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Machine Learning-Driven Calibration of Traffic Models based on a Real-time Video Analysis

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New Technological Solutions, Research Methods, Simulation and Analytical Models That Support the Development of Modern Transport Systems

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26 April 2024

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28 April 2024

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Abstract
Accurate traffic simulation models play a crucial role in developing intelligent transport systems that offer timely traffic information to users and efficient traffic management. However, calibrating these models to represent real-world traffic conditions accurately poses a significant challenge due to the dynamic nature of traffic flow and the limitations of traditional calibration methods. This article introduces a machine learning-based approach to calibrate macroscopic traffic simulation models using real-time traffic video stream data. By leveraging computer vision technologies to extract key traffic parameters from video streams, the approach demonstrated a notable improvement in aligning the generated data from the calibrated simulation model with car sensor data, achieving an average improvement of over 50% compared to the uncalibrated macroscopic model. Moreover, there was a substantial reduction in data drift for the machine learning model integrated into the virtual transport space using vehicle-to-everything technology, resulting in a more than fourfold decrease in the average absolute error of the model.
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Subject: Engineering  -   Transportation Science and Technology

1. Introduction

The current level of development in communication, information, and sensor technologies enables the automation of monitoring and managing complex systems that previously required expert intervention. This automation enhances scalability and responsiveness [1,2,3].
Scalability, real-time monitoring, and control are increasingly feasible and essential for transport systems, leading to improved safety and efficiency in their operations [4]. Intelligent Transport Systems (ITS) utilizing vehicle-to-everything (V2X) technology [5] meet the demands of modern transport systems [6,7,8] by continuously collecting data on road traffic through various sensors [4]. The collected and systematized data, which represents the context of traffic situations, is crucial for determining the evolving requirements of ITS functionality over time [9]. Context data plays a vital role in analyzing sensor data, reasoning, and modeling intelligent systems, significantly impacting the effectiveness of ITS. The interaction diagram of the Physical and Virtual Transport Space (PTS, VTS) within the Metaverse Transportation System provides a comprehensive representation of the context of the entire transport system [10].
The VTS supports computational experiments with feedback optimization relative to the real PTS [10], which connects the operation of many systems at a high level and controls the generation of data facilitating the integration of machine learning (ML) models into ITS operations. VTS can be implemented using various approaches that consider the mobility of their elements. Macroscopic traffic simulation modeling addresses the mobility of elements within transport systems, enabling controlled generation of key traffic flow characteristics.
The Simulation Model of Traffic Flow (SMTF) generates random events representing vehicle appearances on simulated routes based on the context of traffic situations embedded in the model. Predetermined parameters and time within the simulated space define this context [11], influencing movement scenarios, interactions, traffic density, and infrastructure behavior on the road.
Macroscopic traffic models focus on vehicle behavior and statistical characteristics. Therefore, most implementations of these models concentrate on depicting the dynamics of a specific section of the route based on available data [12]. Various software solutions are available to simplify the construction of a macroscopic model, with one notable example being the SUMO (Simulation of Urban Mobility) software widely utilized in research fields, particularly in traffic management and transportation communications [13]. SUMO offers capabilities for constructing, adjusting, and modeling custom traffic flow architectures, along with supporting tools for importing network and demand models of existing route sections.
The demand model determines the frequency of selecting different routes on a specific highway section, including the starting and ending points of vehicles and their type selection. Therefore, the accuracy of this model is crucial in road simulation as it reflects the primary needs of drivers for city navigation [14] and influences the value of the resulting SMTF.
SUMO's versatility enables the study of traffic control strategies and vehicular communication systems [15]. The high-detailed simulation in SUMO is essential for analyzing and optimizing traffic management strategies, evaluating the impact of infrastructure modifications, and examining vehicle interactions in complex urban environments [16]. Additionally, SUMO supports V2X technology modeling, facilitating the development and testing of interoperable automotive applications [17].
However, a significant drawback of such models is their challenge in adapting to dynamic changes in the PTS [18]. The accuracy of the simulated model data may differ significantly from that of real-life PTS data since the simulation's source data relies on information from the OpenStreetMap (OSM) project. Updating the OSM database can be slow and dependent on the location and activity of volunteers in the relevant region [19].
The demand model and vehicle behavior parameters show the most significant differences from real-world traffic data in PTS. The demand model affects how traffic density is distributed over space and time, which can be monitored using data from ITS sensor systems [20]. To address discrepancies between the outdated demand model and current traffic conditions, adjustments can be made to the spatial and temporal distribution of traffic density in the SMTF through calibration of simulation models.
Various calibration techniques can help bridge the gap between the simulated model and actual traffic conditions in FTP. These include direct calibration of the demand model [21,22,23,24,25], calibration of the macroscopic model based on physical processes [26,27,28], and the use of evolutionary algorithms to optimize calibration parameters [29,30,31]. Studies suggest that relying on a single traffic flow model may not capture all relevant phenomena accurately, potentially impacting simulation accuracy [32]. Hybrid traffic flow models, combining microscopic, mesoscopic, and macroscopic approaches [33,34,35,36,37], offer a more comprehensive representation of traffic dynamics with varying levels of scalability.
Another way to enhance simulation accuracy is by integrating macroscopic modeling with ML techniques to improve prediction accuracy and adaptability to changing traffic conditions [38,39,40]. This hybrid approach can provide greater flexibility to changing traffic patterns by combining the overall traffic flow dynamics captured by macroscopic models with ML's ability to handle dynamic changes effectively. By leveraging ML methods instead of traditional statistical approaches, traffic modeling algorithms can achieve higher accuracy and adaptability [41].
In [42], it is demonstrated that ML can be helpful in dynamically calibrating parameters in macroscopic traffic flow models. For instance, ML can generate a set of hyperparameters for calibration through generative adversarial simulation learning. However, a challenge arises in selecting a data source to timely calibrate the VTS to reflect changes in the PTS.
One increasingly popular method for collecting traffic flow data from specific highway sections is the use of Wireless Sensor Networks (WSN) due to their flexibility, scalability, and cost-effectiveness, as highlighted in [43,44,45,46,47,48]. WSNs allow data collection on parameters recorded by sensors from each vehicle connected to the communication network, providing more detailed information about the analyzed route section than analyzing traffic video streams [49]. This richer data can help address a broader range of ITS problems through ML.
Despite the benefits of using WSNs, video recording systems, especially those based on autonomous aerial vehicles, are becoming more prevalent [50,51] thanks to advancements in ML methods for processing video streams [52] and the proliferation of city cameras. This trend enables the creation of extensive and affordable systems for collecting transport network data to build and calibrate simulation models [53,54,55]. Video systems allow data collection from all vehicles without specialized sensors or communication modules. On the other hand, integrating a large number of vehicles into a WSN can present challenges.
However, it is essential to note that a fixed dataset is required to address various challenges in constructing SMTF for specific route sections, conducting computational experiments, and pre-training ML models for integration into VTS [56,57,58]. This dataset cannot always be directly obtained from video streams, and deploying WSNs may be hindered by the lack of vehicles equipped with transceiver systems and sensors.
In our previous work [15], we showcased an application of ML in ITS focusing on specific traffic flow data. The approach involved generating synthetic data to train the ML algorithm within the vehicle-to-infrastructure (V2I) system, leveraging the SUMO simulation model and the Longley-Rice propagation model [59]. The primary objective was to reduce delays in the V2I network, including minimizing network connection time. By creating a method for generating diverse motion scenarios, the algorithm's ability to generalize for antenna radiation tuning was enhanced.
The ML algorithm, trained on the synthetic dataset, exhibited a 94% accuracy in determining the optimal main lobe position crucial for establishing and sustaining a dependable connection between the V2I infrastructure and vehicles. However, when tested on real data extracted through intelligent processing of video streams from the simulated area, the accuracy dropped by over 40% compared to synthetic data. This discrepancy highlighted a significant deviation between the characteristics distribution generated by the simulation model and actual traffic flow data.
This paper proposes a solution to develop SMTFs that closely align with real-world PTS. The methodology involves a hybrid regression calibration of a macroscopic model using SUMO data, leveraging real-time video stream analysis with the ML algorithm to capture vehicle characteristics within the modeled area.
The paper is structured as follows: Section 2 outlines how to represent PTS dynamics within a VTS and details the process for creating and calibrating the proposed SMTF. Section 3 introduces a method for analyzing video streams and extracting relevant data. Section 4 presents simulation results demonstrating the algorithm's performance in calibrating a macroscopic traffic model with new data from the PTS. Additionally, it showcases an experiment assessing the calibrated SUMO model's alignment with real PTS based on video stream data and connected car sensors.

2. Analysis of the Influence of the Dynamics of the PTS on the Operation of the VTS and the Structure of the Proposed ITS

The processes within the transportation flow can vary depending on the specific focus of the study. When examining traffic flow on a specific section of the road, several overarching factors come into play. These include the overall road infrastructure both within and outside the section being studied [60,61,62], as well as temporary factors that can be cyclic, like changes in time of day and seasons [23,63,64], or random, such as variations in weather conditions [65].
These global and temporal factors also fluctuate and influence traffic flow characteristics to different extents, which can make simulation modeling quite complex [23,64]. To simplify this complexity, a limited set of traffic flow parameters is required to develop SMTF and assess the dynamics of each parameter.
In the context of the previous work [15], the selected parameters for addressing the vehicle tracking issue were sensor data that reflect the internal attributes of vehicles while they are in motion. Since these vehicle sensor parameters exhibit a spatial and temporal distribution that aligns with the traffic demand model, analyzing this data offers valuable preliminary insights into the modeled area. Additionally, it supplements Global Navigation Satellite System (GNSS) data in cases where GNSS data is inaccurate or unavailable due to interference or a lack of visible satellites [66,67].
The data used to train the developed algorithm for tracking vehicle movement included the time mark when a request was sent to connect to an intelligent infrastructure facility, the vehicle's speed, and its rotation angle relative to geographic north.
As observed in the VTS analysis from [15], these parameters' dynamics experience temporary fluctuations, leading to deviations in the demand model. These deviations are evident in changes in the frequency of vehicles on various sections of the route over time. During the analysis, a deviation in the demand model was specifically noted, resulting in fluctuations in the frequency of vehicle presence along different segments of the route overall and over specific time intervals.
We divided the simulated area into sectors using the Geohash method [68] of GNSS coordinate space encoding with a code sequence length of 8. Each sector measured 38.2 m by 19.1 m. This level of detail is considered optimal for Vehicle-to-Infrastructure (V2I) technology, which typically has an average range of 600 m [5]. The sector sizes were chosen to match the dimensions of route elements like intersections and turns.
Our analysis of the positioning algorithm involved comparing vehicle coordinates obtained from SUMO with results from video stream analysis. The differences in sector boundary crossing frequencies between the SUMO model and video stream processing data are shown in Figure 1.
Changes in the demand model led to variations in the distribution characteristics of the generated traffic flow parameters. Figure 2 illustrates the deviation in time-averaged vehicle speed values generated compared to data from the video stream.
To address deviations in the SMTF from real-world PTS, we developed a new ML-based simulation model. Initially, SUMO was used to train the model, which was then fine-tuned using data from PTS.

2.1. Dynamics of Traffic Flow as Data Drift

In the context of the VTS intelligent algorithms, changes in the probability distribution of data from the PTS can be seen as data drift [69]. This drift can be categorized into three types when PTS is viewed through a statistical model with input data X and output processing data Y. The first type (or drift of the first kind) is the drift of input data X, which reflects changes in traffic flow density due to daily, weekly, or seasonal cycles [70] and other time-related factors. The second type (the drift of the second kind) is the drift of output data Y, which could manifest as a shift in the simulation model's trace graph relative to the PTS due to external factors. The third type (the drift of the third kind) is simultaneous changes in both input and output data X and Y, indicating the combined influence of global and local factors.
Data drift from PTS dynamics directly impacts the accuracy of simulation modeling, especially when using ML models, as the distribution of input data used for analysis and training becomes outdated [10]. Therefore, calibrating the SMTF is essential to adapt to PTS data drift.
The data calibration process includes four stages [69]:
  • Data extraction: Collecting data fragments from streams to create a current sample of the studied parameter.
  • Extracting critical characteristics from the collected data.
  • Calculating test statistics to evaluate the static deviation degree of the extracted data from the original or current VTS distribution.
  • Determining the statistical significance of the deviation to initiate system adaptation to the new distribution.
These steps can be implemented as a monitoring system for the macroscopic model generated to determine when calibration is necessary.

2.2. Scheme of Operation and Calibration of the Hybrid ITS

As discussed in the Introduction, traffic flow variations are primarily influenced by changes in traffic density over space and time globally (across the entire study area) and locally in specific areas, such as hybrid systems that combine macroscopic and mesoscopic models. This leads to the evolution of the SMTF by transitioning from analyzing a macroscopic model of a controlled route area to studying changes in various sectors across a given territory over time.
The interaction system between the PTS and the VTS, as shown in Figure 3, includes an initial simulation model implemented in SUMO, divided into sectors with both initial global and several local patterns of SMTF timing characteristics. It also incorporates a monitoring system to track the updates of these global or local patterns.
Once the route graph is divided into sectors, an initial temporal dynamics pattern is established through three stages. The first stage involves initializing simulation modeling in SUMO, where fixed parameters are gathered in general and local databases for each sector. The second stage focuses on extracting the global time trend of Yn for each of the n fixed parameters using a statistical method called seasonal trend decomposition using locally estimated scatterplot smoothing (LOESS) [71].
By decomposing the time series of fixed parameter dynamics into seasonal, trend, and residual components, we can pinpoint the trend of the parameter Tn and the seasonal component Sn. These components set the statistical proximity boundaries within which the calibration process of SMTF does not commence.
Y n ( t ) = T n ( t ) + S n ( t ) + R n ( t )
The resulting trend Tn is the foundation for training the global regression model. Additionally, the average duration of seasonal deviations τS was determined, representing the period during which Sn(t) values exceed half of its maximum value max(Sn).
The regression model was chosen based on three key criteria: high accuracy for variables with varying dynamics periods, computational complexity impacting training and retraining speed, and noise resistance to random short-term processes on the route. The Extra Trees Regressor (ET) algorithm was selected for the simulation because it met these criteria [72].
As ET is an ensemble algorithm, a method was employed to adjust trained models considering regional drift to accelerate retraining [69]. This involved updating models by incorporating new classifiers trained on new data while removing some older ones until reaching the desired accuracy threshold on the test sample selected during the calibration stage.
One advantage of ET is that it utilizes the average prediction from all trees in the ensemble, potentially reducing model variance compared to other ensemble algorithms when dealing with noisy data. Additionally, introducing an extra random process in selecting input parameter split points enhances data noise robustness [73].
The third stage involves constructing the initial template of each cluster's dynamics through additional local training on the global ET model using the described ML model adjustment method within the local database of each sector.
Subsequently, the SMTF transitions into run mode while the data drift monitoring system continuously compares fixed parameter distributions over time. The SMTF generates data from ET models, allowing the calibration process to operate simultaneously.
When new data from the PTS is received (either from the video stream analysis system or from the connected vehicle's sensors), it is stored in the global database and then distributed to local databases based on the location of the vehicle when the data was collected. The accumulation of this new data from the PTS happens over a period of time denoted as τS.
Once the new data is collected, extracting key characteristics begins by calculating the trend of the new data T n ' ( t ) and relevant test statistics. This involves determining the maximum absolute difference between two trends for comparison, denoted as max(Sn).
The decision to initiate global or local calibration is based on specific conditions:
sup t | T n ' ( t ) − T n ( t ) | > S n ( t )
If these conditions are met, additional training is conducted on the existing global ET model. The updated model is then incorporated into each sector by additional training on a local dataset, similar to the third stage of constructing the original SMTF. This additional model training occurs in parallel with the operation of the replaced models without causing any interruption. Additional training is only performed on a specific local model if a shift in local data is detected.
Evaluating the simulation's adherence to the established and calibrated SMTF involves a comprehensive process. It involves a statistically comparing the distributions of generated quantities with those obtained from the PTS data. Additionally, the performance of the ML algorithm, which has been extensively trained and integrated into the VTS, is assessed using a test dataset from the PTS. The results of these evaluations are presented in Section 4.

3. Methodology for Analyzing Video Stream Data

In the Introduction, it was mentioned that data from stationary objects (such as video cameras) of road safety infrastructure, or sensors from vehicles connected to the WSN, are used to analyze the ITS transport situation. To create a flexible hybrid SMTF calibration system, separate preprocessing algorithms for each data source must be developed to represent the input data uniformly [74,75].
When preprocessing data from a connected vehicle sensor system, classical steps like data cleaning, integrating data from multiple vehicles in a time-sorted manner, and normalizing parameters under consideration may suffice [76]. However, processing highway video monitoring data poses challenges in obtaining vehicle characteristics directly, which are crucial for many V2X ML applications. An additional algorithm is needed to extract vehicle characteristics from a video stream.

3.1. Algorithm for Extracting Traffic Data from a Video Stream

The data extraction algorithm involves three main steps:
  • Camera calibration and conversion of image coordinates to GNSS coordinates.
  • Tracking and calculation of spatiotemporal characteristics of vehicles.
  • Applying the Kalman filter to smooth the extracted values.
Initially, the YOLOv5 real-time video analytics system [77] was used to analyze the video stream, detecting and tracking the movements of visible vehicles. The YOLO algorithm divides the original image into a grid of N × N cells. If the object’s center falls within the coordinates of a cell, then this cell is considered responsible for determining the object’s location parameters. Each object is defined by five values: center coordinates of the bounding box, its width, height, and confidence level that the box contains the object. For each object class-cell pair, the probability of the cell containing an object of that class must be determined.
The choice of YOLOv5 architecture was made for its high image processing speed and good object detection accuracy with minimal parameters and low learning rate. Training parameters included IoU threshold value of 0.5, image compression to 960 x 960 px, learning rate of 0.001, and SGD optimization algorithm. The training set comprised 3000 images, with 500 in the validation set.
To accurately detect vehicles using YOLOv5 and analyze their parameters, it was essential to address the issue of image distortions caused by various factors and establish a method to convert image coordinates to GNSS coordinates. Figure 4 shows an example of a distorted image.
To calibrate the camera images and map their coordinates to the GNSS coordinate system, the direct linear transformation (DLT) method [78] was employed, along with the POSIT (Pose from Orthographic and Scaling with Iterations) method [79] to calculate the position and orientation of vehicles. The necessary input data for these algorithms included details about the dimensions of the modeled area, reference points with known coordinates in both systems and information about the camera's optical configuration.
The specific section of the route that was simulated represented an intersection measuring 29.4 meters in width and 24.4 meters in length. Reference points were established in the camera coordinates to align with points in the intersection coordinate system: (0, 244), (0, 122), (0, 0), (147, 0), (294, 0), (294, 122), (294, 244), (147, 244).
A graphical representation of corner points from the intersection coordinate system is shown in Figure 5.
Frame marking was conducted after correcting distortions using the Nelder-Mead method implemented through the Python SciPy library in conjunction with the Python OpenCV library. Figure 6 illustrates this process.

3.2. Tracking Algorithm and Indirect Calculation of Vehicle Characteristics

Four straight-line equations were formulated to define the boundaries of the visibility area along the route to improve the accuracy of tracking vehicle trajectories. The centers of objects within this area were identified in each frame, and the distances between these centers in consecutive frames were calculated using the Euclidean metric. When the distance traveled by a vehicle between frames exceeded a set threshold, its movement was recorded, and its trajectory was determined. Figure 7 illustrates the movement of objects in frames t1 and t2.
The distance traveled in pixels between two frames for each object was used to calculate the speed of vehicles as an example of indirect characteristics. This distance allowed for determining the speed at the current time step:
v k m / h = d ( C 1 C 2 ) 3600 ⋅ F P S ,
where d(...) is the calculation of the Euclidean metric, Ci is the selected object center coordinates on the frame's pixel grid, and FPS is the number of frames per second.
One-dimensional Kalman filtering was applied to all indirect characteristic calculations to provide a recursive estimation of the current speed value:
x ˙ k = x ˙ k − 1 + K G ( z k − x ˙ k − 1 ) ,
where zk is the calculated speed value, x ˙ k − 1 is the speed estimate at the previous step, and KG is Kalman Gain, which is calculated:
K G = E E S T t E E S T t + E E M A ,
where EEST is the uncertainty of the current value estimate, and EMEA is the tracking algorithm's error in calculating the speed.

4. Simulation Results of the SMTF Calibration Algorithm and Comparison of Results with PTS

The intersection of Karl Marx and Sverdlov streets in Ufa was chosen as a simulated section for creating and calibrating the SMTF. The coordinates of the video surveillance camera at this location are latitude 54.725376 and longitude 55.940998.
Using OpenStreetMap (OSM) data, a SUMO model was developed with traffic parameters set to Through Traffic Factor = 5 and Count = 12. The initial simulation involved 5000 steps, divided into six parts to establish the SMTF and subsequent calibration during the initial simulation. For example, to extract an indirect parameter of vehicles, we chose the parameters of speed, time of signal transmission from the vehicle to the infrastructure object, and the vehicle's rotation angle relative to the geographic north.
The simulated route area within a 600-meter radius from the camera location was divided into 40 sectors using Geohash coding (see Figure 8).
Traffic speed trends were extracted using LOESS for the first 833 simulation steps (see Figure 9). After averaging the calculated values of τSn, a time interval τS of 60 simulation steps was chosen, approximating a minute of real-time.
In subsequent five iterations generating new data from the SUMO model, the average global and local learning times were 3500 and 110 milliseconds, respectively. Global SMTF calibration initialization occurred in 5 out of 70 drift tracking iterations, while local calibration was observed in 26 cases.
After simulating the SMTF calibration, the model calibration was first tested based on data from an actual video stream of the PTS intersection. Of the 40 sectors in the new dataset, information was only available for six sectors in the center of the intersection. When initializing a new data drift monitoring cycle, global calibration of the model was not required due to a slight divergence in the trends of all parameters under consideration. Local calibration was initiated only for four sectors for the speed parameter, 2 for the signal transmission time parameter, and 1 for the rotation angle.
Data obtained directly from a moving vehicle in the simulated area was recorded using a programmable microcontroller ELM327 from ELM Electronics, which supports OBD-II protocols [80] (p. 15031), to monitor vehicle data in real-time.
The performance of the calibration system was assessed by comparing data from the ELM327 and data generated by the SMTF before and after SMTF calibration. Two methods were used to compare the data: assessing the degree of statistical elimination of drift in data from the SMTF relative to the PTS and assessing the performance of the ML regression model trained on the SMTF data to determine the positions of the main lobe of the radiation pattern for establishing communication between the V2I infrastructure object and the vehicle.
To assess the statistical efficiency of SMTF calibration, the Kolmogorov-Smirnov (K-S) test was used, which is used to compare two samples to confirm that they belong to the same distribution [81] (p. 14). The results of the K-S test showed a decrease in the maximum absolute difference between the distributions of the video stream data and the calibrated SMTF compared to the original model trained on SUMO data. An example of the original velocity distribution obtained from the SUMO model, the velocity distribution from the FTP, and the distribution after model calibration are presented in Figure 10.
Thus, the results of the average level of reduction in the maximum absolute difference between the distributions of vehicle parameters are:
  • for the signal transmission time from the vehicle to the infrastructure object, a reduction of 37.64% was reached;
  • for vehicle speed, a reduction of 72.89% was achieved;
  • for the angle of rotation of the car relative to the geographic north, a reduction of 49.27% was acquired.
To test the stability of the phased array antenna beam steering algorithm when working with data from the PTS, input data, including the specified generated parameters, were created to train the ML model.
A special algorithm was developed to generate the target variable — the number of the sector in which the main lobe of the phased array antenna should be directed — in order to minimize connection delays and maintain a stable communication channel for the car. This algorithm associates clusters with sectors based on the vehicle's location at the time of connection to the V2I network or its movement through the simulated area. The algorithm generated random coordinates within the sector area and assigned properties to simulate a request to connect a vehicle.
Two identical ET models were trained after generating two SMTF data sets - before and after calibration. Their accuracy was assessed on ELM327 data using metrics to measure regression performance: mean absolute error (MAE), root mean square error (MSE), root mean square log error (RMSLE), coefficient of determination (R2), and mean absolute percentage error (MAPE). The average cross-validation results on ELM327 data are presented in Table 1.
A decrease in the MAE, MSE, RMSE, RMSLE, and MAPE metrics indicates a reduction in the discrepancy between the predicted directions of the main lobe of the radiation pattern and the vehicle's location. A significant increase in R2 indicates a decrease in the variance of the dependent variable relative to the independent ones, which indicates a decrease in data drift for the ML model integrated into the VTS.
The results confirm the effectiveness of the calibration algorithm based on global and local regression models and the vehicle data synthesis algorithm using YOLOv5-processed video stream data. Tests also show that the proposed method for extracting vehicle characteristics from a video stream allows data collection without creating a WSN, which requires upgrading city infrastructure and installing sensors on vehicles. This could reduce the costs of implementing urban ITS.

5. Discussion

The developed system for creating SMTF with the possibility of global and local calibration using data from the PTS has demonstrated high adaptability to temporal and spatial deviations from the actual dynamics of traffic flow. The algorithm for extracting vehicle characteristics from video stream analysis ensured high registration accuracy, which was confirmed by tests on the correspondence of the distributions of parameters of the data from the video stream analysis and from the sensor system of the test car (the K-S test will be carried out using data from the AI and the tracker).
In our future work, we plan to introduce a cluster formation algorithm to enhance the spatial accuracy of the simulation model. This algorithm will be based on the selection of elements of the simulated section of the path. Importantly, it will be designed to adapt their boundaries to the operation of specific VTS algorithms, such as the boundaries of the sectors of the beam steering algorithm of the phased array antenna, which plays a crucial role in our model.
An essential part of expanding the areas of application of SMTF will be integrating a microscopic traffic model into it, which will allow for simulation of the movement of specific vehicles within and between the cluster.

6. Conclusions

The proposed method for creating and calibrating a traffic simulation model showcased a significant increase in the statistical alignment between generated vehicle characteristics and actual car data on a simulated highway segment, improving from 37% to 73%. This enhancement was enabled by the approach's ability to calibrate the simulation model globally for overall trend changes and locally for specific route segments, offering flexibility and potentially saving time as local calibration could often replace global adjustments. Additionally, by reducing data drift for machine learning models integrated into the VTS system, the results indicate the algorithm's accuracy in synthesizing vehicle characteristics based on video traffic flow analysis. This capability eliminates the need to deploy WSN, potentially reducing the costs of implementing intelligent transportation systems.

Author Contributions

Conceptualization, E.L., E.G. and G.V.; methodology, E.L.; software, E.L. and A.A.; validation, E.L.; formal analysis, E.L., E.G. and G.V.; investigation, E.L. and A.A.; resources, E.L., E.G. and G.V.; data curation, E.L.; writing—original draft preparation, E.L.; writing—review and editing, E.G. and G.V.; visualization, E.L. and G.V.; supervision, E.G.; project adminis- tration, E.G.; funding acquisition, E.G. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded under the grant of the Russian Science Foundation (Project №21-79- 10407).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

A dataset for training the ML algorithm is available on request to the corresponding author’s e-mail.

Conflicts of Interest

The authors declare no conflict of interest.

Sample Availability

Not applicable.

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Figure 1. Distribution of frequencies of cluster intersections by vehicles in the simulated area: SUMO - according to the SUMO model, Real - according to the PTS model.
Figure 1. Distribution of frequencies of cluster intersections by vehicles in the simulated area: SUMO - according to the SUMO model, Real - according to the PTS model.
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Figure 2. Deviation of speed distribution characteristics obtained from SMTF and PTS.
Figure 2. Deviation of speed distribution characteristics obtained from SMTF and PTS.
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Figure 3. SMTF creation and calibration process.
Figure 3. SMTF creation and calibration process.
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Figure 4. Original image with distortion.
Figure 4. Original image with distortion.
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Figure 5. Graphical representation of corner points from the intersection coordinate system. Values are converted to decimeters.
Figure 5. Graphical representation of corner points from the intersection coordinate system. Values are converted to decimeters.
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Figure 6. YOLOv5 video stream frame marking.
Figure 6. YOLOv5 video stream frame marking.
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Figure 7. Car movement on frames t1 and t2.
Figure 7. Car movement on frames t1 and t2.
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Figure 8. Division of the simulated area into sectors.
Figure 8. Division of the simulated area into sectors.
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Figure 9. Division of the simulated area into sectors.
Figure 9. Division of the simulated area into sectors.
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Figure 10. Cumulative distribution functions of the speed from the PTS and its generated values before and after calibration.
Figure 10. Cumulative distribution functions of the speed from the PTS and its generated values before and after calibration.
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Table 1. Average values of cross-validation of ML models on data from ELM327.
Table 1. Average values of cross-validation of ML models on data from ELM327.
Model MAE MSE RMSE R2 RMSLE MAPE
Trained on SMTF data before calibration 4.1787 4.1787 4.9245 -6.9719 0.7595 1.4117
Trained on SMTF data after calibration 0.0318 0.0189 0.1376 0.9938 0.0266 0.0076
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