Distributed Multi-MMW Radar Fusion for Target Detection and Tracking in Highway Traffic Environment

High-resolution millimeter-wave (MMW) radar is viewed as a low-cost and highly reliable sensor compared to camera, lidar, etc., in moving scenarios and thus has been selected by highway stakeholders as an important roadside detector to detect the movement of trafc vehicles and monitor trafc fow in real time. However, the echo signal of MMW radar in complex highway environment contains not only the signal refected by target but also spurious signals and other interference signals, which signifcantly afects the estimation of the target movement state. To solve this problem, an improved vehicle tracking method is designed to simultaneously estimate the polar angle and polar radius in coordinator of MMW radar. Moreover, considering the movement patterns of target vehicles in dynamic uncertain trafc situations, a set of state space models, such as CA, CV, and CTare combined to represent the vehicle movement. In addition, based on the enhanced detection performance of a single radar, the combination of multiple MMW radars’ information was performed to determine the sequential trajectory of the target vehicle on the continuous road sections; then, the historical trajectory of the target vehicle was correlated and fused. Real experiments in highway scenarios show that the method used in this study is efective in deriving the trajectory of the vehicle and improving the positioning accuracy and reliability when the vehicle performs heavy maneuvers.


Introduction
Te three main modules of the highway system in China, i.e., supervision, communication, and toll collection, have been developed and built independently in the provincial highway segments since 1980, laying a solid foundation for the informatization and intelligence of highways [1]. Starting from 2019, the nationwide interconnection of the nonstop toll system has taken the informatization and intelligence of highways to a new level [2]. With the rapid growth of information, communication, and sensor technology in the past decade, highway intelligence has undergone a lot of technological research and development, demonstration, and promotion and realized the organic integration of industrial Internet, 5G, and sensor technologies to improve the level of refned highway management system. Te focus of modern highway system architecture is on comprehensive trafc fow monitoring as the main feature, making full use of advanced sensors such as radar, lidar, and cameras to track the trajectories of vehicles, providing an efective way to solve trafc integrity, efciency, and environmental problems.
Vehicle tracking and location is the basis for the intelligent highway system to achieve certain functions and applications, especially spatial awareness of trafc fow conditions, vehicle paths, and driving safety based on accurate, robust, and reliable tracking of vehicle movements. In the previous studies, the global positioning system (GPS) is the most widely used recording system for vehicle tracking and provides target locations accurate to the metre and submetre, while the required accuracy for location within the roadway is reported to be 30 cm [3]. Due to the insufcient accuracy of typical GPS positioning, its use in autonomous vehicle applications is limited, so solutions using diferential GPS (DGPS), assisted GPS (AGPS), GPS precise point positioning (GPSPPP), or real-time kinematics GPS (RTK GPS) [4], which can improve GPS accuracy, are emerging. However, in difcult GNSS environments (e.g., tunnels or dense urban areas), signals sufer from various sources of error such as multipath efects, signal blockage due to a limited view of the sky, and uncertainties in satellite clocks and positions. Even the most accurate of the above GNSS, i.e., RTK GPS, may not be practical due to possible signal blockage and a strict requirement on the number of clearly visible satellites for position determination [5], which is insufcient for most vehicle safety applications. Terefore, the development of localization and navigation systems with higher accuracy and lower requirements is of paramount importance before GNSS can qualify as a solution for safety applications. Although the above-given methods have shown that mobile sensors, such as vehicle-based, i.e., GPS probes, and network-based, i.e., cellular phone solutions, can be used to cover a large area road network at an afordable cost, the noisy data and sample size in an adjacent time interval in these mobile probes lead to large discrepancies in the estimation results [6].
In addition to the mobile sensors mentioned above, video detection has been widely used to monitor road trafc [7]. Compared to the frame diference method, background subtraction method, and optical fow algorithm, YOLO algorithms have been developed and are currently used in target detection due to their high speed and accuracy. YOLOv3 with its backbone network DarkNet53, which includes 53 convolutional layers, shows high performance and better accuracy in feature extraction; however, the large number of parameters of DarkNet53 afects the computational performance in actual vehicle monitoring [8]. Te YOLOv3-tiny model reduces the number of network parameters and therefore requires less memory for training, only 34.7 MB, while improving the training speed to enable fast detection. Nevertheless, YOLOv3-tiny is weak in extracting deep features from images and shows poor generalization ability for targets with multiple scene changes or a sudden change in target size [9]. To solve the real-time problem, Huang replaced the backbone feature extraction network with EfcientNet, a lightweight network that can compensate for the scaling of the input image resolution, network width, and network depth, which reduces the model parameters, improves the feature extraction capability, and makes the network more efcient and balanced [10]. Other networks, such as the region-convolution neural network (R-CNN), further improve the recognition accuracy by generating multiple bounding boxes containing targets and then correcting the most appropriate target. Lin proposed a feature pyramid network (FPN), which takes the more abstract top-level features in the neural network and fuses them with feature maps of the same size generated in the forward propagation process of the neural network through lateral connections, which improves the model's ability to recognize small objects without increasing the computational cost [11]. Liu proposed the PANet by adding a bottom-up path aggregation network to the original structure of the FPN. It further improves the recognition accuracy, but the parameters and computational cost of PANet are relatively large [12]. Te above-given feature pyramid networks only add features after up sampling and do not consider the diferent contribution of features at diferent resolutions.
Te MMW radar, which is characterized by its small size and low cost, has also proven itself in terms of its adaptability to the environment and is therefore widely used on highways. By fusing MMW radar data, vehicle trajectories can be detected and tracked, so that microscopic vehicle movements can be perceived, the exact trafc fow can be identifed, and a parallel analysis of trafc conditions can be derived in real-time [13]. Li et al. implements single-target tracking based on the Kalman flter in the polar coordinate system and uses the threshold method to discriminate and assign targets to enable tracking of vehicles with multiple targets [14]. Lohar et al. proposed a convolutional neural network (CNN) model that simulates the point cloud data of the MMW radar and realizes the segmentation of the traversable area of the road [15]. Jin et.al. determine the region of interest of the target image on the radar's projection and then verifes it using the features of symmetry, ground shadow, and vehicle width, which improves the robustness of vehicle identifcation [16]. Wang et al. solved the problem of image distortion due to road refections on rainy days by using radar refection points to extract the horizontal line and calculating the vehicle width from the intersection coordinates with the bounding box to improve the accuracy of vehicle width estimation [17]. Shahian et al. introduced the millimeter-wave radar detection information into the image-based hash coding tracking algorithm to update the scale, but this only applies to the single-target tracking problem and cannot be applied to the target tracking of multiple vehicles in trafc [18]. Recently, the polarized massive multiple-input multiple-output (MIMO) technique has been applied and verifed as a promising solution to millimeter-wave communication and estimation functions [19,20]. Te above-given research based on the fusion of image processing and radar information is mature in the feld of vehicle detection, but it cannot solve the problem of mesoscale changes in vehicle tracking.
In this paper, an improved vehicle tracking method is developed to simultaneously estimate the polar angle and polar radius when coordinating an MMW radar. Considering the motion patterns of target vehicles in dynamic uncertain trafc situations, a series of state space models, such as CA, CV, and CT are combined to represent the vehicle motion. In addition, based on the improved detection performance of a single radar, the combination of the information from multiple MMW radars was performed to determine the sequential trajectory of the target vehicle on the continuous road sections; then, the historical trajectory of the target vehicle was correlated and fused. Te main contributions of this study can be summarized as follows: the fusion of data from multiple MMW radars was integrated and performed in a multiobjective framework to track the sequential trajectory of the target vehicle on the through road sections. Particularly, a multimodel tracking method is proposed to update the vehicle motion information obtained from the MMW radars. Unlike vehicles arriving at the same time are in each lane at the macroscopic level, a more accurate prior probability estimate is obtained at the microscopic level using real-time data GPS. Te key to solving this problem is to identify typical maneuvers that a vehicle performs on a highway, such as driving, accelerating, decelerating, and changing lanes. Tis information can help interpret the scene and assist in identifying risky situations. For example, a lane change or abrupt deceleration can be detected with short latency, resulting in immediate warnings to surrounding vehicles to avoid the risk of near-miss accidents.
In the remainder of the paper, we frst provide an overview of the system architecture and defne the problem in Section 2. Ten, the millimeter-wave radar data compensation method and a set of vehicle models for vehicle tracking are presented in Section 3. Te accuracy and robustness of the proposed method is validated in experimental tests with real data in Section 4, followed by a discussion of the corresponding results. Finally, Section 5 concludes the paper.

Overall Framework
Most roadside millimeter-wave radars use the 77-81 GHz frequency band and can achieve a wide sampling bandwidth, and their resolution is generally high. For large targets, the echo signal from the real target forms a large coordinate point cloud during signal processing due to its large refective area. By emitting millimeter-wave signals outward and receiving the signal refected from the target, the millimeter-wave radar can obtain status information such as the target's range, angle, and speed. To further improve the detection accuracy by algorithm compensation, it is necessary to classify the target point cloud by clustering to prevent the same target from being detected as an object and to reduce the data size. Common clustering methods include K-means, CURE, and DBSCAN. Te target detection and tracking process of millimeter-wave radar mainly includes target detection and target tracking. Te target detection process mainly detects the state of the target and determines the current state information of the target. After the state of the target is determined, it enters the tracking phase. Te tracking methods include Kalman flter, unscented Kalman flter, and particle flter. As shown in Figure 1, the millimeter-wave radar system is mainly composed of the transmit-receive antenna, the RF front end, the signal subsystem, and the processing subsystem.
In radar detection, the relative distance, angle, and speed of the target at the current time can be determined. First, the waveform generator is controlled to generate a control signal for the millimeter-wave radar, which includes the initial frequency and modulation slope of the radar transmit signal. Ten, the control signal is fed into the voltage-controlled oscillator, which then generates a corresponding modulation signal. Part of the modulated signal is amplifed by the power amplifer and then transmitted through the antenna. Te other part is used as a local oscillator signal for subsequent signal mixing. When the transmitted signal reaches the destination, it is refected. Due to the energy loss in signal transmission, the receiving antenna must send the refected signal to the low-noise amplifer for amplifcation after reception, and then the received signal is mixed with the previous signal in the mixer LO to obtain the signal IF. Te function of the mixer is to obtain the instantaneous frequency diference of the input signal. Since there is a time diference between the transmitted signal and the received signal, the frequency diference between them can be obtained after mixing in the signal IF. Ten, the IF signal is processed and calculated in the signal processing subsystem to obtain the state information of the target. After the initial acquisition of the target state information, target confrmation can be performed. To avoid the infuence of refected signals from static objects, static noise denoising is often required in moving target detection. Moving target indication (MTI) is a method for removing static and slowmoving interfering signals. Te purpose of the MTI method is to flter static signals and reduce background noise from moving targets. Since the position of a stationary object remains unchanged, its spectral position is also fxed in the radar's acquisition cycle, while the position of a moving object moves with time and its spectral position changes in the radar's diferent acquisition cycles. Terefore, the signals with multiple cycles are detected to eliminate the fxed interfering signal, and the stationary target is also fltered.
In millimeter-wave radar target detection, the radar analyzes the target's motion state based on transmitted signals and echo signals. Due to the complexity of the road environment, the actual echo signal contains not only the signal refected from the target, but also spurious signals and other interferences that signifcantly afect target detection. Terefore, algorithm compensation is required to improve the accuracy of detection. First, the actual state of the target is determined by target detection. Once the known target track is determined, the track of the existing target is updated based on the new target state information. If there are multiple targets, the new target state must be matched with the existing target track to determine if the new target state belongs to the track of the known target. Ten, the new target is associated with the best matching target track. Ten, the trajectory is tracked and fltered to complete the prediction and correction of the target's trajectory and reduce the mutation and jitter of the trajectory. In the tracking process, new targets are constantly created, old targets are lost, and jamming signals interfere. Tere may be a target signal that does not match the track of the known target, so it is necessary to evaluate the target state by the corresponding algorithm. If the target is known, the tracking state is maintained, else a new target trajectory will be created to represent a new signal.

Millimeter Wave Radar Data Compensation.
Due to the infuence of various obstacles and interferences, target tracking is prone to deviations, resulting in a discrepancy between target tracking and actual target travel. Also, the actual vehicle motion in trafc scenes does not have a constant state but is dynamic and random. To accommodate Mathematical Problems in Engineering diferent vehicle kinematics, various travel patterns, including straights, curves, lane changes, and intersections, can be represented by a combination of linear and nonlinear state models. A general description of the hypothetical models for vehicle n ∈ N during the sampling period (t k− 1 , t k ] can be written as follows: where x n � [p n,x p n,y θ n v n c n a n _ c n ] T , x n (k) describes the predicted state of the vehicle motion. Note that, the subscripts x and y denote the x-axis and the y-axis of each frame, subscript n denotes "of target n," p n,x , p n,y , and θ n are defned on the host vehicle's body-fxed moving frame, and other elements are defned on the ground-based fxed frame. p denotes the relative position, θ denotes the relative yaw angle, v denotes the velocity, c denotes the yaw rate, a denotes the acceleration, and _ c denotes the yaw acceleration. Te variable without subscript n means "variable of the host vehicle." u is the input vector, and f(x n , u) and h(x n , u) are either linear or nonlinear and time-invariant function structure. Te process noise q n and measurement noise r n are mutually uncorrelated zero-mean white Gaussian with covariance Q and R respectively. Note that, difering vehicle motion patterns can be characterized by adjusting f(x n , u), and sensor measurement results z n can be approximately represented by h(x n , u).
When millimeter-wave radar is detected, the measurement trace may easily deviate due to the infuence of various noises and disturbances. In this case, it is necessary to use tracking fltering for processing. Te Kalman flter is an optimal estimation algorithm that can estimate the state of a dynamic system from a set of measurement results containing noise and measurement errors. Te Kalman flter predicts the target state at the next time point based on the previous state and the given motion model and then weights the predicted state and the current state appropriately to obtain the fnal target state. Te fnal target state is considered as to be the closest to the real target state, which combines the motion state and the noise of the current system to avoid the error caused by using only the measurement information. Te rectangular X-Y coordinate system, as shown in Figure 2, is set up with the center of the radar as the origin, while the millimeter-wave radar uses the ρ-θ polar coordinate system with the installation position of the radar on the vehicle as the origin for data measurement.
When the data generated by the millimeter-wave radar are in two-dimensional space and the input measurement vector consists of radial distance, radial velocity, and direction angle, the measurement vector can be written as Te coordinate conversion relationship is shown in formula (2), where x and y are converted radar measurement data representing horizontal and vertical distance, respectively. X(k) is the measurement data that completed the coordinate conversion, which  represents the physical meaning of radial distance, relative radial velocity, and direction angle, and z is the radar deployment angle.
x � ρ cos where the X(k) � because the millimeter-wave radar sampling period is fxed and time is short, the moving target can be estimated approximately in a short time using the basic target motion model so that time compensation can be made for the measurement data acquired by the radar according to the time stamp of the individual millimeterwave radar data. In order to track the target, a model must be created that can describe the target's state of motion at any point in time. Basic target motion models mainly include the uniform linear motion model CV and the uniform linear motion with acceleration model CA. When the target moves on a uniform straight line in the two-dimensional state space, the target state variable can be written as respectively, represent the horizontal and vertical distance of the target and the relative horizontal and vertical velocity refer to the radial distance and radial velocity of the target projected on the x-axis and y-axis in the rectangular coordinate system at time k. Te state-space equation of the target motion can be written in constant velocity (CV) and constant acceleration (CA) linear motion model as follows: where T is the sampling period of radar working cycle after time alignment, I x and I y represent the horizontal and vertical random changes of target speed, and ι x and ι y represent horizontal random change and longitudinal random change of target acceleration, respectively.

Millimeter-Wave Radar Data
Splicing. Te correlation, tracking, and fusion of the measurement data received from multiple millimeter-wave radars is a very complex problem, the measurement data corresponding to the historical targets must be found, and subsequent tracking and fusion processing must be performed. First, the real-time vehicle tracking data are classifed to identify the vehicles that suddenly disappear, or appear, whether it enters the detection area, the nonoverlapping area, or the overlapping area and leaves the detection area. Ten, the vehicles in the overlapping area are sequentially matched at multiple points, and the vehicles that are successfully matched are updated in the global tracking record, while the vehicles that are successfully matched in the sudden disappearance record are deleted. Te vehicles that are not matched are fltered into the sudden disappearance record according to the conditions. Finally, the sudden disappearance set and sudden emergence set are used for moving average prediction and Kalman fltering to address the severe loss of vehicle data in poor road conditions or large vehicle occlusion, and the prediction results are used for the Hungarian multitarget matching. Te successful matching is updated in the global tracking set. At the same time, the successfully matched vehicles are deleted from the group of suddenly disappeared vehicles, and the failed matching is made up in the next iteration.
To enable targeted splicing of the radar track data in each scene, the radar acquisition area is divided into the initial radar acquisition area, the nonoverlapping area, the preoverlapping area, the postoverlapping area, and the area leaving the radar acquisition area, as shown in Figure 3, set the detection area of each radar is (L1 and L2), the L1 and L2, respectively, represent the starting point and end point of the detection area, while the S1, S2, and S3 represents the threshold distance to the detection area, the distance threshold of overlapping area, and threshold distance from the detection area.
If the radar A is the frst radar in the detection area, F is the last radar in the detection area, and the road direction is parallel to the coordinate's X direction, the detection area of radar A, radar F, and other radars can be described in follows: In equation 4, x represents the location of vehicle in the detection area, the inLap value of 1 represents the rear overlap region, 2 means in the nonoverlapping area, 3 represents the front overlap area, 4 represents leaving the radar detection area, and 5 represents the initial entry into the radar detection area. To enable targeted splicing of radar track data in different scenes, diferent sets are used to subdivide radar track data, including sudden disappearance set DAC, sudden appearance set AC, overlap zone set LC, and global tracking set GC. Set the variable t as the current time and set the allowable delay time of the radar track data to a; i.e., the data were received at time t and before time t − a. Te threshold for determining when the track disappears is b, and the criteria for determining that the track enters the sudden disappearance area DAC are described as follows: where Trace v,endT ime is the last arrival time of vehicle v's track Trace, and the track data of vehicle v is not received for the duration b after time Trace v,endT ime . It is assumed that the current time is t and the allowable data delay time is a. Tat is, the data have been received at time t and before time t − a. Te tracking window is the time interval of trajectory splicing analysis. Te length is set as ∆t, and trajectory splicing is performed every ∆t. In the tracking window, the analysis shows that the trajectory suddenly appears set AC, and the judgment conditions for the trajectory entering suddenly appears set AC are Here, Trace v is the track of vehicle v, while the Trace timeDiff represents the time interval length of vehicle v in the tracking window. Te D is the time threshold of trajectory abnormality, Trace startTime is the track start time of the vehicle in the tracking window, e is the time threshold when the trajectory suddenly appears. Te vehicle track in the overlap area is generated by two adjacent radars. Te i-th overlapping area is generated by the i-th radar and the i + 1 radar. Te overlapping area i generated by the i-th radar is called the front overlapping area LC i,front , and the overlapping area i generated by the i + 1 radar is called the rear overlapping area LC i,back . Te judgment conditions for entering LC i,front is set as e i,v,inLap � 3, and the criteria for entering LC i,back are set as e i+1,v,inLap � 1. It should be noted that the e i+1,v,inLap � 3 represents that the track of vehicle v in the i-th radar is in the front overlap area, e i+1,v,inLap � 1 indicates that the track of vehicle v in the i + 1 radar is in the rear overlap area. Global tracking set GC represents all vehicles entering the radar detection area will enter this set and be assigned a globally unique number. For example, the number of vehicles in the frst radar is V1, and the number in the second radar is V11. By analogy, there will be diferent numbers in diferent radars, but there will always be a unique number V1 corresponding to the same vehicle until V1 leaves the radar detection area. Te track splicing process in the overlap area is performed between adjacent radars. For example, for the i-th overlap area, the relevant overlap set is where Point k,time,front represents the time stamp of the kth track point on a track in the front overlap area, Point k,time,back represents the time stamp of the jth track point on a track in the rear overlap area, ∆Time represents the threshold value for judging that two timestamps are close enough.
Point k,speed,front represents the speed value of the kth track point on a track in the front overlap area, while Point k,speed,back represents the speed value of the jth track point on a track in the rear overlap area, ∆Speed represents the threshold value for judging that two speed values are close enough. Lastly, Point k,length,front represents the length of vehicle body collected by the kth track point on a track in the front overlapping area, Point k,length,back represents the vehicle body length collected by the jth track point on a track in the rear overlap area, ∆Length represents the threshold value for judging that two vehicles are close enough, e k,j represents the distance between k locus point and j locus point, and Dist represents the threshold value for judging that the distance between two vehicles is close enough. Ten, the sudden disappearance set DAC could be updated by deleting e i,front corresponding vehicle records from the DAC set if the matches successfully and update the global set GC by searching for Trace i,front,id and changing the e i,back,id if e i,front matches successfully with e i,back . Also, the sudden AC set could be updated after matching by adding the vehicles that failed to match to the sudden AC set according to the conditions. Te rules are as follows:

Experimental Set-Up and Data Set.
Te target measurement and radar data splicing model are formulated and applied to experimental radar data. To verify the suitability of the proposed method for tracking vehicle movements representing various kinematic states and driving patterns in a range of longitudinal and lateral maneuvers, and with accuracy and reliability required to support the applications of ITS, a series of feld tests were conducted in highway scenarios, as shown in Figure 4. Te measurement data were collected by the Jiangxi Trafc Monitoring Command Center. Te dataset was then generated from the recorded measurements by calculating the ground truth position of the target vehicle in sensor coordinates and gating the measurements originating from the vehicle. Tat is, only radar detections in a bounding box exceeding the actual vehicle dimensions by 0.5 m in all directions were paired with the respective ground truth vehicle state. Te entire dataset includes 336,287 data points from approximately 123 minutes of recorded sensor data. On the direction from Yongxiu station to Xinqizhou station, a length of 9.6 km road segment, is equipped with four MMW radar sensors, which are mounted on the gantry or roadside poles. Te MMW radars have an opening angle of about 170 degrees, a range of 500 m, and the sensor axes are rotated by 45 degrees with respect to the setting axis. All radars run at a frequency of 20 Hz and are not synchronized among themselves. Apart from the radar sensors, the test vehicles are equipped with RTK sensors, which combines a precise diferential global positioning system (DGPS) and an inertial measurement unit (IMU). It provides the pose of the vehicles in a global coordinate system and the object motion.
Te ground truth vehicle position of test vehicles in both the ego-vehicle coordinate system and the four sensor coordinate systems, as well as its identifcation results are shown in Figure 5(a). It should be noted that the density of deployment of MMW radar sensors will generate more or less vehicle samples, which may impact on the accuracy of detecting and identifying vehicle trajectory on diferent road segment. In our case, the MMW radar detected vehicle with same ID is ranged from maximum 52 samples to minimum 1 samples, only 23% vehicle trajectories were recorded with more than 10 samples, 6% with more than 16, 0.7% with more than 26, and 0.3% with more than 30, showing the weak continuity of the measured vehicle trajectory. After compensation, the accuracy of vehicle trajectory matched by  Mathematical Problems in Engineering four MMW radars raised from 78.6% to 91.7%. Te accuracy of the proposed vehicle identifcation is further evaluated based on an ROC curve analysis, as shown in Figure 5(b). Te 4-radars detection on the test road segment achieved the highest overall accuracy and AUC result of 0.95, which outperforms the results of 3-radars detection and 2-radars detection. It is believed that the continuity of the MMW radar samples should be efective for detecting vehicle trajectory and providing accurate identifcation in a prompt manner; on the other hand, the higher continuity of the MMW radar samples may conduct to more cost in MMW radar devices.   Figure 6. Due to the Monte Carlo implementation, which involves random generation and propagation of particles, the estimation results are subject to random efects. Te estimation of the vehicle trajectory, velocity, and acceleration are plotted in show that the multimodel based tracking method has a much better estimation power than the single-model based tracking method. It can be seen that the estimation accuracy decreases signifcantly when vehicle takes heavy manipulation; for examples, at t � 43.5 s, driver take deceleration, and at t � 52 s, driver take acceleration maneuver, because the single model cannot adapt to the driver manipulations.
Also, by implementing the IMM algorithm, the MSEs of vehicle location prediction are mostly less than 4 m and those of vehicle speed prediction are mostly smaller than 2 m/s, while the estimation error augmented by applying single-model estimation. It indicates that the proposed IMM tracking method achieves a higher identifcation accuracy. Figure 7 shows the distribution of 181 groups of driving states. Figure 7(a) shows the overall situation of the location distribution of all four driving states. We use diferent shapes for diferent maneuvering behaviors. And, the color is marked on the driving lane of the vehicle. (Figures 7(b)-7(d)) are the individual distributions of sudden acceleration, sudden braking, lane change, and vertical bumpy. Te red circle indicates that the driver accelerates the vehicle at that position, the green square indicates that the driver brakes the vehicle at that position, and the pink diamond indicates that the driver steers the vehicle to change lanes at that position. Te blue fve-pointed star represents the vehicle suddenly moving up at that position. It can be seen that the selected driving state events are independent of each other at the time of their occurrence and their spatial distribution is relatively broad. In Figure 7, the vehicle trajectory and motion patterns can be identifed by MMW radar during the test, a representative detail of these trajectories can be seen with further detail. Te vehicle trajectory profle indicates that during this stretch of 11 s, the vehicle diminishes slowly its speed, until approximately instant 52 s, when brakes are applied, lasting till approximately instant 120 s. After some seconds the driver accelerates to reach velocity values of the same order as previously registered. Figure 7 also presents the details of the vehicle motion patterns over the keep-lane and changelane maneuvering states. As can be clearly seen in Figures 6(a)-6(e), vehicle accelerations, decelerations, and lane changes performed during the trajectory are properly detected by the MMW algorithm. It is believed that the proposed system should be efective for detecting driver behavior and providing accurate identifcation in a prompt manner.

Conclusions
Tis paper presents a vehicle tracking solution based on MMW radars commonly used in digital highway infrastructure systems to improve vehicle tracking and identifcation accuracy and support intelligent highway applications. Te improved vehicle tracking method was developed to simultaneously estimate the polar angle and polar radius in the coordinator of the MMW radar. Considering the movement patterns of target vehicles in dynamic uncertain trafc situations, a series of state space models, such as CA, CV, and CT are also combined to represent vehicle movement. In addition, based on the improved detection performance of a single radar, the combination of the information from multiple MMW radars was performed to determine the sequential trajectory of the target vehicle on the continuous road sections; then the historical trajectory of the target vehicle was correlated and fused. Real experiments in highway scenarios show that the use of MMW radar data is efective in deriving the trajectory of the vehicle and can achieve substantial positioning accuracy and reliability when the vehicle performs severe maneuvers. It is shown that the proposed vehicle maneuver identifcation algorithm is based on the vehicle's own kinematics and the system results are independent of visibility conditions. In the next step, we will further analyze the fused vehicle data and analyze the application scenarios such as vehicle tracking prediction, vehicle driving anomaly recognition, and side collision warning.

Data Availability
Te data used to support the fndings of this study are available from the corresponding author upon request.

Consent
Informed consent was obtained from all subjects involved in the study.

Conflicts of Interest
Te authors declare that there are no conficts of interest.