A vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter

Abstract

The present invention discloses a vehicle parameter estimation method based on a BP neural network and an improved unscented Kalman filter, comprising: determining the state equation and observation equation of the unscented Kalman filter based on an established three-degree-of-freedom vehicle dynamics model; determining the input, state, and observation of the unscented Kalman filter; improving the unscented Kalman filter to obtain a state estimation result of the improved unscented Kalman filter; using the vehicle's front wheel angle and longitudinal acceleration as training inputs, and fitting the BP neural network to obtain a residual value between the state estimation result and the true sensor value; and using the state estimation result and the residual value as the actual output of the vehicle parameter prediction model. The present invention uses an improved unscented particle filter to predict and estimate vehicle dynamics parameters, and uses vehicle state parameters to construct a BP neural network fitting residual, thus addressing the current drawback that high-precision vehicle parameter sensors cannot be installed on vehicles.

Description

Technical Field

[0001] The present invention belongs to the field of automobile dynamics control, and specifically refers to a parameter estimation method based on a BP neural network and an improved unscented Kalman filter. Background Art

[0002] The sideslip angle and yaw rate play a role in assessing and adjusting vehicle posture and stability in vehicle stability control. By monitoring these parameters, appropriate measures can be taken to improve vehicle stability and maneuverability, thereby enhancing driving safety and comfort. In actual production, the relevant commercial sensors are highly accurate but expensive, making them impractical for on-vehicle installation. Therefore, parameter estimation methods are needed to predict and estimate these variables.

[0003] The Kalman filter (KF) is suitable for state estimation and filtering of linear systems. It uses a Gaussian distribution for prediction and update, assuming that both process noise and observation noise are Gaussian, to optimally estimate the system's state. The extended Kalman filter (EKF) is an improvement on the Kalman filter. It approximates nonlinear systems by performing a Taylor series expansion on nonlinear functions, achieving system linearization. However, the first-order Taylor series expansion ignores higher-order terms, resulting in lower estimation accuracy and poor applicability for highly nonlinear problems. The unscented Kalman filter (UKF) is based on the unscented transform. This method studies how to capture the posterior distribution of a highly random variable that has undergone a nonlinear transformation using a fixed sampling point. The computational complexity of the standard UKF is comparable to that of the EKF, but the filtering accuracy is superior to that of the EKF.

[0004] Back propagation neural network (BP neural network for short) is a multi-layer feedforward network trained by error back propagation (error back propagation for short). Its algorithm is called BP algorithm. Its basic idea is gradient descent method, which uses gradient search technology to minimize the mean square error between the actual output value and the expected output value of the network.

[0005] At present, research on vehicle parameter estimation such as the center of mass sideslip angle mainly focuses on how to improve the robustness and accuracy of the algorithm. For example, Chinese invention patent application number CN201810227343.X, patent name "Center of mass sideslip angle estimation method and system based on robust unscented Kalman filter", combines the M estimation algorithm with the UKF algorithm to reduce the influence of outliers, thereby improving the robustness of the filter algorithm to outliers in the observation signal; application number CN202211200764.6, patent name "A vehicle state estimation method and system combining neural network and unscented Kalman filter", uses multiple vehicle sensors to collect data, establishes a neural network and combines unscented Kalman filter to accurately estimate three-dimensional acceleration and three-dimensional angular velocity, so as to achieve accurate estimation of the vehicle's 3D posture, speed and positioning.

[0006] While there is considerable research on parameter estimation using Kalman filters, it's not uncommon to find that many practical problems often rely on Gaussian assumptions about the variables. However, it's often the case that vehicle motion characteristics exhibit non-Gaussian distributions, such as tire slip and braking. Using a Gaussian model for prediction in these situations can introduce estimation errors, reducing prediction accuracy. Therefore, considering model differences in specific vehicle driving conditions is crucial in Kalman filter design. Summary of the Invention

[0007] In view of the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a vehicle parameter estimation method based on a BP neural network and an improved unscented Kalman filter hybrid model to solve the problem of large prediction errors caused by the Gaussian assumption of parameters in the unscented Kalman filter in the prior art and changes in working conditions; the present invention combines the situation where the vehicle parameter characteristics such as tire sideslip and braking are non-Gaussian distributed and the vehicle is in a non-Gaussian white noise working environment, adopts a Monte Carlo importance sampling strategy and an adaptive noise reduction method to improve the prediction effect of the existing unscented Kalman filter on vehicle parameters, outputs the unscented Kalman filter prediction value, and simultaneously uses the BP neural network to fit the residual between the true value and the estimated value of the parameter, combines the predicted value with the optimized residual to achieve a two-way optimization effect, thereby improving the accuracy and stability of parameter estimation.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter of the present invention comprises the following steps:

[0010] 1) Establish a three-degree-of-freedom vehicle dynamics model and determine the state equation and observation equation of the unscented Kalman filter based on the three-degree-of-freedom vehicle dynamics model;

[0011] 2) determining the input quantity, state quantity and observation quantity of the unscented Kalman filter according to the dynamic model in step 1);

[0012] 3) Combining the Monte Carlo sampling method and the adaptive weight distribution formula, the unscented Kalman filter is improved to obtain the state estimation result of the improved unscented Kalman filter

[0013] 4) Collect the true value of the center of mass side slip angle β during vehicle driving under different working conditions a and the true value of the yaw rate γ a The front wheel angle and longitudinal acceleration of the vehicle are used as training inputs, and the residual value Δx between the state quantity estimation result in step 3) and the true value of the sensor is obtained through BP neural network training and fitting. k ;

[0014] 5) The state estimation result obtained in step 3) and the residual value Δx obtained in step 4) are combined k As the actual output of the vehicle parameter prediction model

[0015] Furthermore, the motion equation of the three-degree-of-freedom vehicle dynamics model in step 1) is:

[0016]

[0017] in, is the first-order derivative of the vehicle's center of mass sideslip angle, is the first-order derivative of the vehicle’s yaw rate, is the first-order derivative of the vehicle's longitudinal velocity, β is the vehicle's center of mass sideslip angle, γ is the vehicle's yaw rate, and v x is the longitudinal speed of the vehicle, k1 and k2 are the front wheel cornering stiffness and the rear wheel cornering stiffness respectively, m is the vehicle mass, a and b are the distances from the center of mass to the front and rear axles of the vehicle respectively, δ f is the front wheel angle, I z is the moment of inertia of the vehicle around the z axis, a x is the vehicle longitudinal acceleration.

[0018] Furthermore, the state equation and observation equation of the unscented Kalman filter in step 1) are:

[0019]

[0020] Among them, the subscript k represents the kth moment, k-1 represents the k-1th moment, and x k|k-1 represents the state quantity at time k, z k|k-1 is the observed value at time k, w k-1~(0,Q) is Gaussian white noise with zero mean and covariance Q, v k-1 ~(0,R) is Gaussian white noise with zero mean and covariance R.

[0021] Furthermore, the step 2) specifically includes: selecting the front wheel angle and the vehicle longitudinal acceleration [δ f ,a x ] is the input; the sideslip angle of the center of mass, the yaw rate and the longitudinal speed β, ω r ,v x is the state quantity; lateral acceleration and yaw angular velocity a y ,ω r is the observed quantity.

[0022] Furthermore, the improvement of the unscented Kalman filter in step 3) specifically includes:

[0023] 31) Filter initialization:

[0024] When k = 0, based on the initial state variables, a particle set is generated in the initial distribution prior probability density p(x0) = N(x0, P0) P0 is the initial covariance matrix, and each particle is assigned an equal weight of 1 / N, where N is the number of particles;

[0025] When k>0, the particle set at the previous moment is updated through the state equation and observation equation of the unscented Kalman filter in step 1) to obtain a new particle set at the current moment. The updated particle set is then used to approximate the posterior probability distribution at the current moment. The probability distribution of k at the current moment is described in the form of a weighted sum of particles. Specifically, the process includes: selecting an importance density function, generating prediction particles through importance sampling, calculating and normalizing the particle weights, determining whether resampling is required, and outputting the state estimation result.

[0026] 32) Introduce the importance density function and calculate the importance weight of each particle. Let the importance density function be:

[0027]

[0028] in, is the importance density function of the i-th particle;

[0029] Generate prediction particles by importance sampling, and sample from the importance density function to generate the prediction particles required for particle filtering:

[0030]

[0031] in, is the state value of the current particle, is the particle state sequence of the i-th particle from time 0 to k-1, z 1:k is the observation sequence from time 1 to k, and the importance density function is set to be a normal distribution are the mean and variance of the normal distribution respectively; suppose the initial weights of all particles are N is the total number of particles; based on the particle state at the previous time k-1, the particle state at the current time k is predicted; during the prediction process, the prediction importance density function Sample the particle state to obtain the observation data at time k. Update the weight of each particle based on the conditional probability density of the observation data and state data. The weight update formula is as follows:

[0032]

[0033] in, Observable In particles The likelihood function under the condition indicates the matching degree between the observed data and the particle state. is the likelihood function of the state quantity at time k under the condition of the state quantity at time k-1, which indicates the matching degree of the particle state before and after;

[0034] The importance weight obtained by formula (5) is normalized as follows:

[0035]

[0036] in, is the state of the i-th particle at time k, are the mean and covariance of the reference distribution of the importance density function, is the importance weight of the i-th particle at time k, is the normalized importance weight of the i-th particle at time k;

[0037] 33) Set the threshold N t =N / 3, determine the effective number of particles N e :

[0038]

[0039] in, is the normalized importance weight of the i-th particle at time k;

[0040] According to the set threshold, determine whether the statistics of the sample points are within the threshold range; for sample points that are not within the threshold range, resample and regenerate sample points until the threshold condition is met;

[0041] Resampling generally requires constructing a cumulative distribution function to generate a random index for each particle. The construction formula is as follows:

[0042]

[0043] Where F(i) is the i-th term of the cumulative distribution function, is the normalized weight of all particles in item i;

[0044] For each new particle, generate a uniform random number u in the range [0,1]. i , find the cumulative distribution function that satisfies F(i-1)<u i < index i of F(i), and then take the particle with index i in the original particle set as the new particle;

[0045] After resampling, the weights of all particles are reset to 1 / N to ensure that each particle has the same importance in the next prediction and update step;

[0046] 34) The weighted sum of the predicted particle set is used to output the state estimate. The formula is as follows:

[0047]

[0048] in, are weighted estimates of the state variables.

[0049] Furthermore, in step 31), when k>0, the specific steps include:

[0050] 311) Use unscented Kalman filtering to generate the importance density function for each particle and construct the 2n+1 Sigma point sampling distribution χ for each particle i And the weight distribution formula is:

[0051]

[0052] Where n is the dimension of the state quantity; λ is the scaling factor, λ = α 2 (n+κ)-n, α is a small positive value that determines the distribution of Sigma points; δ is a non-negative weight coefficient that can be used to combine the dynamic errors of high-order terms in the equation. is the state quantity of the i-th Sigma point at time k-1, is the covariance of the i-th Sigma at time k-1, is the weight distribution coefficient when it is approximately the mean, is the weight distribution coefficient of the approximate covariance;

[0053] κ∈R, characterizes the degree of dispersion of Sigma points relative to the mean, R is a real number. The larger κ is, the farther the Sigma points at non-mean locations are from the mean, and the smaller their weights are. For Gaussian problems, κ=3-n. For non-Gaussian problems, adaptive parameters c,ε are introduced, with κ=c(n+ε). If the state distribution is highly non-Gaussian, increase the value of c to increase the number of Sigma points. If the state distribution is highly Gaussian, decrease the value of c to reduce the number of Sigma points.

[0054] 312) Weighted calculation of state quantity at time k The prior distribution of is as follows:

[0055]

[0056] in, is the prior estimate of the state quantity at time k, is the state quantity at time k, is the prior estimate of the covariance of the state quantity at time k, are the weights of the state quantity mean and covariance of each Sigma point, is the variance of the system noise at time k;

[0057] 313) For the state quantity at time k Sigma point sampling and observations of the prior distribution The probability distribution of is as follows:

[0058]

[0059] in, is the prior estimate of the state quantity at time k, is the prior estimate of the covariance of the state quantity at time k, is the Gaussian white noise with zero mean and covariance R of the observed quantity, is the weight distribution coefficient of the approximate mean, 2n is the number of Sigma points, is the observed quantity at time k, is the weighted mean of the observations at time k;

[0060] 314) Calculate the mutual covariance between the state quantity and the observation quantity and the autocovariance of the observation quantity as follows:

[0061]

[0062] in, is the prior estimate of the state quantity at time k, is the state quantity at time k, is the cross-covariance of observations, is the observed autocovariance, is the weight distribution coefficient of the approximate mean square error, is the observed quantity at time k, is the weighted mean of the observations at time k, is the variance of the observation noise;

[0063] 315) Calculate the posterior estimate of the state quantity at time k, the Kalman gain, and the corresponding update steps as follows:

[0064]

[0065] Among them, K i is the Kalman gain of the i-th Sigma point, is the cross-covariance of observations, is the observed autocovariance, is the mean value of the state quantity at time k,

[0066] is the prior estimate of the state quantity at time k, z k is the value of the observation at time k, is the weighted mean of the observations at time k, is the estimated covariance of the state quantity at time k.

[0067] Furthermore, the step 4) specifically includes:

[0068] 41) Determine the network topology and select a single hidden layer topology. Two types of signals are transmitted between different layers: one is the working signal, which is the multiple external input signals that pass through the hidden layer and then output the actual required signal at the output layer; the other is the error signal, which is the difference between the actual output signal and the predicted output signal in the BP neural network. It propagates backward from the output layer to each layer, and there is no interconnection between the same layers.

[0069] 42) Determine the Sigmond function to limit the range of neuron output and integrate the infinite range of possible outputs into the allowed output range. The Sigmond function expression is as follows:

[0070]

[0071] Among them, x is the input feature variable of the hidden layer or output layer, and e is the logarithmic function;

[0072] 43) The working signal propagates forward. The specific process is as follows: the BP neural network receives the input signal, the signal is weighted summed and then converted by the Sigmond function, and then processed by the hidden layer before reaching the output layer. The number of neurons in the output layer matches the number of targets in the problem. The output layer targets are the vehicle's center of mass sideslip angle and yaw rate.

[0073] The output of the i-th node in the input layer is x i ;

[0074] The input of the jth node in the hidden layer is NET j :

[0075]

[0076] The output of the jth node in the hidden layer is y j :

[0077]

[0078] The input of the kth node in the output layer is NET k :

[0079]

[0080] The output of the kth node in the output layer is y k :

[0081]

[0082] Among them, w ij is the connection weight between the i-th node in the input layer and the j-th node in the hidden layer, b j is the threshold of the jth node in the hidden layer, p is the number of nodes in the hidden layer, w jk is the connection weight between the jth node in the hidden layer and the kth node in the output layer, ξ k is the threshold at the kth node in the output layer, and s is the number of nodes in the output layer;

[0083] 44) Back propagation of error signals: Calculate the error between the actual output of the BP neural network data and the expected output of the sample data, and adjust the weights and thresholds of different layers according to the gradient descent method to make the modified neural network close to the expected output value;

[0084] For back propagation, the total error E between the BP neural network prediction value and the true value is set to:

[0085]

[0086] in, is the actual output of the network, for The corresponding expected output;

[0087] 45) iterating steps 43) to 44) in a loop, gradually reducing the calculation error until the error reaches the set target error or the number of loop iterations reaches the set maximum number;

[0088] 46) Obtaining optimal weights and thresholds;

[0089] 47) Fitting vehicle parameter errors: Using sensors to collect and calculate the vehicle's center of mass side slip angle β a and the expected value of the yaw rate γ a , the front wheel angle and longitudinal acceleration are used as the BP neural network input layer parameters, and after the working signal forward propagation process in step 43) above, the center of mass side slip angle β is obtained. k and the predicted value of yaw rate γ k After calculating the error between the predicted value and the expected value, the error is back-propagated according to the gradient descent method in step 44, and the weights and thresholds between each layer are continuously modified to obtain the optimal residual value output Δx k =[Δβ k Δγ k ].

[0090] Furthermore, the step 44) specifically includes two processes: the error is fed back from the output layer to the hidden layer and from the hidden layer to the input layer;

[0091] The error between the predicted value and the expected value of the BP neural network is fed back to the hidden layer from the output layer, and the weights and thresholds between the output layer and the hidden layer are adjusted accordingly;

[0092] Weight w jk Correction value Δw of (n) jk The expression for (n) is:

[0093]

[0094] Threshold ξ k Correction Δξ of (n) k (n) is expressed as:

[0095]

[0096] because:

[0097]

[0098] Arranging the above formulas (23)-(27) yields:

[0099]

[0100] The adjusted weight w jk (n+1) is expressed as:

[0101] w jk (n+1)=w jk (n)+Δw jk (n) (29)

[0102] Adjusted threshold ξ k(n+1) is expressed as:

[0103] ξ k (n+1)=ξ k (n)+Δξ k (n) (30)

[0104] Among them, η is the learning efficiency, n is the number of back propagation times, P is the number of hidden layer nodes, S is the number of output layer nodes, w jk (n+1) is the connection weight between the jth node in the n+1th hidden layer and the kth node in the output layer, ξ k (n+1) is the threshold value of the kth node in the n+1th output layer, f2'(NET k ) is the conversion function between the input value of the hidden layer and the kth node of the output layer, NET k is the input of the kth node in the output layer, y j is the output of the jth node in the hidden layer, is the actual output of the BP neural network, for The corresponding expected output;

[0105] 442) Correct the correction weight and correction threshold from the hidden layer to the input layer;

[0106] Weight correction Δw between the input layer and the hidden layer ij The expression for (n) is:

[0107]

[0108] Threshold b j Correction value Δb of (n) j (n) is:

[0109]

[0110] because:

[0111]

[0112] The corresponding weight and threshold update process is:

[0113]

[0114] Among them, η is the learning efficiency, n is the number of back propagation times, P is the number of hidden layer nodes, S is the number of output layer nodes, w ij (n+1) is the connection weight between the jth node in the n+1th hidden layer and the ith node in the input layer, b j (n+1) is the threshold value at the jth node of the n+1th hidden layer, f1'(NET j) is the conversion function between the input value of the input layer and the jth node of the hidden layer, NET j is the input of the jth node in the hidden layer, y j (n) is the output of the jth node in the nth hidden layer, is the actual output of the network, for The corresponding expected output.

[0115] Beneficial effects of the present invention:

[0116] The present invention uses an improved unscented particle filter to predict and estimate vehicle dynamic parameters, and uses vehicle state parameters to build a BP neural network fitting residual, which to some extent makes up for the defect that high-precision vehicle parameter sensors cannot be installed on vehicles. Its advantages are as follows:

[0117] 1. Robustness: The improved unscented Kalman filter can handle nonlinear and non-Gaussian noise, which is critical for the complexity and uncertainty in vehicle motion and perception. Using the BP neural network to fit the residual can further improve the robustness of the filter and enhance its adaptability to noise and nonlinearity.

[0118] 2. Adaptability: The improved unscented Kalman filter in the present invention introduces an adaptive parameter c to adjust the weight distribution of sigma points in the case of nonlinear distribution. The BP neural network can also automatically adjust the weights and biases to fit the residuals in the best way; it enables adaptation under different vehicle and environmental conditions and improves the accuracy and stability of the estimation.

[0119] 3. The estimation method of the present invention can be applied to various vehicle parameter estimations, such as stiffness parameter estimation and tire parameter estimation, and has high market value and practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 This is a flow chart of the estimation method of the present invention;

[0121] Figure 2 Improved unscented Kalman filter flow chart for the present invention;

[0122] Figure 3 This is the principle block diagram of BP neural network. DETAILED DESCRIPTION

[0123] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0124] Reference Figure 1-Figure 3As shown, a vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter of the present invention comprises the following steps:

[0125] 1) Establish a three-degree-of-freedom vehicle dynamics model and determine the state equation and observation equation of the unscented Kalman filter based on the three-degree-of-freedom vehicle dynamics model;

[0126] The motion equation of the three-degree-of-freedom vehicle dynamics model in step 1) is:

[0127]

[0128] in, is the first-order derivative of the vehicle's center of mass sideslip angle, is the first-order derivative of the vehicle’s yaw rate, is the first-order derivative of the vehicle's longitudinal velocity, β is the vehicle's center of mass sideslip angle, γ is the vehicle's yaw rate, and v x is the longitudinal speed of the vehicle, k1 and k2 are the front wheel cornering stiffness and the rear wheel cornering stiffness respectively, m is the vehicle mass, a and b are the distances from the center of mass to the front and rear axles of the vehicle respectively, δ f is the front wheel angle, I z is the moment of inertia of the vehicle around the z axis, a x is the vehicle longitudinal acceleration.

[0129] Wherein, the state equation and observation equation of the unscented Kalman filter described in step 1) are:

[0130]

[0131] Among them, the subscript k represents the kth moment, k-1 represents the k-1th moment, and x k|k-1 represents the state quantity at time k, z k|k-1 is the observed value at time k, w k-1 ~(0,Q) is Gaussian white noise with zero mean and covariance Q, v k-1 ~(0,R) is Gaussian white noise with zero mean and covariance R.

[0132] 2) determining the input quantity, state quantity and observation quantity of the unscented Kalman filter according to the dynamic model in step 1);

[0133] Wherein, the step 2) specifically includes: selecting the front wheel angle and the vehicle longitudinal acceleration [δ f ,a x ] is the input; the sideslip angle of the center of mass, the yaw rate and the longitudinal speed β, ω r ,v x is the state quantity; lateral acceleration and yaw angular velocity a y ,ωr is the observed quantity.

[0134] 3) Combining the Monte Carlo sampling method and the adaptive weight distribution formula, the unscented Kalman filter is improved to obtain the state estimation result of the improved unscented Kalman filter

[0135] The improvement of the unscented Kalman filter in step 3) specifically includes:

[0136] 31) Filter initialization:

[0137] When k = 0, based on the initial state variables, a particle set is generated in the initial distribution prior probability density p(x0) = N(x0, P0) P0 is the initial covariance matrix, and each particle is assigned an equal weight of 1 / N, where N is the number of particles;

[0138] When k>0, the particle set at the previous moment is updated through the state equation and observation equation of the unscented Kalman filter in step 1) to obtain a new particle set at the current moment. The updated particle set is then used to approximate the posterior probability distribution at the current moment. The probability distribution of k at the current moment is described in the form of a weighted sum of particles. Specifically, the process includes: selecting an importance density function, generating prediction particles through importance sampling, calculating and normalizing the particle weights, determining whether resampling is required, and outputting the state estimation result.

[0139] Specifically, in step 31), when k>0, the specific steps include:

[0140] 311) Use unscented Kalman filtering to generate the importance density function for each particle and construct the 2n+1 Sigma point sampling distribution χ for each particle i And the weight distribution formula is:

[0141]

[0142] Where n is the dimension of the state quantity; λ is the scaling factor, λ = α 2 (n+κ)-n, α is a small positive value that determines the distribution of Sigma points; δ is a non-negative weight coefficient that can be used to combine the dynamic errors of high-order terms in the equation. is the state quantity of the i-th Sigma point at time k-1, is the covariance of the i-th Sigma at time k-1, is the weight distribution coefficient when it is approximately the mean, is the weight distribution coefficient of the approximate covariance;

[0143] κ∈R, characterizes the degree of dispersion of Sigma points relative to the mean, R is a real number. The larger κ is, the farther the Sigma points at non-mean locations are from the mean, and the smaller their weights are. For Gaussian problems, κ=3-n. For non-Gaussian problems, adaptive parameters c,ε are introduced, with κ=c(n+ε). If the state distribution is highly non-Gaussian, increase the value of c to increase the number of Sigma points. If the state distribution is highly Gaussian, decrease the value of c to reduce the number of Sigma points.

[0144] 312) Weighted calculation of state quantity at time k The prior distribution of is as follows:

[0145]

[0146] in, is the prior estimate of the state quantity at time k, is the state quantity at time k,

[0147] is the prior estimate of the covariance of the state quantity at time k, are the weights of the state quantity mean and covariance of each Sigma point, is the variance of the system noise at time k;

[0148] 313) For the state quantity at time k Sigma point sampling and observations of the prior distribution The probability distribution of is as follows:

[0149]

[0150] in, is the prior estimate of the state quantity at time k, is the prior estimate of the covariance of the state quantity at time k, is the Gaussian white noise with zero mean and covariance R of the observed quantity, is the weight distribution coefficient of the approximate mean, 2n is the number of Sigma points, is the observed quantity at time k, is the weighted mean of the observations at time k;

[0151] 314) Calculate the mutual covariance between the state quantity and the observation quantity and the autocovariance of the observation quantity as follows:

[0152]

[0153] in, is the prior estimate of the state quantity at time k, is the state quantity at time k, is the cross-covariance of observations, is the observed autocovariance, is the weight distribution coefficient of the approximate mean square error, is the observed quantity at time k, is the weighted mean of the observations at time k, is the variance of the observation noise;

[0154] 315) Calculate the posterior estimate of the state quantity at time k, the Kalman gain, and the corresponding update steps as follows:

[0155]

[0156] Among them, K i is the Kalman gain of the i-th Sigma point, is the cross-covariance of observations, is the observed autocovariance, is the mean value of the state quantity at time k,

[0157] is the prior estimate of the state quantity at time k, z k is the value of the observation at time k, is the weighted mean of the observations at time k, is the estimated covariance of the state quantity at time k.

[0158] 32) Introduce the importance density function and calculate the importance weight of each particle. Let the importance density function (reference distribution) be:

[0159]

[0160] in, is the importance density function of the i-th particle;

[0161] Generate prediction particles by importance sampling, and sample from the importance density function to generate the prediction particles required for particle filtering:

[0162]

[0163] in, is the state value of the current particle, is the particle state sequence of the i-th particle from time 0 to k-1, z 1:k is the observation sequence from time 1 to k, and the importance density function is set to be a normal distribution are the mean and variance of the normal distribution respectively; suppose the initial weights of all particles are N is the total number of particles; based on the particle state at the previous time k-1, the particle state at the current time k is predicted; during the prediction process, according to the prediction importance density function Sample the particle state to obtain the observation data at time k. Update the weight of each particle based on the conditional probability density of the observation data and state data. The weight update formula is as follows:

[0164]

[0165] in, Observable In particles The likelihood function under the condition indicates the matching degree between the observed data and the particle state. is the likelihood function of the state quantity at time k under the condition of the state quantity at time k-1, which indicates the matching degree of the particle state before and after;

[0166] The importance weight obtained by formula (12) is normalized as follows:

[0167]

[0168] in, is the state of the i-th particle at time k, are the mean and covariance of the reference distribution of the importance density function, is the importance weight of the i-th particle at time k, is the normalized importance weight of the i-th particle at time k;

[0169] 33) Set the threshold N t =N / 3, determine the effective number of particles N e :

[0170]

[0171] in, is the normalized importance weight of the i-th particle at time k;

[0172] According to the set threshold, determine whether the statistics of the sample points are within the threshold range; for sample points that are not within the threshold range, resample and regenerate sample points until the threshold condition is met;

[0173] Resampling generally requires constructing a cumulative distribution function to generate a random index for each particle. The construction formula is as follows:

[0174]

[0175] Where F(i) is the i-th term of the cumulative distribution function, is the normalized weight of all particles in item i;

[0176] For each new particle, generate a uniform random number u in the range [0,1]. i, find the cumulative distribution function that satisfies F(i-1)<u i < index i of F(i), and then take the particle with index i in the original particle set as the new particle;

[0177] After resampling, the weights of all particles are reset to 1 / N to ensure that each particle has the same importance in the next prediction and update step;

[0178] 34) The weighted sum of the predicted particle set is used to output the state estimate. The formula is as follows:

[0179]

[0180] in, are weighted estimates of the state variables.

[0181] 4) Collect the true value of the center of mass side slip angle β during vehicle driving under different working conditions a and the true value of the yaw rate γ a The front wheel angle and longitudinal acceleration of the vehicle are used as training inputs, and the residual value Δx between the state quantity estimation result in step 3) and the true value of the sensor is obtained through BP neural network training and fitting. k ;

[0182] Wherein, the step 4) specifically includes:

[0183] 41) Determine the network topology (input layer - hidden layer - output layer), and choose a single hidden layer topology. Two types of signals are transmitted between different layers: one is the working signal, which is the multiple external input signals that pass through the hidden layer and then output the actual required signal at the output layer; the other is the error signal, which is the difference between the actual output signal and the predicted output signal in the BP neural network. It propagates backward from the output layer to each layer, and there is no interconnection between the same layers.

[0184] 42) Determine the Sigmond function to limit the range of neuron output and integrate the infinite range of possible outputs into the allowed output range. The Sigmond function expression is as follows:

[0185]

[0186] Among them, x is the input feature variable of the hidden layer or output layer, and e is the logarithmic function;

[0187] 43) The working signal propagates forward. The specific process is as follows: the BP neural network receives the input signal, the signal is weighted summed and then converted by the Sigmond function, and then processed by the hidden layer before reaching the output layer. The number of neurons in the output layer matches the number of targets in the problem. The output layer targets are the vehicle's center of mass sideslip angle and yaw rate.

[0188] The output of the i-th node in the input layer is x i ;

[0189] The input of the jth node in the hidden layer is NET j :

[0190]

[0191] The output of the jth node in the hidden layer is y j :

[0192]

[0193] The input of the kth node in the output layer is NET k :

[0194]

[0195] The output of the kth node in the output layer is y k :

[0196]

[0197] Among them, w ij is the connection weight between the i-th node in the input layer and the j-th node in the hidden layer, b j is the threshold of the jth node in the hidden layer, p is the number of nodes in the hidden layer, w jk is the connection weight between the jth node in the hidden layer and the kth node in the output layer, ξ k is the threshold at the kth node in the output layer, and s is the number of nodes in the output layer;

[0198] 44) Back propagation of error signals: Calculate the error between the actual output of the BP neural network data and the expected output of the sample data, and adjust the weights and thresholds of different layers according to the gradient descent method to make the modified neural network close to the expected output value;

[0199] For back propagation, the total error E between the BP neural network prediction value and the true value is set to:

[0200]

[0201] in, is the actual output of the network, for The corresponding expected output;

[0202] 45) iterating steps 43) to 44) in a loop, gradually reducing the calculation error until the error reaches the set target error or the number of loop iterations reaches the set maximum number;

[0203] 46) Obtaining optimal weights and thresholds;

[0204] 47) Fitting vehicle parameter errors: Using sensors to collect and calculate the vehicle's center of mass side slip angle β a and the expected value of the yaw rate γ a , the front wheel angle and longitudinal acceleration are used as the BP neural network input layer parameters, and after the working signal forward propagation process in step 43) above, the center of mass side slip angle β is obtained. k and the predicted value of yaw rate γ k After calculating the error between the predicted value and the expected value, the error is back-propagated according to the gradient descent method in step 44, and the weights and thresholds between each layer are continuously modified to obtain the optimal residual value output Δx k =[Δβ k Δγ k ].

[0205] Specifically, the step 44) includes two processes: the error is fed back from the output layer to the hidden layer and from the hidden layer to the input layer;

[0206] The error between the predicted value and the expected value of the BP neural network is fed back to the hidden layer from the output layer, and the weights and thresholds between the output layer and the hidden layer are adjusted accordingly;

[0207] Weight w jk Correction value Δw of (n) jk The expression for (n) is:

[0208]

[0209] Threshold ξ k Correction Δξ of (n) k (n) is expressed as:

[0210]

[0211] because:

[0212]

[0213] Arranging the above formulas (23)-(27) yields:

[0214]

[0215] The adjusted weight w jk (n+1) is expressed as:

[0216] w jk (n+1)=w jk (n)+Δw jk (n) (29)

[0217] Adjusted threshold ξk (n+1) is expressed as:

[0218] ξ k (n+1)=ξ k (n)+Δξ k (n) (30)

[0219] Among them, η is the learning efficiency, n is the number of back propagation times, P is the number of hidden layer nodes, S is the number of output layer nodes, w jk (n+1) is the connection weight between the jth node in the n+1th hidden layer and the kth node in the output layer, ξ k (n+1) is the threshold value of the kth node in the n+1th output layer, f2'(NET k ) is the conversion function between the input value of the hidden layer and the kth node of the output layer, NET k is the input of the kth node in the output layer, y j is the output of the jth node in the hidden layer, is the actual output of the BP neural network, for The corresponding expected output;

[0220] 442) Correct the correction weight and correction threshold from the hidden layer to the input layer;

[0221] Weight correction Δw between the input layer and the hidden layer ij The expression for (n) is:

[0222]

[0223] Threshold b j Correction value Δb of (n) j (n) is:

[0224]

[0225] because:

[0226]

[0227] The corresponding weight and threshold update process is:

[0228]

[0229] Among them, η is the learning efficiency, n is the number of back propagation times, P is the number of hidden layer nodes, S is the number of output layer nodes, w ij (n+1) is the connection weight between the jth node in the n+1th hidden layer and the ith node in the input layer, b j (n+1) is the threshold value at the jth node of the n+1th hidden layer, f1'(NET j) is the conversion function between the input value of the input layer and the jth node of the hidden layer, NET j is the input of the jth node in the hidden layer, y j (n) is the output of the jth node in the nth hidden layer, is the actual output of the network, for The corresponding expected output.

[0230] 5) The state estimation result obtained in step 3) and the residual value Δx obtained in step 4) are combined k As the actual output of the vehicle parameter prediction model

[0231] The present invention has many specific application paths. 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 can be made without departing from the principles of the present invention. These improvements should also be considered as the scope of protection of the present invention.

Claims

1. A vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter, characterized in that: Here are the steps: 1) Establish a three-degree-of-freedom vehicle dynamics model and determine the state equation and observation equation of the unscented Kalman filter based on the three-degree-of-freedom vehicle dynamics model; 2) determining the input quantity, state quantity and observation quantity of the unscented Kalman filter according to the dynamic model in step 1); 3) Combining the Monte Carlo sampling method and the adaptive weight distribution formula, the unscented Kalman filter is improved to obtain the state estimation result of the improved unscented Kalman filter 4) Collect the true value of the center of mass side slip angle β during vehicle driving under different working conditions a and the true value of the yaw rate γ a The front wheel angle and longitudinal acceleration of the vehicle are used as training inputs, and the residual value Δx between the state quantity estimation result in step 3) and the true value of the sensor is obtained through BP neural network training and fitting. k ; 5) The state estimation result obtained in step 3) and the residual value Δx obtained in step 4) are combined k As the actual output of the vehicle parameter prediction model 2. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 1, characterized in that: The motion equation of the three-degree-of-freedom vehicle dynamics model in step 1) is: in, is the first-order derivative of the vehicle's center of mass sideslip angle, is the first-order derivative of the vehicle’s yaw rate, is the first-order derivative of the vehicle's longitudinal velocity, β is the vehicle's center of mass sideslip angle, γ is the vehicle's yaw rate, and v x is the longitudinal speed of the vehicle, k1 and k2 are the front wheel cornering stiffness and the rear wheel cornering stiffness respectively, m is the vehicle mass, a and b are the distances from the center of mass to the front and rear axles of the vehicle respectively, δ f is the front wheel angle, I z is the moment of inertia of the vehicle around the z axis, a x is the vehicle longitudinal acceleration.

3. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 1, characterized in that: The state equation and observation equation of the unscented Kalman filter in step 1) are: Among them, the subscript k represents the kth moment, k-1 represents the k-1th moment, and x k|k-1 represents the state quantity at time k, z k|k-1 is the observed value at time k, w k-1 ~(0,Q) is Gaussian white noise with zero mean and covariance Q, v k-1 ~(0,R) is Gaussian white noise with zero mean and covariance R.

4. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 1, characterized in that: The step 2) specifically includes: selecting the front wheel angle and the vehicle longitudinal acceleration [δ f ,a x ] is the input; the sideslip angle β, yaw angular velocity ω r and longitudinal speed v x is the state quantity; lateral acceleration a y and yaw angular velocity ω r is the observed quantity.

5. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 1, characterized in that: The improvement of the unscented Kalman filter in step 3) specifically includes: 31) Filter initialization: When k = 0, based on the initial state variables, a particle set is generated in the initial distribution prior probability density p(x0) = N(x0, P0) P0 is the initial covariance matrix, and each particle is assigned an equal weight of 1 / N, where N is the number of particles; When k>0, the particle set at the previous moment is updated through the state equation and observation equation of the unscented Kalman filter in step 1) to obtain a new particle set at the current moment. The updated particle set is then used to approximate the posterior probability distribution at the current moment. The probability distribution of k at the current moment is described in the form of a weighted sum of particles. Specifically, the process includes: selecting an importance density function, generating prediction particles through importance sampling, calculating and normalizing the particle weights, determining whether resampling is required, and outputting the state estimation result. 32) Introduce the importance density function and calculate the importance weight of each particle. Let the importance density function be: in, is the importance density function of the i-th particle; Generate prediction particles by importance sampling, and sample from the importance density function to generate the prediction particles required for particle filtering: in, is the state value of the current particle, is the particle state sequence of the i-th particle from time 0 to k-1, z 1:k is the observation sequence from time 1 to k, and the importance density function is set to be a normal distribution are the mean and variance of the normal distribution respectively; suppose the initial weights of all particles are N is the total number of particles; based on the particle state at the previous time k-1, the particle state at the current time k is predicted; during the prediction process, according to the prediction importance density function Sample the particle state to obtain the observation data at time k. Update the weight of each particle based on the conditional probability density of the observation data and state data. The weight update formula is as follows: in, Observable In particles The likelihood function under the condition indicates the matching degree between the observed data and the particle state. is the likelihood function of the state quantity at time k under the condition of the state quantity at time k-1, which indicates the matching degree of the particle state before and after; The importance weight obtained by formula (5) is normalized as follows: in, is the state of the i-th particle at time k, are the mean and covariance of the reference distribution of the importance density function, is the importance weight of the i-th particle at time k, is the normalized importance weight of the i-th particle at time k; 33) Set the threshold N t =N / 3, determine the effective number of particles N e : in, is the normalized importance weight of the i-th particle at time k; According to the set threshold, determine whether the statistics of the sample points are within the threshold range; for sample points that are not within the threshold range, resample and regenerate sample points until the threshold condition is met; Resampling generally requires constructing a cumulative distribution function to generate a random index for each particle. The construction formula is as follows: Where F(i) is the i-th term of the cumulative distribution function, is the normalized weight of all particles in item i; For each new particle, generate a uniform random number u in the range [0,1]. i , find the cumulative distribution function that satisfies F(i-1)<u i < index i of F(i), and then take the particle with index i in the original particle set as the new particle; After resampling, the weights of all particles are reset to 1 / N to ensure that each particle has the same importance in the next prediction and update step; 34) The weighted sum of the predicted particle set is used to output the state estimate. The formula is as follows: in, are weighted estimates of the state variables.

6. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 5, characterized in that: In step 31), when k>0, the specific steps include: 311) Use unscented Kalman filtering to generate the importance density function for each particle and construct the 2n+1 Sigma point sampling distribution χ for each particle i And the weight distribution formula is: Where n is the dimension of the state quantity; λ is the scaling factor, λ = α 2 (n+κ)-n, α is a small positive value that determines the distribution of Sigma points; δ is a non-negative weight coefficient that can be used to combine the dynamic errors of high-order terms in the equation. is the state quantity of the i-th Sigma point at time k-1, is the covariance of the i-th Sigma at time k-1, is the weight distribution coefficient when it is approximately the mean, is the weight distribution coefficient of the approximate covariance; κ∈R, characterizes the degree of dispersion of Sigma points relative to the mean, R is a real number. The larger κ is, the farther the Sigma points at non-mean locations are from the mean, and the smaller their weights are. For Gaussian problems, κ=3-n. For non-Gaussian problems, adaptive parameters c,ε are introduced, with κ=c(n+ε). If the state distribution is highly non-Gaussian, increase the value of c to increase the number of Sigma points. If the state distribution is highly Gaussian, decrease the value of c to reduce the number of Sigma points. 312) Weighted calculation of state quantity at time k The prior distribution of is as follows: in, is the prior estimate of the state quantity at time k, is the state quantity at time k, is the prior estimate of the covariance of the state quantity at time k, are the weights of the state quantity mean and covariance of each Sigma point, is the variance of the system noise at time k; 313) For the state quantity at time k Sigma point sampling and observations of the prior distribution The probability distribution of is as follows: in, is the prior estimate of the state quantity at time k, is the prior estimate of the covariance of the state quantity at time k, is the Gaussian white noise with zero mean and covariance R of the observed quantity, is the weight distribution coefficient of the approximate mean, 2n is the number of Sigma points, is the observed quantity at time k, is the weighted mean of the observations at time k; 314) Calculate the mutual covariance between the state quantity and the observation quantity and the autocovariance of the observation quantity as follows: in, is the prior estimate of the state quantity at time k, is the state quantity at time k, is the cross-covariance of observations, is the observed autocovariance, is the weight distribution coefficient of the approximate mean square error, is the observed quantity at time k, is the weighted mean of the observations at time k, is the variance of the observation noise; 315) Calculate the posterior estimate of the state quantity at time k, the Kalman gain, and the corresponding update steps as follows: Among them, K i is the Kalman gain of the i-th Sigma point, is the cross-covariance of observations, is the observed autocovariance, is the mean value of the state quantity at time k, is the prior estimate of the state quantity at time k, z k is the value of the observation at time k, is the weighted mean of the observations at time k, is the estimated covariance of the state quantity at time k.

7. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 1, characterized in that: The step 4) specifically includes: 41) Determine the network topology and select a single hidden layer topology. Two types of signals are transmitted between different layers: one is the working signal, which is the multiple external input signals that pass through the hidden layer and then output the actual required signal at the output layer; the other is the error signal, which is the difference between the actual output signal and the predicted output signal in the BP neural network. It propagates backward from the output layer to each layer, and there is no interconnection between the same layers. 42) Determine the Sigmond function to limit the range of neuron output and integrate the infinite range of possible outputs into the allowed output range. The Sigmond function expression is as follows: Among them, x is the input feature variable of the hidden layer or output layer, and e is the logarithmic function; 43) The working signal propagates forward. The specific process is as follows: the BP neural network receives the input signal, the signal is weighted summed and then converted by the Sigmond function, and then processed by the hidden layer before reaching the output layer. The number of neurons in the output layer matches the number of targets in the problem. The output layer targets are the vehicle's center of mass sideslip angle and yaw rate. The output of the i-th node in the input layer is x i ; The input of the jth node in the hidden layer is NET j : The output of the jth node in the hidden layer is y j : The input of the kth node in the output layer is NET k : The output of the kth node in the output layer is y k : Among them, w ij is the connection weight between the i-th node in the input layer and the j-th node in the hidden layer, b j is the threshold of the jth node in the hidden layer, p is the number of nodes in the hidden layer, w jk is the connection weight between the jth node in the hidden layer and the kth node in the output layer, ξ k is the threshold at the kth node in the output layer, and s is the number of nodes in the output layer; 44) Calculate the error between the actual output of the BP neural network data and the expected output of the sample data, and adjust the weights and thresholds of different layers according to the gradient descent method to make the modified neural network close to the expected output value; For back propagation, the total error E between the BP neural network prediction value and the true value is set to: in, is the actual output of the network, for The corresponding expected output; 45) iterating steps 43) to 44) in a loop, gradually reducing the calculation error until the error reaches the set target error or the number of loop iterations reaches the set maximum number; 46) Obtaining optimal weights and thresholds; 47) Fitting vehicle parameter errors: Using sensors to collect and calculate the vehicle's center of mass side slip angle β a and the expected value of the yaw rate γ a , the front wheel angle and longitudinal acceleration are used as the BP neural network input layer parameters, and after the working signal forward propagation process in step 43) above, the center of mass side slip angle β is obtained. k and the predicted value of yaw rate γ k After calculating the error between the predicted value and the expected value, the error is back-propagated according to the gradient descent method in step 44, and the weights and thresholds between each layer are continuously modified to obtain the optimal residual value output Δx k =[Δβ k Δγ k ].

8. The vehicle parameter estimation method based on BP neural network and improved unscented Kalman filter according to claim 7, characterized in that: The step 44) specifically includes two processes: the error is fed back from the output layer to the hidden layer and from the hidden layer to the input layer; The error between the predicted value and the expected value of the BP neural network is fed back to the hidden layer from the output layer, and the weights and thresholds between the output layer and the hidden layer are adjusted accordingly; Weight w jk Correction value Δw of (n) jk The expression for (n) is: Threshold ξ k Correction Δξ of (n) k (n) is expressed as: because: Arranging the above formulas (23)-(27) yields: The adjusted weight w jk (n+1) is expressed as: In jk (n+1)=in jk (n)+Δw jk (n) (29) Adjusted threshold ξ k (n+1) is expressed as: x k (n+1)=ξ k (n)+Dx k (n) (30) Among them, η is the learning efficiency, n is the number of back propagation times, P is the number of hidden layer nodes, S is the number of output layer nodes, w jk (n+1) is the connection weight between the jth node in the n+1th hidden layer and the kth node in the output layer, ξ k (n+1) is the threshold value of the kth node in the n+1th output layer, f2'(NET k ) is the conversion function between the input value of the hidden layer and the kth node of the output layer, NET k is the input of the kth node in the output layer, y j is the output of the jth node in the hidden layer, is the actual output of the BP neural network, for The corresponding expected output; 442) Correct the correction weight and correction threshold from the hidden layer to the input layer; Weight correction Δw between the input layer and the hidden layer ij The expression for (n) is: Threshold b j Correction value Δb of (n) j (n) is: because: The corresponding weight and threshold update process is: Among them, η is the learning efficiency, n is the number of back propagation times, P is the number of hidden layer nodes, S is the number of output layer nodes, w ij (n+1) is the connection weight between the jth node in the n+1th hidden layer and the ith node in the input layer, b j (n+1) is the threshold value at the jth node of the n+1th hidden layer, f1'(NET j ) is the conversion function between the input value of the input layer and the jth node of the hidden layer, NET j is the input of the jth node in the hidden layer, y j (n) is the output of the jth node in the nth hidden layer, is the actual output of the network, for The corresponding expected output.

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