4D radar odometry method for high dynamic scenarios

Abstract

This invention provides a 4D radar odometry method for high-dynamic scenarios, relating to the field of autonomous driving perception and sensor fusion technology. The method includes: acquiring raw point cloud data using a 4D millimeter-wave radar-based perception system; extracting corresponding clustering parameters from the raw point cloud data, wherein the clustering parameters include search radii in different directions and minimum neighborhood density; clustering the raw point cloud data using the DBSCAN clustering method based on the clustering parameters to obtain different point cloud clusters; extracting static points from the different point cloud clusters; and calculating the vehicle speed based on the static points using an angle-distance weighted least squares method. This technical solution effectively improves the accuracy of vehicle speed measurement.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving perception and sensor fusion technology, and more specifically, to a 4D radar odometry method for high dynamic scenarios. Background Technology

[0002] Accurate measurement of vehicle speed by odometers is a crucial link in ensuring the safety and reliability of autonomous driving technology. Traditional radar odometers primarily obtain raw point cloud data from sensors such as LiDAR and cameras. They utilize methods like Random Sample Consensus (RANSAC) or fixed-radius DBSCAN clustering to perform tasks such as object unit segmentation and dynamic / static point segmentation. Finally, based on static background points, the vehicle speed is calculated using the least squares method, serving as input for subsequent processes such as loop closure detection and mapping. However, traditional radar odometers have revealed several problems that urgently need to be addressed: 1. Current mainstream perception systems heavily rely on LiDAR and visual sensors. LiDAR performance deteriorates sharply in adverse weather conditions such as rain, snow, fog, and dust; visual sensors are greatly affected by lighting conditions (such as glare and darkness). In extreme weather or complex scenarios, the accuracy of the raw point cloud acquired by the odometer decreases, leading to increased errors in the calculated vehicle speed and negatively impacting the stability of the autonomous driving system. 2. The RANSAC method fails in highly dynamic scenarios, exhibiting significant errors and being ill-suited for handling complex road scenarios involving a mixture of multiple velocity models. The traditional DBSCAN method, limited by a fixed search radius, is prone to issues such as multiple segmentations of the same object, difficulty in clustering distant objects, and misclassification of noise points. 3. When calculating vehicle speed, the ordinary least squares method is sensitive to outliers and susceptible to noise interference, resulting in unstable estimation results and poor robustness and low accuracy of the speed estimates.

[0003] Odometers are located at the front end of a SLAM system, and high-quality speed calculation results are crucial for the system's back end and the entire SLAM system. Therefore, developing an odometer method that is adaptable to all scenarios, has strong processing capabilities for raw point cloud data, and provides high accuracy in calculating vehicle speed has become an urgent problem to solve, addressing the aforementioned technical challenges. Summary of the Invention

[0004] In view of this, the present invention proposes a 4D radar odometry method for high dynamic scenarios to solve the problems existing in the prior art.

[0005] To achieve the above objectives, this invention proposes a 4D radar odometry method for high-dynamic scenarios, comprising: A perception system based on 4D millimeter-wave radar is used to acquire raw point cloud data; Clustering parameters are extracted from the original point cloud data, including search radii in different directions and minimum neighborhood density. Based on the clustering parameters, the original point cloud data is clustered using the DBSCAN clustering method to obtain different point cloud clusters. Static points are extracted from different point cloud clusters; The vehicle speed is calculated from the static point using the least squares method with angle-distance weighting.

[0006] Optionally, the perception system based on 4D millimeter-wave radar includes 4D millimeter-wave radar, depth camera, and lidar; multimodal point cloud data is acquired through 4D millimeter-wave radar, depth camera, and lidar, and the multimodal point cloud data is fused to generate raw point cloud data.

[0007] Optionally, the process of extracting the search radius includes: Based on different raw point cloud data, an adaptive search radius function is used to extract search radii in different directions. The adaptive search radius function includes:

[0008] in, It is the radial search radius. It is the search radius in the azimuth direction. It is the search radius in the direction of elevation. It is the radial distance from the target point to the radar; It is the direction of elevation; It is radial resolution. It is the azimuth resolution. It is the resolution at the elevation angle; , , It is the radial adjustment coefficient. , , It is the azimuth direction adjustment coefficient. , , It is the elevation angle adjustment coefficient.

[0009] Optionally, the extraction process of the minimum neighborhood density includes: Based on the anisotropic neighborhood corresponding to the search radius in different directions, the corresponding minimum neighborhood density is calculated using the minimum neighborhood density function, where the minimum neighborhood density function is:

[0010] in, MinPts; Anisotropic neighborhoods representing search radii in different directions. This indicates the number of points within that neighborhood; It is a percentage factor.

[0011] Optionally, the process of extracting the static points includes: Based on the point cloud clusters, calculate the assumed velocity, group the point cloud clusters according to the assumed velocity, generate point cloud groups, and select the point cloud in the outermost and most widely distributed point cloud group as static points.

[0012] Optionally, the vehicle speed can be calculated from the static point using the angle-distance weighted least squares method.

[0013] The angle weights and distance weights in different directions are calculated based on the static point. The angle weights and distance weights in different directions are then combined to generate corresponding combined weights. The vehicle speed in different directions is calculated based on the static point using the least squares method according to the combined weights.

[0014] Optionally, the calculation process for the angle weights includes:

[0015]

[0016]

[0017] in, It is the direction angle. It's the angle of elevation; This is the point used to calculate the forward speed of the vehicle. Angle weights; This is the point used to calculate the lateral velocity of the vehicle. Angle weights; This is the point used to calculate the vertical velocity of the vehicle. Angle weights.

[0018] Optionally, the calculation process of the distance weight includes:

[0019] Where R is the distance from the target point to the radar.

[0020] Optionally, the process of generating the combined weights includes:

[0021]

[0022]

[0023] in, It is the combined weight used when calculating the forward speed of the vehicle; It is the combined weight used when calculating the lateral speed of the vehicle; It is the combined weight used when calculating the vertical velocity of the vehicle; It is a distance weight; It is the angle weight when calculating the forward speed of the vehicle; It is the angle weight when calculating the lateral velocity of the vehicle; It is the angle weight when calculating the forward speed of the vehicle; It is the fusion coefficient.

[0024] Optionally, the calculation process for the vehicle speed includes:

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] in, It is the location at the data point location. The unit line-of-sight vector of the radar echo; It is a block diagonal weight matrix; The vehicle speed is estimated using the weighted least squares method. This represents a single line-of-sight coefficient parameter. Representing the observed quantity, This represents the view weight matrix. Represents the observation matrix, Represents the weight matrix. This represents the radial velocity measured at the i-th radar echo point.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention improves the accuracy of vehicle speed measurement and establishes a continuous and stable motion perception foundation through a series of steps, including multimodal perception based on 4D millimeter-wave radar, adaptive DBSCAN algorithm clustering, static point extraction based on speed grouping and maximum distribution, and weighted least squares speed measurement. This effectively enhances the safety, reliability, and all-scenario adaptability of the autonomous driving system. Attached Figure Description

[0034] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 This is a flowchart of the odometer method based on 4D millimeter-wave radar in an embodiment of the present invention; Figure 2 This is a flowchart of the adaptive DBSCAN clustering method in an embodiment of the present invention; Figure 3 This is a flowchart of the static point determination method based on velocity grouping and maximum distribution in an embodiment of the present invention; Figure 4 This is a weight structure diagram of the weighted least squares method in the embodiments of the present invention. Detailed Implementation

[0035] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0036] This invention discloses an odometer method based on 4D millimeter-wave radar. The method includes: constructing a multi-sensor, multi-modal perception system using a camera, lidar, and 4D millimeter-wave radar; continuously adjusting the search radius using an adaptive DBSCAN clustering algorithm based on sensor data to transform the original disordered point cloud into structured object units with cluster labels; determining static background clusters using a static point judgment method based on speed grouping and maximum distribution; and calculating the vehicle speed using weighted least squares (LSQ) based on a point cloud map with clear distinction between static and dynamic points, assigning different weights to different static points according to distance, azimuth, and elevation angles. This invention improves the accuracy of vehicle speed measurement and establishes a continuous and stable motion perception foundation through a series of steps including multi-modal perception based on 4D millimeter-wave radar, adaptive DBSCAN clustering, static point extraction based on speed grouping and maximum distribution, and weighted least squares speed measurement. This effectively enhances the safety, reliability, and all-scenario adaptability of the autonomous driving system.

[0037] To achieve the above-mentioned technical objectives, this invention proposes an odometer method based on 4D millimeter-wave radar, comprising the following steps: Step 1: Construct a multimodal perception system that integrates 4D millimeter-wave radar, optical camera, and lidar, and collect raw point clouds; Step 2: Based on the original point cloud data, the adaptive DBSCAN algorithm is used to automatically adjust the search radius in the radial, azimuth, and elevation directions and form the minimum neighborhood density (MinPts) required for effective clustering. High-precision clustering is then performed to construct a clear point cloud map with cluster labels. Step 3: Based on the velocity grouping and maximum distribution detection method, accurately extract static points from the point cloud map for velocity measurement; Step 4: Based on the static background, calculate the vehicle speed using the angle-distance weighted least squares method.

[0038] Furthermore, step 1 specifically includes: A multi-dimensional perception system consisting of 4D millimeter-wave radar, camera, and lidar is constructed. This system includes various sensors, specifically 4D millimeter-wave radar, camera, and lidar. The all-scene adaptability of 4D millimeter-wave radar and the high precision of lidar complement each other. Through aligned point-level correlation fusion, a high-information-density original point cloud map is jointly constructed. Optical camera data is used for visual semantic assistance.

[0039] Furthermore, the adaptive DBSCAN method in step 2 specifically includes: The radial search radius, azimuth search radius, and elevation search radius are adjusted based on the radial distance and elevation angle from the target point to the radar. Then, the MinPts (Minimum Points) are determined based on the number of point clouds within the effective area of ​​the search radius. Finally, the original points are clustered to construct object units with cluster labels. Specifically: An adaptive search radius function is used to determine the radial, azimuth, and elevation search radii. The effective region is determined based on the search radius. The minimum number of points (MinPts) within the effective region is determined. Finally, the DBSCAN method is used for clustering based on the search radius and MinPts. For any data point in the point cloud... The formula for the adaptive search radius function is:

[0040] in, It is the radial search radius; This data point Radial distance to the radar; It is radial resolution; , , It is the radial adjustment coefficient.

[0041]

[0042] in, It is the search radius in the azimuth direction; It is the radial distance from the target point to the radar; It is the azimuth resolution; It is a point The direction of the elevation angle; , , It is the azimuth direction adjustment coefficient.

[0043]

[0044] in, It is the search radius in the direction of elevation. It is the radial distance from the target point to the radar; It is the resolution at the elevation angle; , , It is the elevation angle adjustment coefficient.

[0045] MinPts function:

[0046] in, MinPts; Indicates using , , Anisotropic neighborhood of a given point This indicates the number of points within that neighborhood; It is a percentage factor. .

[0047] Furthermore, step 3, the detection method based on velocity distribution and maximum distribution, specifically includes: Assuming all clusters are static, multiple hypothetical vehicle velocities are calculated backwards. These hypothetical velocities are then grouped based on their numerical similarity. Following the general rule that "static objects are usually located outside of dynamic objects," the velocity group occupying the outermost edge of the space is determined, thus identifying the static point. Specifically: First, assuming all clusters are static, according to radar kinematics principles, if an object is stationary in the physical world, its positional change between two consecutive point cloud frames is entirely caused by the radar's own motion. Multiple hypothetical vehicle velocities are calculated by reverse engineering, and these velocities are grouped based on their numerical similarity. Based on the prior rule that "in a vehicle driving scenario, static objects are usually distributed on both sides of the road, i.e., outside of dynamic objects," the velocity groups occupying the largest outer distribution on the point cloud map can be initially distinguished from static points by tracking and detecting them. It should be noted that this step aims to extract high-confidence static points from the point cloud for robust motion estimation in subsequent radar odometry. Point cloud clusters not marked as static points may belong to dynamic objects, edge points of static objects, noise points, or points with ambiguous velocity. For these points, appropriate subsequent processing strategies can be selected according to specific application requirements, rather than simply classifying them all as dynamic points.

[0048] Furthermore, step 4, the weighted least squares method for calculating the vehicle speed, specifically includes: When calculating forward, lateral, and vertical velocities, angle and distance weights are introduced, and a combined weighted average is used to calculate the vehicle's speed. Specifically: Using the static points identified in step 3, and based on the influence of the distance from the static points to the radar, the azimuth angle and elevation angle of the static points on the forward speed, lateral speed and vertical speed of the vehicle, an angle-distance combination weight is designed, and different points are assigned different combination weights to calculate the vehicle speed.

[0049] Furthermore, regarding the angle weights in the weighted least squares method in step 4, the formula for the angle weight function is:

[0050]

[0051]

[0052] in, It is the direction angle. It's the angle of elevation; This is the point used to calculate the forward speed of the vehicle. Angle weights; This is the point used to calculate the lateral velocity of the vehicle. Angle weights; This is the point used to calculate the vertical velocity of the vehicle. Angle weights.

[0053] Furthermore, regarding the distance weights in the weighted least squares method in step 4... The distance weighting function formula is:

[0054] Where R is the distance from the target point to the radar.

[0055] Furthermore, regarding the angle-distance combination weighting in step 4 using the weighted least squares method, the formula for the angle-distance combination weight function is:

[0056]

[0057]

[0058] in, It is the combined weight used when calculating the forward speed of the vehicle; It is the combined weight used when calculating the lateral speed of the vehicle; It is the combined weight used when calculating the vertical velocity of the vehicle; It is a distance weight; It is the angle weight when calculating the forward speed of the vehicle; It is the angle weight when calculating the lateral velocity of the vehicle; It is the angle weight when calculating the forward speed of the vehicle; It is the fusion coefficient. .

[0059] Furthermore, regarding the calculation of the vehicle speed using the weighted least squares method in step 4, the formula for calculating the vehicle speed is as follows:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] in, It is the location at the data point location. The unit line-of-sight vector of the radar echo, These represent the x, y, and z coordinates of data point i, respectively. It is a block diagonal weight matrix; The vehicle speed is estimated using the weighted least squares method. This represents a single line-of-sight coefficient parameter. Representing the observed quantity, This represents the view weight matrix. Represents the observation matrix, Represents the weight matrix. This represents the radial velocity measured at the i-th radar echo point.

[0068] The above technical solution is described in detail below: Figure 1 A general flowchart of the odometry method based on 4D millimeter-wave radar is shown. Figure 1 As shown, firstly, the 4D millimeter-wave radar, lidar, and camera output point cloud and image data respectively to describe environmental information. For each echo point in the point cloud, adaptive search radii in the radial, azimuth, and elevation directions are calculated based on its radial distance and angle, thus constructing an anisotropic neighborhood. Subsequently, using this neighborhood definition, the adaptive DBSCAN algorithm is used to cluster the point cloud. Based on the velocity grouping-maximum distribution static point differentiation method, the velocity patterns occupying the outermost spatial distribution are tracked and detected using multi-frame point cloud images to determine static background points. For each echo point, its angle-distance combination weight is determined according to radial distance, direction, and elevation angle, and then the vehicle speed is calculated using the weighted least squares method.

[0069] Figure 2 The flowchart of the adaptive DBSCAN algorithm is shown. Specifically, it includes: For an echo point in the radar Cartesian coordinate system Using a search radius related to three directions To define its anisotropic neighborhood .use This represents the number of points that satisfy the anisotropic neighborhood condition, thus determining MinPts for point cloud clustering. The specific formula is:

[0070] in, It is the radial search radius. It is the search radius in the azimuth direction. It is the search radius in the direction of elevation. It is the radial distance from the target point to the radar; It is the direction of elevation; It is radial resolution. It is the azimuth resolution. It is the resolution at the elevation angle; , , It is the radial adjustment coefficient. , , It is the azimuth direction adjustment coefficient. , , It is the elevation angle adjustment coefficient.

[0071]

[0072] in, MinPts; Indicates using , , Anisotropic neighborhood of a given point This indicates the number of points within that neighborhood; It is a percentage factor. .

[0073] Figure 3 A flowchart illustrating the method for determining static points based on velocity grouping and maximum distribution is presented. Specifically, it includes: For the clustered point cloud map, we first assume that each cluster is a static cluster, and calculate multiple hypothetical velocities. Then, we divide the point cloud clusters corresponding to hypothetical velocities with similar values ​​into a velocity group. Finally, we select the velocity group with the widest spatial distribution to determine the static cluster.

[0074] Figure 4 This diagram illustrates the structure of the combined weights used in the weighted least squares method. Specifically, it includes: For each static point, distance weights and angle weights are calculated based on its distance, orientation angle, and elevation angle. These weights are then combined into an angle-distance combined weight. Finally, the vehicle speed is calculated using the weighted least squares method. The specific formula is as follows:

[0075]

[0076]

[0077] in, It is the direction angle. It's the angle of elevation; This is the point used to calculate the forward speed of the vehicle. Angle weights; This is the point used to calculate the lateral velocity of the vehicle. Angle weights; This is the point used to calculate the vertical velocity of the vehicle. Angle weights.

[0078]

[0079] Where R is the distance from the target point to the radar;

[0080]

[0081]

[0082] in, It is the combined weight used when calculating the forward speed of the vehicle; It is the combined weight used when calculating the lateral speed of the vehicle; It is the combined weight used when calculating the vertical velocity of the vehicle; It is a distance weight; It is the angle weight when calculating the forward speed of the vehicle; It is the angle weight when calculating the lateral velocity of the vehicle; It is the angle weight when calculating the forward speed of the vehicle; It is the fusion coefficient. .

[0083] The above technical solution first uses the raw point cloud information collected by 4D millimeter-wave radar-camera-LiDAR as input data for the odometer. Then, the adaptive DBSCAN algorithm is used to determine the radial search radius, azimuth search radius, elevation search radius, and MinPts. The raw point cloud is then clustered to construct structured object units with cluster labels, and static background points are determined through velocity grouping and maximum distribution. Finally, based on the distance, azimuth, and elevation of the static points, angle-distance combination weights are calculated and assigned to each static point on the point cloud map to calculate the vehicle's speed. This invention's perception system complements the advantages of 4D millimeter-wave radar and LiDAR, enabling the collection of richer raw point cloud information. 4D millimeter-wave radar is less affected by adverse weather conditions and has strong adaptability to complex scenes; LiDAR offers high accuracy, and the camera can provide semantic information. Through their combined effect, this invention's perception system is more accurate, more robust, and adaptable to all scenarios.

[0084] The adaptive DBSCAN method used in this invention outperforms the RANSAC method and the traditional fixed-radius DBSCAN method in clustering. The adaptive DBSCAN method automatically adjusts the search radius and MinPts, avoiding significant problems common in the traditional DBSCAN method, such as multiple segmentations of the same object and difficulty in clustering distant objects. In field experiments, the adaptive DBSCAN method shows lower mean error, MSE (mean square error), and RMSE (root mean square error) than the RANSAC method. Furthermore, in two complex scenarios—"two or more vehicles ahead with almost identical speeds and linear directions of movement" and "large vehicles obstructing the view"—the DBSCAN method outperforms the RANSAC method.

[0085] The weighted least squares method employed in this invention significantly improves the accuracy of vehicle speed estimation. Ordinary least squares treats all points equally, but radar speed measurement error is proportional to the square of the target distance. Therefore, ordinary least squares is susceptible to the influence of distant points and noise, leading to large errors in speed estimation. This invention's least squares method takes into account the influence of target point distance, azimuth, and elevation angles on vehicle speed calculation. Therefore, it designs an angle-distance weighted function to minimize the impact of noise points on speed calculation, significantly improving the accuracy of vehicle speed calculation.

[0086] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A 4D radar odometry method for high dynamic scenarios, characterized in that, include: A perception system based on 4D millimeter-wave radar is used to acquire raw point cloud data; Clustering parameters are extracted from the original point cloud data, including search radii in different directions and minimum neighborhood density. Based on the clustering parameters, the original point cloud data is clustered using the DBSCAN clustering method to obtain different point cloud clusters; Static points are extracted from different point cloud clusters; The vehicle speed is calculated from the static point using the least squares method with angle-distance weighting.

2. The method according to claim 1, characterized in that, The perception system based on 4D millimeter-wave radar includes 4D millimeter-wave radar, depth camera, and lidar; it acquires multimodal point cloud data through 4D millimeter-wave radar, depth camera, and lidar, and then fuses the multimodal point cloud data to generate raw point cloud data.

3. The method according to claim 1, characterized in that, The process of extracting the search radius includes: Based on different raw point cloud data, an adaptive search radius function is used to extract search radii in different directions. The adaptive search radius function includes: ， in, It is the radial search radius. It is the search radius in the azimuth direction. It is the search radius in the direction of elevation. It is the radial distance from the target point to the radar; It is the direction of elevation; It is radial resolution. It is the azimuth resolution. It is the resolution at the elevation angle; , , It is the radial adjustment coefficient. , , It is the azimuth direction adjustment coefficient. , , It is the elevation angle adjustment coefficient.

4. The method according to claim 1, characterized in that, The extraction process of the minimum neighborhood density includes: Based on the anisotropic neighborhood corresponding to the search radius in different directions, the corresponding minimum neighborhood density is calculated using the minimum neighborhood density function, where the minimum neighborhood density function is: ， in, MinPts; Anisotropic neighborhoods representing search radii in different directions. This indicates the number of points within that neighborhood; It is a percentage factor.

5. The method according to claim 1, characterized in that, The process of extracting the static points includes: Based on the point cloud clusters, calculate the assumed velocity, group the point cloud clusters according to the assumed velocity, generate point cloud groups, and select the point clouds in the outermost and most widely distributed point cloud group as static points.

6. The method according to claim 1, characterized in that, The vehicle speed is calculated using the least squares method with angle-distance weighting based on the static point. The angle weights and distance weights in different directions are calculated based on the static point. The angle weights and distance weights in different directions are then combined to generate corresponding combined weights. The vehicle speed in different directions is calculated based on the static point using the least squares method according to the combined weights.

7. The method according to claim 6, characterized in that, The calculation process for the angle weight includes: ， ， ， in, It is the direction angle. It's the angle of elevation; This is the point used to calculate the forward speed of the vehicle. Angle weights; This is the point used to calculate the lateral velocity of the vehicle. Angle weights; This is the point used to calculate the vertical velocity of the vehicle. Angle weights.

8. The method according to claim 6, characterized in that, The calculation process for the distance weight includes: ， Where R is the distance from the target point to the radar.

9. The method according to claim 6, characterized in that, The process of generating the combined weights includes: ， ， ， in, It is the combined weight used when calculating the forward speed of the vehicle; It is the combined weight used when calculating the lateral speed of the vehicle; It is the combined weight used when calculating the vertical velocity of the vehicle; It is a distance weight; It is the angle weight when calculating the forward speed of the vehicle; It is the angle weight when calculating the lateral velocity of the vehicle; It is the angle weight when calculating the forward speed of the vehicle; It is the fusion coefficient.

10. The method according to claim 1, characterized in that, The calculation process for the vehicle speed includes: ， ， ， ， ， ， ， ， in, It is the location at the data point location. The unit line-of-sight vector of the radar echo; It is a block diagonal weight matrix; The vehicle speed is estimated using the weighted least squares method. This represents a single line-of-sight coefficient parameter. Representing the observed quantity, This represents the view weight matrix. Represents the observation matrix, Represents the weight matrix. This represents the radial velocity measured at the i-th radar echo point.

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