Method and device for estimating vehicle mass center side slip angle, and vehicle

Abstract

This application provides a method, apparatus, and vehicle for estimating the sideslip angle of a vehicle's center of gravity. The method includes at least: acquiring vehicle operating state data; determining input data from the operating state data for inputting into a preset estimator; wherein the input data is used to characterize the degree of lateral change of the vehicle; and processing the input data using the preset estimator to determine the real-time sideslip angle of the vehicle's center of gravity.

Description

Technical Field

[0001] This application relates to vehicle technology, and in particular to a method, apparatus, and vehicle for estimating the sideslip angle of a vehicle's center of gravity. Background Technology

[0002] In the development of automobiles, the performance of vehicle active safety control systems increasingly relies on the accurate perception of the vehicle's motion state. Among these parameters, the center-of-gravity sideslip angle, as a core parameter for measuring a vehicle's lateral stability and sideslip tendency, directly affects the control effectiveness of key functions such as electronic stability control and direct yaw moment control. Due to the high cost and difficulty in mass production and deployment of high-precision sensors (such as inertial navigation systems), algorithm-based methods for estimating the center-of-gravity sideslip angle have become the mainstream technical approach.

[0003] In related technologies, data-driven methods are generally used to estimate the centroid sideslip angle by employing machine learning models such as deep neural networks and training them with historical data. However, such methods require a large amount of high-quality labeled data, which is difficult and risky to acquire, especially under extreme operating conditions. At the same time, the model structure is complex, has poor generalization ability, and consumes a lot of onboard computing resources, making it difficult to meet real-time control requirements. Summary of the Invention

[0004] To address the aforementioned problems, this application provides at least one method, apparatus, and vehicle for estimating the vehicle's center of gravity sideslip angle. This solution achieves high-precision and high-real-time performance estimation of the center of gravity sideslip angle even with small sample data.

[0005] The technical solution of this application is implemented as follows: In a first aspect, this application provides a method for estimating the sideslip angle of a vehicle's center of gravity. The method includes: acquiring vehicle operating state data; determining input data from the operating state data for inputting into a preset estimator; wherein the input data is used to characterize the degree of lateral change of the vehicle; and processing the input data using the preset estimator to determine the real-time sideslip angle of the vehicle's center of gravity.

[0006] Secondly, this application provides a device for estimating the sideslip angle of a vehicle's center of gravity. The device includes: an acquisition unit for acquiring vehicle operating state data; a determination unit for determining input data from the operating state data for inputting into a preset estimator; wherein the input data is used to characterize the degree of lateral change of the vehicle; and a processing unit for processing the input data using the preset estimator to determine the real-time sideslip angle of the vehicle's center of gravity.

[0007] Thirdly, this application provides a vehicle, a sensor, and a controller. The sensor is used to acquire vehicle operating status data, and the controller is used to process the operating status data to implement the method provided in the first aspect.

[0008] Fourthly, this application also provides a storage medium storing a computer program or instructions that, when executed by a processor, implement any of the methods provided in the first aspect above.

[0009] Fifthly, this application also provides a computer program product comprising a computer program or instructions that, when executed by a processor, implement any of the methods provided in the first aspect above.

[0010] This scheme first acquires vehicle operating status data, then extracts input data that characterizes the degree of lateral change of the vehicle, which serves as input to a preset estimator. The preset estimator then processes the input data to output the vehicle's real-time centroid sideslip angle. This method avoids the strong dependence of traditional models on tire nonlinear parameters by constructing a lightweight machine learning estimator that integrates vehicle physical characteristics. It also overcomes the requirement of massive training data for purely data-driven methods, achieving high-precision, high-real-time centroid sideslip angle estimation even with small sample data. Attached Figure Description

[0011] Figure 1 A schematic flowchart of an optional method for estimating the vehicle center of gravity sideslip angle provided in an embodiment of this application; Figure 2 A schematic flowchart of an optional process for estimating the centroid sideslip angle provided in an embodiment of this application; Figure 3 This is a schematic diagram of an optional structure of the vehicle center of gravity sideslip angle estimation device provided in the embodiments of this application.

[0012] It should be noted that the terms "first" and "second" mentioned above are only used to distinguish between different options and do not represent the degree of superiority or inferiority of the options or their priority in the implementation process. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the specific technical solutions of the application will be further described in detail below with reference to the accompanying drawings of the embodiments of this application. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application.

[0014] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0015] In the following description, the terms "first," "second," and "third" are used only to distinguish different objects and do not represent a specific order of objects, nor are they constituting a chronological order. It is understood that "first," "second," and "third" may be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0016] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0017] This application provides a method, apparatus, vehicle, storage medium, and program product for estimating the sideslip angle of a vehicle's center of gravity. The following describes various embodiments of the method, apparatus, vehicle, storage medium, and program product for estimating the sideslip angle of a vehicle's center of gravity provided in this application.

[0018] To facilitate understanding, some technical terms will be explained first.

[0019] In a first aspect, embodiments of this application provide a method for estimating the sideslip angle of a vehicle's center of gravity. This control method can be executed by a device for estimating the sideslip angle of the vehicle's center of gravity. The device for estimating the sideslip angle of the vehicle's center of gravity can be deployed in an electronic device or a vehicle and implemented through a program stored in a memory by a processor.

[0020] To facilitate understanding, some of the technical terms involved in this embodiment will be explained first.

[0021] Side slip angle: This refers to the lateral offset of the vehicle's center of gravity relative to its direction of travel. It is a key parameter characterizing vehicle handling stability, sideslip tendency, and extreme maneuverability. This angle increases significantly when the vehicle experiences sideslip or oversteer / understeer, directly impacting driving safety and control performance. In vehicle dynamics models, the side slip angle is typically calculated as the ratio of lateral velocity to longitudinal velocity.

[0022] Kernel functions: In machine learning, a kernel function is a function used to calculate the inner product of two data points in a high-dimensional feature space without explicitly mapping the data to a high-dimensional space. It indirectly calculates similarity in the feature space by performing operations in the original input space. In this application, kernel functions are used to construct kernel matrices, transforming the problem of an infinite-dimensional feature space into solving a system of linear equations in finite dimensions. This avoids complex feature extraction and high-dimensional computation, significantly reducing algorithm complexity and achieving lightweight, real-time online estimation.

[0023] Constrained optimization problems refer to mathematical optimization problems that require satisfying a set of pre-defined constraints while optimizing the objective function. In this application, the constrained optimization problem has two main objectives: first, to minimize the error between the actual lateral velocity and the estimated lateral velocity; and second, to homogenize the estimator parameters to prevent some parameters from becoming too large and causing model instability. By introducing Lagrange multipliers, the original constrained optimization problem is transformed into an unconstrained Lagrangian function optimization problem, thereby deriving an optimal estimator framework with analytical expressions.

[0024] Analytical expression: This refers to an expression whose result can be directly calculated using an explicit mathematical formula, without the need for iteration or numerical approximation. This application, through mathematical derivation of kernel functions and Lagrange multipliers, ultimately obtains a linear expression based on the kernel matrix of the training data, used for real-time calculation of lateral velocity estimates. This analytical form minimizes the computational load of the estimation process, fully meeting the stringent millisecond-level real-time requirements of automotive embedded systems.

[0025] Small sample data-driven: This refers to methods that require only a small amount of high-quality, representative training data to complete model training. Unlike traditional deep learning, which relies on massive amounts of labeled data, this application transforms the infinite-dimensional feature problem into a system of linear equations based on finite training data through constrained optimization and kernel function matrix derivation. Therefore, only a small amount of real vehicle test data covering normal and typical extreme conditions needs to be collected to train a high-precision estimator, significantly reducing the data acquisition threshold and calibration cost.

[0026] Machine learning incorporating physical mechanisms refers to methods that integrate domain expertise (such as vehicle dynamics models) and physical laws (such as lateral response errors) into the design of machine learning models. This application is not a pure black-box model; its input vector and scheduling vector are designed based on in-depth analysis of the vehicle system dynamics model, ensuring that the model has good physical interpretability and generalization ability, especially maintaining high estimation accuracy under unseen extreme conditions.

[0027] The following section uses a vehicle as an example to explain the method for estimating the vehicle's center of gravity sideslip angle.

[0028] refer to Figure 1 The process may include, but is not limited to, S101 to S103 described below.

[0029] S101, The vehicle acquires the vehicle's operating status data.

[0030] Operational status data refers to vehicle status data related to the degree of lateral change in the vehicle. For example, operational status data includes at least vehicle speed and steering wheel angle, and may also include other data. These include wheel speed signals, front wheel steering angle signals, yaw rate signals, longitudinal speed signals, lateral acceleration signals, and tire force signals. Specifically, wheel speed signals are provided by wheel speed sensors installed on each wheel and are used to calculate the vehicle's longitudinal speed and lateral slip ratio; front wheel steering angle signals are collected by steering angle sensors, reflecting the driver's steering intention; yaw rate signals are output from the gyroscope in the inertial measurement unit, characterizing the vehicle's rotational rate around its vertical axis; and longitudinal speed and lateral acceleration signals are calculated by combining wheel speed information with accelerometer data from the inertial measurement unit.

[0031] All sensor data is sampled at high frequencies (e.g., above 100Hz) and transmitted via bus or Ethernet to the vehicle control unit or domain controller for processing. For example, during high-speed cornering, the left front wheel speed signal is 80 km / h, the right front wheel speed signal is 78 km / h, the front wheel steering angle signal is 15 degrees, the yaw rate signal is 0.5 rad / s, and the lateral acceleration signal is 2.5. These data together constitute a complete description of the vehicle's current motion state. Another example is during emergency avoidance on a slippery road surface, where the four wheel speed signals differ significantly. The front wheel steering angle signal suddenly increases to 30 degrees, the yaw rate signal reaches 1.2 rad / s, and the peak lateral acceleration signal reaches 3.0 m / s². In this situation, the vehicle control unit or domain controller needs to respond quickly to prevent loss of control.

[0032] In practical implementation, acquiring vehicle operating status data is fundamental to the entire estimation process, ensuring the reliability of data sources for subsequent feature extraction and model computation. Multi-source sensor fusion not only improves data accuracy but also enhances the system's robustness to abnormal signals. For example, if a wheel speed signal malfunctions, compensation estimation can be performed using the other three wheel speed signals and the longitudinal speed signal, preventing the estimation system from collapsing due to a single point of failure. Simultaneously, high-frequency sampling ensures dynamic response capabilities, meeting the millisecond-level latency requirements of vehicle control. The technical advantage of acquiring vehicle operating status data lies in constructing a comprehensive, accurate, and real-time vehicle status perception system, providing the necessary input conditions for subsequent accurate estimation of the centroid sideslip angle.

[0033] S102, The vehicle determines the input data from the operating status data to input the preset estimator.

[0034] The input data is used to characterize the degree of lateral change of the vehicle.

[0035] Operational status data can be uniformly organized into input data. This data can be divided into two categories based on its impact on the vehicle's lateral deformation. For example, the input data could include: first feature data and second feature data. The first feature data has a greater impact on the vehicle's lateral deformation than the second feature data.

[0036] The preset estimator is an intelligent formula trained in advance using a small amount of high-quality data by solving equations. When running on the vehicle, it acts like a high-speed calculator, instantly calculating the precise sideslip angle by inputting real-time data, combining the lightweight efficiency of a physical model with the adaptive capabilities of a data-driven model.

[0037] In practical implementation, the core of determining the input data for the preset estimator from the vehicle's operating status data lies in extracting physically meaningful and statistically representative feature variables from the raw sensor data to form an input vector. According to the vehicle dynamics model analysis, the key factors affecting lateral speed include: the front wheel steering angle signal δ at the current moment, the yaw rate signal r, the four wheel speed signals, the estimated lateral speed at historical moments, and the difference between the ideal lateral acceleration based on the driver's input and the actual lateral acceleration (i.e., the lateral response error).

[0038] Among them, the steering wheel angle δ(k) and yaw rate r(k) serve as the core control inputs, directly determining the vehicle's steering behavior; the four wheel speed signals reflect the actual driving state of the vehicle and are used to calculate the longitudinal speed and lateral slip ratio; the estimated lateral speed at historical moments reflects the temporal dependence of the system, because the current state in a discrete system is often affected by the state at the previous moment.

[0039] In addition, to enhance the model's adaptability under extreme conditions, a lateral response error Δa_y(k) is introduced. The lateral response error Δa_y(k) is close to zero when the vehicle is stable, but increases significantly when there is oversteering or understeering. Therefore, it is used as part of the scheduling vector p(k) to dynamically adjust the estimator weights.

[0040] In practical implementation, input data for the preset estimator is determined from the target vehicle's operational status data. By constructing an input vector that integrates physical mechanisms, the generalization ability and robustness of the estimator are significantly improved. For example, when the target vehicle enters an S-curve at 80 km / h, the front wheel steering angle signal changes continuously, and the yaw rate signal fluctuates significantly. The system can promptly capture the changing trend of the lateral response error Δa_y(k) and adjust the model parameters to adapt to nonlinear conditions.

[0041] For example, when making a sharp turn on an icy or snowy road, the actual lateral acceleration signal is much lower than the ideal value due to the decrease in tire adhesion, and the lateral response error Δa_y(k) increases sharply. The scheduling vector p(k) is updated accordingly, allowing the estimator to automatically reduce its dependence on traditional model parameters and rely more on the data-driven mechanism, thereby avoiding model divergence. The technical effect of determining the input data for the preset estimator from the target vehicle's operating state data is that it achieves an effective transformation from raw data to structured input features, ensuring that the estimator can fully perceive the lateral dynamic changes of the target vehicle, and maintain high-precision estimation, especially under extreme conditions.

[0042] S103. The vehicle uses a preset estimator to process the input data to determine the vehicle's real-time centroid sideslip angle.

[0043] In one possible implementation, a preset estimator is trained as a model for estimating the real-time centroid sideslip angle. Thus, when input data is fed into the preset estimator, the preset estimator estimates the real-time centroid sideslip angle based on the input data and directly outputs the real-time centroid sideslip angle.

[0044] In another possible implementation, a preset estimator is trained as a model for estimating the lateral velocity of a real-time vehicle. Thus, input data is fed into the preset estimator, which estimates the lateral velocity of the vehicle based on the input data and outputs the lateral velocity. Then, based on the estimated lateral velocity and the longitudinal velocity, the vehicle's center of gravity sideslip angle is determined.

[0045] This scheme first acquires vehicle operating status data, then extracts input data that characterizes the degree of lateral change of the vehicle, which serves as input to a preset estimator. The preset estimator then processes the input data to output the vehicle's real-time centroid sideslip angle. This method avoids the strong dependence of traditional models on tire nonlinear parameters by constructing a lightweight machine learning estimator that integrates vehicle physical characteristics. It also overcomes the requirement of massive training data for purely data-driven methods, achieving high-precision, high-real-time centroid sideslip angle estimation even with small sample data.

[0046] The input data is explained below.

[0047] The input data includes first feature data and second feature data; the first feature data includes first historical data related to the vehicle's lateral motion, and the second feature data includes first real-time data related to the vehicle's lateral response difference, which is determined based on the difference between the actual lateral acceleration and the desired lateral acceleration.

[0048] The first feature data (input vector) forms the "state memory foundation" of the estimator. It mainly contains historical moment data directly related to the vehicle's lateral motion, such as the front wheel steering angle and yaw rate at the previous and current moments, as well as the estimated lateral velocity at the previous moment (or even the moment before that). The selection of this data strictly follows the time-dependent characteristics of the vehicle's lateral dynamics differential equations and discrete systems, essentially providing the machine learning model with initial state values ​​and evolutionary trajectory information for lateral motion, enabling the estimator to capture the dynamic changes in lateral velocity.

[0049] The second feature data (scheduling vector) serves as the estimator's "condition-aware antenna." It focuses on reflecting in real-time how close the vehicle is to its handling limits. Its most innovative feature is the lateral response difference—the deviation between the vehicle's actual lateral acceleration and the ideal lateral acceleration expected based on the driver's front wheel steering angle input. A significant increase in this difference indicates that the tires have entered a highly nonlinear region or are approaching their adhesion limits. Using this difference and its rate of change (ΔΔa_y) as real-time features is equivalent to telling the estimator "whether the current condition is linear or nonlinear," allowing the model to adaptively adjust the estimation weights based on the vehicle's stability margin, significantly improving the estimation robustness under extreme conditions.

[0050] In some embodiments, the first feature data is the data after weighting the first historical data with first weight data, and the second feature data is the data after weighting the first real-time data with second weight data.

[0051] Both the first weighted data (Wx) and the second weighted data (Wp) are diagonal positive semi-definite matrices, applied to the first historical data and the first real-time data, respectively. Their most basic functions are dimensional normalization and feature selection. Since the original features contain physical quantities with different dimensions such as angle, velocity, and acceleration, and their numerical ranges vary significantly (e.g., yaw rate is only 0-1 rad / s, while wheel speed can reach over 100 m / s), without weighted scaling, large numerical features would dominate the kernel function calculation results, causing information from smaller numerical features to be overwhelmed. By independently scaling the diagonal matrices, all features can be mapped to similar orders of magnitude, allowing the estimator to utilize each physical feature equally. Simultaneously, high weights are assigned to core physical quantities (such as yaw rate and historical lateral velocity), while low weights are assigned to secondary or redundant features. This eliminates invalid interference under small sample conditions, enabling the limited data to focus on learning the most critical patterns.

[0052] The weight matrix is ​​not a fixed constant, but dynamically adjusted according to global states such as vehicle speed, steering angle, and yaw rate, achieving adaptive feature enhancement based on operating conditions. For example, under extreme conditions such as high speed or large steering, the system automatically increases the weight of the "lateral response difference" and its rate of change, making the estimator more sensitive to sudden changes in tire nonlinearity; while in the low-speed linear region, the weight is appropriately reduced to avoid excessive amplification of sensor noise. This dynamic weighting strategy enables the same estimator framework to maintain optimal estimation performance across the entire operating condition range from the linear region to the extreme nonlinearity. Its deeper physical meaning is that the weight matrix is ​​essentially a "mathematical implementation of feature engineering." It not only undertakes the basic function of data preprocessing, but also deeply integrates prior knowledge of vehicle dynamics into the machine learning framework through adaptive adjustment based on operating conditions, ultimately achieving an organic unity between "small sample data-driven" and "strong physical consistency."

[0053] In some embodiments, the first feature data includes at least one of the following: historical estimated lateral speed, historical front wheel steering angle, and historical yaw rate.

[0054] Historical estimated lateral velocity refers to the velocity component corresponding to the vehicle's sideslip angle, estimated by the system within one or more sampling periods prior to the current moment. Historical estimated lateral velocity is typically derived from the lateral velocity estimate of the previous moment and reflects the continuity of the vehicle's motion over time; it is a crucial component in constructing the input vector. Due to the inertial nature of vehicle motion, the current lateral velocity is closely related to the historical estimated lateral velocity of the previous moment. Therefore, incorporating historical estimated lateral velocity into the input vector can effectively improve the estimation model's adaptability to dynamic changes. For example, when the vehicle is making continuous turns, ignoring historical estimated lateral velocity information may lead to jumps or lags in the estimated values; introducing historical estimated lateral velocity can smooth the transition and enhance stability.

[0055] The historical front wheel steering angle refers to the instantaneous steering angle of the vehicle's front wheels relative to the vehicle's coordinate system. The value of the historical front wheel steering angle directly reflects the driver's steering intention and the intensity of the vehicle's steering input. The historical front wheel steering angle is one of the core control variables affecting the vehicle's lateral dynamics, transmitting forces to the ground through the tires and thus altering the vehicle's lateral acceleration and yaw rate. Including the historical front wheel steering angle in the input vector helps the model capture the direct impact of steering operations on lateral velocity, especially in conditions such as sharp turns or lane changes, enabling more accurate prediction of changes in vehicle state.

[0056] Historical yaw rate refers to the angular velocity of a vehicle's rotation around its vertical axis, representing the overall rotational motion of the vehicle. Historical yaw rate is a key indicator for measuring changes in vehicle attitude, and its magnitude is closely related to the vehicle's steering response and sideslip tendency. Incorporating historical yaw rate into the input vector can help the prediction model understand the vehicle's current dynamic behavior, such as whether it is drifting, fishtailing, or in a stable driving state. For example, when the historical yaw rate is large and continues to increase, it may indicate that the vehicle is approaching its handling limits; in this case, the prediction model should assign higher weights to adjust the estimation strategy.

[0057] These three features together form the foundation of the input vector, and there is a close physical relationship between them. The historical estimated lateral velocity has a time-series dependency with the current lateral velocity, reflecting the dynamic characteristics of the system; the historical front wheel steering angle serves as a control input, driving the vehicle to generate lateral acceleration, which in turn affects the lateral velocity; and the historical yaw rate serves as the system output response, reflecting the vehicle's responsiveness to steering inputs. The combination of these three features forms a complete input-state-output closed-loop description, giving the machine learning model stronger physical interpretability and generalization ability.

[0058] In practical applications, the dynamic characteristics of a vehicle can be acquired in real time by onboard sensors (such as IMU and steering angle sensors), and then filtered and synchronized by the signal processing module before being input into the estimator. For example, during high-speed cornering, the vehicle state estimation system continuously acquires the system's historical front wheel steering angle, system's historical yaw rate, and system's historical estimated lateral velocity at each moment, and combines the above data into an input vector for subsequent kernel function calculations.

[0059] In this embodiment, by using historical estimated lateral velocity, historical front wheel steering angle, and historical yaw rate as the first feature data, not only is the temporal continuity of vehicle motion preserved, but the coupling relationship between key control inputs and system response is also fully considered. This improves the model's adaptability to complex dynamic conditions, thereby enhancing estimation accuracy and ultimately improving the stability and reliability of the vehicle's active safety control system under extreme conditions.

[0060] The second feature data includes at least one of the following: the vehicle lateral response difference at the current time, and the rate of change of the vehicle steering response difference at the current time.

[0061] The current vehicle lateral response difference refers to the difference between the actual lateral acceleration generated by the vehicle at the current sampling moment and the desired lateral acceleration expected based on the driver's steering input. The formula for calculating the current vehicle lateral response difference is: actual lateral acceleration minus desired lateral acceleration. The desired lateral acceleration is calculated based on the vehicle's wheelbase and historical front wheel steering angle, i.e.: desired lateral acceleration = historical front wheel steering angle × longitudinal velocity² / vehicle wheelbase. Essentially, the current vehicle lateral response difference reflects the vehicle's error in responding to driver commands. When the vehicle is in a stable state, the current vehicle lateral response difference is close to zero; when the vehicle approaches or enters extreme operating conditions, due to insufficient tire adhesion or increased nonlinear effects, the current vehicle lateral response difference will significantly increase, reflecting the vehicle's tendency to sideslip or lose control.

[0062] The rate of change of the vehicle's steering response difference at the current moment refers to the rate at which the vehicle's lateral response difference changes over time; it is calculated by discrete differentiation of the vehicle's lateral response difference at the current moment. This rate of change reflects the severity of the vehicle's dynamic response and is an important basis for judging whether the vehicle is rapidly approaching its extreme operating conditions. For example, during emergency avoidance, if the vehicle's lateral response difference increases rapidly at the current moment, it indicates that the vehicle is experiencing a severe change in lateral force, and the vehicle control system should immediately initiate intervention measures.

[0063] These two parameters together constitute the core of the scheduling vector, and there is a logically progressive relationship between them. The lateral response difference of the vehicle at the current moment provides the static deviation of the current state, while the rate of change of the steering response difference of the vehicle at the current moment reveals the dynamic trend. Combining these two parameters allows for a multi-dimensional assessment of the vehicle's handling limits. For example, if the lateral response difference of the vehicle at the current moment is small, but the rate of change of the steering response difference of the vehicle at the current moment is large, it indicates that although the vehicle is not completely unstable, it is approaching its limits with high acceleration, requiring early warning. Conversely, if the lateral response difference of the vehicle at the current moment is large, but the rate of change of the steering response difference of the vehicle at the current moment is small, it may already be in a stable slip state, requiring different control strategies.

[0064] In practice, the system calculates the two parameters mentioned above in each control cycle and passes the scheduling vector as input to the estimator. For example, in the chassis control system of a certain intelligent electric vehicle, the controller collects IMU data and steering angle signals every 10ms, calculates the difference in vehicle lateral response and its rate of change at the current moment, and then combines it with other input features to call a pre-trained kernel function model to output the estimated lateral speed value in real time.

[0065] In this embodiment, by using the vehicle's lateral response difference at the current moment and the rate of change of that difference as the second feature data, the degree to which the vehicle approaches its handling limits can be effectively quantified. This allows for dynamic adjustment of the estimator's weight allocation, thereby improving the model's robustness and accuracy under nonlinear conditions, and ultimately enhancing the real-time response capability and safety of the vehicle's active safety control system.

[0066] In some embodiments, the historical estimated lateral speed, historical front wheel steering angle, and historical yaw rate each include data from two adjacent historical moments.

[0067] Historical estimated lateral velocity refers to the lateral velocity value calculated by the system based on the vehicle dynamics model or previous estimates up to the current moment. Historical estimated lateral velocity reflects the vehicle's lateral motion state at one or more recent time points and is a crucial component in constructing the input vector. It contains data from two consecutive historical time points—estimates from the previous time point (k-1) and the time point before that (k-2)—to capture trends in lateral velocity changes, thereby improving the estimator's adaptability to dynamic conditions. For example, when a vehicle is making a sharp turn, continuous historical estimated lateral velocity data helps the system determine whether it is currently in an acceleration / slippage or deceleration / right-side-off phase, thus optimizing the accuracy of the current lateral velocity estimate.

[0068] Historical front wheel steering angle refers to the steering angle of the vehicle's front wheels relative to the vehicle's coordinate system up to the current moment. The historical front wheel steering angle is a key control input affecting the vehicle's lateral acceleration and yaw rate, directly related to the driver's steering intentions. In this invention, the historical front wheel steering angle includes data from two consecutive historical moments, namely the angle values ​​at the previous moment (k-1) and the moment before that (k-2), reflecting the continuity and rate of change of front wheel steering operations. For example, when a vehicle enters a curve, continuous historical front wheel steering angle data can help the system determine whether the steering is smooth or sudden, thereby more accurately predicting the vehicle's response behavior.

[0069] Historical yaw rate refers to the angular velocity of a vehicle's rotation around its center of mass up to the current moment. It characterizes the overall rotational trend of the vehicle and is an important indicator for assessing vehicle stability. In this invention, the historical yaw rate includes data from two consecutive historical moments, namely the yaw rate values ​​at the previous moment (k-1) and the moment before that (k-2), used to analyze the dynamic process of vehicle attitude changes. For example, when a vehicle experiences a fishtail or understeer, continuous historical yaw rate data can reveal the intensification or mitigation of the rotational trend, providing the control system with a more comprehensive state perception.

[0070] The inclusion of data from two consecutive historical moments for each of the historical estimated lateral velocity, historical front wheel steering angle, and historical yaw rate means that the input vector construction system considers the values ​​from two points prior to the current moment. This design not only enhances the temporal dimension of the input vector but also improves the estimator's generalization ability to nonlinear conditions. For example, when the vehicle approaches its handling limits, continuous historical estimated lateral velocity, historical front wheel steering angle, and historical yaw rate data can more accurately capture sudden changes in tire force and drastic changes in vehicle attitude, thus avoiding estimation errors caused by single-point data.

[0071] Furthermore, the inclusion of data from two consecutive historical moments for each of the historical estimated lateral velocity, historical front wheel steering angle, and historical yaw rate, combined with the lateral response error index in the scheduling vector, further enhances the estimator's sensitivity to extreme conditions. By comparing the response differences between the current and historical moments, the system can dynamically adjust the estimation weights to ensure estimation accuracy in highly dynamic scenarios. This design, which integrates physical mechanisms and time-series information, enables the estimator to exhibit excellent real-time performance and robustness even under small-sample training conditions.

[0072] In this embodiment, the historical estimated lateral velocity, historical front wheel steering angle, and historical yaw rate are each limited to data containing two consecutive historical moments. This enriches the temporal dimension of the input vector, enabling more accurate capture of the changing trends in vehicle motion, and thus improving the accuracy and stability of lateral velocity estimation under extreme conditions.

[0073] In some embodiments, the second feature data further includes at least one of the following: the wheel speed of the vehicle's wheels at the current moment; the longitudinal velocity at the current moment; the longitudinal acceleration at the current moment; and the lateral acceleration at the current moment.

[0074] The wheel speed of the vehicle at the current moment can be determined as the first feature set, and the longitudinal velocity, longitudinal acceleration, and lateral acceleration at the current moment can be determined as the second feature set.

[0075] The first feature set refers to the data set containing wheel speed information of each wheel of the vehicle. Its function is to provide the wheel-end motion state of the vehicle at the current moment. Wheel speed is a fundamental variable in vehicle dynamics analysis, directly affecting the calculation of key state parameters such as lateral acceleration and yaw rate. In this application, the first feature set specifically emphasizes the wheel speed of each wheel of the vehicle at the current moment, i.e., real-time acquisition of the rotational speed signals of the four wheels, used as the initial input for constructing the scheduling vector. The wheel speed data of each wheel of the vehicle is usually acquired by wheel speed sensors (such as Hall effect sensors or magnetoresistive sensors), which have high sampling frequency and high accuracy, and can accurately reflect tire slip ratio and driving / braking state.

[0076] The second feature set refers to the data set containing parameters of the vehicle's longitudinal and lateral motion states. Its purpose is to provide a macroscopic description of the vehicle's overall dynamic behavior. The second feature set includes three parameters: the vehicle's longitudinal velocity, longitudinal acceleration, and lateral acceleration at the current moment. The vehicle's longitudinal velocity reflects the speed of its forward motion, its longitudinal acceleration reflects the acceleration or deceleration trend, and its lateral acceleration is directly related to its steering performance and sideslip risk. These three parameters together constitute the core indicators of the vehicle's motion state and are crucial for assessing whether the vehicle is in stable driving or under extreme conditions.

[0077] In real-world scenarios, when a vehicle makes a sharp turn on a slippery surface, the system reads the wheel speed of the vehicle's wheels in real time (first feature set), and simultaneously collects the longitudinal velocity, longitudinal acceleration, and lateral acceleration at the current moment (second feature set). For example, if the rear wheel speed is detected to be significantly higher than the front wheel speed, and the lateral acceleration at the current moment reaches a threshold, it indicates that the vehicle may be about to fishtail. In this case, the system will automatically assign higher weights to the scheduled vectors, prompting the estimator in the system to respond quickly and improving the estimation accuracy of the center of gravity sideslip angle.

[0078] In this embodiment, the first feature set is defined as the wheel speed of the vehicle at the current moment, and the second feature set is defined as including at least one of the vehicle's longitudinal velocity, longitudinal acceleration, and lateral acceleration at the current moment. This allows for accurate capture of the coordinated motion state of the vehicle's wheels and the entire vehicle, enabling multi-level modeling of the vehicle's dynamic characteristics and improving the estimator's adaptability and accuracy under different driving conditions.

[0079] In this embodiment, the second feature data is structurally expanded by introducing a first feature set and a second feature set. This enables refined classification and multi-dimensional representation of vehicle motion states, thereby enhancing the physical interpretability and information density of the scheduling vector. Consequently, it significantly improves the accuracy and real-time performance of the centroid sideslip angle estimation method under complex and extreme conditions, meeting the high-performance requirements of intelligent chassis control systems.

[0080] The following section explains the preset estimator.

[0081] The preset estimator is an analytical estimator, and it is trained and built based on data that characterizes the degree of lateral change of the vehicle.

[0082] This pre-defined estimator is essentially an analytical machine learning model built by embedding prior knowledge of vehicle dynamics into a kernel function framework. Its training process does not require massive amounts of data, only a small amount of high-quality real-vehicle data covering both normal and extreme operating conditions. For example, a constrained optimization problem can be constructed (with the objective of minimizing the weighted sum of estimation error and model complexity), and Lagrange multipliers can be introduced to transform the infinite-dimensional feature mapping into a system of linear equations with a finite-dimensional kernel matrix for solving—using the kernel function to calculate the similarity between features, directly obtaining the optimal estimator with a closed analytical expression. During training, the input data is carefully designed as "first feature data" (containing state memories such as historical lateral velocity and yaw rate) and "second feature data" (containing operating condition perception indicators such as lateral response difference and its rate of change), enabling the model to automatically determine the linear / nonlinear region of the vehicle based on the degree of lateral change, thereby achieving physically consistent adaptive estimation.

[0083] Compared to deep neural networks that rely on massive amounts of labeled data and complex backpropagation training, this analytical estimator achieves a fundamental leap in four dimensions: data efficiency, computational real-time performance, extreme generalization ability, and engineering interpretability.

[0084] At the data level, neural networks need to cover hundreds of thousands of samples covering all working conditions to implicitly learn the nonlinear characteristics of tires, while this solution only needs a small amount (usually hundreds of sets) of representative data to directly solve the model parameters through a system of linear equations, reducing the data acquisition cost and calibration cycle by more than an order of magnitude. At the computational level, neural network forward inference involves hundreds of thousands of floating-point multiply-accumulate operations and activation function calls, posing a severe challenge to the computing power of automotive microcontrollers. In contrast, the analytical solution of this scheme is only a lightweight kernel function accumulation operation, with a computation time of up to microseconds, which fully meets the stringent real-time requirements of millisecond-level control cycles. At the generalization level, pure black-box models are prone to producing abnormal outputs that violate physical laws under untrained conditions. However, this solution, due to the deep integration of physical indicators such as lateral response error, can maintain the estimation trend consistent with the actual dynamic behavior of the vehicle even in the extreme nonlinear region, thus avoiding the risk of "overfitting-failure" of neural networks. At the engineering implementation level, this solution has clear physical interpretability—each feature and weight corresponds to a clear vehicle dynamics meaning, which makes it easy for engineers to trace problems and perform calibration and debugging. However, the "black box" nature of neural networks makes it difficult for them to pass the stringent requirements of functional safety certification.

[0085] In summary, neural networks use massive amounts of data to "brute-force" mapping relationships, while this approach uses physical knowledge to analyze patterns. The former has significant value in academic research, while the latter is more robust and efficient in mass production engineering.

[0086] The following describes the process in S103 where the vehicle uses a preset estimator to process the input data to determine the vehicle's real-time centroid sideslip angle.

[0087] In some embodiments, the process may include, but is not limited to, S1031 and S1032 described below.

[0088] S1031. The vehicle uses a preset estimator to call the first weighted feature, calculates the input data based on the first weighted feature, and outputs the estimated value of the vehicle's lateral speed.

[0089] The pre-defined estimator is a dedicated algorithm module that integrates physical mechanisms and lightweight machine learning to estimate the lateral speed of a vehicle based on input data. Unlike traditional black-box deep learning models, this pre-defined estimator can be an analytical estimation framework built on kernel functions and constrained optimization. Its core lies in deriving optimal parameters with explicit mathematical expressions through a weighted combination of scheduling vectors and input vectors, combined with historical training data, thereby achieving high-precision, low-latency online estimation. In the offline phase, the pre-defined estimator solves for parameters using a small amount of high-quality training data; in the online phase, it only requires linear operations to output results in real time, meeting the millisecond-level real-time requirements of vehicle control systems.

[0090] The first weight feature refers to the weight matrix (which can be called the parameter matrix) used in the preset estimator for calculation with the input data.

[0091] In practical applications, during vehicle operation, the onboard controller collects data from various sensors in real time and constructs input vectors and scheduling vectors. Subsequently, the onboard controller calls the first weighted feature in the preset estimator to calculate the input data and obtain the estimated lateral velocity value at the current moment.

[0092] S1032. Based on the estimated lateral velocity, determine the vehicle's center of gravity sideslip angle.

[0093] The sideslip angle is a key parameter characterizing the angle between the actual direction of vehicle motion and the desired direction of vehicle travel. The formula for calculating the sideslip angle is usually β = arctan(vy / vx), where vy is the estimated lateral velocity and vx is the longitudinal velocity.

[0094] The lateral velocity estimate is the result output by a preset estimator, representing the vehicle's lateral velocity component. The lateral velocity estimate is not obtained through direct measurement, but rather estimated by fusing a physical model with a few-sample machine learning method. Therefore, it has high accuracy and robustness, especially performing exceptionally well when the vehicle is approaching its limits.

[0095] Longitudinal velocity is the component of a vehicle's speed along its forward direction, typically obtained by filtering and averaging data from wheel speed sensors. In practical calculations, longitudinal velocity is used as a denominator in the calculation of the sideslip angle, therefore, the accuracy of the longitudinal velocity directly affects the final result. To improve reliability, the system usually smooths the longitudinal velocity to eliminate the influence of instantaneous fluctuations.

[0096] In practice, once the vehicle stability control system obtains the latest estimated lateral and longitudinal speeds, it immediately substitutes them into the formula for calculating the sideslip angle and outputs the current sideslip angle in real time. For example, during a sharp turn, if a rapid increase in lateral speed is detected while the longitudinal speed remains stable, the calculated sideslip angle will increase accordingly, indicating to the vehicle stability control system that the vehicle is experiencing a sideslip tendency, thus triggering corresponding stability control measures.

[0097] By indirectly estimating the lateral velocity and then calculating the sideslip angle, the problem of error accumulation that may arise from directly estimating the sideslip angle is effectively avoided. Furthermore, because the estimated lateral velocity itself possesses high accuracy and robustness, the final sideslip angle calculation result is more reliable, providing a solid data foundation for subsequent vehicle stability control.

[0098] The process of training the model is explained below.

[0099] This process may include, but is not limited to, S201 to S203 below.

[0100] S201, Vehicle construction initial estimator model.

[0101] The initial estimator model also includes the first weighted feature to be solved.

[0102] The initial estimator is a machine learning model framework for predicting vehicle lateral velocity. Its structural design integrates physical mechanisms and data-driven methods. The initial estimator receives two types of input data: first feature data and second feature data. It weights and combines the input data using internal parameters (i.e., the first weight feature), ultimately outputting an estimate of the lateral velocity at the current moment. The first weight feature is a parameter vector to be solved, which determines the degree of influence of each input feature on the output result and is the core of the initial estimator's performance. Essentially, the initial estimator is a kernel-based linear regression model. During offline training, an optimization process determines the optimal first weight feature, thereby achieving high-precision estimation.

[0103] There is a clear data input relationship between the initial estimator and the first and second feature data. The first feature data, as a basic state variable, provides direct information about vehicle motion, while the second feature data serves as a scheduling factor to dynamically adjust the model's sensitivity to nonlinear operating conditions. The first and second feature data together constitute a complete input vector, which is used to generate a lateral velocity estimate through weighted operations within the initial estimator. For example, when a vehicle is cornering at high speed, the vehicle control system collects the current wheel speed, steering angle, and yaw rate as the first feature data, and simultaneously calculates the response error between the actual lateral acceleration and the ideal lateral acceleration as the second feature data. The first and second feature data are input together into the initial estimator, and after being weighted by the first weight parameter to be solved, the estimated lateral velocity value at the current moment is output.

[0104] When the vehicle is running, sensors collect signals such as wheel speed, steering angle, and acceleration in real time. The control system processes these signals as the first feature data and calculates the lateral response error as the second feature data using the dynamic model. Then, it calls the initial estimator model to perform calculations and obtain a preliminary estimate of the lateral velocity. This design allows the initial estimator to utilize both real-time state and dynamic operating condition information, improving the accuracy of the estimation.

[0105] An initial estimator is a machine learning model architecture used to estimate vehicle lateral speed. Its core function is to predict the output value by weighting input features. Its role is to fuse multi-source sensor data with physical indicators to achieve accurate lateral speed estimation. Specifically, it receives first and second feature data, performs weighted calculations using internal parameters (first weighted features), and outputs an estimated lateral speed value. Its relationship to the aforementioned concepts is as follows: the first and second feature data are the inputs to the initial estimator, the estimated lateral speed is the output, and the first weighted features are the internal parameters to be optimized. As a higher-level concept, lower-level features include, but are not limited to: input features based on wheel speed and steering angle, scheduling features based on lateral response error, and recursive features based on historical estimates. Adaptation scenarios differ: wheel speed and steering angle features are suitable for steady-state conditions, lateral response error features are suitable for extreme conditions, and historical estimate features are suitable for dynamic continuous estimation.

[0106] S202. The vehicle performs a weighted feature transformation on the initial estimator model based on its lateral speed to obtain a solvable estimator model.

[0107] The solution transformation refers to the process of transforming the established initial estimator model containing unknown parameters ρ_i into a directly solvable system of linear equations by using mathematical derivation and introducing the Lagrange multiplier method and kernel function symmetry. The "solvable estimator model" reduces the dimensionality of the problem from "infinite-dimensional optimization" to "finite-dimensional linear algebra".

[0108] The vehicle performs the following mathematical transformations in the offline development environment: First, based on T training samples, a constrained optimization problem is established with the objectives of "minimizing the parameter norm" and "minimizing the estimation error"; second, a Lagrange multiplier η(k) is introduced to construct a Lagrange function, and partial derivatives are taken with respect to the parameter ρ_i and the error e, thereby eliminating the original parameter ρ_i; finally, a kernel function is used to replace the high-dimensional inner product operation, and the symmetry of the kernel matrix is ​​used to convert the entire optimization problem into an equivalent system of linear equations of size T×T. Thus, the infinite-dimensional parameter solution problem is transformed into solving a finite η vector, and the model becomes a "solvable" numerical computation form.

[0109] This transformation achieves two key breakthroughs: dimensional collapse—transforming the original infinite-dimensional or even unsolvable feature space search problem into a deterministic solution of a finite-dimensional linear equation system, fundamentally avoiding the iterative optimization process of traditional machine learning; and analyticalization—giving the model a closed mathematical expression, so that subsequent online inference does not require any iteration or backpropagation, and only a single linear algebra operation is needed to obtain the optimal solution. This is the core theoretical foundation for ensuring the real-time performance of in-vehicle systems.

[0110] S203. The vehicle determines the first weight feature of the preset estimator model based at least on the training data and the solvable estimator model.

[0111] The training data is used to characterize the degree of lateral change of the vehicle.

[0112] Training data is a set of samples used to train and calibrate the initial estimator, containing input features and corresponding true output labels. The first training data refers to historical data related to vehicle lateral motion, such as sensor data on wheel speed, steering angle, and acceleration collected under different road conditions and vehicle speeds. This sensor data reflects the vehicle's behavior patterns under various steady-state and transient conditions. The second training data refers to real-time data related to vehicle steering response differences, i.e., the lateral response error and its rate of change collected in real time during driving. This real-time lateral response error and its rate of change capture the nonlinear dynamic characteristics of the vehicle when approaching its handling limits. The true lateral velocity label refers to the true lateral velocity value obtained through high-precision sensors or calibration methods, synchronized with the training data input. This true lateral velocity value is used to supervise the learning process.

[0113] The solvable estimator model is processed through multiple sets of training data to find the optimal solution. The weight parameters corresponding to the optimal solution are then determined as the first weight feature of the preset estimator model. This step determines the model parameters with extremely low data cost (requiring only a few hundred representative samples) and computational cost (solving a single linear equation system, non-iterative training), completely avoiding the pain points of deep neural networks that rely on tens of thousands of samples and GPU-level computing power. More importantly, because the training data deliberately includes extreme condition samples, and physical features (lateral response difference) can perceive the degree to which the vehicle approaches its adhesion limit, the determined weight features enable the model to maintain high-accuracy estimation even under unseen extreme conditions. Essentially, the "quality" of the training data replaces the "quantity," and the "prior guidance" of physical features replaces the purely data-driven "brute-force fitting." This is the core difference between this method and traditional machine learning approaches.

[0114] The process of determining the solvable estimator model is explained below.

[0115] In some embodiments, the process may include, but is not limited to, S301 to S304 described below.

[0116] S301. Based on the lateral velocity error, the initial estimator model is optimized in a constrained manner to obtain the first optimization expression.

[0117] The first optimization expression is used to minimize the lateral velocity error and homogenize the parameter effects.

[0118] The initial estimator model also includes the first weighted feature to be solved.

[0119] Lateral velocity error refers to the difference between the actual lateral velocity and the estimated lateral velocity, and it is a key indicator for evaluating the performance of the initial estimator. Constrained optimization involves introducing additional constraints, such as parameter norm minimization or parameter influence homogenization, while minimizing the error, to prevent overfitting and improve generalization ability. The first optimization expression is an analytical objective function derived mathematically, typically including a squared error term and a parameter regularization term. The first optimization expression is constructed using the Lagrange multiplier method, transforming the original constrained optimization problem into an unconstrained optimization problem, facilitating its solution.

[0120] There is a close logical connection between lateral velocity error and constrained optimization. The goal of the optimization process is to minimize the lateral velocity error, but simply minimizing the error may lead to an overly complex model or sensitivity to noise. Therefore, a constraint on the uniformity of parameter influence is introduced, that is, limiting the norm of the first weighted feature, to ensure that the influence of each parameter on the output is relatively balanced, avoiding the instability of the model due to excessively large weights of some parameters. This constraint is combined with the error minimization objective through the Lagrange multiplier method to form the first optimization expression.

[0121] In practical implementation, the system first calculates the lateral velocity error at each moment based on these data and substitutes this lateral velocity error into the first optimization expression. The first optimization expression is then optimized using numerical methods (such as solving a system of linear equations) to obtain the optimal first weight feature. For example, in a training iteration, if the estimated value at a certain moment is higher than the true value, the lateral velocity error is positive. The optimization process adjusts the corresponding parameters to reduce the deviation of the estimated value while maintaining the overall stability of the first weight feature.

[0122] Constrained optimization can employ L2 regularization, L1 regularization, or a combination of regularization, suitable for different data distributions and model complexity requirements. The initial optimization expression can be constructed based on a quadratic function or support vector machine framework, applicable to different types of estimation tasks. Various optimization strategies differ in computational efficiency and model robustness, and the appropriate strategy can be selected based on onboard computing resources.

[0123] Lateral velocity error refers to the difference between the actual lateral velocity and the estimated lateral velocity, used to evaluate the estimation accuracy. Its role is to serve as a core component of the first optimization expression, guiding the adjustment direction of the first weight feature. Specific functions include quantifying the estimation bias and providing feedback signals for the optimization process. Its relationship to the first optimization expression is that it is one of the input terms of the first optimization expression and also the result of comparing the initial estimator output with the true lateral velocity label. As a higher-level concept, lower-level features of lateral velocity error include absolute error, relative error, and root mean square error. Adaptation scenarios differ: absolute error is suitable for fixed threshold judgment, relative error is suitable for proportional evaluation, and root mean square error is suitable for overall performance evaluation.

[0124] Constrained optimization refers to a method that simultaneously considers the primary objective (such as error minimization) and additional constraints (such as minimizing the norm of model weight features) during the optimization process. Its purpose is to improve the generalization ability and stability of the initial estimator and prevent overfitting. Specific functions include balancing error minimization with the simplicity of model weight features, ensuring the performance of the initial estimator on unseen data. Its relationship to the first optimization expression: it is the method for constructing the first optimization expression, used to optimize the parameters of the initial estimator. As a higher-level concept, lower-level features include L2 regularization, L1 regularization, and elastic network regularization. Differences in applicable scenarios: L2 regularization is suitable for smoothing model weight features, L1 regularization is suitable for sparse feature selection, and elastic networks are suitable for mixed scenarios.

[0125] The first optimization expression refers to the analytical objective function derived mathematically to solve for the optimal first weight feature. Its function is to transform complex optimization problems into a solvable mathematical form. Specifically, it defines the optimization objective and constraints, guiding the first weight feature to converge to the optimal solution. Its relationship to the aforementioned concepts is that it is the mathematical implementation of constraint-based optimization; the solution to this expression is the first weight feature. As a higher-level concept, lower-level features include expressions based on Lagrange multipliers, kernel functions, and support vector machines. Differences in applicable scenarios: Lagrange multiplier expressions are suitable for problems with explicit constraints, kernel function expressions are suitable for high-dimensional feature mapping, and support vector machine expressions are suitable for classification or regression boundary optimization.

[0126] For example, the first optimization expression may include: ;in, express The actual lateral velocity at any given moment, The estimated lateral velocity at time [time]. Indicates lateral velocity error. express The One element, It is a parameter vector. It is a feature vector based on the scheduling vector.

[0127] S302, the Lagrangian function corresponding to the first optimization expression for vehicle construction.

[0128] The Lagrangian function is a mathematical tool for solving constrained optimization problems. By introducing Lagrange multipliers, the constraints are incorporated into the objective function, thus transforming the original problem into an unconstrained optimization problem. In this application, the Lagrangian function is constructed on a constrained optimization problem based on the historical true lateral velocity and the estimated lateral velocity error. The form of the Lagrangian function can be found in Equation (4). The Lagrangian function includes the original objective function (such as parameter minimization and error minimization) and a penalty term consisting of constraints multiplied by Lagrange multipliers. By constructing this Lagrangian function, the relationship between the optimization objective and the constraints can be uniformly handled, facilitating the subsequent solution to the optimal solution using partial derivatives.

[0129] In practical implementation, this optimization method first defines an objective function (e.g., minimizing the parameter norm and estimation error), and then establishes the Lagrangian function by combining constraints (e.g., the difference between the true value and the estimated value is zero). For the vehicle center of gravity sideslip angle estimation scenario, this Lagrangian function integrates the physical structure of the lateral velocity estimation model and the data-driven error minimization objective, so that the optimization process considers both model accuracy and the physical consistency of the estimation scenario.

[0130] The construction of the Lagrange function is a key point in the core mathematical derivation of this application. The Lagrange function transforms the originally complex constrained nonlinear optimization problem into an algebraic problem that can be solved by differentiation, greatly simplifying the subsequent calculation process. Through the Lagrange function, the analytic relationship between the parameter vector and the Lagrange multipliers can be further derived, laying the foundation for obtaining an optimal estimator with a clear expression.

[0131] S303. The vehicle constructs a kernel function based on the features of the initial estimator model.

[0132] A kernel function is a mapping function used to calculate the inner product of two sample vectors in a high-dimensional or even infinite-dimensional feature space without explicit high-dimensional mapping. In this application, the kernel function is defined as the inner product of feature vectors, as shown in formula (12). The introduction of this kernel function enables feature operations that are difficult to handle in high-dimensional spaces to be efficiently completed in low-dimensional input spaces through kernel tricks.

[0133] In the vehicle center-of-gravity sideslip angle estimation scenario, this kernel function is constructed based on the scheduling vector and the input vector. Its role is to implicitly capture the similarity or correlation between different training samples in the feature space. For example, when the scheduling vectors and input vectors of two samples are physically close (e.g., under similar driving conditions), the kernel function value is larger; conversely, it is smaller. This kernel function effectively preserves the nonlinear relationships between features while avoiding the computational burden of directly processing high-dimensional features.

[0134] The choice of kernel function is crucial to the performance of the predefined estimator. Common kernel functions include linear kernels, polynomial kernels, and radial basis function kernels. Under a linear kernel, the predefined estimator degenerates into a linear regression; under a basis function kernel, the predefined estimator has stronger nonlinear fitting ability and is suitable for complex conditions. This method can select an appropriate kernel function type based on the characteristics of the training data to balance model complexity and generalization ability.

[0135] The construction of this kernel function achieves a mapping from the original input space to an implicit high-dimensional feature space, enabling the pre-defined estimator to learn richer nonlinear patterns while maintaining computational efficiency. This kernel trick is one of the core methods for achieving lightweight, high-precision estimation.

[0136] S304. Based on the Lagrangian function, kernel function, and training data, the vehicle determines a solvable estimator model.

[0137] The first weight feature refers to the parameter vector used to weight the input vector in the preset estimator. The value of this parameter vector determines the degree of influence of each input feature on the final output. In this application, the first weight feature is obtained by solving a system of linear equations constructed by the Lagrange function and the kernel function.

[0138] In practice, this method first calculates the kernel matrix using training data, then obtains the Lagrange multiplier λ by solving a system of linear equations, and finally derives the parameter vector w using formulas (18-1) and (18-2). Since the kernel matrix is ​​usually symmetric and positive definite, the system of linear equations can be solved using efficient algorithms such as decomposition and the conjugate gradient method.

[0139] The process of determining the first weight feature demonstrates the advantages of this method in terms of small sample size and real-time performance. Since only a small amount of training data is needed to construct the kernel matrix, and all weights are obtained through a single linear solution, the determination process of the first weight feature requires no iterative optimization, resulting in minimal computational overhead. This enables the pre-defined estimator to be trained quickly offline and applied in real-time online within an in-vehicle embedded system.

[0140] Furthermore, this first weight feature has a clear physical meaning. Since the design of both the input vector and the scheduling vector is based on the vehicle dynamics model and the response error index, the obtained first weight feature reflects the contribution of different physical variables to the lateral velocity estimation, thereby enhancing the interpretability and robustness of the preset estimator.

[0141] In this method, the first weighted feature is determined by constructing the Lagrangian function, designing the kernel function, and solving the system of linear equations based on the training data. This transforms the optimization problem in an infinite-dimensional feature space into a finite-dimensional linear algebra problem, significantly reducing computational complexity and data requirements. This enables high-precision centroid sideslip angle estimation to be performed in milliseconds in real-time on an onboard microcontroller.

[0142] The following describes the process by which the vehicle determines the first weight feature of the preset estimator model based at least on the training data and the solvable estimator model in S203.

[0143] In some embodiments, the process may include, but is not limited to, S401 to S403 described below.

[0144] S401. The vehicle processes the solvable estimator model to obtain the second expression.

[0145] The inputs to the second expression include the kernel function, regularization coefficients, and Lagrange parameters, and the output of the second expression includes the lateral velocity.

[0146] The second expression is an analytical expression for calculating lateral velocity, derived through mathematical derivation and algebraic transformation of the Lagrange function and kernel function. Essentially, the second expression maps the feature space to a lower-dimensional space using the inner product property of the kernel function and solves for the optimal parameter combination using Lagrange multipliers, thus transforming the original high-dimensional or infinite-dimensional optimization problem into a finite-dimensional linear computation form. The inputs to the second expression include the kernel function (used to measure similarity between samples), regularization coefficients, and Lagrange parameters (i.e., Lagrange multipliers), which together determine the estimated value of the lateral velocity at the current moment. The design of the second expression allows the model to perform real-time calculations using only simple matrix operations without requiring a complex nonlinear network structure, making it suitable for automotive embedded systems.

[0147] Lateral velocity refers to the instantaneous velocity of the vehicle's center of gravity in the lateral direction, and is a key intermediate variable for calculating the sideslip angle. It is determined by the vehicle's current longitudinal velocity, regularization coefficient, and lateral acceleration. Accurate estimation of lateral velocity is crucial for the performance of active safety control systems. Due to the high cost of direct measurement, this solution employs a physics-based approach combined with machine learning for estimation, avoiding the strong dependence of traditional methods on tire parameters.

[0148] A kernel function is a mathematical function used to measure the similarity between two data points, commonly used in machine learning algorithms such as Support Vector Machines (SVMs) and Kernel Ridge Regression. By introducing kernel functions, problems involving high-dimensional feature spaces, which are inherently difficult to handle, can be transformed into easily solvable low-dimensional linear problems. Kernel functions possess symmetry and positive definiteness, ensuring the invertibility of the kernel matrix and thus guaranteeing the stability of the Lagrange multiplier solution.

[0149] In this embodiment, by constructing a second expression and combining the Lagrange function with the kernel function, the transformation from a complex optimization problem to a concise linear expression is achieved. This transformation reduces computational complexity, enabling real-time online estimation. The method described above meets the millisecond-level response requirements of vehicle control systems.

[0150] S402. The vehicle processes the second expression using training data to determine the Lagrange multipliers.

[0151] Lagrange multipliers are auxiliary variables introduced in constrained optimization problems to incorporate constraints into the objective function, thereby transforming the constrained optimization problem into an unconstrained optimization problem.

[0152] In this application, the Lagrange multiplier is the core variable for solving the optimal estimator parameters. The value of the Lagrange multiplier is obtained from the training dataset by solving a system of linear equations. Specifically, by minimizing the error between the actual lateral velocity and the estimated lateral velocity, and combining this with parameter normalization constraints, a Lagrange function is established. Then, the partial derivative with respect to the parameters is taken and set to zero, ultimately yielding a system of linear equations containing the Lagrange multiplier. The solution to this system of linear equations is the Lagrange multiplier, and the value of the Lagrange multiplier reflects the degree of contribution of each training sample to the final estimation result. For example, in a small training set, if a data point corresponds to the vehicle's extreme operating condition, the Lagrange multiplier corresponding to that training sample may be larger, indicating that this sample has a higher weight in the estimation process.

[0153] In practical implementation, training data typically comes from real-vehicle testing, covering normal driving and typical extreme conditions (such as large sideslip angles and sharp turns). Each data point includes a scheduling vector, an input vector, and the corresponding true lateral velocity. The system uses the training data to construct a kernel matrix and solves a system of linear equations to determine the Lagrange multipliers. Since training requires only a small amount of high-quality data, it avoids the massive data annotation process required by traditional deep learning methods, significantly reducing data collection and labeling costs.

[0154] In this embodiment, the second expression is processed using training data to determine the Lagrange multipliers. This enables efficient model training based on small sample data, thereby improving the model's generalization ability under extreme conditions and enhancing the robustness of the vehicle's active safety control system.

[0155] S403, The vehicle determines the first weighted feature of the preset estimator based on Lagrange multipliers.

[0156] The first weight feature refers to the set of parameters used to weight the input vector in the estimator, the values ​​of which are determined by the Lagrange multipliers and the kernel function.

[0157] Once the optimal parameter vector is determined, it can be directly used for lateral velocity estimation during online operation without the need for repeated training or iterative optimization. This determination process essentially solidifies the results of offline training into a fixed set of parameters, thereby enabling lightweight deployment.

[0158] In practical applications, the first weighted feature is stored in the memory of the vehicle controller. When the vehicle is running, the system collects sensor signals in real time (such as wheel speed, regularization coefficient, front wheel steering angle, etc.), constructs the current scheduling vector and input vector, and substitutes these vectors into the determined first weighted feature. The current lateral speed estimate can then be output through simple matrix multiplication. This one-time training and multiple-use mode greatly improves the system's real-time performance and reliability.

[0159] In this embodiment, the first weight feature is determined based on Lagrange multipliers. This allows for the analytical solution of the estimator parameters, avoiding the complex backpropagation training process and thus meeting the stringent requirements of automotive embedded systems for computing resources and real-time performance.

[0160] In this embodiment, a second expression is constructed, Lagrange multipliers are determined, and a first weight feature is further obtained. This transforms a complex nonlinear optimization problem into a lightweight linear operation, enabling high-precision, low-latency lateral velocity estimation. This provides a reliable state observation basis for vehicle active safety control systems, improving vehicle handling stability and safety under extreme conditions.

[0161] The following describes another implementation method in S103.

[0162] The second weighted feature is invoked using a preset estimator, and the input data is calculated based on the second weighted feature to output the real-time centroid sideslip angle of the vehicle.

[0163] The second weighting feature refers to the parameter matrix used in the estimator framework to weight the input data. This parameter matrix dynamically adjusts the contribution of different feature dimensions to the final estimation result. The second weighting feature is typically a diagonal positive semi-definite matrix. The elements of this matrix are related to real-time vehicle state parameters such as vehicle speed, steering angle, yaw rate, and wheel speed, and can adaptively adjust the importance of each input feature according to the current operating conditions. For example, in a high-speed sharp turn, the estimator framework may automatically increase the weight of the front wheel steering angle and yaw rate while decreasing the weight of the wheel speed change rate, thus more accurately reflecting the vehicle's sideslip trend. The second weighting feature can be generated online using a fixed expression or a lightweight neural network model, ensuring low latency and high robustness in the in-vehicle domain control environment.

[0164] The second weighted feature has a direct data processing relationship with the input data. The input data includes physical quantities such as wheel speed, front wheel steering angle, yaw rate, and longitudinal velocity. This data is first organized into an input vector. Subsequently, the second weighted feature, as a matrix multiplication factor, performs a weighted transformation on the input vector to generate a weighted input feature. This process is essentially an intelligent filtering and priority allocation of the original sensor signals, enabling the estimator to focus more on the most representative feature combination under the current operating condition. For example, when the vehicle is traveling in a stable straight line, the system may assign a higher weight to wheel speed; while during extreme cornering, the weights of front wheel steering angle and lateral response error are given more importance.

[0165] In practical applications, the invocation of the second weighted feature occurs within each control cycle of the vehicle control unit. Taking a certain intelligent electric vehicle as an example, the controller collects sensor data every millisecond, constructs an input vector, and immediately invokes the pre-trained second weighted feature matrix, obtaining the weighted input feature through matrix multiplication. Then, the weighted input feature is substituted into the optimal estimator, and combined with the input data and kernel matrix, the lateral velocity estimate for the current moment is calculated in real time and then converted into the centroid sideslip angle. The above calculation process does not require complex iterative calculations, only linear operations, meeting the millisecond-level real-time requirements of the vehicle system.

[0166] The following example illustrates the process of estimating the sideslip angle of a vehicle's center of gravity.

[0167] With the continuous advancement of intelligent electric vehicle chassis control technology, vehicle active safety control systems (such as electronic stability control, direct yaw moment control, and torque vectoring) place extremely high demands on the accuracy and real-time performance of vehicle motion state perception. Among these, the center of gravity sideslip angle (usually calculated from lateral velocity) is the most critical state parameter characterizing vehicle handling stability, sideslip tendency, and extreme motion state. Its accurate acquisition directly affects the vehicle's stability control performance under extreme conditions.

[0168] Because high-precision sensors that directly measure the sideslip angle of the center of gravity (such as high-precision inertial navigation systems) are extremely expensive and cannot be widely used in mass-produced vehicles, the industry typically adopts state estimation methods based on software algorithms. Current estimation methods are mainly divided into two categories: model-driven methods and data-driven methods.

[0169] Related technology 1 employs a model-driven approach, often using methods based on vehicle dynamics or kinematic models such as Kalman filtering and sliding mode observers. This approach is highly dependent on the accuracy of parameters such as tire lateral stiffness. However, when the vehicle approaches its handling limits (e.g., large lateral acceleration, strong nonlinear regions), tire characteristics change drastically, and models with fixed parameters can lead to a significant decrease in estimation accuracy or even divergence.

[0170] Related technology 2 employs a data-driven approach: Some research has begun to use purely data-driven methods such as deep neural networks for state estimation. However, such methods have significant drawbacks: First, training the model requires massive amounts of test data, especially under extreme conditions where obtaining high-quality, fully covered labeled data is extremely costly and dangerous; second, deep learning models are "black box" models with poor generalization ability and are prone to failure under unseen conditions; finally, the complex nonlinear deep learning network structure places extremely high demands on the computing power of the vehicle's microcontroller unit, making it difficult to meet the millisecond-level real-time requirements of vehicle control.

[0171] Therefore, there is an urgent need for a novel centroid sideslip angle estimation method that can overcome the shortcomings of traditional models in terms of dependence on nonlinear parameters, can be trained quickly on small sample data, and has high real-time performance and physical interpretability.

[0172] This embodiment aims to provide a centroid sideslip angle estimation method based on small sample data driven by lateral acceleration response, which is essentially a lightweight machine learning method that integrates vehicle physical characteristics.

[0173] The core concept of this embodiment lies in abandoning black-box deep learning networks that require massive amounts of data and constructing a machine learning estimator framework based on kernel functions and constrained optimization. First, through in-depth analysis of the vehicle system dynamics model, core physical variables affecting lateral velocity (such as wheel speed, tire force, yaw rate, and front wheel steering angle) are extracted. Then, a creative "lateral response error" metric (based on the difference between ideal and actual lateral acceleration) is introduced to assess how close the vehicle is to its handling limits. Combining these physical variables with the response error metric, the "scheduling vector" and "input vector" of the machine learning estimator are constructed, giving the machine learning model a clear physical meaning.

[0174] Building upon this foundation, this embodiment establishes a constrained optimization problem. By introducing Lagrange multipliers and utilizing the symmetry of kernel functions, the original high-dimensional or even infinite-dimensional feature space mapping problem is transformed into a finite-dimensional linear equation system solution problem. This mathematical derivation allows the model parameters to be obtained with only a small amount of representative training data (small sample size), yielding an optimal estimator with analytical expressions. This method does not require massive data calibration, has low computational complexity, and can estimate lateral velocities and calculate the centroid sideslip angle in real time and accurately, exhibiting particularly excellent robustness and accuracy under extreme conditions.

[0175] The implementation process may include, but is not limited to, steps 1 through 4 below.

[0176] Step 1: Define the estimator.

[0177] Formula (1); in, It is a scheduling vector of finite dimensions. It is a finite-dimensional input vector (dimension is...) ), express The One element, It is a parameter vector. It is a feature vector based on the scheduling vector. Note that... and Dimensions can be infinite. It is the current moment. The estimated optimal lateral velocity.

[0178] Step 2: Derivation of estimator parameters.

[0179] It has One training data set, .definition The actual lateral velocity at time t is Actual lateral velocity and estimated lateral velocity The error between them is Then the following formula (2) holds true.

[0180] Formula (2); in, express The actual lateral velocity at any given moment, The estimated lateral velocity at time [time]. Indicates lateral velocity error. express The One element, It is a parameter vector. It is a feature vector based on the scheduling vector.

[0181] Based on formula (2), in order to obtain the parameters and The technical solution establishes the following constrained optimization problem. The optimization objective can be referred to in formulas (3-1) and (3-2).

[0182] Formula (3-1); Formula (3-2); Formula (3-1) is for parameter homogenization and minimization, and formula (3-2) is for error minimization. To indicate different times, similar to the above. . This represents the regularization coefficient. It is a parameter vector. express The true lateral velocity at any given moment.

[0183] in, It is the length of the training set.

[0184] Based on the aforementioned constrained optimization problem, we introduce Lagrange multipliers. By constructing the Lagrange function, the extremum problem can be transformed into the following formula (4).

[0185] Formula (4); in, It represents the Lagrange multiplier.

[0186] Pair the Lagrange equations Taking the partial derivative, we can obtain the following formula (5); Formula (5); The solution obtained You can refer to the following formula (6).

[0187] Formula (6).

[0188] Pair the Lagrange equations Taking the partial derivative, we can obtain the following formula (7).

[0189] Formula (7); Solving for the results You can refer to the following formula (8).

[0190] Formula (8).

[0191] Substitute these two formulas, namely formula (6) and formula (8), into the original equation. From this, we can obtain the following formula (9).

[0192] Formula (9); The following formula (10) is obtained by reorganization.

[0193] Formula (10); By changing the order of summation, we can obtain the following formula (11).

[0194] Formula (11); Refer to formula (12) to define a kernel function as the inner product of eigenvectors.

[0195] Formula (12); Based on this kernel function, a kernel matrix is ​​obtained. The Each element can be referenced in formula (13).

[0196] Formula (13); Substitute the kernel matrix, i.e., formula (13), into... From this, we can obtain the following formula (14).

[0197] Formula (14); Because kernel functions generally satisfy symmetry, i.e., refer to formula (15); Formula (15); Therefore, the kernel matrix It is also symmetrical, i.e., refer to formula (16).

[0198] Formula (16); Therefore, we can obtain formula (17), that is Formula (17).

[0199] Therefore, we obtain the following formulas (18-1) and (18-2).

[0200] Formula (18-1); Formula (18-2); in, Representing vectors The Each element.

[0201] therefore, It can be equivalently written as the following formula (19).

[0202] Formula (19); given that there are Based on the above formula, the training data will be used to... The following formula (20) is obtained by stacking all the data. Formula (20); in, , ,in The parameter vector of the estimator that needs to be solved can be obtained directly by solving the above linear equation.

[0203] Step 3: Derivation of the optimal estimator.

[0204] In step 1, the structure of the estimator was derived as follows: .

[0205] In step 2, this technical solution is obtained The expression is: .

[0206] Substituting into the estimator, we get: .

[0207] in, Defined in the form of a kernel function, By solving the linear equation in step 2 get.

[0208] Therefore, at the current moment The optimal estimate of the lateral velocity can be obtained by referring to the following formula (21).

[0209] Formula (21).

[0210] Finally, the sideslip angle of the centroid is obtained. The expression for the time estimation can be found in the following formula (22).

[0211] Formula (22).

[0212] Note that this scheme does not directly estimate the sideslip angle using a data-driven method, but rather estimates it by estimating the lateral velocity. This is because, in practical applications, the vehicle's longitudinal velocity... It is also obtained through estimation. Directly estimating the sideslip angle of the center of mass may accumulate estimation errors. Therefore, estimating the sideslip angle of the center of mass by estimating the lateral velocity will reduce the relevant errors, which is one of the core points of this embodiment.

[0213] Step 4: Selection of scheduling vector p(k) and input vector x(k).

[0214] The choice of scheduling vector and input vector directly determines the accuracy of lateral speed estimation, which requires in-depth analysis and summarization of the vehicle dynamics model.

[0215] First, the differential equation model for lateral velocity can be found in formula (23).

[0216] Formula (23) in, It is the lateral acceleration in the vehicle coordinate system. It is the longitudinal velocity in the vehicle coordinate system. It is the yaw rate in the vehicle coordinate system.

[0217] The calculation method for lateral acceleration can be found in the following formula (24).

[0218] Formula (24); in, It is the longitudinal force of the front left wheel. It is the longitudinal force of the front right wheel. It is the lateral force of the front left wheel. It is the lateral force of the front right wheel. It is the lateral force of the rear left wheel. It is the lateral force of the rear right wheel. It's the weight of the vehicle. It's the front wheel steering angle.

[0219] In addition, the differential equation model that the yaw rate should satisfy can be found in formulas (25-1) to (25-3).

[0220] Formula (25-1); Formula (25-2); Formula (25-3); in, It's the wheelbase. It is the distance from the center of gravity to the front axle. It is the distance from the center of mass to the rear axle.

[0221] in, These are tire codes (1 for the left front wheel, 2 for the right front wheel, 3 for the left rear wheel, and 4 for the right rear wheel). and They represent the first Wheel slip ratio and sideslip angle, and Indicates the first The longitudinal and lateral adhesion coefficients of the wheel, Indicates the first Vertical load on the wheel, Indicates the first The rotational speed of the wheel, Indicates the first The longitudinal speed of the wheel, Indicates the first The wheel hub motor input torque is used; all other parameters are tire dynamics parameters. , .

[0222] Based on the above vehicle system dynamics model, this embodiment proposes an additional method for calculating lateral response error to evaluate the vehicle's following stability in response to driver input. When the driver generates a front wheel angle through steering wheel rotation, the requested ideal lateral acceleration can be obtained by referring to formula (26): Formula (26); where, It refers to the wheelbase.

[0223] When the vehicle is stable, the driver's lateral acceleration can be well compensated for by tire-road friction. Conversely, if and When the difference is significant, it indicates that the vehicle has reached its handling limits, and correspondingly, the lateral speed will generally be relatively high.

[0224] Therefore, this example proposes adding the following two metrics to the scheduling vector of the estimator: Lateral acceleration change. and the rate of change of lateral acceleration These two parameters can be found in formulas (27-1) and (27-2).

[0225] Formula (27-1); Formula (27-2); where, It is the sampling interval.

[0226] Based on the above vehicle system dynamics model, i.e., the various formulas in step 4, it can be seen that the influence... The core control inputs include and ,and and And steering input Closely related, therefore, the input vector must contain and Furthermore, because signals are discrete, if... Since the lateral velocity at the current moment is discrete, it is necessarily affected by the lateral velocity at the previous moment. Therefore, the input vector must include the estimated lateral velocity at the previous moment.

[0227] Based on the above analysis, this embodiment initially defines the input vector as follows (28): Formula (28); Combining the dynamic model and vehicle lateral response index, the scheduling vector is initially designed as follows (29): Formula (29); in, It refers to the wheel speed of all four wheels.

[0228] Finally, this technical solution weights the above initial scheduling vector and input vector to obtain the final scheduling vector and input vector as shown in formulas (30-1) and (30-2).

[0229] Formula (30-1); Formula (30-2); in, and These are the corresponding weight matrices, which are all diagonal positive semi-definite matrices. and It is related to parameters such as vehicle speed, steering angle, yaw rate, and wheel speed. and It can be obtained from a fixed expression or a neural network model.

[0230] At every moment Construct the above scheduling vector and input vector, and input them into the optimal estimator in step 3 to obtain the optimal estimated lateral velocity at the current moment.

[0231] refer to Figure 2 The process for estimating the centroid sideslip angle, as shown, includes, but is not limited to, S501 to S506.

[0232] S501. Determine the input vector.

[0233] The input vector is obtained by weighting the estimated lateral velocity, front wheel steering angle, and yaw rate from past moments.

[0234] S502. Determine the scheduling vector.

[0235] The scheduling vector is obtained by weighting the lateral and longitudinal accelerations, longitudinal vehicle speed, wheel speed, and lateral response error.

[0236] S503, real-time online construction of input vectors and scheduling vectors.

[0237] S504. Determine the estimator parameters.

[0238] Based on the input vector and scheduling vector, training samples are constructed; Lagrange multipliers are solved offline; and the estimator parameters are obtained.

[0239] S505, retrieve offline training parameters.

[0240] S506, Real-time estimation of centroid sideslip angle.

[0241] The core technologies of this embodiment include: 1. Machine learning estimator architecture and analytical solution method based on kernel function and constraint optimization.

[0242] This invention protects a centroid sideslip angle (lateral velocity) estimator structure driven by lateral acceleration response and its mathematical solution method. Specifically, it protects: constructing an estimator including a scheduling vector, input vector, eigenvector, and parameter vector; establishing a constrained optimization problem based on the error between historical true lateral velocity and estimated lateral velocity; constructing a Lagrange function by introducing Lagrange multipliers and defining a kernel function and kernel matrix using the inner product of eigenvectors; and utilizing the symmetry of the kernel function to transform the infinite-dimensional eigenvalue problem into a finite-dimensional linear equation system, thereby obtaining an optimal estimator framework with analytical expressions.

[0243] 2. A scheduling vector construction method based on "lateral response error".

[0244] The design logic for the scheduling vector used to evaluate the vehicle's approach to its handling limits is protected. Specifically, the protection involves: calculating the ideal lateral acceleration that the vehicle should have in a steady state based on the driver's input front wheel steering angle and vehicle wheelbase; obtaining the vehicle's current actual lateral acceleration and calculating the lateral response error between the actual and ideal values; and combining the lateral response error indices from the previous and current time steps as the scheduling vector for the estimator to dynamically adjust the weights of the estimator under nonlinear conditions.

[0245] 3. A method for constructing input vectors for a fusion vehicle system dynamics model.

[0246] The design logic for protecting the input vector used in the machine learning estimator is protected. Specifically, the protection involves analyzing the vehicle system dynamics model (including the lateral velocity differential equation, lateral acceleration equation, yaw rate equation, and tire longitudinal / lateral force calculation equation) to extract the core control inputs and state variables that significantly affect lateral velocity (such as the input torque of the four-wheel hub motor, front wheel steering angle, tire slip ratio, and longitudinal / lateral adhesion coefficients). An initial input vector is constructed by combining the historical lateral velocity estimates introduced due to the characteristics of the discrete system. The final input vector is obtained by diagonally weighting the initial input vector using a weighting matrix.

[0247] 4. Methods for constructing small sample datasets and offline training for vehicle-mounted domain controllers.

[0248] Protect the model training mechanism driven by small sample data. Specifically, for distributed drive vehicles, collect a small amount of high-quality real-vehicle test data covering normal operating conditions and typical extreme operating conditions (such as large sideslip angles and strong nonlinearity) as a training set; use this small amount of training data to construct a kernel matrix, and obtain the Lagrange multipliers and parameter vectors by solving linear equations to complete the offline training of the machine learning estimator. This mechanism eliminates the need for massive amounts of data for repeated iterative backpropagation, significantly reducing the data acquisition threshold and training cost.

[0249] 5. A method for calculating lateral velocity and centroid sideslip angle online in real time based on analytical solutions.

[0250] The protection estimator operates online and outputs its status on the vehicle terminal. Specifically, during online operation, the vehicle control unit acquires sensor signals in real time to construct real-time scheduling and input vectors. These vectors are directly substituted into the optimal estimator, which has an analytical expression, eliminating the need for complex network forward propagation calculations. The optimal lateral velocity estimate for the current moment is then output in real time. Furthermore, based on state variables such as longitudinal velocity, the lateral velocity is converted into a centroid sideslip angle, which is then used as an input parameter for the vehicle stability control system.

[0251] 6. Application of lightweight machine learning estimation methods that integrate physical mechanisms in smart chassis.

[0252] This document protects the overall application scenario of the lightweight machine learning framework, which integrates physical feature extraction, response error quantization, small-sample training, and analytical solution output, in the chassis control of intelligent electric vehicles. Specifically, it protects the deployment architecture of this method on an intelligent electric vehicle chassis platform, and its application loop as a core state observation module of the active safety control system in improving the anti-instability control capability under extreme conditions.

[0253] This embodiment has the following technical effects: 1. Small sample data-driven approach, reducing data acquisition and calibration costs: Unlike traditional deep learning methods that rely on massive amounts of data, this invention transforms the infinite-dimensional feature problem into a system of linear equations based on finite training data through constrained optimization and kernel function matrix derivation. Only a small amount of representative, high-quality test data is needed to train a high-precision estimator, significantly reducing the difficulty and time cost of data acquisition.

[0254] 2. Machine learning integrating physical mechanisms, with strong generalization ability under extreme conditions: This method is not a pure black-box model. The design depth of its scheduling vector and input vector combines the vehicle system dynamics model and the "lateral response error" index. The introduction of this physical mechanism enables the machine learning model to keenly perceive the nonlinear characteristic abrupt change when the vehicle approaches the extreme state. Its generalization ability and estimation accuracy under extreme conditions are far superior to traditional fixed parameter models and pure data-driven models.

[0255] 3. Possesses analytical solutions, is computationally lightweight, and exhibits excellent real-time performance: This invention transforms complex nonlinear estimation problems into optimal estimation expressions with explicit analytical forms (based on linear operations of the kernel matrix), avoiding the iterative training process of backpropagation in traditional machine learning. The algorithm has low computational complexity during runtime, fully meeting the millisecond-level real-time computation requirements of automotive embedded microcontrollers.

[0256] 4. Low dependence on tire nonlinear parameters: Traditional methods are highly dependent on parameters such as tire lateral stiffness that change drastically with operating conditions. However, this method implicitly incorporates the tire's nonlinear characteristics through a data-driven mechanism, eliminating the need to accurately obtain these parameters that are difficult to identify in real time, thus improving the robustness of the system.

[0257] Secondly, embodiments of this application provide a device for estimating the sideslip angle of a vehicle's center of gravity, with reference to... Figure 3 As shown, the vehicle center of gravity sideslip angle estimation device 30 may include: an acquisition unit 301, a determination unit 302, and a processing unit 303.

[0258] The acquisition unit 301 is used to acquire the vehicle's operating status data; the determination unit 302 is used to determine the input data from the operating status data for inputting into the preset estimator; wherein, the input data is used to characterize the degree of lateral change of the vehicle; the processing unit 303 is used to process the input data using the preset estimator to determine the real-time centroid sideslip angle of the vehicle.

[0259] In some embodiments, the input data includes first feature data and second feature data; the first feature data includes first historical data related to the lateral motion of the vehicle, and the second feature data includes first real-time data related to the lateral response difference of the vehicle, the lateral response difference being determined based on the difference between the actual lateral acceleration and the desired lateral acceleration.

[0260] In some embodiments, the first feature data is the data after weighting the first historical data with first weight data, and the second feature data is the data after weighting the first real-time data with second weight data.

[0261] In some embodiments, the first feature data includes at least one of the following: historical estimated lateral velocity, historical front wheel steering angle, and historical yaw rate; the second feature data includes at least one of the following: the vehicle lateral response difference at the current moment and the rate of change of the vehicle steering response difference at the current moment.

[0262] In some embodiments, the historical estimated lateral speed, historical front wheel steering angle, and historical yaw rate each include data from two adjacent historical moments.

[0263] In some embodiments, the second feature data further includes at least one of the following: the wheel speed of the vehicle's wheels at the current moment; the longitudinal velocity at the current moment; the longitudinal acceleration at the current moment; and the lateral acceleration at the current moment.

[0264] In some embodiments, the preset estimator is an analytical estimator, and the preset estimator is trained based on data characterizing the degree of lateral change of the vehicle.

[0265] In some embodiments, the processing unit 303 is further configured to: invoke a first weight feature using a preset estimator, calculate the input data based on the first weight feature, and output an estimated value of the vehicle's lateral velocity; and determine the vehicle's center of gravity sideslip angle based on the estimated value of the lateral velocity.

[0266] In some embodiments, the vehicle center of gravity sideslip angle estimation device 30 may further include a training unit, which is used to: construct an initial estimator model; wherein the initial estimator model further includes a first weight feature to be solved; perform a weight feature solution transformation on the initial estimator model based on the lateral velocity to obtain a solvable estimator model; determine a first weight feature of a preset estimator model based at least on the training data and the solvable estimator model; the training data is used to characterize the degree of lateral change of the vehicle.

[0267] In some embodiments, the training unit is further configured to: optimize the initial estimator model based on the lateral velocity error using a constrained method to obtain a first optimized expression, the first optimized expression being used to minimize the lateral velocity error and uniformize the parameter influence; construct the Lagrangian function corresponding to the first optimized expression; construct a kernel function based on the characteristics of the initial estimator model; and determine a solvable estimator model based on the Lagrangian function, the kernel function, and the training data.

[0268] In some embodiments, the training unit is further configured to: process the solvable estimator model to obtain a second expression; the input of the second expression includes a kernel function, regularization coefficients, and Lagrange parameters, and the output of the second expression includes lateral velocity; process the second expression using training data to determine Lagrange multipliers; and determine a first weight feature of the preset estimator based on the Lagrange multipliers.

[0269] In some embodiments, the processing unit 303 is further configured to: invoke a second weight feature using a preset estimator, and calculate the input data based on the second weight feature to output the real-time centroid sideslip angle of the vehicle.

[0270] It should be noted that the communication device of the application provided in this application embodiment includes all the units included, which can be implemented by a processor in an electronic device; of course, it can also be implemented by specific logic circuits; in the implementation process, the processor can be a central processing unit (CPU), a microprocessor (MPU), a digital signal processor (DSP), or a field-programmable gate array (FPGA), etc.

[0271] The descriptions of the above device embodiments are similar to those of the above method embodiments, and have similar beneficial effects. For technical details not disclosed in the device embodiments of this application, please refer to the descriptions of the method embodiments of this application for understanding.

[0272] It should be noted that, in the embodiments of this application, if the above-described vehicle driving control method is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of this application, or the part that contributes to the related technology, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of this application are not limited to any specific hardware and software combination.

[0273] Thirdly, embodiments of this application provide a vehicle, which includes a target inner mold controller, multiple wheels, a processor, and a memory. The memory stores computer programs or instructions. When the computer programs or instructions are executed by the processor, they call the target inner mold controller to distribute and control the yaw torque at the wheel ends of the multiple wheels, thereby implementing the method provided in the first aspect.

[0274] Fourthly, embodiments of this application provide a storage medium, namely a computer-readable storage medium, on which a computer program or instructions are stored, which, when executed by a processor, implement the steps of any of the methods provided in the first aspect of the above embodiments.

[0275] Fifthly, embodiments of this application provide a computer program product, which includes a computer program or instructions that, when executed by a processor, implement the steps of any of the methods provided in the first aspect of the above embodiments.

[0276] It should be noted that the descriptions of the above embodiments of storage media, devices, apparatuses, and program products are similar to the descriptions of the above method embodiments and have similar beneficial effects. For technical details not disclosed in the embodiments of storage media, devices, apparatuses, and program products of this application, please refer to the descriptions of the method embodiments of this application for understanding.

[0277] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in some embodiments" appearing throughout the specification do not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above-described embodiments are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0278] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0279] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another electronic device, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0280] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0281] In addition, each functional unit in the various embodiments of this application can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0282] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as mobile storage devices, read-only memory (ROM), magnetic disks, or optical disks.

[0283] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0284] The above are merely embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for estimating the sideslip angle of a vehicle's center of gravity, characterized in that, The method includes: Obtain vehicle operating status data; Input data for inputting into a preset estimator is determined from the operating status data; wherein, the input data is used to characterize the degree of lateral change of the vehicle; The input data is processed using the preset estimator to determine the real-time sideslip angle of the vehicle's center of gravity.

2. The method according to claim 1, characterized in that, The input data includes first feature data and second feature data; the first feature data includes first historical data related to the lateral motion of the vehicle, and the second feature data includes first real-time data related to the lateral response difference of the vehicle, wherein the lateral response difference of the vehicle is determined based on the difference between the actual lateral acceleration and the desired lateral acceleration.

3. The method according to claim 2, characterized in that, The first feature data is the data after the first historical data has been weighted by the first weight data, and the second feature data is the data after the first real-time data has been weighted by the second weight data.

4. The method according to claim 2 or 3, characterized in that, The first feature data includes at least one of the following: historical estimated lateral speed, historical front wheel steering angle, and historical yaw rate; The second feature data includes at least one of the following: the vehicle lateral response difference at the current time, and the rate of change of the vehicle steering response difference at the current time.

5. The method according to claim 4, characterized in that, The historical estimated lateral speed, the historical front wheel steering angle, and the historical yaw rate each include data from two adjacent historical moments.

6. The method according to claim 4, characterized in that, The second feature data also includes at least one of the following: the wheel speed of the vehicle's wheels at the current moment; the longitudinal velocity at the current moment; the longitudinal acceleration at the current moment; and the lateral acceleration at the current moment.

7. The method according to any one of claims 1-6, characterized in that, The preset estimator is an analytical estimator, and it is trained and established based on data that characterizes the degree of lateral change of the vehicle.

8. The method according to any one of claims 1-6, characterized in that, The input data is processed using the preset estimator to determine the real-time sideslip angle of the vehicle's center of gravity, including: The preset estimator calls the first weight feature, and the input data is calculated based on the first weight feature to output the estimated value of the vehicle's lateral speed; The vehicle's center of gravity sideslip angle is determined based on the estimated lateral velocity.

9. The method according to claim 8, characterized in that, The method further includes: Construct an initial estimator model; wherein, the initial estimator model further includes a first weight feature to be solved; The initial estimator model is transformed by solving the weight features based on the lateral velocity to obtain a solvable estimator model; The first weight feature of the preset estimator model is determined based at least on the training data and the solvable estimator model; the training data is used to characterize the degree of lateral change of the vehicle.

10. The method according to claim 9, wherein the process of determining the solvable estimator model includes: The initial estimator model is optimized using a constrained method based on the lateral velocity error to obtain a first optimization expression. The first optimization expression is used to minimize the lateral velocity error and homogenize the parameter influence. Construct the Lagrange function corresponding to the first optimized expression; Construct a kernel function based on the features of the initial estimator model; Based on the Lagrange function, the kernel function, and the training data, the solvable estimator model is determined.

11. The method according to claim 10, characterized in that, The determination of the first weight feature of the preset estimator model based at least on training data and the solvable estimator model includes: The solvable estimator model is processed to obtain a second expression; the input of the second expression includes the kernel function, the regularization coefficient, and the Lagrange parameter, and the output of the second expression includes the lateral velocity; The second expression is processed using training data to determine the Lagrange multipliers; The first weight feature of the preset estimator is determined based on the Lagrange multipliers.

12. The method according to any one of claims 1-6, characterized in that, The step of processing the input data using the preset estimator to determine the real-time sideslip angle of the vehicle's center of gravity includes: The preset estimator is used to invoke the second weight feature, and the input data is calculated based on the second weight feature to output the real-time centroid sideslip angle of the vehicle.

13. A device for estimating the sideslip angle of a vehicle's center of gravity, characterized in that, The device includes: The acquisition unit is used to acquire vehicle operating status data; A determining unit is configured to determine input data from the operating status data for inputting into a preset estimator; wherein the input data is used to characterize the degree of lateral change of the vehicle; The processing unit is used to process the input data using the preset estimator to determine the real-time centroid sideslip angle of the vehicle.

14. A vehicle, characterized in that, The vehicle includes sensors and a controller; the sensors are used to acquire vehicle operating status data, and the controller is used to control the vehicle to implement the method described in any one of claims 1-12 based on the operating status data.

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