Road adhesion coefficient estimation method based on adaptive unscented Kalman filtering

Abstract

The invention discloses a road adhesion coefficient estimation method based on adaptive unscented Kalman filtering, and the method comprises the steps: obtaining the static parameters of a vehicle and the driving parameters of the vehicle in the driving process, and carrying out the modeling of the vehicle based on a seven-degree-of-freedom dynamic model, modeling a vehicle tire based on a Dugoff tire model on the basis of the seven-degree-of-freedom dynamic model to obtain a nonlinear system of the vehicle; estimating a road adhesion coefficient in the Dugoff tire model based on an adaptive unscented Kalman filter algorithm and a seven-degree-of-freedom dynamic model to obtain a road adhesion coefficient estimation value; according to the adaptive unscented Kalman filtering algorithm, a proportion correction coefficient is introduced in an unbiased transformation link, and an adaptive noise coefficient is introduced in a standard UKF. According to the method, a proportion correction coefficient and an adaptive coefficient are introduced into an adaptive unscented Kalman filtering algorithm, so that the response capability and estimation precision of a sudden change state are enhanced.

Description

Technical Field

[0001] The invention relates to the technical field of automobile active safety, and in particular to a road adhesion coefficient estimation method based on adaptive unscented Kalman filtering. Background Art

[0002] In modern automobile safety systems, the road adhesion coefficient is an important parameter that determines vehicle stability and safety. Accurately estimating the road adhesion coefficient can effectively improve the vehicle's handling and stability under different working conditions. Current road adhesion coefficient estimation methods are generally divided into cause-based estimation methods (such as direct measurement of road surface characteristics) and result-based estimation methods (such as inference through vehicle dynamics response).

[0003] In contrast, estimation methods based on vehicle dynamic response are more economical and universal. This type of method infers the road adhesion coefficient by analyzing parameters such as vehicle acceleration, tire slip rate, and yaw rate, and can provide effective adhesion coefficient estimation without using additional expensive equipment. Among the existing result-based estimation methods, Kalman filters and extended Kalman filters are widely used in state estimation of nonlinear systems. However, the extended Kalman filter requires linearization of nonlinear equations, which introduces linearization errors and affects the accuracy of the estimation. In addition, when the vehicle is traveling on a complex or rapidly changing road surface, the traditional Kalman filter method may not be able to adapt to the rapid changes in the environment, resulting in inaccurate adhesion coefficient estimation.

[0004] In order to solve the above problems, the Unscented Kalman Filter (UKF) was proposed as an improved filtering method, which handles nonlinear problems through unbiased transformation and avoids linearization errors. However, the UKF may have "non-local effects" in the Sigma point sampling process in high-dimensional states, resulting in instability of the covariance matrix. Summary of the invention

[0005] Technical purpose: In view of the defects in the prior art, the present invention discloses a road adhesion coefficient estimation method based on an adaptive unscented Kalman filter. A proportional correction coefficient and an adaptive coefficient are introduced into the adaptive unscented Kalman filter algorithm to enhance the responsiveness to sudden changes and the estimation accuracy.

[0006] Technical solution: In order to achieve the above technical objectives, the present invention adopts the following technical solution.

[0007] A road adhesion coefficient estimation method based on adaptive unscented Kalman filtering comprises the following steps:

[0008] S1. Obtain static parameters of the vehicle and driving parameters of the vehicle during driving, model the vehicle based on a seven-degree-of-freedom dynamics model, and model the vehicle tire based on a Dugoff tire model on the basis of the seven-degree-of-freedom dynamics model to obtain a nonlinear system of the vehicle, wherein the nonlinear system includes the seven-degree-of-freedom dynamics model and the Dugoff tire model, which together describe the nonlinear relationship between the longitudinal, lateral, yaw and tire forces of the vehicle;

[0009] S2. Based on the adaptive unscented Kalman filter algorithm and the seven-degree-of-freedom dynamic model, the road adhesion coefficient in the Dugoff tire model is estimated to obtain the estimated value of the road adhesion coefficient; the adaptive unscented Kalman filter algorithm introduces a proportional correction coefficient in the unbiased transformation link, and introduces an adaptive noise coefficient in the standard UKF.

[0010] Beneficial effects: The present invention introduces a proportional correction coefficient and an adaptive coefficient into the adaptive unscented Kalman filter algorithm to enhance the responsiveness to sudden changes and the estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0012] Figure 2 is a schematic diagram of the Dugoff tire model used in the embodiment of the present invention;

[0013] Figure 3 is a schematic diagram of a seven-degree-of-freedom vehicle dynamics model used in an embodiment of the present invention;

[0014] Figure 4 It is a framework diagram of a road adhesion coefficient estimation model designed in an experiment according to an embodiment of the present invention;

[0015] Figures 5 to 18 It is a simulation effect diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0016] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0017] Example

[0018] As attached Figure 1 As shown, a method for estimating a road adhesion coefficient based on an adaptive unscented Kalman filter in this embodiment includes the following steps:

[0019] S1. Obtain static parameters of the vehicle and driving parameters of the vehicle during driving, model the vehicle based on a seven-degree-of-freedom dynamics model, and model the vehicle tire based on a Dugoff tire model on the basis of the seven-degree-of-freedom dynamics model to obtain a nonlinear system of the vehicle, wherein the nonlinear system includes the seven-degree-of-freedom dynamics model and the Dugoff tire model, which together describe the nonlinear relationship between the longitudinal, lateral, yaw and tire forces of the vehicle;

[0020] Among them, the driving parameters include tire slip rate λ, vehicle longitudinal acceleration a x , vehicle lateral acceleration a y , vehicle yaw rate Wheel moment of inertia J, wheel angular acceleration The vehicle's front wheel turning angle δ; the vehicle's moment of inertia around the z-axis I z ; Static parameters include vehicle mass m, distance between front wheels B f , the distance between the rear wheels B r , effective rolling radius of the tire R, front wheelbase of the vehicle L f 、Vehicle rear wheelbase L r ;

[0021] The vehicle is modeled based on the seven-degree-of-freedom dynamics model, including the longitudinal motion equation, lateral motion equation, yaw motion equation, and wheel rotation equations corresponding to the four wheels; the seven-degree-of-freedom dynamics model uses the center of mass of the vehicle as the origin of the coordinate system, the longitudinal axis is the forward direction of the vehicle, and the forward direction is defined as positive; the horizontal axis is the lateral direction of the vehicle, and the left direction is defined as positive; at the same time, the torque in the horizontal plane is defined as counterclockwise positive. In addition, considering the particularity of the simulation scenario, the following assumptions are made for the established seven-degree-of-freedom dynamics model: the influence of aerodynamics is ignored; the movement of the vehicle in the vertical direction is ignored; the pitch and roll movement of the vehicle are ignored; and the physical properties of each tire are the same.

[0022] The longitudinal motion equation is:

[0023]

[0024] Among them, a x is the longitudinal acceleration of the vehicle, γ is the yaw angle of the vehicle, v x The first derivative of v x 、v y are the longitudinal and lateral speeds of the vehicle respectively; δ is the front wheel turning angle of the vehicle, F xFL is the longitudinal force of the left front tire of the vehicle, F xFR is the longitudinal force of the left rear tire of the vehicle, F xRL is the longitudinal force of the right front tire of the vehicle, FxRR is the longitudinal force of the right rear tire of the vehicle, F yFL is the lateral force of the left front tire of the vehicle, F yFR is the lateral force of the left rear tire of the vehicle;

[0025] The lateral motion equation is:

[0026]

[0027] Among them, a y is the vehicle lateral acceleration, v y The first derivative of yRL is the lateral force of the right front tire of the vehicle, F yRR is the lateral force of the right rear tire of the vehicle;

[0028] The yaw motion equation is:

[0029]

[0030] in, is the first-order derivative of γ; I z is the inertia of the vehicle around the z-axis, Γ is the yaw moment of the vehicle around the z-axis; L f is the front wheelbase of the vehicle, L r B is the rear wheelbase of the vehicle; f is the distance between the front wheels, B r is the distance between the rear wheels;

[0031] Wheel rotation equation:

[0032]

[0033] Where J is the rotational inertia of the wheel and R is the effective rolling radius of the tire. dFL，FR is the driving torque between the left front tire and the left rear tire of the vehicle, T bFL，FR is the braking torque between the left front tire and the left rear tire of the vehicle; F xRL，RR is the lateral force between the right front tire and the right rear tire of the vehicle, F bRL，RR is the braking torque between the right front tire and the right rear tire of the vehicle; is the angular acceleration of the left front tire and the left rear tire of the vehicle, also w FL，FR The first derivative of FL，FR is the angular velocity of the left front tire and the left rear tire of the vehicle; is the angular acceleration of the right front tire and the right rear tire of the vehicle, also w RL，RR The first derivative of RL，RR is the angular velocity of the right front tire and the right rear tire of the vehicle;

[0034] The vehicle tire is modeled based on the Dugoff tire model; the Dugoff tire model is used to describe the longitudinal and lateral forces of the tire, and the tire force is normalized based on the tire stiffness and slip rate. In this embodiment, the automobile tire modeling adopts the Dugoff model, which only focuses on the slip rate and stiffness, and does not need to consider the radial deformation of the wheel, the yaw angle and the wheel speed, so as to solve the normalized tire force. Compared with the magic tire model, the Dugoff tire model requires fewer parameters and less calculation.

[0035] The Dugoff tire model includes the tire longitudinal force equation and the tire lateral force equation;

[0036] The tire longitudinal force equation and tire lateral force equation are:

[0037]

[0038] Among them, F x is the tire longitudinal force, F y is the tire lateral force, μ is the road adhesion coefficient, λ is the tire slip rate, α is the tire side slip angle, C x , C y F is the longitudinal and lateral stiffness of the tire. z is the tire vertical force, f(L) is the value function related to the boundary value, L is the boundary value, is the preset value, which is used to describe the nonlinear characteristics caused by the tire slip rate, and ε is the speed influence coefficient;

[0039] Normalizing the above formula can get the new Dugoff tire model formula:

[0040]

[0041] in, They represent the normalized representation of the longitudinal and lateral forces on the tire, respectively, and the influence of the road adhesion coefficient can be ignored.

[0042] The tire force is normalized based on the tire stiffness and tire slip rate, and the calculation formula is:

[0043]

[0044]

[0045] Among them, F zFL is the vertical load on the left front wheel, g is the acceleration of gravity, L r is the distance from the center of mass to the rear axle, l is the total wheelbase from the front axle to the rear axle, a x is the acceleration of the vehicle in the forward direction, h g is the height of the vehicle's center of mass, B f is the front wheelbase of the vehicle, FzFR is the vertical load on the left rear wheel, F zRL is the vertical load on the right front wheel, B r is the rear wheelbase of the vehicle, F zRR is the vertical load on the right rear wheel;

[0046] When the vehicle is in driving state, the calculation formula of tire slip rate is:

[0047]

[0048] Among them, v ij is the longitudinal velocity of each wheel, ω ij is the angular velocity of each wheel, R is the effective rolling radius of the tire, λ ij is the tire slip rate of each wheel. The calculation formula of the wheel center speed is:

[0049]

[0050] Among them, v cFL 、v cFR v cRL 、v cRR is the speed at the center of the left front wheel, right front wheel, left rear wheel, and right rear wheel; ω FL ,ω FR ,ω RL ,ω RR are the angular velocities of the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. f is the front wheelbase of the vehicle;

[0051] The formula for calculating the tire slip angle is:

[0052]

[0053] Among them, α FL , α FR , α RL , α RR They are the tire slip angles of the front wheel, right front wheel, left rear wheel, and right rear wheel respectively;

[0054] S2. Based on the adaptive unscented Kalman filter algorithm and the seven-degree-of-freedom dynamic model, the road adhesion coefficient in the Dugoff tire model is estimated to obtain the estimated value of the road adhesion coefficient; the adaptive unscented Kalman filter algorithm introduces a proportional correction coefficient in the unbiased transformation link to eliminate the "non-local effect" in the sampling process, and introduces an adaptive noise coefficient in the standard UKF, and uses the updated covariance matrix to control the filter gain in real time, thereby improving the adaptive ability of the adaptive unscented Kalman filter algorithm to sudden changes.

[0055] To estimate the vehicle's motion parameters and road adhesion coefficient, it is necessary to consider the vehicle's longitudinal, lateral, and yaw motions. The tire state has a direct impact on the road adhesion coefficient, and the rotation of the four wheels also needs to be considered. Therefore, it is necessary to estimate the road adhesion coefficient μ in combination with the seven-degree-of-freedom dynamics model.

[0056] Unbiased transformation is an important part of the standard UKF filtering method, which is used to deal with nonlinear problems. It first selects a Sigma point set to approximate the statistical characteristics of the original state, and then performs a nonlinear transformation on these points to obtain the statistics of the transformed state. Finally, the best estimate of the nonlinear problem is obtained by weighted calculation of the mean and covariance of these transformed points.

[0057] The nonlinear system of the present invention can be represented by y=f(x), and the state vector refers to the system state variable that needs to be estimated in the adaptive unscented Kalman filter algorithm. In the present invention, the state vector is usually a plurality of parameters related to the vehicle motion, including: the longitudinal speed of the vehicle, the lateral speed of the vehicle, the yaw rate of the vehicle, the steering angle or sideslip angle of the wheel, the longitudinal force of the wheel, the lateral force of the wheel, the slip rate of the tire, the sideslip angle of the tire, and the road adhesion coefficient. Assume T x are the mean and variance of the state vector x respectively. To satisfy the statistical characteristics of calculating y, a Sigma vector χ is first set i , i = 0, 1, ...., 2L′, and then weighted to get the corresponding mean and covariance weights Where L′ is the number of Sigma points of the sampling strategy. The UT transformation process for the symmetric sampling strategy is as follows:

[0058]

[0059] λ′=α 2 (L′+k)-L′

[0060] Among them, λ′ is the scale parameter, χ0 represents the first Sigma point, and χ i represents the i-th Sigma point; Represents the value of the i-th row of the square root of the matrix; is the mean weight corresponding to the first simga point, is the covariance weight of the first sigma point, is the covariance weight of the i-th sigma point, is the mean weight of the i-th sigma point; α is used to calculate the Sigma point The distribution range near x, k is the second-order proportional parameter, and β is the previous state of the distribution of x.

[0061] However, in this UKF algorithm, as the dimension L′ increases, the distance between the Sigma point and the mean point It will also increase, resulting in the "non-local effect" that occurs during sampling. In addition, the nonlinearity of the measurement equation function directly affects the overall filtering accuracy of the algorithm. In order to solve this "non-local effect" and ensure the semi-positive definiteness of the covariance matrix, the present invention considers performing proportional sampling correction on the previously obtained Sigma point set. The corrected formula is as follows:

[0062]

[0063] Among them, X (i) (k|k) is the state vector of the i-th Sigma point estimated at time k under the condition of time k, X (i) (k+1|k) is the state vector of the i-th Sigma point estimated conditionally at time k+1, X (0) is the state vector of the first Sigma point, X (i) is the state vector of the i-th Sigma point, 2L′ is the dimension of the state, X (i) (k, k) is the state vector of the i-th Sigma point at time k; a1 is the proportional correction parameter, which takes a value of [0, 1], X (i) (k+1|k) is the state vector of the i-th Sigma point conditionally estimated at time k+1 at time k, and f(·) is the nonlinear transformation function of the system state quantity.

[0064] The transformed Sigma point is brought into the observation equation for nonlinear analysis, which means that in the adaptive unscented Kalman filter algorithm, the state vector generated by the Sigma point is nonlinearly mapped through the tire mechanics model and the vehicle dynamics model to obtain the output of the measurement space (such as tire force, slip rate, etc.).

[0065] Substitute the set Sigma point into the nonlinear transformation function f(·) to obtain the transformed Sigma point set The calculation formula is:

[0066]

[0067] χ i is the i-th Sigma point, is the i-th Sigma point after transformation; the transformed Sigma point is then weighted to estimate The approximate mean and variance are calculated as:

[0068]

[0069] in, is the mean of the measured predicted values ​​after the proportional correction coefficient is introduced, P yy is the measurement prediction covariance matrix after the scale correction coefficient is introduced.

[0070] After introducing the proportional correction coefficient, the process of the adaptive unscented Kalman filter algorithm of the present invention is as follows:

[0071] The nonlinear system established by the present invention can be expressed by the following expression:

[0072]

[0073] Where f(·) is the nonlinear transformation function, h(.) is the measurement model; x k is the state variable at time k, x k+1 is the state variable at time k+1, u k is the input variable at time k, y k is the output variable at time k, w k 、v k are the process noise and output noise at time k, respectively. The subscript k represents the time. Input variables such as the longitudinal force of the tire (F xFL 、F xFR 、F xRL 、F xRR ), lateral force of the tire (F yFL 、F yFR 、F yRL 、F yRR ), tire slip rate λ, tire side slip angle α, and vehicle front wheel steering angle δ. Output variables such as state estimation State covariance matrix P, Kalman gain K, prediction residual m k , updated filter state, updated covariance matrix, sigma point set χ, measured prediction value and the observation covariance matrix S.

[0074] S2.1, filter initialization, time k = 0:

[0075]

[0076] in, is the initial estimated state vector, which is the state estimate obtained by a filter (such as a Kalman filter) according to the system model and initial conditions. x0 is the initial true state vector, which is the actual state of the system. It is usually not directly observable and can only be obtained by estimation. E[·] is the expectation operator representation. P0 is the initial covariance matrix.

[0077] S2.2, for k = 1, 2 ...:

[0078] S2.2.1. Obtain 2L′+1 Sigma points according to UT transformation theory:

[0079]

[0080] Among them, χ(k-1) is the state variable of the Sigma point at time k-1, is the predicted state vector at time k-1, P i (k-1) is the prediction covariance matrix of the i-th Sigma point at time k-1, λ is the scale parameter, and 2L′+1 is the number of Sigma points.

[0081] S2.2.2. Time update:

[0082] The obtained Sigma point set is then used to calculate the transformed Sigma point set through the three state equations: the longitudinal motion equation, the lateral motion equation, and the yaw motion equation:

[0083] χ(k|k-1)=f(χ(k-1),u(k-1))

[0084] Among them, χ(k|k-1) is the state variable predicted at time k at time k-1, and u(k-1) is the input variable at time k-1. The state variable provides detailed distribution information of the system state at a certain moment; the state vector is a statistical summary and optimized estimate of this distribution information. Both play a role in the adaptive unscented Kalman filter algorithm: the state variable is used to propagate the nonlinear system state, while the state vector is used for specific prediction and updated output.

[0085] According to the UT transformation theory, the prediction mean calculation formula for the mean weighted calculation state is:

[0086]

[0087] Among them, χ i (k|k-1) is the i-th column of the matrix χ(k|k-1), i=0, 1, ..2L′, 2L′+1 is the total number of sigma points, is the state vector at time k predicted at time k-1.

[0088] According to the UT transformation theory, the calculation formula for the prediction variance of the covariance weighted calculation state is:

[0089]

[0090] Among them, P(k|k-1) is the covariance matrix of time k predicted at time k-1, The state vector at time k predicted at time k-1 is the weighted average of all possible distributions of the state at time k-1, that is, the centralized estimation of the system state by the adaptive unscented Kalman filter algorithm in the prediction stage. k is the process noise covariance matrix;

[0091] Substitute the transformed Sigma point into the observation equation for nonlinear analysis:

[0092] ζ(k|k-1)=h(χ(k-1))

[0093] Among them, ξ(k|k-1) is the process matrix at time k predicted at time k-1, and X(k-1) is the state variable at time k-1;

[0094] Then the predicted value of the observed variable is estimated by the weighted sum method:

[0095]

[0096] in, is the observed variable at time k predicted at time k-1, ξ i (k|k-1) is the i-th column of the matrix ξ(k|k-1), i=0, 1, ..., 2L′.

[0097] S2.2.3, Measurement Update:

[0098] When performing UT transformation, the present invention introduces a proportional correction coefficient to eliminate the "non-local effect" in the sampling process. Although this correction is effective, in practical applications, the UKF filtering algorithm is sensitive to the initial value of the filter, which may cause the filter to diverge.

[0099] Therefore, the present invention introduces an adaptive noise coefficient on the basis of the proportional correction coefficient to optimize the original algorithm. The noise adaptive coefficient can not only estimate and correct the uncertain system model noise and noise statistical parameters, but also use the measured value to correct the predicted value. Therefore, the traditional prediction covariance is updated as follows:

[0100] Calculate the updated state covariance matrix P yy :

[0101]

[0102] Compute the cross-covariance matrix:

[0103]

[0104] Among them, α k is the adaptive noise coefficient at time k, with a value range of 0<α k ≤1,ζ i(k|k-1) is the i-th column of ζ(k|k-1), ζ(k|k-1) is the process matrix at time k predicted at time k-1, which changes with the changes of system state and observation function, so it needs to be re-estimated in each step of filtering calculation, R k is the measurement noise covariance matrix at time k, is the observed variable at time k predicted at time k-1, P xy (k|k-1) is the cross covariance matrix at time k predicted at time k-1.

[0105] Choosing a suitable adaptive noise coefficient is crucial because it can not only adjust the weight balance between the state equation estimate and the observation information, but also effectively suppress the adverse effects of abnormal interference on the estimation results. k The values ​​of are as follows:

[0106]

[0107] Among them, trace represents the sum calculation of the diagonal elements of the matrix, P yy is the covariance matrix of the observation residuals, also known as the state covariance matrix, which is used to quantify the uncertainty or error distribution between the predicted observations and the true observations; the calculation formula for the prediction residuals is:

[0108]

[0109] Among them, Z (i) (k+1|k) is the predicted value of the measurement at time k+1 predicted by the i-th sigma point at time k. is the weighted mean of the measured predicted values ​​at time k+1 predicted at time k. The measured value z(k+1) is the actual observed physical quantity, such as the sensor output during vehicle driving, including actual measured dynamic data such as acceleration and turning angle.

[0110] Calculate the updated filter feedback gain:

[0111]

[0112] Among them, K(k) is the Kalman gain matrix at time k, P xy (k|k-1) is the cross-covariance matrix at time k predicted at time k-1, P yy The inverse matrix of

[0113] Calculate the filtered value after the state update:

[0114]

[0115] in, is the updated state vector at time k, is the state vector at time k predicted at time k-1, and y(k) is the measurement residual; The observed variable at time k predicted at time k-1;

[0116] Calculate the state posterior variance matrix:

[0117] P(k|k)=P(k|k-1)-K(k)P yy K(k) T

[0118] Among them, P(k|k) is the updated covariance matrix at time k, and P(k|k-1) is the covariance matrix at time k predicted at time k-1.

[0119] The present invention obtains various driving parameters during vehicle driving, combines the seven-degree-of-freedom vehicle dynamics model and the Dugoff tire model, and solves the normalized tire force. On this basis, an adaptive unscented Kalman filter algorithm is adopted, a proportional correction coefficient is introduced to eliminate the non-local effect in the sampling process, and the updated covariance matrix is ​​optimized in combination with the adaptive coefficient, and the filter gain is controlled in real time, thereby improving the algorithm's adaptive ability in the case of sudden changes in the road adhesion coefficient. The present invention uses Carsim and Simulink to perform simulation verification of various road conditions. The results show that compared with traditional filtering algorithms, this method greatly reduces the computational complexity while ensuring accuracy, and improves the convergence speed and estimation accuracy.

[0120] Reference Figure 4 As shown, this embodiment uses Carsim and Simulink for joint simulation to verify the accuracy of the algorithm. The vehicle model provided in Carsim is used for relevant parameters such as vehicle mass, front wheel distance, and rear wheel distance to set the vehicle operating conditions; the Dugoff tire model and the seven-degree-of-freedom vehicle dynamics model are established in Simulink, and the algorithm is established; through the joint simulation of Carsim and Simulink, the convergence and estimation accuracy of AUKF (i.e., the adaptive unscented Kalman filter algorithm described in the present invention) compared with the traditional UKF algorithm (unscented Kalman filter algorithm) in road adhesion coefficient estimation under different road conditions are reflected, and the specific analysis is as follows:

[0121] In order to verify the effect of the AUKF filtering algorithm under actual braking conditions, this embodiment designs a series of experiments, covering low adhesion coefficient roads, high adhesion coefficient spliced ​​roads and transitional road conditions. Through these experiments, the performance of the UKF algorithm and the AUKF algorithm are compared and analyzed. In order to facilitate the presentation of the comparison effect, the present invention simultaneously experiments with high adhesion coefficients and low adhesion coefficients by splicing the road surface. The spliced ​​road surface is to set the left and right halves of the road surface with different adhesion coefficients. When the vehicle speed is above 48km / h, the road adhesion coefficient of dry cement and dry asphalt roads is 0.8; when the road surface is wet, it is 0.5. In the simulation, a specific vehicle model in Carsim is selected, and it is set according to the relevant parameters listed in Table 1.

[0122] Table 1. Vehicle parameters

[0123]

[0124]

[0125] For low adhesion road surface simulation verification, the road adhesion coefficient of the left front wheel and the left rear wheel is set to 0.5, the initial vehicle speed is 16m / s, i.e. 57.6km / h, the throttle opening is 0, the gear is neutral, the wheel cylinder pressure is 0.45MPa, and the simulation time is 1s. The simulation results and error results of the left front wheel and the left rear wheel before and after improvement are shown as follows: Figure 5 , Figure 6 , Figure 7 , Figure 8 shown.

[0126] Keeping other parameters of Carsim unchanged, changing the road adhesion coefficient to 0.8, and conducting simulation experiments on the right front wheel and right rear wheel. The simulation results are shown in the figure. Similar to the low adhesion coefficient road condition, the convergence speed is faster, the estimation error is improved by about 2%-3%, and the maximum estimation error is significantly reduced. The simulation results and error results of the right front wheel and right rear wheel before and after the improvement are shown in the figure. Fig. 9 , Fig.10 , Fig.11 , Fig.12 shown.

[0127] To simulate the sudden change of the road adhesion coefficient, this embodiment sets the road adhesion coefficient to suddenly change from 0.8 to 0.5 at the 5th second, i.e., the scene where it suddenly rains while the vehicle is driving. Other parameters remain unchanged, and the simulation results are shown in the figure. When the road adhesion coefficient suddenly changes, the AUKF algorithm can converge to the set value faster, and there is a slight improvement in the estimation error. The simulation results before and after the improvement of the left front wheel and the right front wheel are shown in the figure. Fig.13 As shown, Fig.13 The simulation results around 5 seconds are as follows Fig.14As shown; the error results before and after the front wheel improvement are as follows Fig.15 As shown in Figure 2, the simulation results of the left rear wheel and the right rear wheel before and after improvement are as follows: Fig.16 As shown, Fig.16 The simulation results around 5 seconds are as follows Fig.17 As shown; the error results of the rear wheel before and after improvement are as follows Fig.18 shown.

[0128] By analyzing and comparing the simulation curves, both the AUKF algorithm and the UKF algorithm tend to converge to the set standard value. However, compared with UKF, the AUKF algorithm converges faster and has higher accuracy. Because this embodiment introduces a noise adaptive coefficient on the basis of the standard UKF to adjust abnormal disturbances, thereby correcting the system estimation results. In the road adhesion coefficient estimation experiment of the left front wheel and the left rear wheel, the estimation error of AUKF is significantly smaller than that of UKF. Except for the maximum estimation error, there is a difference of about 2%.

[0129] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A road adhesion coefficient estimation method based on adaptive unscented Kalman filtering, characterized in that: The following steps are involved: S1. Obtain static parameters of the vehicle and driving parameters of the vehicle during driving, model the vehicle based on a seven-degree-of-freedom dynamics model, and model the vehicle tire based on a Dugoff tire model on the basis of the seven-degree-of-freedom dynamics model to obtain a nonlinear system of the vehicle, wherein the nonlinear system includes the seven-degree-of-freedom dynamics model and the Dugoff tire model, which together describe the nonlinear relationship between the longitudinal, lateral, yaw and tire forces of the vehicle; S2. Based on the adaptive unscented Kalman filter algorithm and the seven-degree-of-freedom dynamic model, the road adhesion coefficient in the Dugoff tire model is estimated to obtain the estimated value of the road adhesion coefficient; the adaptive unscented Kalman filter algorithm introduces a proportional correction coefficient in the unbiased transformation link, and introduces an adaptive noise coefficient in the standard UKF.

2. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 1, characterized in that: In a nonlinear system, the longitudinal motion equation is: Among them, a x is the longitudinal acceleration of the vehicle, γ is the yaw angle of the vehicle, v x The first derivative of v x 、v y are the longitudinal and lateral speeds of the vehicle respectively; δ is the front wheel turning angle of the vehicle, F xFL is the longitudinal force of the left front tire of the vehicle, F xFR is the longitudinal force of the left rear tire of the vehicle, F xRL is the longitudinal force of the right front tire of the vehicle, F xRR is the longitudinal force of the right rear tire of the vehicle, F yFL is the lateral force of the left front tire of the vehicle, F yFR is the lateral force of the left rear tire of the vehicle; The lateral motion equation is: Among them, a y is the vehicle lateral acceleration, v y The first derivative of yRL is the lateral force of the right front tire of the vehicle, F yRR is the lateral force of the right rear tire of the vehicle; The yaw motion equation is: in, is the first-order derivative of γ; I z is the inertia of the vehicle around the z-axis, Γ is the yaw moment of the vehicle around the z-axis; L f is the front wheelbase of the vehicle, L r B is the rear wheelbase of the vehicle; f is the distance between the front wheels, B r is the distance between the rear wheels; Wheel rotation equation: Where J is the rotational inertia of the wheel, R is the effective rolling radius of the tire; T dFL，FR is the driving torque between the left front tire and the left rear tire of the vehicle, T bFL，FR is the braking torque between the left front tire and the left rear tire of the vehicle; F xRL，RR is the lateral force between the right front tire and the right rear tire of the vehicle, T bRL，RR is the braking torque between the right front tire and the right rear tire of the vehicle; is the angular acceleration of the left front tire and the left rear tire of the vehicle, also w FL，FR The first derivative of FL，FR is the angular velocity of the left front tire and the left rear tire of the vehicle; is the angular acceleration of the right front tire and the right rear tire of the vehicle, also w RL，RR The first derivative of RL，RR is the angular velocity of the right front tire and the right rear tire of the vehicle; the Dugoff tire model formula includes: in, They represent the normalized representation of the longitudinal and lateral forces on the tire, respectively, and F x is the tire longitudinal force, F y is the tire lateral force, μ is the road adhesion coefficient, λ is the tire slip rate, F z is the tire vertical force, f(L) is the value function related to the boundary value, L is the boundary value, C x , C y is the longitudinal and lateral stiffness of the tire, and α is the tire slip angle.

3. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 1, characterized in that: The adaptive unscented Kalman filter algorithm introduces a proportional correction coefficient in the unbiased transformation link. The corrected formula includes: Among them, X (i) (k|k) is the state vector of the i-th Sigma point estimated at time k under the condition of time k, X (i) (k+1|k) is the state vector of the i-th Sigma point estimated conditionally at time k+1, X (0) is the state vector of the first Sigma point, X (i) is the state vector of the i-th Sigma point, 2L′ is the dimension of the state, X (i) (k, k) is the state vector of the i-th Sigma point at time k; a1 is the proportional correction parameter, X (i) (k+1|k) is the state vector of the i-th Sigma point conditionally estimated at time k+1 at time k, and f(·) is the nonlinear transformation function of the system state quantity.

4. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 3, characterized in that: After introducing the proportional correction coefficient, the calculation formula of the nonlinear system includes: Where f(·) is the nonlinear transformation function, h(·) is the measurement model; x k is the state variable at time k, x k+1 is the state variable at time k+1, u k is the input variable at time k, y k is the output variable at time k, w k 、v k are the process noise and output noise at time k, respectively. The subscript k represents the time. The input variables include the longitudinal force of the tire, the lateral force of the tire, the slip rate of the tire, the sideslip angle of the tire, and the front wheel turning angle of the vehicle. The output variables include the state estimate, the state covariance matrix, the Kalman gain, the prediction residual, the updated filter state, the updated covariance matrix, the sigma point set, the measurement prediction value, and the observation covariance matrix.

5. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 4, characterized in that: The calculation process of the adaptive unscented Kalman filter algorithm includes: S2.1, filter initialization, time k = 0: in, is the initial estimated state vector, x0 is the initial true state vector, E[·] is the expectation operator representation, and P0 is the initial covariance matrix; S2.2, for k = 1, 2 ...: S2.2.

1. Obtain 2L′+1 Sigma points according to UT transformation theory: S2.2.2, time update: the obtained Sigma point set is then used to calculate the transformed Sigma point set through the three state equations of longitudinal motion equation, lateral motion equation and yaw motion equation; S2.2.3, Measurement update: Based on the proportional correction coefficient, an adaptive noise coefficient is introduced to achieve update.

6. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 5, characterized in that: According to the UT transformation theory, 2L+1 Sigma points are obtained, and the calculation formula is: Among them, χ(k-1) is the state variable of the Sigma point at time k-1, is the predicted state vector at time k-1, P i (k-1) is the prediction covariance matrix of the i-th Sigma point at time k-1, λ is the scale parameter, and 2L′+1 is the number of Sigma points.

7. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 5, characterized in that: The adaptive noise coefficient is introduced based on the proportional correction coefficient. The calculation formula includes: Calculate the updated state covariance matrix P yy : Compute the cross-covariance matrix: Among them, α k is the adaptive noise coefficient at time k, with a value range of 0<α k ≤1,ζ i (k|k-1) is the i-th column of ζ(k|k-1), ζ(k|k-1) is the process matrix at time k predicted at time k-1, R k is the measurement noise covariance matrix at time k, is the observed variable at time k predicted at time k-1, P xy (k|k-1) is the cross covariance matrix at time k predicted at time k-1; W i (c) is the covariance weight of the i-th sigma point, χ i (k|k-1) is the i-th column of the matrix χ(k|k-1), i=0,1,..2L′, 2L′+1 is the total number of sigma points, is the state vector at time k predicted at time k-1.

8. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 6, characterized in that: α k The formulas for determining the value of include: Among them, trace represents the sum calculation of the diagonal elements of the matrix, P yy is the covariance matrix of the observed residuals; the calculation formula for the predicted residuals is: Among them, Z (i) (k+1|k) is the predicted value of the measurement at time k+1 predicted by the i-th sigma point at time k. It is the weighted mean of the measured predicted values ​​at time k+1 predicted at time k.

9. The method for estimating road adhesion coefficient based on adaptive unscented Kalman filtering according to claim 6, characterized in that: The formula for measuring update in S2.2.3 includes: Calculate the updated filter feedback gain: Among them, K(k) is the Kalman gain matrix at time k, P xy (k|k-1) is the cross covariance matrix, P yy The inverse matrix of Calculate the filtered value after the state update: in, is the updated state vector at time k, is the state vector at time k predicted at time k-1, and y(k) is the measurement residual; The observed variable at time k predicted at time k-1; Calculate the state posterior variance matrix: P(k|k)=P(k|k-1)-K(k)P yy K(k) T Among them, P(k|k) is the updated covariance matrix at time k, and P(k|k-1) is the covariance matrix at time k predicted at time k-1.

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