changes of the camera and radar, the control module drives the electric mechanism to adjust the position of the retractable calibration plate, ensuring that the relative position and attitude between the camera and radar are always kept in the optimal state.

10. An automatic camera-radar position offset calibration system based on a calibration board according to claim 9, characterized in that: The telescopic calibration plate includes a fixed base, a rotating platform is provided above the fixed base, a camera-radar sensor is provided above the rotating platform, and a number of fixed ends of telescopic rods are connected around the rotating platform. The movable ends of the telescopic rods are provided with calibration plates.