Vehicle Driving State Estimation Method Based on Piecewise Affine Identification Tire Model

Abstract

The present invention discloses a method for estimating the driving state of a vehicle based on a piecewise affine identification tire model, including steps such as a tire longitudinal slip and sideslip characteristic experiment, conducting a tire longitudinal slip and sideslip characteristic experiment, constructing a piecewise affine identification model of the tire longitudinal slip and sideslip mechanical characteristics according to the experimental data, constructing a mathematical model for estimating the driving state of a vehicle dynamic piecewise affine system, and estimating the vehicle driving state parameters, etc. Beneficial effects: The technical solution of the present invention completes the piecewise affine identification of the tire longitudinal slip and sideslip mechanical characteristics, constructs a mathematical model for estimating the state of the intelligent vehicle lateral dynamics system based on the identified model combined with the tire longitudinal relaxation length, and uses the adaptive cubature Kalman filter algorithm to adopt the maximum a posteriori probability to estimate the statistical values of the process noise and measurement noise, effectively improving the estimation accuracy and stability, and providing reference value for the subsequent vehicle dynamics control system.

Description

Technical Field

[0001] The present invention relates to a method for estimating a vehicle driving state, in particular to a method for estimating a vehicle driving state based on a piecewise affine identification tire model, and belongs to the technical field of vehicle control. Background Art

[0002] With the continuous increase in the number of social automobiles, the environmental problems brought about have an increasingly serious impact on human society. Electric vehicles have attracted wide social attention due to their advantages in energy conservation and environmental protection. Among them, distributed drive electric vehicles are considered to be a good platform for realizing autonomous driving technology because they have no complex transmission mechanism and the torque can be accurately controlled.

[0003] In recent years, with the application of various advanced control systems, such as: adaptive cruise control system, lane keeping system, etc., the principle of which is the direct application of yaw moment control on mass-produced vehicles. However, users' requirements for vehicle driving stability and safety performance are constantly increasing, requiring the vehicle to maintain good stability and reliability under relatively harsh driving conditions. In a closed-loop vehicle dynamics control architecture, reliable driving state estimation parameter input is the premise for intelligent vehicles to achieve high-precision dynamics control. Vehicle control parameters such as: yaw angular velocity, sideslip angle of the center of mass, longitudinal and lateral velocities, and four-wheel longitudinal forces are the basis for intelligent vehicle trajectory tracking and direct yaw moment control and are also the key factors for completing the vehicle dynamics control. However, as the only component of the vehicle in contact with the ground, the model accuracy of the tire directly affects the estimation performance and control accuracy of the vehicle system. There is a complex coupling relationship between the longitudinal force and the lateral force of the tire when driving at high speed on a wet and slippery road surface. In previous studies, the factors considered were usually not comprehensive enough. Therefore, the vehicle is prone to disadvantages such as low estimation accuracy and poor stability under many special driving conditions.

[0004] With the continuous development of the vehicle motion control system, especially the higher requirements for the motion control performance of electric vehicles under all-conditions road driving conditions. At present, the failure to construct an accurate dynamic characteristic model for the tire results in limited improvement of the system control performance. At the same time, from the perspective of vehicle dynamics control integration, the model should not only accurately describe the physical essence of the objective system but also be suitable for the application of dynamics control theory. Even though a complex mechanism model can effectively reflect the nonlinear relationship between variables in the controlled process, it may cause inconvenience for the design of the control system. Therefore, although there have been studies on complex mechanism models of tire longitudinal slip and sideslip mechanical characteristics, most of them are complex in form and difficult to fit parameters. Studying only the mechanical characteristics of the tire without considering subsequent motion control system integration on this basis, therefore, it is impossible to accurately fit the nonlinear mechanical characteristics of the tire under composite conditions, thus affecting the design of the subsequent vehicle motion control system based on this. Summary of the Invention

[0005] Objective of the Invention: Aiming at the problem of estimating the driving state of a distributed drive electric vehicle under extreme working conditions in the prior art, the present invention proposes a method for estimating the driving state of a vehicle based on a piecewise affine identification tire model.

[0006] Technical Solution: A method for estimating the driving state of a vehicle based on a piecewise affine identification tire model includes the following steps:

[0007] Step 1, Tire Longitudinal Slip and Lateral Force Characteristics Experiment: Conduct a tire longitudinal slip and lateral force characteristics experiment to obtain experimental data on the non-linear relationship between the tire longitudinal force and lateral force and the tire operating parameters.

[0008] Step 2, Construct a Piecewise Affine Identification Model of Tire Longitudinal Slip and Lateral Force Mechanical Characteristics: According to the non-linear relationship between the tire longitudinal force and lateral force and the tire operating parameters, construct a piecewise affine identification model of tire longitudinal slip and lateral force mechanical characteristics through piecewise affine identification.

[0009] Step 3, Construct a Mathematical Model for Estimating the Driving State of a Vehicle Dynamics Piecewise Affine System: Based on the piecewise affine identification model of tire longitudinal slip and lateral force mechanical characteristics, and at the same time, according to the three-degree-of-freedom model of the vehicle including longitudinal motion, lateral motion, and yaw motion of the vehicle and combining the longitudinal relaxation lengths of each tire, construct a mathematical model for estimating the driving state of a vehicle dynamics piecewise affine system.

[0010] Step 4, Estimate Vehicle Driving State Parameters: Based on the constructed mathematical model for estimating the driving state of a vehicle dynamics piecewise affine system, use the adaptive cubature Kalman filter algorithm to estimate the statistical values of the process noise covariance and measurement noise covariance using the maximum a posteriori probability criterion.

[0011] The technical solution of the present invention effectively improves the estimation accuracy and stability by completing the piecewise affine identification of tire longitudinal slip and lateral force mechanical characteristics, constructing a mathematical model for estimating the state of the vehicle lateral dynamics system based on the identified model and combining the longitudinal relaxation lengths of the tires, and using the maximum a posteriori probability to estimate the statistics of the process noise and measurement noise, providing a reference value for the subsequent vehicle dynamics control system.

[0012] Preferred Option: To ensure the accuracy of the experimental data, in the tire longitudinal slip and lateral force characteristics experiment in Step 1, the tire vertical load is set to 8060 N, the change range of the tire lateral deviation angle is set to [-10° to 10°], and the slip rate is controlled to [-1 to 0.5].

[0013] Preferred Option: To enable the piecewise affine identification of tire longitudinal slip and lateral force mechanical characteristics, the method for piecewise affine identification of tire longitudinal slip and lateral force mechanical characteristics in Step 2 includes four links: model definition, data clustering, parameter estimation of the affine sub-model, and solution of the hyperplane coefficient matrix.

[0014] Preferred option, the method for defining the model is as follows:

[0015] Construct the model mathematical expression

[0016]

[0017] where y j ∈R p is the output of the system, θ i (i = 1,..., s) are the parameters of each sub-model, x j ∈R n is the regression vector of the system, which always contains the past input and output of the system, x j is expressed as:

[0018]

[0019] where n y and n u represent the order of the piecewise affine model, u j is the system input, n = pn y + mn u .χ i (i = 1,…, s) is a complete partition of the regression set χ, and each region is a convex polyhedron subset, written as:

[0020] χ i ={F i x j + g i ≤ 0}

[0021] where F i and g i are the hyperplane coefficient matrices; let H i =[F i g i ,(i = 1,..., s) then the convex polyhedron region is rewritten as:

[0022] χ i ={H i [x j 1] T ≤ 0}

[0023] Preferred option, the method for data clustering is as follows:

[0024] Divide the original data set into s uncorrelated clusters, and adopt the statistical data clustering method based on the Gaussian mixture model. Assume that N data samples are expressed as:

[0025]

[0026] Based on the Gaussian mixture model, the data sample zj The probability density is expressed as:

[0027]

[0028] For Φ = (α, μ, Σ), where the scalar parameter α := (α1, α2, …, α s ) satisfies dimensional vector and the (n + p)×(n + p) dimensional covariance matrix Σ := (Σ1, Σ2, …, Σ s ), the function p i (z; μ i , Σ i ) is used to define the expression of the multivariate Gaussian density, specifically as follows:

[0029]

[0030] When the optimal parameter Ф is obtained, the data sample j is assigned to the cluster Γ i The probability is expressed as:

[0031]

[0032] The said probability is used as the criterion for data clustering. For the remaining part, the optimal parameter Ф is found based on the maximum likelihood estimation method; for N data samples, the optimal parameter Ф that maximizes the log-likelihood function is found:

[0033]

[0034] Using the Expectation-Maximization (EM) algorithm, the maximum value is obtained by iteratively updating the parameter Ф. The EM algorithm consists of two steps, namely the Expectation step (E-step) and the Maximization step (M-step); in the M-step, it involves maximizing the log-likelihood function, which is redefined in the E-step of each iteration;

[0035] The execution process of the EM algorithm is as follows:

[0036] Starting from several initial parameters of Ф (0) , the EM algorithm improves the maximum value,

[0037] EM algorithm:

[0038] 1) Initialize Φ (0) = (α (0) , μ (0) , Σ (0) ) and at the same time set the iteration counter l = 0 and set ε > 0,

[0039] 2) Φ (l) = (α (l) , μ (l) , Σ (l))Perform the following steps:

[0040] Step E: Calculate j = 1, 2, …, N, i = 1, 2, …, s

[0041]

[0042] Step M: Update Φ (l) =(α (l) , μ (l) , Σ (l) ) Calculate

[0043]

[0044] 3) If the specified convergence condition is satisfied

[0045]

[0046] then set l * = l + 1, and the optimal estimate of Ф is obtained as Φ * = Φ (l*) Otherwise, input l = l + 1 and return to step 2);

[0047] The number of sub - models cannot be known in advance, and an estimation of the number of sub - models based on the information criterion related to maximum likelihood estimation is further introduced;

[0048] First, two positive integers s min and s max are given such that the number of sub - models is in the interval [s min , s max . Secondly, for all s = s min , …, s max , calculate the parameter estimate Ф s , Ф s represents the estimate of Ф under the fixed s; the estimate of s is obtained by the following formula:

[0049]

[0050] where J(Ф s , s) represents the criterion shown as follows: Based on the existing model - selection information criterion, the consistent Akaike information criterion (CAIC) and MDL criterion are adopted; the above criteria have the following form:

[0051] J(Φ s , s)= - 2L(Φ s )+ A(N)D(s)

[0052] In the formula, L(Ф s ) is the Ф sThe logarithmic likelihood function, the second term of the criterion represents the penalty for the data and the number of clusters, where D(s) represents the number of independent parameters in Ф s The expression is:

[0053]

[0054] And A(N) is a function of the number of data samples N, which are respectively

[0055]

[0056] Preferred option, the method for estimating the affine sub-model parameters is as follows:

[0057] After completing the data clustering task, according to the set Г i The parameters of the affine sub-model are estimated by the least squares algorithm through the data points collected therein; N data samples are divided into s non-overlapping clusters, so it is assumed that there are N i Samples in the i-th cluster, denoted as j i1 , j i2 , …, j iNi ; The first subscript represents the number of clusters, and the second subscript represents the number of samples in the i-th cluster. According to the above description, the following equations and variables are obtained:

[0058]

[0059] x j Is the autoregressive vector of the PWA model, N i Is the N i Samples in the i-th subset, denoted as j iN1 , j iN2 , …, j iNi , Using the least squares algorithm, the parameters of each affine sub-model are estimated according to the following formula:

[0060]

[0061] Preferred option, the method for solving the hyperplane coefficient matrix is as follows:

[0062] First, find two adjacent clusters Г i And Г j , Define the basic equation for calculation as follows:

[0063]

[0064] Secondly, combined with the improved approximate support vector machine (PSVM) algorithm, the interface coefficient matrix is obtained by solving the following optimization problem:

[0065]

[0066] s.t.W i (F i x i -eg i )=λ i -ξ i

[0067] where V i and W i are diagonal matrices, ξ i is the error vector, e is the unit vector. When W i = 1, V i = v (v is the penalty factor), λ i = 1, while when W i = -1, V i = v(n + / n - ), λ i = a i (a i is a positive number), n + is the number of positive samples, n - is the number of negative samples. When 0 < a i < 1, the classification hyperplane moves towards the negative sample direction; when a i > 1, the classification hyperplane moves towards the positive sample direction;

[0068] By adjusting the value of a i , the deviation of the classification hyperplane is adjusted;

[0069] According to the KKT (Karush - Kuhn - Tucher) conditions, the following Lagrangian equation can be constructed:

[0070]

[0071] where η i is the Lagrangian coefficient. Using the Lagrangian conditional extremum, the following equations are further obtained:

[0072]

[0073] Based on the above equations, it can be further obtained that:

[0074]

[0075] On this basis, it can be further obtained that:

[0076]

[0077] Subtracting the above two formulas, it can be obtained that:

[0078]

[0079] Multiply both sides of the above formula by W i , and we can get:

[0080]

[0081] Combining the above formula, we can get:

[0082]

[0083] So

[0084]

[0085] Calculate the hyperplane coefficient matrices F i and g j .

[0086] Preferred option, the method for constructing the mathematical model for estimating the driving state of the vehicle dynamics piecewise affine system in step 3 is as follows:

[0087] (1) The mathematical expressions for the three-degree-of-freedom vehicle model of the vehicle's longitudinal motion, lateral motion, and yaw motion are constructed as follows:

[0088]

[0089] where F xij and F yij represent the longitudinal force and lateral force of the tire respectively. The first subscript i = f or r represents the front axle or the rear axle, and the second subscript j = l or r represents the left and right wheels. δ is the front wheel steering angle, B is the wheelbase of the vehicle, I z is the moment of inertia of the vehicle, l f and l r are the distances between the front and rear axles of the vehicle, v x , v y and r are the longitudinal speed, lateral speed, and yaw angular velocity of the vehicle respectively, a x and a y represent the longitudinal acceleration and lateral acceleration of the vehicle respectively;

[0090] a x and a y are expressed as:

[0091]

[0092] where m is the body mass;

[0093] The sideslip angle of the center of mass and the slip ratio of each wheel are expressed as:

[0094]

[0095] where, w i , λ ij and v ij are the wheel angular velocity, wheel slip ratio and wheel center point velocity respectively, R is the wheel radius, and the subscripts "fl", "fr", "rl", "rr" represent the left front wheel, right front wheel, left rear wheel and right rear wheel respectively;

[0096] The longitudinal relaxation length expression is written as:

[0097]

[0098] where, ε xij represents the relaxation length of each wheel, F xij_M is the tire force calculated by the piecewise affine tire model, and ε xij represents the elastic hysteresis during the contact process between the tire and the road surface;

[0099] The relaxation length of the wheel is expressed as:

[0100]

[0101] where, C fx is the longitudinal stiffness of the longitudinal force at zero point, and C x is the tire lateral stiffness;

[0102] The longitudinal forces and lateral forces of the four tires are expressed as follows:

[0103]

[0104] where, F xfl_M , F xfr_M , F xrl_M and F xrr_M represent the longitudinal forces of the left front wheel tire, right front wheel tire, left rear wheel tire and right rear wheel tire calculated according to the piecewise affine tire model respectively; F yfl_M , F yfr_M , F yrl_M and F yrr_M represent the lateral forces of the left front wheel tire, right front wheel tire, left rear wheel tire and right rear wheel tire calculated according to the piecewise affine tire model respectively; in the above formula, M i , N i and b i are the parameters of the vehicle longitudinal force on different affine sub-models, and M j , N j and b jParameters of vehicle lateral force on different affine sub-models. The superscripts x on M, N, and b represent longitudinal direction, and y represents lateral direction. 1 - 4 represent the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively. α1 and α3 are the sideslip angles of the front wheels and rear wheels respectively, and λ1, λ2, λ3, and λ4 are the slip ratios of each wheel;

[0105] The sideslip angles of the front and rear wheels of the tire are expressed as:

[0106]

[0107] The non-linear state space of the vehicle system is expressed as:

[0108]

[0109] Among them, x(t) is the vehicle state variable, u(t) is the system input variable, w(t) is the system noise, v(t) is the measurement noise, z(t) is the measurement variable, f(·) is the state transition equation, and h(·) is the measurement equation;

[0110] Specifically, it is expressed as follows:

[0111]

[0112] Among them, L1 - L 36 is a time-varying parameter obtained according to the area of each wheel in the affine sub-model region, and is specifically expressed as:

[0113]

[0114] Preferred option. The method for estimating vehicle driving state parameters in step 4 is as follows:

[0115] The standard square root cubature Kalman filter algorithm is as follows.

[0116] The discrete non-linear system is expressed as:

[0117]

[0118] Among them, x k is the system state vector, z k is the system measurement vector, f(·) and h(·) are the system state transfer equation and measurement equation, w k-1 and v k represent the system process noise and measurement noise;

[0119] 1) Initialization

[0120] The initial value of the system and the square root factor S of the error covariance matrix 0|0 are set as:

[0121] S 0|0 = [Chol(P 0|0 )] T

[0122] where P 0|0 is the error covariance matrix, and Chol(·) is the Cholesky decomposition.

[0123] 2) Time update

[0124] Calculate and transfer the sigma points according to the state transition function:

[0125]

[0126] where S k-1|k-1 is the square root obtained by Cholesky decomposition of P k-1|k-1 , S k-1|k-1 = [Chol(P k-1|k-1 )] T , ξ i is the i-th column of the sigma point weight matrix , I n is the n×n identity matrix, and n is the dimension of the state variables.

[0127] Calculate the predicted value of the state and the square root factor of its error covariance matrix:

[0128]

[0129] Tria(·) represents the orthogonal triangular matrix decomposition, and the weighted center matrix is defined as:

[0130]

[0131] 3) Measurement update

[0132] Update the sigma points by using the state predicted value and the square root S k|k-1 of the predicted error covariance at time k, and perform the following transfer according to the following measurement equation:

[0133]

[0134] Calculate the square root factor of the predicted measurement value and its innovation covariance matrix as follows:

[0135]

[0136] The weighted center matrix Z k|k-1 is defined as:

[0137]

[0138] The calculation of the measurement covariance matrix and the cross-covariance matrix is as follows:

[0139]

[0140] The weighted center matrix X k|k-1 is defined as

[0141]

[0142] The Kalman gain matrix can be expressed as

[0143]

[0144] Update the square root factor and the error covariance matrix of the state variable at time k:

[0145]

[0146] Assume that the process noise covariance Q, the measurement noise covariance R, and the system state x k are all unknown variables, and the maximum a posteriori estimate is obtained by maximizing the conditional density function:

[0147] J * = p[X k , Q, R|Z k

[0148] where X k = {x1, x2, …, x k}, Z k = {z1, z2, …, z k},

[0149] According to the properties of conditional probability, we get

[0150]

[0151] p[Z k has nothing to do with the maximization of J * , and the maximum a posteriori estimates of Q, R, and x k are equivalently obtained by maximizing the following density function

[0152] J = p[X k , Q, R, Z k

[0153] = p[Z k |X k , Q, R] p[X k |Q, R] p[Q, R]

[0154] ​​where p[Q,R] is obtained from the prior information and regarded as a known constant. According to the probability multiplication rule:

[0155]

[0156] In the formula, n is the dimension of the state variable, and C1 = 1 / (2π) n(k+1 / 2 is a constant,

[0157] we get:

[0158]

[0159] In the formula, m is the dimension of the measurement variable, and C2 = 1 / (2π) mk / 2 is a constant. Further, we get:

[0160]

[0161] where

[0162]

[0163] The logarithmic operation does not change the extreme points of the function. J and ln J have the same maximum value. Taking the logarithm of the above formula, we get:

[0164]

[0165] Assume and are known. Taking the partial derivatives of ln J with respect to Q and R, we have the following relationship:

[0166]

[0167] Smoothing estimation and cannot be obtained. Use the state estimation and or the state prediction to replace. Denote the sub-optimal estimated values of the noise covariance Q k-1 and R k as

[0168]

[0169] Define the measurement innovation as

[0170]

[0171] Then we have the following relationship

[0172]

[0173] Therefore, we get

[0174]

[0175] Known According to the standard volume Kalman filter algorithm, the noise covariance Q k-1 and R k has an expectation of

[0176]

[0177]

[0178] When the noise statistics are constant or change little, it is considered that Q k-1 = Q j-1 and R k = R j , and rewriting the above formula gives:

[0179]

[0180] The noise covariance Q k-1 and R k has a statistical estimate of:

[0181]

[0182] Beneficial effects: The technical solution of the present invention effectively improves the estimation accuracy and stability by completing the piecewise affine identification of the longitudinal slip and side slip mechanical characteristics of the tire, constructing a mathematical model for the state estimation of the lateral dynamics system of an intelligent vehicle based on the identified model combined with the longitudinal relaxation length of the tire, and using the adaptive volume Kalman filter algorithm to estimate the statistical values of the process noise and measurement noise by the maximum a posteriori probability, providing a reference value for the subsequent vehicle dynamics control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0183] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts;

[0184] Figure 1 is the flowchart of the piecewise affine identification of the longitudinal slip and side slip mechanical characteristics of the tire of the present invention;

[0185] Figure 2 is the flowchart of the state estimation based on the piecewise affine system of the present invention;

[0186] Figure 3 is the flowchart of the vehicle state estimation of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0187] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0188] As shown in the figure, a method for estimating the vehicle driving state based on a piecewise affine identification tire model includes the following steps:

[0189] Step 1, Tire longitudinal slip and side slip characteristic experiment. Conduct a tire longitudinal slip and side slip characteristic experiment to obtain experimental data on the non-linear relationship between the tire longitudinal force and lateral force and the tire operating parameters.

[0190] In the tire longitudinal slip and side slip characteristic experiment, the tire vertical load is set to 8060 N, the change range of the tire side slip angle is set to [-10° to 10°], and the slip rate is controlled to [-1 to 0.5].

[0191] Step 2, Construct a piecewise affine identification model of the tire longitudinal slip and side slip mechanical characteristics. According to the non-linear relationship between the tire longitudinal force and lateral force and the tire operating parameters, construct a piecewise affine identification model of the tire longitudinal slip and side slip mechanical characteristics through piecewise affine identification.

[0192] It is analyzed that under a specific vertical load, the tire longitudinal force and lateral force are mainly affected by three factors: the tire slip rate, the side slip angle, and the road surface adhesion coefficient. In addition, from the experimental results, it is also obtained that the ratio of the tire longitudinal force to the lateral force is approximately equal to the ratio of the road surface adhesion coefficients. Therefore, the modeling of the tire longitudinal slip and side slip characteristics is confirmed as a three-dimensional piecewise affine identification problem. Based on the test data, piecewise affine identification of the non-linear mechanical characteristics of the tire is carried out. The method for piecewise affine identification of the tire longitudinal slip and side slip mechanical characteristics includes four links: model definition, data clustering, affine sub-model parameter estimation, and hyperplane coefficient matrix solution.

[0193] The method of the model definition is as follows:

[0194] Construct the model mathematical expression

[0195]

[0196] where y j ∈R p is the output of the system, θ i (i = 1,..., s) are the parameters of each sub-model, x j ∈R n is the regression vector of the system, which always includes the past input and output of the system, x jExpressed as:

[0197]

[0198] where n y and n u represent the order of the piecewise affine model, u j is the system input, n = pn y + mn u .χ i (i = 1,…, s) is a complete partition of the regression set χ, and each region is a convex polyhedron subset, written as:

[0199] χ i ={F i x j + g i ≤ 0}

[0200] where F i and g i are hyperplane coefficient matrices; let H i =[F i g i , (i = 1,..., s) then the convex polyhedron region is rewritten as:

[0201] χ i ={H i [x j 1] T ≤ 0}

[0202] The method of data clustering is as follows:

[0203] The original data set is divided into s uncorrelated clusters, and a statistical data clustering method based on the Gaussian mixture model is adopted. Assume that N data samples are expressed as:

[0204]

[0205] Based on the Gaussian mixture model, the probability density of the data sample z j is expressed as:

[0206]

[0207] For Φ = (α, μ, ∑) where the scalar parameter α := (α1, α2,…, α s ) satisfies (n + p)-dimensional vector and (n + p)×(n + p)-dimensional covariance matrix Σ := (Σ1, Σ2,…, Σ s ), the function p i (z; μ i , Σ i ) is used to define the expression of the multivariate Gaussian density, specifically as follows:​​​​​​​​​​​​​​​​​​​​​

[0208]

[0209] After obtaining the optimal parameter Ф, the data sample j is partitioned into the cluster Γ i The probability is expressed as:

[0210]

[0211] The said probability serves as the criterion for data clustering. For the remaining part, the optimal parameter Ф is found based on the maximum likelihood estimation method; according to N data samples, the optimal parameter Ф that maximizes the log-likelihood function is found:

[0212]

[0213] For the single Gaussian model, the optimal parameter Ф that maximizes the above function value can be obtained through derivation. However, for the Gaussian mixture model adopted, this method is not feasible. Therefore, the Expectation-Maximization (EM) algorithm is used to obtain the maximum value by iteratively updating the parameter Ф. The EM algorithm consists of two steps, namely the Expectation step (E-step) and the Maximization step (M-step); in the M-step, it involves maximizing the log-likelihood function, which is redefined in the E-step of each iteration;

[0214] The execution process of the EM algorithm is as follows:

[0215] Starting from several initial parameters of Ф (0) the EM algorithm improves the maximum value,

[0216] EM algorithm:

[0217] 1) Initialize Φ (0) =(α (0) , μ (0) , Σ (0) ) At the same time, set the iteration counter l = 0 and set ε > 0,

[0218] 2) Φ (l) =(α (l) , μ (l) , Σ (l) ) Execute the following steps:

[0219] E-step:: Calculate j = 1, 2, …, N, i = 1, 2, …, s

[0220]

[0221] M-step: Update Φ (l) =(α (l) , μ (l) , Σ(l) ) Calculation

[0222]

[0223]

[0224] 3) If the specified convergence condition is satisfied

[0225]

[0226] Then set l * = l + 1, and the optimal estimate of Ф is obtained as Φ * = Φ (l*) Otherwise, input l = l + 1 and return to step 2);

[0227] From the above description, it can be seen that the data clustering process is based on the known number of affine submodels. However, since the number of submodels cannot be known in advance in actual situations, an estimation of the number of submodels based on the information criterion related to maximum likelihood estimation is further introduced;

[0228] First, two positive integers s min and s max are given such that the number of submodels is within the interval [s min , s max . Secondly, for all s = s min , …, s max , the parameter estimate Ф s , Ф s represents the estimate of Ф under the fixed s; the estimate of s is obtained by the following formula:

[0229]

[0230] where J(Ф s , s) represents the criterion shown below: Based on the existing model selection information criterion, the consistent Akaike information criterion (CAIC) and MDL criterion are adopted; the above criteria have the following forms:

[0231] J(Φ s , s) = -2L(Φ s ) + A(N)D(s)

[0232] In the formula, L(Ф s ) is the log-likelihood function of Ф s defined by the above formula, and the second term of the criterion represents the penalty for the data and the number of clusters, where D(s) represents the number of independent parameters in Ф s , and its expression is:

[0233]

[0234] where \(A(N)\) is a function of the number \(N\) of data samples, respectively

[0235]

[0236] The method for estimating the parameters of the affine sub - model is as follows:

[0237] After completing the data clustering task, according to the set \(\Gamma\) i the parameters of the affine sub - model are estimated by the least - squares algorithm through the data points collected in it; \(N\) data samples are divided into \(s\) non - overlapping clusters. Therefore, it is assumed that there are \(N_i\) samples in the \(i\) - th cluster, which are respectively denoted as \(j_{i1}\), \(j_{i2}\), …, \(j_{iN_i}\); the first subscript represents the number of clusters, and the second subscript represents the number of samples in the \(i\) - th cluster. According to the above description, the following equations and variables are obtained: i i1 i2 iNi ; where \(x\) is the autoregressive vector of the PWA model, \(N_i\) is the \(N_i\) samples in the \(i\) - th subset, which are respectively denoted as \(j_{i1}\), \(j_{i2}\), …, \(j_{iN_i}\). Using the least - squares algorithm, the parameters of each affine sub - model are estimated according to the following formula:

[0238]

[0239] x j is the autoregressive vector of the PWA model, \(N_i\) i is the \(N_i\) samples in the \(i\) - th subset i which are respectively denoted as \(j_{i1}\), iN1 iN2 iNi , …, \(j_{iN_i}\). Using the least - squares algorithm, the parameters of each affine sub - model are estimated as follows:

[0240]

[0241] After the above steps, data clustering and parameter estimation of each affine sub - model have been realized. The last step is to calculate the hyperplane coefficient matrix for classifying two adjacent clusters \(\Gamma_i\) and \(\Gamma_j\). Once the data samples are divided into \(s\) non - overlapping clusters, by calculating the hyperplane coefficient matrix that separates the data points in \(\Gamma_i\) from the data points in \(\Gamma_j\), for any pair \(i,j\) with \(i\neq j\), the entire set can be reconstructed. This work is actually to solve \(s(s - 1) / 2\) pattern recognition problems. According to the principle of statistical learning methods, the improved proximal support vector machine method is selected to solve this problem. Then this method is used to calculate the hyperplane coefficient matrix. i j i and \(\Gamma_j\) j . The method for solving the hyperplane coefficient matrix is as follows:

[0242] The method for solving the hyperplane coefficient matrix is as follows:

[0243] First, find two adjacent clusters \(\Gamma_i\) i and \(\Gamma_j\) j , and define the basic equation for calculation as follows: ​​​​​​​

[0244]

[0245] Secondly, combined with the improved approximate support vector machine (PSVM) algorithm, the interface coefficient matrix is obtained by solving the following optimization problem:

[0246]

[0247] s.t. W i (F i x i - eg i ) = λ i - ξ i

[0248] where V i and W i are diagonal matrices, ξ i is the error vector, e is the unit vector. When W i = 1, V i = v (v is the penalty factor), λ i = 1, while when W i = -1, V i = v(n + / n - ), λ i = a i (a i is a positive number), n + is the number of positive samples, n - is the number of negative samples. When 0 < a i < 1, the classification hyperplane moves towards the negative sample direction. When a i > 1, the classification hyperplane moves towards the positive sample direction;

[0249] By adjusting the value of a i , the deviation of the classification hyperplane is adjusted;

[0250] According to the KKT (Karush - Kuhn - Tucher) conditions, the following Lagrangian equation can be constructed:

[0251]

[0252] where η i is the Lagrangian coefficient. Using the Lagrangian conditional extreme value, the following equations can be further obtained:

[0253]

[0254] Based on the above equations, the following can be further obtained:

[0255]

[0256] On this basis, further obtain:

[0257]

[0258] Subtract the above two formulas to obtain:

[0259]

[0260] Multiply both sides of the above formula by W i , to obtain:

[0261]

[0262] Combined with the above formula, it can be obtained:

[0263]

[0264] So

[0265]

[0266] Calculate the hyperplane coefficient matrix F i and g j .

[0267] Step 3: Construct a mathematical model for estimating the driving state of a vehicle dynamics piecewise affine system, a piecewise affine identification model based on the longitudinal slip and lateral force characteristics of tires. At the same time, according to the three-degree-of-freedom vehicle model of vehicle longitudinal motion, lateral motion, and yaw motion, combined with the longitudinal relaxation length of each tire, construct a mathematical model for estimating the driving state of a vehicle dynamics piecewise affine system;

[0268] The method for constructing a mathematical model for estimating the driving state of a vehicle dynamics piecewise affine system is as follows:

[0269] (1) The mathematical expressions for constructing a three-degree-of-freedom vehicle model of vehicle longitudinal motion, lateral motion, and yaw motion are as follows:

[0270]

[0271] where F xij and F yij respectively represent the longitudinal force and lateral force of the tire. The first subscript i = f or r represents the front axle or the rear axle, and the second subscript j = l or r represents the left and right wheels. δ is the front wheel steering angle, B is the vehicle's front and rear wheel track, I z is the moment of inertia of the vehicle, l f and l r are the distances between the front and rear axles of the vehicle, v x , v y and r are the longitudinal speed, lateral speed, and yaw angular velocity of the vehicle respectively, a xand a y represent the longitudinal acceleration and lateral acceleration of the vehicle respectively;

[0272] a x and a y are expressed as:

[0273]

[0274] where m is the vehicle body mass;

[0275] The sideslip angle of the center of mass and the slip ratios of each wheel are expressed as:

[0276]

[0277] where w i , λ ij and v ij are the angular velocity of the wheel, the slip ratio of the wheel, and the velocity of the center point of the wheel, R is the wheel radius, and the subscripts "fl", "fr", "rl", "rr" represent the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively;

[0278] The expression of the longitudinal relaxation length is written as:

[0279]

[0280] where ε xij represents the relaxation length of each wheel, F xij_M is the tire force calculated by the piecewise affine tire model, and ε xij represents the elastic hysteresis during the contact process between the tire and the road surface;

[0281] In the existing research on the estimation of the longitudinal force of the wheel, the longitudinal relaxation length, as a key parameter, greatly affects the longitudinal dynamics modeling. The relaxation length of the wheel is expressed as:

[0282]

[0283] where C fx is the longitudinal stiffness of the longitudinal force at zero point, and C x is the tire lateral stiffness;

[0284] The longitudinal forces and lateral forces of the four tires are expressed as follows:

[0285]

[0286] where F xfl_M , F xfr_M , F xrl_M and F xrr_Mrespectively represent the longitudinal forces of the left front tire, right front tire, left rear tire, and right rear tire calculated according to the piecewise affine tire model; F yfl_M 、F yfr_M 、F yrl_M and F yrr_M respectively represent the lateral forces of the left front tire, right front tire, left rear tire, and right rear tire calculated according to the piecewise affine tire model; in the above formula, M i 、N i and b i are the parameters of the vehicle longitudinal force on different affine sub-models, M j 、N j and b j are the parameters of the vehicle lateral force on different affine sub-models. The superscripts x of M, N, and b represent longitudinal, and y represents lateral. 1-4 respectively represent the left front wheel, right front wheel, left rear wheel, and right rear wheel. α1 and α3 are the sideslip angles of the front wheels and rear wheels respectively, and λ1, λ2, λ3, and λ4 are the slip ratios of each wheel;

[0287] The sideslip angles of the front wheels and rear wheels of the tire are expressed as:

[0288]

[0289] The nonlinear state space of the vehicle system is expressed as:

[0290]

[0291] where x(t) is the vehicle state variable, u(t) is the system input variable, w(t) is the system noise, v(t) is the measurement noise, z(t) is the measurement variable, f(·) is the state transition equation, and h(·) is the measurement equation;

[0292] Specifically, it is expressed as follows:

[0293]

[0294] where L1-L 36 is a time-varying parameter obtained according to the affine sub-model region where each wheel is located, and is specifically expressed as:

[0295]

[0296] Step 4: Estimate the vehicle driving state parameters. Based on the established mathematical model for estimating the driving state of the vehicle dynamics piecewise affine system, the statistical values of the process noise covariance and measurement noise covariance are estimated using the adaptive cubature Kalman filter algorithm with the maximum a posteriori probability criterion.

[0297] The method for estimating the vehicle driving state parameters is as follows:

[0298] The standard square-root cubature Kalman filter algorithm is as follows. The discrete nonlinear system is expressed as:

[0299]

[0300] where x k is the system state vector, z k is the system measurement vector, f(·) and h(·) are the system state transition equation and measurement equation, w k-1 and v k represent the system process noise and measurement noise;

[0301] 1) Initialization

[0302] The system initial value and the square root factor S of the error covariance matrix 0|0 are set as:

[0303] S 0|0 = [Chol(P 0|0 )] T

[0304] where P 0|0 is the error covariance matrix, Chol(·) is the Cholesky decomposition,

[0305] 2) Time update

[0306] Calculate and transfer the cubature points according to the state transition function:

[0307]

[0308] where S k-1|k-1 is the square root obtained by Cholesky decomposition of P k-1|k-1 , S k-1|k-1 = [Chol(P k-1|k-1 )] T , ξ i is the i-th column of the cubature point weight matrix , I n is the n×n identity matrix, and n is the dimension of the state variable;

[0309] Calculate the predicted value of the state and the square root factor of its error covariance matrix:

[0310]

[0311] Tria(·) represents the orthogonal triangular matrix decomposition, and the weighted center matrix is defined as:

[0312]

[0313] 3) Measurement update

[0314] By using the state prediction value and the square root S of the prediction error covariance at time k k|k-1 Update the volume points and perform the following transfer according to the following measurement equation:

[0315]

[0316] The square root factor of the measurement prediction value and its innovation covariance matrix are calculated as follows:

[0317]

[0318] Weighted center matrix Z k|k-1 Is defined as:

[0319]

[0320] The measurement covariance matrix and the cross-covariance matrix are calculated as follows:

[0321]

[0322] Weighted center matrix X k|k-1 Is defined as

[0323]

[0324] The Kalman gain matrix can be expressed as

[0325]

[0326] Update the square root factor and the error covariance matrix of the state variable at time k:

[0327]

[0328] When the prior statistical values of the noise statistics are unknown, it is difficult to guarantee its estimation accuracy. An adaptive algorithm based on maximum a posteriori probability estimation is proposed to estimate the statistical values of the process noise and the measurement noise. Assume that the process noise covariance Q, the measurement noise covariance R, and the system state x k Are all unknown variables, and the maximum a posteriori estimate is obtained by maximizing the conditional density function:

[0329] J * = p[X k ,Q,R|Z k

[0330] Where X k = {x1,x2,…,x k},Z k ​={z1,z2,…,z k},

[0331] According to the properties of conditional probability, we obtain

[0332]

[0333] p[Z k is independent of the maximization of J. The maximum a posteriori estimates of Q, R, and x * are equivalently obtained by maximizing the following density function k J = p[X

[0334] J = p[X k , Q, R, Z k

[0335] = p[Z k |X k , Q, R] p[X k |Q, R] p[Q, R]

[0336] where p[Q, R] is obtained from prior information and regarded as a known constant. According to the probability multiplication rule:

[0337]

[0338] In the formula, n is the dimension of the state variable, and C1 = 1 / (2π) n(k+1 / 2 is a constant,

[0339] We obtain:

[0340]

[0341] In the formula, m is the dimension of the measurement variable, and C2 = 1 / (2π) mk / 2 is a constant. Further, we obtain:

[0342]

[0343] where

[0344]

[0345] The logarithmic operation does not change the extreme points of the function. J and ln J have the same maximum value. Taking the logarithm of the above formula, we get:

[0346]

[0347] Assume and are known. Taking the partial derivatives of ln J with respect to Q and R, we have the following relationship:

[0348] ​

[0349] For a real-time dynamic system, information after a certain moment cannot be known. Therefore, smooth estimation and cannot be obtained. Instead, state estimation and or state prediction is used. The suboptimal estimated values of the noise covariances Q k-1 and R k are expressed as

[0350]

[0351] Define the measurement innovation as

[0352]

[0353] Then there is the following relationship

[0354]

[0355] Therefore, it is obtained that

[0356]

[0357] It is known that According to the standard cubature Kalman filter algorithm, the expectations of the noise covariances Q k-1 and R k are

[0358]

[0359] When the noise statistics are constant or change little, it is considered that Q k-1 = Q j-1 and R k = R j , and the above formula is rewritten as:

[0360]

[0361] The statistical estimates of the noise covariances Q k-1 and R k are:

[0362]

[0363] Flash the designed system state estimation algorithm onto the in-vehicle control unit of the distributed drive electric vehicle. Obtain the parameters required for the measurement equation through the existing sensors on the mass-produced vehicle. The yaw rate can be output through the vehicle's ESP, the longitudinal acceleration can be output by the vehicle's longitudinal acceleration sensor, the lateral acceleration can be output by the vehicle's lateral acceleration sensor, and the wheel speed sensor can output the wheel speed. Based on these signal parameters and the proposed system state estimation algorithm, calculate the yaw rate, sideslip angle of the center of mass, longitudinal and lateral velocities, and longitudinal forces of the four wheels in real time.

[0364] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

Claims

1. A method for estimating a vehicle driving state based on a piecewise affine identified tire model, characterized in that It includes the following steps: Step 1, Tire longitudinal slip and side slip characteristic experiment: Conduct a tire longitudinal slip and side slip characteristic experiment to obtain experimental data on the non-linear relationship between the tire longitudinal force and lateral force and the tire operating parameters. Step 2, Construct a piecewise affine identification model of the tire longitudinal slip and side slip mechanical characteristics: According to the non-linear relationship between the tire longitudinal force and lateral force and the tire operating parameters, construct a piecewise affine identification model of the tire longitudinal slip and side slip mechanical characteristics through piecewise affine identification. Step 3, Construct a mathematical model for estimating the driving state of the vehicle dynamics piecewise affine system: Based on the piecewise affine identification model of the tire longitudinal slip and side slip mechanical characteristics, and at the same time, according to the three-degree-of-freedom model of the vehicle's longitudinal motion, lateral motion and yaw motion, combined with the longitudinal relaxation length of each tire, construct a mathematical model for estimating the driving state of the vehicle dynamics piecewise affine system. The method for constructing the mathematical model for estimating the driving state of the vehicle dynamics piecewise affine system is as follows: (1) The mathematical expressions for the three-degree-of-freedom vehicle model of the vehicle's longitudinal motion, lateral motion and yaw motion are as follows: where F xij and F yij represent the longitudinal force and the lateral force of the tire respectively. The first subscript i = f or r represents the front axle or the rear axle, and the second subscript j = l or r represents the left and right wheels. δ is the front wheel steering angle, B is the wheelbase of the vehicle, I z is the moment of inertia of the vehicle, l f and l r are the distances between the front and rear axles of the vehicle, v x , v y and r are the longitudinal speed, the lateral speed and the yaw angular velocity of the vehicle respectively, a x and a y represent the longitudinal acceleration and the lateral acceleration of the vehicle respectively; a x and a y is expressed as: Where, m is the vehicle body mass; The sideslip angle of the center of mass and the slip rate of each wheel are expressed as: where w i , λ ij and v ij are the angular velocity of the wheel, the wheel slip ratio, and the velocity of the wheel center point, R is the wheel radius, and the subscripts "fl", "fr", "rl", and "rr" represent the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively; The expression of the longitudinal relaxation length is written as: Among them, ε xij represents the slack length of each wheel, and F xij_M is the tire force calculated by the piecewise affine tire model, and ε xij represents the elastic hysteresis during the contact process between the tire and the road surface; The relaxation length of the wheel is expressed as: Among them, C fx is the longitudinal stiffness of the longitudinal force at zero point, and C x is the lateral stiffness of the tire; The longitudinal forces and lateral forces of the four tires are expressed as the following formula: Among them, F xfl_M , F xfr_M , F xrl_M and F xrr_M respectively represent the longitudinal forces of the left front wheel tire, the right front wheel tire, the left rear wheel tire, and the right rear wheel tire calculated according to the piecewise affine tire model; F yfl_M , F yfr_M , F yrl_M and F yrr_M respectively represent the lateral forces of the left front wheel tire, the right front wheel tire, the left rear wheel tire, and the right rear wheel tire calculated according to the piecewise affine tire model; in the above formula, M i , N i and b i are the parameters of the vehicle longitudinal force on different affine sub-models, M j , N j and b j are the parameters of the vehicle lateral force on different affine sub-models. The superscripts x of M, N, and b represent longitudinal, y represents lateral, 1-4 respectively represent the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, α1 and α3 are the sideslip angles of the front wheels and the rear wheels respectively, and λ1, λ2, λ3, and λ4 are the slip ratios of each wheel; The sideslip angles of the front and rear wheels of the tire are expressed as: The non-linear state space of the vehicle system is expressed as: Where, x(t) is the vehicle state variable, u(t) is the system input variable, w(t) is the system noise, v(t) is the measurement noise, z(t) is the measurement variable, f(·) is the state transition equation, and h(·) is the measurement equation; Specifically, it is expressed as follows: wherein, L1-L 36 are time-varying parameters obtained according to the affine sub-model regions where each wheel is located Specifically, it is expressed as: Step 4, Estimate the vehicle driving state parameters: Based on the constructed mathematical model for estimating the driving state of the vehicle dynamics piecewise affine system, use the adaptive cubature Kalman filter algorithm to estimate the statistical values of the process noise covariance and measurement noise covariance using the maximum a posteriori probability criterion.

2. The vehicle driving state estimation method based on the piecewise affine identification tire model according to claim 1, characterized in that: In the tire longitudinal slip and side slip characteristic experiment in Step 1, the tire vertical load is set to 8060N, the variation range of the tire sideslip angle is set to [-10° to 10°], and the slip rate is controlled to [-1 to 0.5].

3. The vehicle driving state estimation method based on a piecewise affine identification tire model according to claim 1, wherein: The method for piecewise affine identification of the tire longitudinal slip and side slip mechanical characteristics in Step 2 includes four links: model definition, data clustering, parameter estimation of the affine sub-model, and solution of the hyperplane coefficient matrix.

4. The vehicle driving state estimation method based on the piecewise affine identification tire model according to claim 3, characterized in that, The method for model definition is as follows: Construct the model mathematical expression where y j ∈R p is the output of the system, θ i is the parameter of each sub-model, i = 1, ..., s, where s is the number of affine sub-models, and x j ∈R n is the regression vector of the system, which always contains the past input and output of the system, and x j is expressed as: where n y and n u represent the order of the piecewise affine model, u j is the system input, n = pn y + mn u .χ i , i = 1, …, s, where s is the number of affine submodels, is a complete partition of the regression set χ, and each region is a convex polyhedron subset, written as: χ i ={F i x j +g i ≤0} where F i and g i are hyperplane coefficient matrices; let H i = [F i g i , i = 1, ..., s, where s is the number of affine submodels, then the convex polyhedron region can be rewritten as: χ i = {H i [x j 1] T ≤ 0}.

5. The vehicle driving state estimation method based on the piecewise affine identification tire model according to claim 4, wherein The method for data clustering is as follows: Divide the original data set into s uncorrelated clusters, and use the statistical data clustering method based on the Gaussian mixture model. Assume that N data samples are expressed as: Based on the Gaussian mixture model, the probability density of the data sample z j is expressed as: For Φ = (α, μ, Σ) where the scalar parameter α := (α1, α2, …, α s ) satisfies (n + p)-dimensional vector and (n + p)×(n + p)-dimensional covariance matrix Σ := (Σ1, Σ2, …, Σ s ), the function p i (z; μ i , Σ i ) is used to define the expression of the multivariate Gaussian density as follows: When the optimal parameter Ф is obtained, the probability that the data sample j is divided into the cluster Γ i is expressed as: The probability is used as the standard for data clustering. For the remaining part, find the best parameter Ф based on the maximum likelihood estimation method; according to N data samples, find the best parameter Ф that can make the log-likelihood function reach the maximum value: Using the Expectation-Maximization (EM) algorithm, the maximum value is obtained by iteratively updating the parameter Ф. The EM algorithm consists of two steps, namely the Expectation (E) step and the Maximization (M) step. In the M step, it involves maximizing the log-likelihood function, which is redefined in each iteration of the E step. The execution process of the EM algorithm is as follows: Starting from several initial parameters of Ф (0) the EM algorithm increases the maximum value EM algorithm: 1) Initialize Φ (0) = (α (0) , μ (0) , Σ (0) ) Also set the iteration counter l = 0 and set ε > 0, 2) Φ (l) = (α (l) , μ (l) , Σ (l) ) performs the following steps: Step E: Calculate Step M: Update Φ (l) =(α (l) , μ (l) , Σ (l) ) Calculate 3) If the specified convergence condition is satisfied Then set l * = l + 1, and the optimal estimate of Ф is obtained as Φ * = Φ (l*) Otherwise, input l = l + 1 and return to step 2); Since the number of sub-models cannot be known in advance, an estimation of the number of sub-models based on the information criterion related to maximum likelihood estimation is further introduced. First, two positive integers s min and s max are given such that the number of submodels is in the interval [s min , s max . Next, for all s = s min , …, s max , the parameter estimate Ф s is calculated, where Ф s denotes the estimate of Ф for a fixed s; the estimate of s is obtained by the following formula: where J(Ф s , s) represents the following criteria: based on the existing model selection information criteria, the CAIC information criterion and the MDL criterion are adopted; the above criteria have the following forms: J(Φ s , s) = -2L(Φ s ) + A(N)D(s) where L(Ф s ) is the log-likelihood function of Ф defined by the above formula, and the second term of the criterion represents the penalty on the data and the number of clusters, where D(s) represents the number of independent parameters in Ф s , and its expression is: s ​ And A(N) is a function of the number of data samples N, which are respectively 6. The vehicle driving state estimation method based on the piecewise affine identification tire model according to claim 5, characterized in that The method for estimating the affine sub-model parameters is as follows: After completing the data clustering task, according to the set Г i The data points collected in are used to complete the estimation of the parameters of the affine sub-model through the least squares algorithm; N data samples are divided into s non-overlapping clusters. Therefore, it is assumed that there are N i samples in the i-th cluster, which are respectively denoted as j i1 , j i2 , …, j iNi ; The first subscript represents the number of clusters, and the second subscript represents the number of samples in the i-th cluster. According to the above description, the following equations and variables are obtained: x j is the autoregressive vector of the PWA model, N i is the N i samples in the i-th subset, respectively denoted as j iN1 , j iN2 , …, j iNi , using the least squares algorithm, estimate the parameters of each affine sub-model according to the following formula:

7. The vehicle driving state estimation method based on the piecewise affine identification tire model according to claim 6, characterized in that, The method for solving the hyperplane coefficient matrix is as follows: First, find two adjacent clusters Γ i and Γ j , and define the basic equation for calculation as follows: Secondly, combined with the improved approximate support vector machine (PSVM) algorithm, the interface coefficient matrix is obtained by solving the following optimization problem: s.t.W i (F i x i -eg i )=λ i -ξ i where V i and W i are diagonal matrices, ξ i is the error vector, e is the unit vector. When W i = 1, V i = v, where v is the penalty factor, λ i = 1, and when W i = -1, V i = v(n + / n - ), λ i = a i , where a i is a positive number, n + is the number of positive samples, n - is the number of negative samples. When 0 < a i < 1, the classification hyperplane moves towards the negative sample direction, and when a i > 1, the classification hyperplane moves towards the positive sample direction; Adjust the deviation of the classification hyperplane by adjusting the value of a i ; According to the KKT (Karush-Kuhn-Tucker) conditions, the following Lagrangian equation can be constructed: where η i is the Lagrange coefficient. By using the Lagrange conditional extreme value, the following equations can be further obtained: Based on the above equation, it can be further obtained: On this basis, it can be further obtained: Subtracting the above two formulas, we can get: Multiply both sides of the above formula by W i , and we can get: Combined with the constraint condition W of the optimization problem i (F i x i -eg i ) = λ i -ξ i It can be obtained that: So Calculate the hyperplane coefficient matrix F i and g j .

8. The vehicle driving state estimation method based on the piecewise affine identification tire model according to claim 1, characterized in that The method for estimating the vehicle driving state parameters in step 4 is as follows: The standard square root cubature Kalman filter algorithm is as follows. The discrete non-linear system is expressed as: where, x k is the system state vector, z k is the system measurement vector, f(·) and h(·) are the system state transition equation and measurement equation, w k-1 and v k represent the system process noise and measurement noise; 1) Initialization System initial value and the square root factor S of the error covariance matrix 0|0 are set to: S 0|0 = [Chol(P 0|0 )] T where P 0|0 is the error covariance matrix, Chol(·) is the Cholesky decomposition, 2) Time update Calculate and transfer the cubature points according to the state transition function: Among them, S k-1|k-1 is the square root obtained by Cholesky decomposition of P k-1|k-1 , S k-1|k-1 = [Chol(P k-1|k-1 )] T , ξ i is the i-th column of the cubature point weight matrix , I n is the n×n identity matrix, where n is the dimension of the state variable; Calculate the predicted value of the state and the square root factor of its error covariance matrix: Tria(·) represents the orthogonal triangular matrix factorization, and the weighted center matrix is defined as: 3) Measurement update By using the state prediction value and the square root S of the prediction error covariance at time k k|k-1 Update the cubature points and perform the following transformation according to the following measurement equation: The square root factor of the predicted measurement value and its innovation covariance matrix are calculated as follows: Weighted center matrix Z k|k-1 is defined as: The measurement covariance matrix and the cross-covariance matrix are calculated as follows: Weighted central matrix X k|k-1 is defined as The Kalman gain matrix is expressed as Update the square root factor of the state variable and the error covariance matrix at time k: Assume that the process noise covariance Q, the measurement noise covariance R, and the system state x k are all unknown variables, and the maximum a posteriori estimate is obtained by maximizing the conditional density function: J * = p[X k , Q, R|Z k ​ where X k = {x1, x2, …, x k}, Z k = {z1, z2, …, z k} According to the properties of conditional probability, we get p[Z k is independent of the maximization of J * , and the maximum a posteriori estimates of Q, R, and x k are equivalently obtained by maximizing the following density function J = p[X k , Q, R, Z k ​ = p[Z k |X k , Q, R] p[X k |Q, R] p[Q, R] where p[Q,R] is obtained from the prior information and is regarded as a known constant. According to the probability multiplication rule: where n is the dimension of the state variable, and C1 = 1 / (2π) n(k+1 / 2 is a constant We get: where m is the dimension of the measurement variable, and C2 = 1 / (2π) mk / 2 is a constant, and further we get: where The logarithmic operation does not change the extreme points of the function. J and ln J have the same maximum value. Taking the logarithm of the above formula, we get: Hypothesis and Given that, taking the partial derivatives of ln J with respect to Q and R, there are the following relationships: Smoothing estimation and cannot be obtained. Use state estimation and or state prediction instead. Represent the sub-optimal estimated values of the noise covariances Q k-1 and R k as Define the measurement innovation as Then there is the following relationship Therefore, we get Known According to the standard volume Kalman filtering algorithm, the noise covariance Q k-1 and R k has an expectation of When the noise statistics are constant or change little, it is considered that Q k-1 = Q j-1 and R k = R j , and rewriting the above formula gives: Obtain the noise covariance Q k-1 and R k The statistical estimates of which are as follows:

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