A distributed two-stage roadside multi-millimeter wave radar cooperative calibration method

Abstract

The application belongs to the field of highway roadside sensor calibration, and provides a distributed two-stage roadside multi-millimeter wave radar cooperative calibration method, which comprises engineering coordinate system construction, radar equipment installation, radar calibration equation construction, road estimation curve fitting, rotation parameter optimization, matching track data determination, X-direction motion equation and Y-direction motion equation fitting, stretching parameter optimization, radar calibration equation updating and periodic online cooperative calibration. The application improves the calibration accuracy of the radar by constructing the radar calibration equation and optimizing the rotation parameter and the stretching parameter, has strong adaptability and flexibility, can be integrated into the existing intelligent transportation system, is compatible with different radar models and configurations, and does not need to make large-scale modification to the existing infrastructure.

Description

Technical Field

[0001] This invention relates to the field of roadside sensor calibration for highways, and in particular to a distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method. Background Technology

[0002] Installing continuous millimeter-wave radar along highways to extract vehicle trajectory data is a key technology for providing a digital twin foundation in smart highways. Millimeter-wave radar calibration, which involves converting the collected raw data to the required coordinate system, is a necessary prerequisite for using radar data. Large-scale radar clusters involve the calibration of multiple millimeter-wave radars. The calibration results not only need to be reasonable for each individual radar but also need to maximize the coordination between the calibration results of different radars.

[0003] Existing calibration solutions for millimeter-wave radar on highways mainly fall into two categories: static target-based calibration, which requires fixed reflectors and is dangerous and inefficient in highway environments; and dynamic calibration, which involves aligning high-precision trajectory data from other data sources with the trajectory data synchronously acquired by the millimeter-wave radar. While this dynamic calibration method significantly improves safety compared to traditional static calibration methods and is not dependent on closed roads, it is currently mainly used for single-radar calibration. Applying it to multiple radar systems may require substantial organizational costs. In multi-radar collaborative operation, even slight radar rotation can cause significant fluctuations in trajectory data. In highway environments, sensors inevitably experience positional fluctuations due to vibration, wind, or aging equipment, making repeated calibration procedures cumbersome. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method, which solves the problems of insufficient utilization of highway alignment and vehicle motion consistency information between radars, and low degree of automation in existing technologies.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method includes:

[0007] Based on the pre-collected horizontal curve data of the target road segment, an engineering coordinate system and a discretized representation of the road alignment are constructed, and the radar equipment is aligned to the target installation position using RTK measurement equipment;

[0008] Construct radar calibration equations;

[0009] The radar equipment is used to collect the first trajectory data of vehicles on the target road segment, and RANSAC robust regression is used to fit the first trajectory data to obtain the road estimation curve.

[0010] The road estimation curve is transformed into an engineering estimation curve using the rotation parameters of the radar calibration equation. The Nelder-Mead optimization algorithm is then used to determine the rotation parameters of the radar calibration equation when the variance of the engineering estimation curve and the discretized representation of the road alignment is minimized, thus obtaining the optimized rotation parameters.

[0011] Within the overlapping area of ​​adjacent radar devices, two sets of second trajectory data of the same vehicle are identified and matched, and the two sets of second trajectory data are matched using a distance sorting method to obtain matched trajectory data;

[0012] The motion features of the second trajectory data in the X and Y directions are extracted, and the motion features are fitted with a time-based cubic polynomial function using the least squares method to obtain the motion equations in the X and Y directions.

[0013] Calculate the difference between the observed values ​​of the X-axis motion equation and the Y-axis motion equation and the fitted values ​​of the matched trajectory data at the same time to obtain the X-axis residual and the Y-axis residual. Input the X-axis residual and the Y-axis residual into the optimization target, and use the Nelder-Mead optimization algorithm to determine the stretching parameter of the radar calibration equation when the output result of the optimization target is minimized, so as to obtain the optimized stretching parameter.

[0014] The optimized rotation parameters and optimized stretching parameters are updated to the radar calibration equation, and the updated radar calibration equation is used to calibrate the vehicles in the target road segment.

[0015] The radar calibration equation is periodically calibrated online by returning to the step "using the radar equipment to collect the first trajectory data of vehicles on the target road segment, and using RANSAC robust regression to fit the first trajectory data to obtain the road estimation curve" at fixed time intervals.

[0016] Preferably, the horizontal curve data includes: straight line parameters, curve parameters, and turning angle parameters.

[0017] Preferably, the radar calibration equation is: B = AH;

[0018] in, B is the transformed coordinate point; A is the original coordinate point acquired by the radar equipment; H is the transformation matrix; θ is the rotation parameter; α is the stretching parameter; c1 and c2 are the coordinates of the radar equipment in the X and Y directions in the engineering coordinate system, respectively.

[0019] Preferably, the expression for the optimization objective is:

[0020]

[0021] Where γ and β are the error weights in the X and Y directions, respectively; e x e y These are the X-axis residual and the Y-axis residual, respectively; n is the number of data points; i is e x and e y The corresponding point number.

[0022] Preferably, the distance between adjacent station numbers in the engineering coordinate system is less than or equal to 2m.

[0023] Preferably, the first trajectory data includes: a time field, a horizontal coordinate field, a vertical coordinate field, and a velocity field.

[0024] Preferably, the road estimation curve, the X-axis motion equation, and the Y-axis motion equation are all cubic equations in three variables.

[0025] Preferably, the fixed time is 30 minutes.

[0026] Preferably, the installation spacing between adjacent radar devices is 350m; the length of the overlapping area is 100m.

[0027] Preferably, the error between the actual installation position of the radar device and the target installation position is less than 1 cm.

[0028] The present invention discloses the following technical effects:

[0029] This invention provides a distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method. By constructing radar calibration equations and optimizing rotation and stretching parameters, it solves the problems of insufficient utilization of highway alignment and vehicle motion consistency information between radars and low degree of automation in existing technologies, and realizes adaptive calibration that quickly determines the monitored road conditions and trajectory data. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 A schematic diagram of the distributed two-stage roadside multi-millimeter-wave radar collaborative calibration process provided in an embodiment of the present invention;

[0032] Figure 2 This is an illustration of a distributed millimeter-wave radar deployment scenario and overlapping area provided in an embodiment of the present invention;

[0033] Figure 3 A simplified technical diagram provided for an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the calibration process provided in an embodiment of the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] The purpose of this invention is to provide a distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method to solve the problems of insufficient utilization of highway alignment and vehicle motion consistency information between radars and low degree of automation in the existing technology.

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] Figure 1 This is a schematic diagram of the distributed two-stage roadside multi-millimeter-wave radar collaborative calibration process provided in an embodiment of the present invention, as shown below. Figure 1 As shown, this invention provides a distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method, including:

[0039] Step 100: Construct an engineering coordinate system and a discretized representation of the road alignment based on the pre-collected horizontal curve data of the target road segment, and use RTK measurement equipment to align the radar equipment to the target installation position;

[0040] Step 200: Construct the radar calibration equations;

[0041] Step 300: Use radar equipment to collect the first trajectory data of vehicles on the target road segment, and use RANSAC robust regression to fit the first trajectory data to obtain the road estimation curve;

[0042] Step 400: Transform the road estimation curve into an engineering estimation curve using the rotation parameters of the radar calibration equation, and use the Nelder-Mead optimization algorithm to determine the rotation parameters of the radar calibration equation when the variance of the engineering estimation curve and the discretized representation of the road alignment is minimized, thus obtaining the optimized rotation parameters.

[0043] Step 500: In the overlapping area of ​​adjacent radar devices, identify and match two sets of second trajectory data of the same vehicle, and use the distance sorting method to match the two sets of second trajectory data to obtain the matched trajectory data;

[0044] Step 600: Extract the motion features of the second trajectory data in the X and Y directions, and use the least squares method to fit the motion features with a time-based cubic polynomial function to obtain the motion equations in the X and Y directions.

[0045] Step 700: Calculate the difference between the observed values ​​of the X-axis motion equation and the Y-axis motion equation and the fitted values ​​of the matched trajectory data at the same time to obtain the X-axis residual and the Y-axis residual. Input the X-axis residual and the Y-axis residual into the optimization target, and use the nelder-mead optimization algorithm to determine the stretching parameters of the radar calibration equation when the output result of the optimization target is minimized, and obtain the optimized stretching parameters.

[0046] Step 800: Update the optimized rotation parameters and optimized stretching parameters to the radar calibration equation, and use the updated radar calibration equation to calibrate the vehicles on the target road segment;

[0047] Step 900: Return to step "Use radar equipment to collect the first trajectory data of vehicles on the target road segment, and use RANSAC robust regression to fit the first trajectory data to obtain the road estimation curve" at fixed time intervals to perform periodic online collaborative calibration of the radar calibration equation.

[0048] Specifically, horizontal curve data includes: straight line parameters, curve parameters, and turning angle parameters.

[0049] Furthermore, the radar calibration equation is: B = AH;

[0050] in, B is the transformed coordinate point; A is the original coordinate point acquired by the radar equipment; H is the transformation matrix; θ is the rotation parameter; α is the stretching parameter; c1 and c2 are the coordinates of the radar equipment in the X and Y directions in the engineering coordinate system, respectively.

[0051] Specifically, the expression for the optimization objective is:

[0052]

[0053] Where γ and β are the error weights in the X and Y directions, respectively; ex e y These are the X-axis residuals and Y-axis residuals, respectively; n is the number of data points; i is e^(-π / 2). x and e y The corresponding point number.

[0054] Preferably, the distance between adjacent station numbers in the engineering coordinate system is less than or equal to 2m.

[0055] Specifically, the first trajectory data includes: a time field, a horizontal axis field, a vertical axis field, and a velocity field.

[0056] Preferably, the road estimation curve, the X-axis motion equation, and the Y-axis motion equation are all cubic equations in three variables.

[0057] Optionally, the fixed time is 30 minutes.

[0058] Specifically, the installation spacing between adjacent radar devices is 350m; the length of the overlapping area is 100m.

[0059] Preferably, the error between the actual installation position of the radar equipment and the target installation position is less than 1 cm.

[0060] Furthermore, a relatively simple distance sorting method was used when matching the second trajectory data. When two vehicles were detected to be less than 5m apart for five consecutive times, they were considered to be successfully matched.

[0061] Specifically, using the horizontal curve data of highways, including parameters such as straight lines, curves, and turning angles, the station-by-station coordinates of the road centerline can be calculated, yielding a discrete representation of the road. The corresponding station coordinate system points are {(k1,b1),(k2,b2),…,(k m ,b m The spacing between each station number is generally no more than 2m, and the corresponding engineering coordinates G are given. road :{(x g1 ,y g1 ),(x g2 ,y g2 )…(x gm ,y gm This coordinate system represents the road alignment reference line within the radar's detection area. Where m is the number of discrete road points; k... m b m These represent the station number and the transverse position of the road section, respectively; x gm y gm This represents the horizontal and vertical positions of the corresponding points in the engineering coordinate system.

[0062] Furthermore, the initial calibration equation involves placing an RTK device below the installed radar equipment and collecting the latitude and longitude coordinates of the corresponding radar equipment. At this point, a series of latitude and longitude coordinate system positions of the radar installations can be recorded as {(lat r1 ,long r1 ),(lat r2 ,long r2 )…(lat rd ,long rd )}, convert the coordinates to the corresponding radar position in the engineering coordinate system {(x r1 ,y r1 ),(x r2 ,y r2 )…(x rd ,y rd The corresponding station coordinate system can be read from the drawings or on-site as {(k)}. r1 ,b r1 ),(k r1 ,b r1 )…(k rd ,b rd )}. Among them, lat rd 、long rd These represent the longitude and latitude positions of the radar in the latitude and longitude coordinate system, respectively; x rd y rd k represents the horizontal and vertical positions of the corresponding points in the engineering coordinate system. rd b rd The station number and the lateral position of the corresponding point in the station coordinate system are given. r indicates the radar and d represents the radar number.

[0063] Specifically, radar calibration involves coordinate system transformation. The original coordinate point recorded in the radar is A, which is [X...]. A ,Y A [,1], where X A Y A These represent all the initial positions of the radar's first trajectory data in the engineering coordinate system, with 1 representing the offset. To facilitate the calculation of displacements in the calibration relationship, the required coordinate points after transformation are recorded as B as [X]. B ,Y B ], X B Y B These represent the positions of the radar's first trajectory data after calibration in the engineering coordinate system. The calibration process for millimeter-wave radar involves solving a transformation matrix H such that B = AH. To express the calibration equation, the radar calibration process is defined as a change in two dimensions: rotation and stretching. The core parameters are transformed into estimating two parameters, θ and α. The transformation matrix can be represented as follows:

[0064]

[0065] Furthermore, the radar collects and accumulates raw trajectory data over a period of time. This data includes the vehicle's trajectory data in the radar coordinate system, denoted as Tra. rd The content includes {T rd ,X rd ,Y rd V rd …} represent the time T when the vehicle was detected. rd Horizontal and vertical position and velocity data X rd ,Y rd V rd Where 'r' identifies the radar data and 'd' represents the radar number. All data acquired by the radar is in its own coordinate system; the radar's coordinate system is then transformed to its corresponding position in the engineering coordinate system.

[0066] Preferably, the trajectory data is fitted with the corresponding cubic curve y = ax using RANSAC. 3 +bx 2 The four parameters in +cx+d are a, b, c, and d. RANSAC can effectively reduce the influence of outliers in the initial data on the results. This fitting process can be expressed as... in Let represent the above fitting process, where i represents the trajectory dataset of the i-th radar, and θ is the parameter to be optimized. The fitted curve is represented by the estimated road geometry curve feature points G. est :{(x e1 ,y e1 ),(x e2 ,y e2 )…(x em ,y em )} where x em ,y em The corresponding feature points of the fitted road set correspond to the road feature points obtained by discretization in the previous step.

[0067] Furthermore, the fitted curve G est This can represent the movement trend of vehicles along the road alignment, and it should also be consistent with the alignment of the highway, that is, the curve and the station-by-station coordinates G obtained from S1. road We should maintain consistency.

[0068] Furthermore, the optimization equation for the first stage is expressed as minVar(G est -G road ), and θ' is obtained by optimization. Var represents the variance of the two.

[0069] Specifically, within the overlapping area of ​​two radars, trajectory data of the same vehicle detected by different radars are identified and matched; the matched trajectory data is called Tra. match Including vehicle location X match Y match and speed V match Time T match Extract the vehicle's motion features in the X and Y directions, and fit the vehicle's trajectory in the X and Y directions using a cubic polynomial function of time t: P y =a3t 3 +a2t 2 +a1t+a0 and P x =b3t 3 +b2t 2 +b1t+b0, where a i and b i (i = 0, 1, 2, 3) are the coefficients of the polynomial, which are determined using the least squares method.

[0070] Furthermore, the residuals in the fitting process are calculated, which are the differences between the observed values ​​and the fitted values: e x =P x -x match e y =P y -y match , where x match y match These represent the vehicle positions in the X and Y directions, respectively, within the matched trajectory data. An optimization objective is established to minimize the sum of squared residuals to ensure that the motion state of the same vehicle detected by both radars remains consistent within the overlapping region:

[0071]

[0072] By optimizing the above objective function, the longitudinal scaling parameter α of the radar is determined, which further compensates for errors caused by manufacturing tolerances or installation errors, making the motion patterns of adjacent radar vehicles consistent and enhancing the radar's collaborative working capability.

[0073] Preferably, for all radars, taking pairs of opposing radars as the research objects, the optimization parameters are solved every 30 minutes. The above steps are repeated to complete the calibration of all radars. The calibration of all radars is completed periodically.

[0074] Furthermore, the following explanation will be provided in conjunction with the specific accompanying drawings:

[0075] refer to Figure 2In this embodiment, multiple distributed radars are used. The deployment and overlapping sensing ranges of the radars are shown in the figure. A pair of radars are selected with an installation distance of approximately 350m between them, and the overlap area is approximately 100m long. The implementation scenario is a typical section of a highway.

[0076] S1: In this embodiment, the precise installation location of the radar must first be determined so that the data detected by the radar can be accurately matched with the actual road geometry during the subsequent calibration process. For this purpose, this embodiment uses horizontal curve data from highways. This data includes parameters such as straight lines, curves, and turning angles, which are key information describing the coordinates of the road centerline at each stake. Specific data generally comes from design drawings. The result of the discretization of the road alignment at this point is G. road :{(x g1 ,y g1 ),(x g2 ,y g2 )…(x gm ,y gm In this embodiment, discrete points are set at intervals of 2m.

[0077] Specifically, after the radar is installed, RTK measuring equipment is used to align the radar installation position and collect its latitude and longitude coordinates. This ensures that the deviation between the radar installation position and the designed position is within the centimeter level, and the latitude and longitude coordinates are converted into engineering coordinates. In this embodiment, the station coordinate system and engineering coordinate system results of the radar installation point are shown in Table 1. This initialization method determines the relative positional relationship between the radar and the road, ensuring a benchmark for subsequent radar calibration procedures.

[0078] Table 1

[0079]

[0080]

[0081] S2: In this embodiment, the original coordinate point recorded by the radar is A. In the original radar coordinate system, the radar is generally used as the origin. The coordinate point after calibration transformation is B, and all radar coordinate systems are unified into the engineering coordinate system. Each radar needs to be calibrated using the following transformation matrix, which contains unknowns α, θ, c1, and c2.

[0082]

[0083] Specifically, taking radar points 1 and 2 as examples, c1 and c2 are taken as 148765.3 and 228130 respectively; 149220.3 and 229811.3 respectively; the physical meaning is to move the radar position from its original position to the corresponding c1 and c2 positions. At this time, the unknowns only include α and θ, which serve as the solution objectives for the subsequent optimization.

[0084] S3: The first stage of optimization minimizes the difference between the vehicle trajectory detected by the radar and the actual road geometry by optimizing the radar's rotation parameters. This process is as follows: Figure 3 As shown, the pre-collected trajectory data is processed to remove outliers, including filtering to remove points that significantly deviate from the normal trajectory, thus improving fitting accuracy. RANSAC robust regression is then applied to the trajectory data to obtain the estimated road curve G. est This represents the curve shape of the road where the radar is located. The curve equation fitted to radar points 1 and 2 is similar to y. A = This type of form, where x A ,y A All of these represent the original coordinate system of the radar.

[0085] Furthermore, this fitting process can be expressed as: in Let represent the above fitting process, where i represents the trajectory dataset of the i-th radar, and θ is the parameter to be optimized. The fitted curve is represented by the estimated road geometry curve feature points G. est :{(x e1 ,y e1 ),(x e2 ,y e2 )…(x em ,y em )} where x em ,y em The corresponding feature points of the fitted road set correspond to the road feature points discretized in the previous step. To make the estimated results as similar to the actual results as possible, we solve for minVar(G). est -G road Specifically, aligning x and subtracting the corresponding y is performed.

[0086] Furthermore, in this embodiment, the Nelder-Mead optimization algorithm is used to solve the problem. The optimized parameters θ1 and θ2 for radar points 1 and 2 are obtained as 0.4958 and 3.5468, respectively. The optimization results are as follows: Figure 4 As shown, the initial alignment of the radar and road coordinate systems is achieved as a result of the first optimization step. However, due to factors such as the radar's elevation angle, there are still some misalignments in the longitudinal direction of the road. Therefore, further calibration is required.

[0087] S4: The second stage of optimization optimizes the longitudinal scaling parameter α of the radar to ensure that the motion state of the same vehicle detected by the two radars remains consistent within the overlapping area. The purpose of step S4 is to identify and match the trajectory data of the same vehicle detected by the two radars within the overlapping area. This process is as follows: Figure 3 As shown, the overlap area between radars is a key prerequisite for kinematic consistency optimization. Since millimeter-wave radar cannot perceive the vehicle's geometric information, especially at the far end of its detection range, the vehicle's reflection centroid cannot reflect its geometric centroid to some extent. Therefore, this embodiment pays special attention to longitudinal distance matching in this step, while also considering the lateral distance of vehicles within the same lane. Only trajectory data that can be detected by both radars and are successfully matched are retained, while incomplete or excessively erroneous trajectory pairs are discarded. In this embodiment, 100 successfully paired trajectory pairs are retained.

[0088] The matched trajectory data is divided into horizontal and vertical axes, and the position and time are fitted separately. The following objective function is optimized. To minimize the deviation in the lateral fitting of the road, β = 2 and γ = 1 are set in this example. The corresponding optimization equation is as follows:

[0089] Furthermore, using the same Nelder-mead algorithm, the scaling parameters α1 and α2 for radar points 1 and 2 are obtained as 1.02 and 1.03, respectively. The optimization results are shown below. Figure 4 As shown, the vehicle maintains better kinematic consistency within the same overlapping area.

[0090] S5: In this embodiment, periodic online calibration of all radars ensures the long-term stability of the entire radar network and the accuracy of the data. Before calibration, the normal operation of all radar hardware and the accuracy of the initial calibration parameters are first ensured. The calibration cycle between each pair of radars is set to 30 minutes. This periodic calibration ensures that the system can adapt to changes in road conditions, such as fluctuations in traffic flow and weather changes, thereby maintaining the real-time updating and accuracy of the calibration parameters.

[0091] The beneficial effects of this invention are as follows:

[0092] (1) This invention innovatively combines two stages: road geometric similarity optimization and motion consistency optimization, to improve the calibration accuracy of radar pairs. In the first stage, the radar rotation parameters are optimized by utilizing road geometric features and vehicle trajectory data detected by the radar, ensuring that the radars are roughly aligned. In the second stage, the longitudinal scaling parameters of the radars are further optimized by analyzing the motion consistency between different radars, ensuring a high degree of consistency in the vehicle motion data detected within the radar overlap area. This two-stage method fully utilizes different prior knowledge and, combined with the transformation matrix, improves the efficiency of calibration.

[0093] (2) The calibration method of this invention has strong adaptability and flexibility. It can be easily integrated into existing intelligent transportation systems, requiring only consideration of trajectory data and existing road infrastructure conditions. It is compatible with different radar models and configurations without requiring large-scale modifications to existing infrastructure. This flexibility allows the method of this invention to be quickly deployed in different road and traffic environments, and has broad application prospects. In summary, the distributed two-stage calibration method of this invention demonstrates advantages in calibration efficiency, adaptability to different traffic environments, cost-effectiveness, and system stability, providing a new adaptive calibration solution for roadside millimeter-wave radar in intelligent transportation systems.

[0094] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0095] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method, characterized in that, include: Based on the pre-collected horizontal curve data of the target road segment, an engineering coordinate system and a discretized representation of the road alignment are constructed, and the radar equipment is aligned to the target installation position using RTK measurement equipment; Construct radar calibration equations; The radar equipment is used to collect the first trajectory data of vehicles on the target road segment, and RANSAC robust regression is used to fit the first trajectory data to obtain the road estimation curve. The road estimation curve is transformed into an engineering estimation curve using the rotation parameters of the radar calibration equation. The Nelder-Mead optimization algorithm is then used to determine the rotation parameters of the radar calibration equation when the variance of the engineering estimation curve and the discretized representation of the road alignment is minimized, thus obtaining the optimized rotation parameters. Within the overlapping area of ​​adjacent radar devices, two sets of second trajectory data of the same vehicle are identified and matched, and the two sets of second trajectory data are matched using a distance sorting method to obtain matched trajectory data; The motion features of the second trajectory data in the X and Y directions are extracted, and the motion features are fitted with a time-based cubic polynomial function using the least squares method to obtain the motion equations in the X and Y directions. Calculate the difference between the observed values ​​of the X-axis motion equation and the Y-axis motion equation and the fitted values ​​of the matched trajectory data at the same time to obtain the X-axis residual and the Y-axis residual. Input the X-axis residual and the Y-axis residual into the optimization target, and use the Nelder-Mead optimization algorithm to determine the stretching parameter of the radar calibration equation when the output result of the optimization target is minimized, so as to obtain the optimized stretching parameter. The optimized rotation parameters and optimized stretching parameters are updated to the radar calibration equation, and the updated radar calibration equation is used to calibrate the vehicles in the target road segment. The radar calibration equation is periodically calibrated online by returning to the step "using the radar equipment to collect the first trajectory data of vehicles on the target road segment, and using RANSAC robust regression to fit the first trajectory data to obtain the road estimation curve" at fixed time intervals.

2. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The horizontal curve data includes: straight line parameters, curve parameters, and turning angle parameters.

3. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The radar calibration equation is: B = AH; in, B is the transformed coordinate point; A is the original coordinate point acquired by the radar equipment; H is the transformation matrix; θ is the rotation parameter; α is the stretching parameter; c1 and c2 are the coordinates of the radar equipment in the X and Y directions in the engineering coordinate system, respectively.

4. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The expression for the optimization objective is: Where γ and β are the error weights in the X and Y directions, respectively; e x e y These are the X-axis residual and the Y-axis residual, respectively; n is the number of data points; i is e x and e y The corresponding point number.

5. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The distance between adjacent station numbers in the engineering coordinate system is less than or equal to 2m.

6. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The first trajectory data includes: a time field, a horizontal axis field, a vertical axis field, and a velocity field.

7. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The road estimation curve, the X-axis motion equation, and the Y-axis motion equation are all cubic equations in three variables.

8. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The fixed time is 30 minutes.

9. The distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The installation spacing between adjacent radar devices is 350m; the length of the overlapping area is 100m.

10. A distributed two-stage roadside multi-millimeter-wave radar collaborative calibration method according to claim 1, characterized in that, The actual installation position of the radar equipment is less than 1 cm away from the installation position of the target.

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