A method and device for predicting the lateral motion state of vehicles based on the sliding window mechanism

Abstract

This invention relates to a method and apparatus for predicting the lateral motion state of a vehicle based on a sliding window mechanism, comprising: Step S1: obtaining a pre-configured sliding window length, and initializing a vehicle lateral motion state prediction model based on the sliding window length and historical data; Step S2: upon receiving the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio, and vehicle lateral motion state, generating a system evolution matrix of the prediction model based on the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio, and vehicle lateral motion state, wherein the system evolution matrix of the prediction model acts on the vehicle lateral motion state prediction model, and the vehicle lateral motion state includes the vehicle lateral velocity and the vehicle yaw rate; Step S3: correcting the vehicle lateral motion state prediction model based on the generated system evolution matrix; Step S4: predicting the vehicle lateral motion state based on the corrected vehicle lateral motion state prediction model. Compared with the prior art, this invention has the advantages of requiring fewer parameters and being able to adapt to dynamic changes in operating conditions.

Description

Technical Field

[0001] This invention relates to the field of vehicle lateral motion control, and in particular to a method and device for predicting the lateral motion state of a vehicle based on the sliding window mechanism. Background Technology

[0002] The lateral motion of a vehicle mainly includes lateral velocity and yaw rate. In traditional technology, the lateral velocity and yaw rate are generally obtained using dynamic modeling methods based on Newton's laws of motion. However, this method involves many time-varying vehicle parameters, such as vehicle mass, tire longitudinal stiffness, lateral stiffness, and vehicle center of gravity position. The large number of parameters involved makes it easy to obtain these data in experimental scenarios, but in actual working conditions, the accuracy will decrease due to unpredictable changes in the vehicle's health and the condition of its components.

[0003] To address this issue, some OEMs have researched using machine learning techniques to identify or predict the lateral motion of vehicles through readily available indirect parameters. However, machine learning methods require a large amount of data, and model training is time-consuming and labor-intensive. Developers outside of OEMs find it difficult to obtain sufficient data for training. Furthermore, relying on machine learning to predict the lateral motion of vehicles, which clearly exhibits Newtonian mechanical properties, is not economical.

[0004] Therefore, in order to solve the problems of the traditional dynamic modeling method based on Newton's laws of motion, some people in the field have adopted a mechanism-data fusion method based on a fixed window to reduce the problem of too many types of parameters. However, the mechanism-data fusion method based on a fixed window is not very adaptable to the working conditions and requires multiple selections and modeling of window data, which puts greater pressure on the computing power of the already insufficient vehicle computing equipment. Summary of the Invention

[0005] The purpose of this invention is to provide a method and device for predicting the lateral motion state of a vehicle based on the sliding window mechanism. Based on the sliding window mechanism, the vehicle lateral motion state prediction model can be updated using the measured values ​​of the vehicle's front wheel steering angle, front wheel slip ratio, and lateral motion state. On the one hand, fewer parameters are required, and on the other hand, the accuracy of predicting the lateral motion state of the vehicle during dynamic changes and changes in operating conditions is improved through the sliding window method.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for predicting the lateral motion state of a vehicle based on a sliding window mechanism includes:

[0008] Step S1: Obtain the pre-configured sliding window length, and initialize the vehicle lateral motion state prediction model based on the sliding window length and historical data;

[0009] Step S2: After receiving the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state, generate the system evolution matrix of the prediction model based on the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state. The system evolution matrix of the prediction model acts on the vehicle lateral motion state prediction model, and the vehicle lateral motion state includes the vehicle lateral velocity and the vehicle yaw rate.

[0010] Step S3: Correct the vehicle lateral motion state prediction model based on the system evolution matrix of the prediction model;

[0011] Step S4: Predict the lateral motion state of the vehicle based on the modified vehicle lateral motion state prediction model.

[0012] The update process of the vehicle lateral motion state prediction model includes:

[0013] The first input to the control system is the vehicle's front wheel steering angle.

[0014] Lateral movement of the vehicle

[0015] The second input to the control system includes the reciprocal of the vehicle's longitudinal speed, the vehicle's longitudinal speed, and the vehicle's front wheel slip ratio.

[0016] The mathematical formula for the vehicle lateral motion state prediction model is:

[0017]

[0018] Where: x k+1 This represents the lateral motion state of the vehicle predicted in step k+1. For the knth d The vector formed by the measured values ​​of the vehicle's lateral motion state from step +1 to step k, U k For the knth d The vector formed by the measured values ​​of the first input quantity from step k to step (k-1), U(ρ) k ) is the knth d Step k-1 System planning parameter vector ρ k With input u k The product of the Kronecker operators, X k For the knth d The vector consisting of the measured values ​​of the vehicle's lateral motion state from step k to step (k-1), X(ρ k ) is the knth d Step k-1 System planning parameter vector ρk With lateral motion state quantity x k The product of Kronecker operators, Ω k For the knth d The data segment up to step k-1, u k Let ρ be the input to the control system in step k. k Let x be the planning parameter vector of the control system in step k. k This represents the lateral motion state of the vehicle measured at step k.

[0019] The knth d Step k-1 System planning parameter vector ρ k With input u k Kronecker operator product U(ρ) k The mathematical expression for ) is:

[0020]

[0021] in: For kn d The measured value of the second input quantity. For the knth d The measured value of the first input quantity. This is the measured value of the second input quantity in step k-1. This is the measured value of the first input quantity in step k-1. Let be the dimension of the matrix.

[0022] The knth d Step k-1 System planning parameter vector ρ k With lateral motion state quantity x k The product of the Kronecker operators X(ρ) k The mathematical expression for ) is:

[0023]

[0024] in: For kn d The measured value of the second input quantity. No. kn d Measured values ​​of the lateral motion state of the vehicle. This is the measured value of the second input quantity in step k-1. This represents the measured value of the vehicle's lateral motion state at step k-1. Let be the dimension of the matrix.

[0025] A vehicle lateral motion state prediction device based on a sliding window mechanism includes a memory, a processor, and a program stored in the memory. When the processor executes the program, it performs the following steps:

[0026] Step S1: Obtain the pre-configured sliding window length, and initialize the vehicle lateral motion state prediction model based on the sliding window length and historical data;

[0027] Step S2: After receiving the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state, generate the system evolution matrix of the prediction model based on the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state. The system evolution matrix of the prediction model acts on the vehicle lateral motion state prediction model, and the vehicle lateral motion state includes the vehicle lateral velocity and the vehicle yaw rate.

[0028] Step S3: Correct the vehicle lateral motion state prediction model based on the system evolution matrix of the prediction model;

[0029] Step S4: Predict the lateral motion state of the vehicle based on the modified vehicle lateral motion state prediction model.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. Based on the sliding window mechanism, the vehicle's lateral motion state prediction model can be updated using the measured values ​​of the vehicle's front wheel steering angle, front wheel slip ratio, and lateral motion state. On the one hand, fewer parameters are required, and on the other hand, the accuracy of predicting the vehicle's lateral motion state during dynamic changes and changes in operating conditions is improved through the sliding window method.

[0032] 2. Based on the designed lateral motion state of the vehicle, this model has both physical interpretability and strong adaptability to data-driven methods. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the technical route of the vehicle lateral motion state prediction model on which the present invention is based;

[0034] Figure 2 This is a schematic diagram showing the relationship between tire longitudinal force and slip ratio.

[0035] Figure 3 This is a schematic diagram of the main steps of the method of the present invention;

[0036] Figure 4 A schematic diagram illustrating the effect of sliding window length on model error.

[0037] Figure 5 A schematic diagram comparing model errors with different sliding window lengths;

[0038] Figure 6 For the standard path tracking condition, the sliding window length n d A schematic diagram of the model representation with a value of 50;

[0039] Figure 7 For the sliding window length n in the case of a road with small curvature d A schematic diagram of the model representation with a value of 50;

[0040] Figure 8 A schematic diagram showing the model representation of a fixed window of different lengths for a road with small curvature.

[0041] Figure 9 This diagram illustrates the comparison of the model performance of sliding window and fixed window algorithms for road conditions with high curvature. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0043] The vehicle lateral motion state prediction method based on the sliding window mechanism proposed in this application is a novel vehicle lateral motion state prediction model obtained from the vehicle lateral dynamics modeling method based on the sliding window mechanism and data fusion. The vehicle lateral dynamics modeling method based on the sliding window mechanism and data fusion proposes a data sliding window-based modeling architecture, which possesses both the interpretability of physical laws and the condition adaptability of data-driven methods. Figure 1 As shown, based on the traditional vehicle lateral dynamics model, a discrete-domain linear variable parameter control model for vehicle lateral dynamics is derived. The adjustment parameters are the measurable longitudinal vehicle speed and front wheel slip ratio. The new model achieves effective separation between vehicle-related time-varying parameters and the real-time measurable adjustment parameters. This model is derived from Newton's laws of motion and has physical interpretability. Based on the discrete-domain linear variable parameter model, a system evolution matrix based on data (steering wheel angle, longitudinal speed, wheel speed) is derived. A data sliding window mechanism is designed to collect data at each moment and update the data within the sliding window, achieving real-time updating of the system evolution matrix and giving the model adaptability to operating conditions.

[0044] Based on the laws of vehicle motion and Newton's laws of motion, the traditional lateral dynamics model of a vehicle can be described by the following equation:

[0045]

[0046]

[0047] Where: m represents the vehicle mass, I z δ represents the moment of inertia of the vehicle about the z-axis. fThis represents the front wheel steering angle. Unlike traditional tire force models, a novel tire force model is proposed here. This model integrates nonlinear terms into the tire stiffness, designs the tire stiffness as a time-varying parameter, and preserves the linear relationship between tire force and slip ratio / side slip angle, as shown in the figure. The tire force can be expressed by the following formula:

[0048]

[0049] Where: i takes the value f or r, f represents the front wheel, r represents the rear wheel, superscript / subscript x represents longitudinal direction, and superscript / subscript y represents lateral direction. λ represents the corresponding tire stiffness. i The tire slip ratio, r i w represents the effective radius of the tire. i The speed of tire rotation, v x α represents the longitudinal velocity of the vehicle. i Indicates the tire slip angle, v y L represents the lateral speed of the vehicle. i γ represents the distance from the front or rear axle to the center of mass, and γ represents the vehicle's yaw rate.

[0050] like Figure 2 The diagram shows the relationship between tire longitudinal force and slip ratio. The above system is derived into a state-space equation, with a discrete time step T. s Discretization yields the following system:

[0051] x k+1 =A k (ρ k )x k +B k (ρ k )u k

[0052] x = [υ y γ] T u=δ f , ρ=[ρ1 ρ2 ρ3] T =[1 / υ x υ x λ f ] T

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] Note that in the above formulas, A1, B0, and B3 are time-varying vehicle-related system parameters, which are separate from the adjustment parameter ρ. The above system is derived based on physical laws, possesses intuitive physical interpretability, and can describe the vehicle's motion patterns under different operating conditions.

[0059] By introducing the Kronecker product operator, the above discrete system can be further simplified:

[0060]

[0061] Assuming a set of data can be collected Define the window length of the sliding window as n d Define the following data matrix to form a window:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] Based on the data and using the physical rules of the linear variable parameter transverse dynamics model, the following relationship can be obtained:

[0068]

[0069] The system evolution matrix can be calculated as follows:

[0070]

[0071] Therefore, the vehicle lateral motion state prediction model based on mechanism-data fusion can be derived as follows:

[0072]

[0073] Finally, a sliding window mechanism for data is designed, that is, at each moment, when a new data point... After collection, the oldest data points are discarded, and a window of data is formed and updated. This process is repeated at different times to update the system matrix in real time, implementing a sliding window mechanism for the system evolution matrix, and ultimately achieving online prediction of the vehicle's lateral motion state, as detailed below:

[0074] A method for predicting the lateral motion state of a vehicle based on the sliding window mechanism, such as... Figure 3 As shown, it includes:

[0075] Step S1: Obtain the pre-configured sliding window length, and initialize the vehicle lateral motion state prediction model based on the sliding window length and historical data;

[0076] Step S2: After receiving the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state, generate the system evolution matrix of the prediction model based on the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state. The system evolution matrix of the prediction model acts on the vehicle lateral motion state prediction model, and the vehicle lateral motion state includes the vehicle lateral velocity and the vehicle yaw rate.

[0077] Step S3: Correct the vehicle lateral motion state prediction model based on the system evolution matrix of the prediction model;

[0078] Step S4: Predict the lateral motion state of the vehicle based on the modified vehicle lateral motion state prediction model.

[0079] Based on the sliding window mechanism, the vehicle lateral motion state prediction model can be updated using the measured values ​​of the vehicle's front wheel steering angle, front wheel slip ratio, and lateral motion state. On the one hand, fewer parameters are required, and on the other hand, the accuracy of predicting the vehicle's lateral motion state during dynamic changes and changes in operating conditions is improved through the sliding window method.

[0080] In this embodiment, the vehicle lateral motion state prediction model update process includes:

[0081] The first input to the control system is the vehicle's front wheel steering angle.

[0082] Lateral movement of the vehicle

[0083] The second input to the control system includes the reciprocal of the vehicle's longitudinal speed, the vehicle's longitudinal speed, and the vehicle's front wheel slip ratio.

[0084] The mathematical formula for the vehicle lateral motion state prediction model is as follows:

[0085]

[0086] Where: x k+1 This represents the lateral motion state of the vehicle predicted in step k+1. For the knth d The vector formed by the measured values ​​of the vehicle's lateral motion state from step +1 to step k, U k For the knth d The vector formed by the measured values ​​of the first input quantity from step k to step (k-1), U(ρ) k ) is the knth d Step k-1 System planning parameter vector ρ kWith input u k The product of the Kronecker operators, X k For the knth d The vector consisting of the measured values ​​of the vehicle's lateral motion state from step k to step (k-1), X(ρ k ) is the knth d Step k-1 System planning parameter vector ρ k With lateral motion state quantity x k The product of Kronecker operators, Ω k For the knth d The data segment up to step k-1, u k Let ρ be the input to the control system in step k. k Let x be the planning parameter vector of the control system in step k. k This represents the lateral motion state of the vehicle measured at step k.

[0087] The knth d Step k-1 System planning parameter vector ρ k With input u k Kronecker operator product U(ρ) k The mathematical expression for ) is:

[0088]

[0089] in: For kn d The measured value of the second input quantity. For the knth d The measured value of the first input quantity. This is the measured value of the second input quantity in step k-1. This is the measured value of the first input quantity in step k-1. Let be the dimension of the matrix.

[0090] The knth d Step k-1 System planning parameter vector ρ k With lateral motion state quantity x k The product of the Kronecker operators X(ρ) k The mathematical expression for ) is:

[0091]

[0092] in: For kn d The measured value of the second input quantity. No. kn d Measured values ​​of the lateral motion state of the vehicle. This is the measured value of the second input quantity in step k-1. This represents the measured value of the vehicle's lateral motion state at step k-1. Let be the dimension of the matrix.

[0093] Taking the measured value of the second input quantity in step k-1 as an example, its specific value is as follows:

[0094] Furthermore, simulation experiments were conducted on the vehicle lateral motion state prediction model provided in this application, and the test results for its various indicators are as follows: Figures 4 to 9 As shown.

[0095] Figure 4 , Figure 5 and Figure 6 The impact of different sliding window lengths on the accuracy of this prediction method is demonstrated. This is applied to conventional paths (including straightaways, curves with varying curvature, acceleration, and deceleration). Figure 4 The analysis results of the prediction error (i.e., lateral velocity error and yaw rate error) of the proposed model as a function of the sliding window length are presented. It shows that as the sliding window length increases, the amount of data used for model prediction increases, and the prediction error of the dynamic signal gradually decreases. When the sliding window length increases to a certain value, the prediction error is in a steady state, indicating that the model achieves accurate prediction. Figure 5 The diagram illustrates the specific predictive performance of lateral velocity error (top image) and yaw rate error (bottom image) under normal operating conditions for three different sliding window lengths; scenarios with good prediction results (such as n) are also shown. d =50) Display as follows Figure 6 As shown.

[0096] Figure 7-9 The prediction results of the method proposed in this patent and the fixed window method under different road curvatures were compared. Figure 7 and Figure 8 The road includes a 50m straight section and a curved section. The radius R of the curved section is 1000m, and the curvature is 1 / R. From Figure 7 As can be seen, the solution proposed in this patent can achieve good prediction results using only a 50-point window, while Figure 8 The results show that, for the same prediction effect, the fixed window method requires a window length of 1000 points. Figure 9 The prediction results of the sliding window and fixed window methods are presented under the condition of large curvature road (front wheel steering angle can reach 40 degrees), showing that the sliding window prediction method has strong adaptability.

[0097] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, 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 steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for predicting the lateral motion state of a vehicle based on the sliding window mechanism, characterized in that, include: Step S1: Obtain the pre-configured sliding window length, and initialize the vehicle lateral motion state prediction model based on the sliding window length and historical data; Step S2: After receiving the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state, generate the system evolution matrix of the prediction model based on the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state. The system evolution matrix of the prediction model acts on the vehicle lateral motion state prediction model, and the vehicle lateral motion state includes the vehicle lateral velocity and the vehicle yaw rate. Step S3: Correct the vehicle lateral motion state prediction model based on the system evolution matrix generated by the prediction model; Step S4: Predict the lateral motion state of the vehicle based on the modified vehicle lateral motion state prediction model; The mathematical formula for the vehicle lateral motion state prediction model is: in: x k+1 For the first k +1 step prediction of the vehicle's lateral motion state For the first k - n d +1 step to the next k The vector formed by the measured values ​​of the lateral motion state of the vehicle, U k For the first k - n d Step to the first k The vector composed of the measured values ​​of the first input quantity in step -1, U( ρ k ) is the first k - n d Step to the first k -1-step system planning parameter vector ρ k With input u k The product of the Kronecker operators, X k For the first k - n d Step to the first k The vector consisting of the measured values ​​of the vehicle's lateral motion state in step -1, X(ρ k ) is the first k - n d Step to the first k -1-step system planning parameter vector ρ k With lateral motion state quantity x k The product of Kronecker operators, Ω k For the first k - n d Step to the first k -1 step data segment, u k For the first k The input of the step control system ρ k For the first k The planning parameter vector of the step control system, x k For the first k The lateral motion state of the vehicle is obtained by step measurement.

2. The method for predicting the lateral motion state of a vehicle based on the sliding window mechanism according to claim 1, characterized in that, The update process of the vehicle lateral motion state prediction model includes: The first input to the control system is the vehicle's front wheel steering angle. The vehicle's lateral movement. The second input to the control system includes the reciprocal of the vehicle's longitudinal speed, the vehicle's longitudinal speed, and the vehicle's front wheel slip ratio.

3. The method for predicting the lateral motion state of a vehicle based on the sliding window mechanism according to claim 1, characterized in that, The first k - n d Step to the first k -1-step system planning parameter vector ρ k With input u k The product of the Kronecker operators U ( ρ k The mathematical expression for ) is: in: for k - n d The measured value of the second input quantity. For the first k - n d The measured value of the first input quantity. For the first k -1 step, the measured value of the second input quantity. For the first k -1 step, the measured value of the first input quantity. Let be the dimension of the matrix.

4. The method for predicting the lateral motion state of a vehicle based on the sliding window mechanism according to claim 1, characterized in that, The first k - n d Step to the first k -1-step system planning parameter vector ρ k With lateral motion state quantity x k The product of the Kronecker operators X(ρ) k The mathematical expression for ) is: in: for k - n d The measured value of the second input quantity. No. k - n d Measured values ​​of the lateral motion state of the vehicle. For the first k -1 step, the measured value of the second input quantity. For the first k -1 step, measured value of the vehicle's lateral motion state. Let be the dimension of the matrix.

5. A vehicle lateral motion state prediction device based on sliding window mechanism, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it performs the following steps: Step S1: Obtain the pre-configured sliding window length, and initialize the vehicle lateral motion state prediction model based on the sliding window length and historical data; Step S2: After receiving the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state, generate the system evolution matrix of the prediction model based on the latest collected vehicle front wheel steering angle, vehicle front wheel slip ratio and vehicle lateral motion state. The system evolution matrix of the prediction model acts on the vehicle lateral motion state prediction model, and the vehicle lateral motion state includes the vehicle lateral velocity and the vehicle yaw rate. Step S3: Correct the vehicle lateral motion state prediction model based on the system evolution matrix of the prediction model; Step S4: Predict the lateral motion state of the vehicle based on the modified vehicle lateral motion state prediction model; The mathematical formula for the vehicle lateral motion state prediction model is: in: x k+1 For the first k +1 step prediction of the vehicle's lateral motion state For the first k - n d +1 step to the next k The vector formed by the measured values ​​of the lateral motion state of the vehicle, U k For the first k - n d Step to the first k The vector composed of the measured values ​​of the first input quantity in step -1, U( ρ k ) is the first k - n d Step to the first k -1-step system planning parameter vector ρ k With input u k The product of the Kronecker operators, X k For the first k - n d Step to the first k The vector consisting of the measured values ​​of the vehicle's lateral motion state in step -1, X(ρ k ) is the first k - n d Step to the first k -1-step system planning parameter vector ρ k With lateral motion state quantity x k The product of Kronecker operators, Ω k For the first k - n d Step to the first k -1 step data segment, u k For the first k The input of the step control system ρ k For the first k The planning parameter vector of the step control system, x k For the first k The lateral motion state of the vehicle is obtained by step measurement.

6. The vehicle lateral motion state prediction device based on sliding window mechanism according to claim 5, characterized in that, The update process of the vehicle lateral motion state prediction model includes: The first input to the control system is the vehicle's front wheel steering angle. The vehicle's lateral movement. The second input to the control system includes the reciprocal of the vehicle's longitudinal speed, the vehicle's longitudinal speed, and the vehicle's front wheel slip ratio.

7. The vehicle lateral motion state prediction device based on sliding window mechanism according to claim 5, characterized in that, The first k - n d Step to the first k -1-step system planning parameter vector ρ k With input u k The product of the Kronecker operators U ( ρ k The mathematical expression for ) is: in: for k - n d The measured value of the second input quantity. For the first k - n d The measured value of the first input quantity. For the first k -1 step, the measured value of the second input quantity. For the first k -1 step, the measured value of the first input quantity. Let be the dimension of the matrix.

8. The vehicle lateral motion state prediction device based on sliding window mechanism according to claim 5, characterized in that, The first k - n d Step to the first k -1-step system planning parameter vector ρ k With lateral motion state quantity x k The product of the Kronecker operators X(ρ) k The mathematical expression for ) is: in: for k - n d The measured value of the second input quantity. No. k - n d Measured values ​​of the lateral motion state of the vehicle. For the first k -1 step, the measured value of the second input quantity. For the first k -1 step, measured value of the vehicle's lateral motion state. Let be the dimension of the matrix.

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