A vehicle state estimation method based on improved adaptive extended Kalman filter

Abstract

This invention discloses a vehicle state estimation method based on an improved adaptive extended Kalman filter, comprising: establishing a three-degree-of-freedom vehicle dynamics model; solving the dynamic equations based on the vehicle dynamics model; estimating the tire's lateral stiffness using the recursive least squares method to obtain the tire's real-time lateral stiffness; designing a fuzzy adaptive extended Kalman filter based on the dynamic equations; wherein the fuzzy adaptive extended Kalman filter can correct the observation noise present in the estimation process in real time; the real-time lateral stiffness of the tire is used as the tire lateral stiffness value in the fuzzy adaptive extended Kalman filter; and the vehicle state parameters are estimated using the fuzzy adaptive extended Kalman filter. The vehicle state estimation method provided by this invention can continuously correct the tire's lateral stiffness and adjust the observation noise in real time, effectively improving the estimation accuracy of vehicle state parameters.

Description

Technical Field

[0001] This invention belongs to the field of vehicle state parameter estimation technology, and specifically relates to a vehicle state estimation method based on an improved adaptive extended Kalman filter. Background Technology

[0002] Safety has always been a crucial factor for car owners when evaluating vehicles. Vehicle active safety control systems collect vehicle status parameters through various sensors installed on the vehicle and provide real-time feedback to the driver, enhancing their ability to proactively avoid hazards while driving. Furthermore, in the event of a sudden vehicle malfunction or a traffic accident, the active safety system can intervene to smoothly decelerate the vehicle to a stop, preventing rollovers or longitudinal tilting that could lead to more serious consequences.

[0003] In the closed-loop control of active safety systems, the most crucial step is estimating the vehicle's driving state. A prerequisite for active control is that sensors must accurately measure real-time state parameters of the vehicle during its movement. These parameters include longitudinal speed, lateral speed, sideslip angle, and yaw rate, and transmit this information to the active safety system. Accurate acquisition of these parameters improves the accuracy of the active safety system's control, enabling the vehicle to drive more stably and safely under various road conditions. To reduce the cost of using sensors, a common approach is to construct a vehicle driving state estimator based on the vehicle's dynamics model to estimate the state parameters required for active safety control. This method offers high model accuracy, effectively describes the vehicle's overall motion characteristics, and achieves good estimation results. However, since some parameters and observation noise change in real time during vehicle operation, directly inputting fixed values ​​into the model will negatively impact the accuracy of the state estimation. Summary of the Invention

[0004] The purpose of this invention is to provide a vehicle state estimation method based on an improved adaptive extended Kalman filter, which can overcome the disadvantage of fixed lateral stiffness in the process of estimating vehicle state parameters using extended Kalman filter, and can adjust the observation noise in real time, effectively improving the estimation accuracy of vehicle state parameters.

[0005] The technical solution provided by this invention is as follows:

[0006] A vehicle state estimation method based on an improved adaptive extended Kalman filter includes:

[0007] Establish a three-degree-of-freedom vehicle dynamics model;

[0008] Solve the dynamic equations based on the vehicle dynamics model;

[0009] The tire's lateral stiffness is estimated using the recursive least squares method to obtain the tire's real-time lateral stiffness.

[0010] Design of a fuzzy adaptive extended Kalman filter based on dynamic equations;

[0011] The fuzzy adaptive extended Kalman filter can correct the observation noise in the estimation process in real time; the fuzzy adaptive extended Kalman filter uses the real-time lateral stiffness of the tire as the tire lateral stiffness value.

[0012] The fuzzy adaptive extended Kalman filter is used to estimate vehicle state parameters.

[0013] Preferably, the kinetic equation is:

[0014]

[0015] Where u is the longitudinal vehicle speed; is the derivative of the longitudinal vehicle speed; v is the lateral vehicle speed; ω is the derivative of the lateral vehicle speed; ω is the yaw rate. a is the derivative of the yaw rate; y This is lateral acceleration; a x J is the longitudinal acceleration; z Let Γ be the moment of inertia about the z-axis in the vehicle dynamics model; Γ is the yaw moment.

[0016] Preferably, the method for estimating the tire's lateral stiffness is as follows:

[0017] The linear regression equation for tire lateral force and lateral stiffness is determined as follows:

[0018]

[0019] In the formula, Y k Let w be the set of system output samples at time k. k To identify the parameter set for the system, Let V be the sample set at time k. k The system noise at time k;

[0020] in,

[0021]

[0022] In the formula, C αf and C αr Here, θ represents the lateral stiffness of the front and rear wheels, respectively, and ω represents the yaw rate of the vehicle. Let δ be the derivative of the vehicle's yaw rate, m be the vehicle's mass, L be the wheelbase, and δ be the yaw rate of the vehicle. f The front wheel steering angle is u, and the longitudinal vehicle speed is u. This is the derivative of the lateral vehicle speed.

[0023] The tire's lateral stiffness is obtained using the forgetting factor recursive algorithm formula of the recursive least squares method:

[0024] The recursive algorithm formula is as follows:

[0025]

[0026] In the formula, G k P is the gain vector at time k; k P k-1 Let be the error covariance matrices at times k and k-1, respectively, and λ be the forgetting factor. Let be the sample set at time k-1.

[0027] Preferably, the forgetting factor λ ranges from [0.98, 1].

[0028] Preferably, the method for designing a fuzzy adaptive extended Kalman filter is as follows:

[0029] The extended Kalman filter is derived based on the dynamic equations;

[0030] The difference e between the theoretical variance and the actual variance in the extended Kalman filter and the derivative of e ec are used as the two inputs of the fuzzy controller, and the output of the fuzzy controller is the adjustment factor U.

[0031] The filter factor U output by the fuzzy controller at time k is multiplied by the observation noise covariance matrix to obtain an estimate of the observation noise covariance matrix at that time; thus realizing the fuzzy adaptation of the extended Kalman filter algorithm.

[0032] The beneficial effects of this invention are:

[0033] (1) The three-degree-of-freedom vehicle dynamics model built in this invention takes into account the nonlinear dynamics of the vehicle driving process and fully characterizes the main behavioral features of the vehicle during the driving process.

[0034] (2) The side stiffness estimator based on the recursive least squares method of this invention can continuously correct the side stiffness of the tire. At the same time, based on the fuzzy adaptive extended Kalman filter, it can correct the observation noise in the estimation process in real time, effectively reducing the error when using the Kalman filter to estimate vehicle state parameters. Attached Figure Description

[0035] Figure 1This is a flowchart of the vehicle state estimation method based on the improved adaptive extended Kalman filter described in this invention.

[0036] Figure 2 This is a schematic diagram of a three-degree-of-freedom vehicle dynamics model.

[0037] Figure 3 This is a graph of the membership function of input e in fuzzy control.

[0038] Figure 4 This is a membership function graph of the input ec in fuzzy control.

[0039] Figure 5 This is a graph of the membership function of the output U in fuzzy control.

[0040] Figure 6 The figure shows the estimated yaw rate under steering conditions.

[0041] Figure 7 This is a diagram showing the estimated sideslip angle of the center of gravity under steering conditions.

[0042] Figure 8 This is a diagram showing the longitudinal speed estimation results under steering conditions.

[0043] Figure 9 The figure shows the estimation results of the yaw rate under the serpentine working condition.

[0044] Figure 10 The figure shows the estimation results of the centroid sideslip angle under the serpentine working condition.

[0045] Figure 11 The image shows the longitudinal speed estimation results under the serpentine driving condition.

[0046] Figure 12 The figure shows the estimation results of the yaw rate under the double-track change condition.

[0047] Figure 13 The figure shows the estimation results of the centroid sideslip angle under the double-tracking condition.

[0048] Figure 14 This is a diagram showing the longitudinal speed estimation results under the double lane change condition. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0050] like Figure 1 As shown, this invention provides a vehicle state estimation method based on an improved adaptive extended Kalman filter, the specific process of which is as follows.

[0051] I. Establishing a three-degree-of-freedom vehicle dynamics model

[0052] The Y-plane is defined by the left and right center symmetry planes of the vehicle. The Z-plane is defined by a plane perpendicular to the Y-plane and parallel to the longitudinal beam plane or the floor surface. The X-plane is defined by a plane perpendicular to both the Y and Z-planes and passing through the center of the front wheels in the ready-to-drive state. The established dynamic model is as follows: Figure 2 As shown, this includes the vehicle's longitudinal, lateral, and yaw motions, and the following assumptions are made about the model:

[0053] (1) Ignoring the influence of the suspension system, the vehicle body only moves in a plane parallel to the ground.

[0054] (2) Ignore the influence of the steering system and directly use the front wheel steering angle δ as the input;

[0055] (3) Ignore the difference in front and rear track width;

[0056] (4) Assume the car's forward speed remains constant;

[0057] (5) Assume the lateral acceleration of the car is a y <0.4g;

[0058] (6) Assume the road surface is flat and has no inclination angle.

[0059] II. Solving the dynamic equations based on the vehicle dynamics model

[0060] The aforementioned dynamic equation is:

[0061]

[0062]

[0063]

[0064] In the formula, u is the longitudinal vehicle speed; is the derivative of the longitudinal vehicle speed; v is the lateral vehicle speed; ω is the derivative of the lateral vehicle speed; ω is the yaw rate. a is the derivative of the yaw rate; y This is lateral acceleration; a x J is the longitudinal acceleration; z Let Γ be the moment of inertia about the z-axis in the vehicle dynamics model; Γ is the yaw moment.

[0065] In the above formula, parameter a y a x The calculation methods for Γ are as follows:

[0066]

[0067]

[0068]

[0069] In the formula, i = f or r represents the front wheel or the rear wheel; j = l or r represents the left wheel or the right wheel; F x_ij For the longitudinal force of the four wheels; F y_ij The lateral force of the four wheels; δ ij d1 and d2 are the wheel angles; m is the total mass of the vehicle; d1 and d2 are the front and rear track widths; a and b are the distances from the center of gravity to the front and rear axles, respectively.

[0070] Based on the established dynamic equations, the formulas for calculating other parameters are as follows:

[0071]

[0072]

[0073]

[0074] In the formula, α ij The sideslip angle of the four wheels; v ij F represents the linear velocity of the four wheels. z_ij β is the normal force on the tire; L is the wheelbase; h is the height of the center of gravity; β is the sideslip angle of the center of gravity.

[0075] From the above formula, the differential equation required to design the estimation algorithm can be derived as follows:

[0076]

[0077]

[0078]

[0079]

[0080] In the formula, γ is the yaw rate of the vehicle; β is the sideslip angle; δ f Front wheel steering angle; a and b are the distances from the front and rear axles to the vehicle's center of gravity, respectively; C αf and C αr These are the lateral stiffnesses of the front and rear wheels, respectively; I z Let m be the moment of inertia of the center of mass about the z-axis; m be the total mass of the vehicle; a x and a y These are the vehicle's longitudinal acceleration and lateral acceleration, respectively.

[0081] III. Real-time estimation of tire lateral stiffness using recursive least squares method

[0082] When the tire slip angle is small, the lateral force is approximately linearly related to the slip angle, and its lateral stiffness relationship can be expressed as:

[0083] F yi =C αi (μ)α i (14)

[0084] In the formula, i = f or r represent the front and rear wheels, respectively; F y C is the lateral force of the tire. αi (μ) represents the tire lateral stiffness; α represents the tire lateral angle; and μ represents the road adhesion coefficient.

[0085] Under normal circumstances, the higher the road surface adhesion coefficient, the greater the tire's lateral stiffness. Since the linearized tire model has high fitting accuracy when the tire slip angle is small, within the allowable error range, assuming the left and right wheel rotation angles of the front and rear axles are equal, a small angle assumption can be used to approximate the following:

[0086]

[0087]

[0088] In the formula, ω is the yaw rate of the vehicle; δ f β is the front wheel steering angle; β is the center of gravity sideslip angle.

[0089] Having already calculated the vehicle's longitudinal and lateral accelerations, and combining the vehicle's yaw moment and the lateral force on the tires, using the vehicle's equations of motion and Newton's second law, we can obtain the following formula:

[0090]

[0091]

[0092] Substituting equation (18) into equation (17), eliminating the value of β, and setting the vehicle wheelbase to L, we obtain the following formula:

[0093]

[0094] in:

[0095]

[0096]

[0097] After determining the intermediate variables X1 and X2, the tire lateral stiffness C can be calculated. αf and C αr The required formula is as follows:

[0098]

[0099]

[0100] The linear regression equation for the relationship between lateral force and lateral stiffness of a tire is as follows:

[0101]

[0102] In the formula, Y k Let w be the set of system output samples at time k. k Let k be the set of system identification parameters. Let V be the sample set at time k. k Let V be the system noise at time k, and assume it follows a uniform distribution, and V k ~(0,σ2). Comparing equations (19) and (24), the corresponding relationship can be obtained as follows:

[0103]

[0104]

[0105]

[0106] The formula for the forgetting factor recursive algorithm of recursive least squares is as follows:

[0107]

[0108]

[0109]

[0110] In the formula, G k P is the gain vector at time k; k Let P0 = δI be the error covariance matrix of the system at time k, initialized as P0 = δI, where δ is a positive decimal. In reality, new data is often more meaningful than old data. Therefore, a forgetting factor λ∈[0,1] is introduced in the recursive least squares method, with a value generally between 0.98 and 1, to evaluate the impact of data on the current model, making the impact of data larger as time goes on. For static data, i.e., when all data can be given at once, there is no need to consider the forgetting factor. In one embodiment, the value of λ is taken as 0.99.

[0111] IV. Designing a fuzzy adaptive extended Kalman filter based on dynamic equations to estimate vehicle state parameters.

[0112] The state transition equations and observation equations for the extended Kalman filter are as follows:

[0113] x k =f(x) k-1 ,u k-1 ,w k-1 (31)

[0114] z k =h(x k-1 ,v k-1 (32)

[0115] In the formula, x k Let z be the state vector of the system at time k; k Let f be the observation vector of the system at time k; f and h represent x, respectively. k and z k Nonlinear function; u k-1 w represents the control input of the system at time k-1. k-1 v represents the process noise of the system at time k-1; k-1 The system at time k-1 is observation noise.

[0116] The filtering equation is as follows:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] In the formula, F represents the prior state estimate of the system at time k; k-1 H is the state transition matrix of the system at time k-1; k Let k be the output matrix of the system at time k; Let Q be the prior estimation error covariance matrix of the system at time k; k-1 Let K be the process noise covariance matrix of the system at time k-1; k R is the state gain matrix of the system at time k; k Let be the observation noise covariance matrix of the system at time k; P represents the posterior state estimate of the system at time k-1; k Let ' be the posterior estimation error covariance matrix of the system at time k.

[0123] The system's state transition matrix F and output matrix H need to be represented by the Jacobian matrices after partial derivatives of the functions f and h, respectively, as follows:

[0124]

[0125] Combining equations (11), (12), (13), and (14), the state transition matrix F and output matrix H of the corresponding model can be obtained as follows:

[0126]

[0127]

[0128] In the formula, T is the sampling time, with a value of 0.001, and the error covariance matrix P(t) = I 3×3 The process noise covariance matrix Q = 0.1 × I 3×3 The observation noise covariance matrix R = 0.001.

[0129] Based on the designed extended Kalman filter estimation algorithm, the theoretical variance of the error is taken:

[0130]

[0131] Take the actual variance of the error:

[0132]

[0133] Calculate the difference between the theoretical variance and the actual variance:

[0134] e = P a -P t (43)

[0135] The variance difference *e* and its derivative *ec* are taken as the two inputs to the fuzzy control, and the output is the adjustment factor *U*. The fuzzy sets of input and output are defined as follows:

[0136] e = {PB, PM, PS, Z, NS, NM, NB}

[0137] ec = {PB, PM, Z, NM, NB}

[0138] U={PVB,PB,PMB,PSB,PM,PSM,PS,PVS}

[0139] Where PB is positive (large), PM is positive (medium), PS is positive (small), Z is zero, NS is negative (small), NM is negative (medium), NB is negative (large), PVB is positive (higher-large), PMB is positive (medium-large), PSB is positive (elementary-large), PSM is positive (medium-small), and PVS is positive (higher-small). The input and output membership functions are based on experience as follows: Figure 3 , Figure 4 , Figure 5As shown in Table 1, the inputs e have triangular membership functions NB, Z, and PB, and Gaussian membership functions NM, NS, PS, and PM; the inputs ec have triangular membership functions NM and PM, and generalized bell membership functions NB, Z, and PB; the outputs U have triangular membership functions PVS, PS, PSM, PSB, PMB, PB, and PVB, and generalized bell membership function PM. The fuzzy rules are established as shown in Table 1. Multiplying the filter factor U output by the fuzzy controller at time k with the current R yields the estimated value R of the observation noise covariance matrix at that time. k This enables real-time adjustment of the observation noise covariance matrix, achieving fuzzy adaptation of the extended Kalman filter algorithm.

[0140] Table 1 Fuzzy Control Rules

[0141]

[0142] Example

[0143] The effectiveness of this method was tested using a co-simulation platform built with Carsim and Simulink. First, the corresponding vehicle model and driving conditions were selected using Carsim. The vehicle parameters for the simulation experiment are shown in Table 2.

[0144] Table 2 Simulation Vehicle Parameters

[0145]

[0146]

[0147] During vehicle operation, the vehicle speed was set to a constant 40 km / h, the road adhesion coefficient was set to a constant 0.85, the sampling time was 20 s, and the sampling step size was 0.001 s. Simulations were conducted under three driving conditions: steering, serpentine maneuvers, and double lane change, and the results were compared and analyzed.

[0148] Taking the steering condition as an example: Figure 6-8 As shown, FAEKF+RLS represents the estimation curve of the improved adaptive extended Kalman filter, and EKF represents the estimation curve of the extended Kalman filter. From... Figure 6 It can be seen that in the estimation of yaw rate, the maximum error of the extended Kalman filter estimation is 12.3%, while the maximum error of the improved adaptive extended Kalman filter estimation is 5.4%. Figure 7 From this, it can be seen that in the estimation of the centroid sideslip angle, the maximum error of the extended Kalman filter estimation is 15.7%, while the maximum error of the improved adaptive extended Kalman filter estimation is 6.7%. Figure 8It can be seen that in the estimation of longitudinal vehicle speed, the maximum error of the extended Kalman filter estimation is 2.1%, and the maximum error of the improved adaptive extended Kalman filter estimation is 0.7%.

[0149] In both serpentine and double-line-shifting operating conditions, by Figure 9-14 It can be seen that the estimates obtained by using the improved fuzzy adaptive extended Kalman filter to estimate vehicle state parameters are more accurate than those obtained by using the extended Kalman filter alone. Simulation results under three different operating conditions demonstrate that this method has a good effect in the field of vehicle state parameter estimation and can improve the estimation accuracy of state parameters.

[0150] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A vehicle state estimation method based on improved adaptive extended Kalman filter, characterized in that, The method comprises the following steps: establishing a three-degree-of-freedom vehicle dynamics model; solving a dynamics equation based on the vehicle dynamics model; estimating the tire side stiffness by using a recursive least square method to obtain real-time tire side stiffness; designing a fuzzy adaptive extended Kalman filter based on the dynamics equation; the fuzzy adaptive extended Kalman filter can correct the observation noise in the estimation process in real time; the real-time tire side stiffness is used as the tire side stiffness value in the fuzzy adaptive extended Kalman filter; using the fuzzy adaptive extended Kalman filter to estimate the vehicle state parameters; the dynamics equation is: where u is the longitudinal vehicle speed; is the derivative of the longitudinal vehicle speed; v is the lateral vehicle speed; is the derivative of the lateral vehicle speed; ω is the yaw rate; is the derivative of the yaw rate; a y is the lateral acceleration; a x is the longitudinal acceleration; J z is the moment of inertia about the z-axis in the vehicle dynamics model; Γ is the yaw moment; the method for estimating the tire side stiffness is: determining a linear regression equation of the tire lateral force and the tire side stiffness is: In the formula, Y k is the system output sample set at time k, w k is the system identification parameter set, is the sample set at time k, V k is the system noise at time k; wherein where C αf and C αr are the cornering stiffness of the front and rear wheels, respectively, ω is the yaw rate of the vehicle, is the derivative of the yaw rate of the vehicle, m is the mass of the vehicle, L is the wheelbase, δ f is the front wheel steering angle, u is the longitudinal vehicle speed, is the derivative of the lateral vehicle speed; according to a forgetting factor recursive algorithm formula of the recursive least square method, the tire side stiffness is obtained: the recursive algorithm formula is: In the formula, G k is the gain vector at time k; P k , P k-1 are the error covariance matrices at times k and k-1, respectively, and λ is a forgetting factor, is the sample set at time k-1.

2. The method of claim 1, wherein, the value range of the forgetting factor λ is [0.98, 1].

3. The improved adaptive extended Kalman filter based vehicle state estimation method according to claim 1 or 2, characterized in that, the method for designing the fuzzy adaptive extended Kalman filter is: obtaining an extended Kalman filter based on the dynamics equation; taking the difference e between the theoretical variance and the actual variance in the extended Kalman filter and the derivative ec of e as two inputs of the fuzzy controller, and taking the output of the fuzzy controller as an adjustment factor U; multiplying the filter factor U output by the fuzzy controller at the k moment and the observation noise covariance matrix to obtain the estimated value of the observation noise covariance matrix at the moment; and realizing the fuzzy adaptive of the extended Kalman filter algorithm.

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