A high-precision redrawing and key parameter acceleration extrapolation method for vehicle lane-changing trajectory

Abstract

The application discloses a kind of vehicle lane-changing trajectory high-precision redrawing and key parameter acceleration extrapolation method, which comprises the following steps: obtaining the sampling data set of real-time dynamic driving scene;Filtering complete lane-changing scene of multi-vehicle interaction;Filtering pretreatment of original noisy data;Based on midpoint step-by-step lane-changing assumption, construct lane-changing trajectory model, take the time when crossing lane line as node, segment modeling for lane-changing process, based on the lane-changing trajectory model of horizontal and vertical decoupling, carry out trajectory feature parameter identification, mine trajectory feature parameter distribution law, condense lane-changing scene parameter distribution characteristics;Based on Gaussian mixture model, extract lane-changing scene parameter distribution characteristics, propose joint probability model of scene multidimensional parameters;Extract lane-changing scene distribution gradient information;Carry out Hamilton monte carlo sampling;Form lane-changing acceleration test scene library.The application realizes dimensionality reduction and high-precision redrawing of lane-changing trajectory, completes key scene parameter extrapolation and the construction of high-precision and efficient lane-changing acceleration test scene library.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent driving simulation, in particular to a vehicle lane-changing trajectory high-precision redrawing and key parameter acceleration extrapolation method. BACKGROUND

[0002] It is of great significance to develop and apply intelligent driving systems to build a high-precision and efficient acceleration simulation test scene library. In recent years, in order to further improve the test efficiency, the concept of acceleration test has been gradually applied to the virtual simulation test of intelligent driving systems. In addition to fully utilizing computer computing power through parallel testing, it is also necessary to develop effective methods to improve test efficiency, such as reducing the parameter dimension of the test scene, using a small number of representative scenes to reduce the number of test scenes, etc. However, reducing the parameter dimension also reduces the data accuracy, which inevitably brings bias to the test results, and it is difficult to balance between reducing the number of scenes and ensuring the coverage of the scenes.

[0003] Lane changing is one of the most basic driving conditions, which has higher risk than following conditions, and is the focus of simulation test. To build a lane-changing acceleration simulation test scene library, firstly, the parameter dimension needs to be reduced. The traditional decoupling planning assumes that the longitudinal velocity is constant, which is applicable to a small number of conditions, and can maintain a certain accuracy when fitting the lane-changing trajectory in natural driving data, but loses the characteristics of the actual lane-changing trajectory. The integrated trajectory planning method assumes a lane-changing trajectory model, with the coupling of lateral velocity, longitudinal velocity and lane-changing time, which overall meets the expectations of safety and comfort of the driver, i.e. retains certain driving style characteristics, but the accuracy is greatly lost. Secondly, a small number of scenes are needed to represent natural driving data, i.e. the distribution of the scene library composed of a small number of scenes is highly close to the distribution of the natural driving data set, so as to ensure the credibility of the test results.

[0004] The traditional lane-changing trajectory longitudinal uniform speed assumption or uniform acceleration assumption sets the longitudinal velocity unchanged or the vehicle uniformly accelerated during the cut-in process, and determines the lane-changing time and the whole lane-changing process. It is further believed that the occurrence of a collision event is also determined. Since the longitudinal motion is greatly simplified, the lane-changing scene constructed is close to the following scene to some extent, and the longitudinal motion becomes the main factor affecting the test results. The longitudinal characteristics of the lane-changing trajectory are lost due to the uniform speed or uniform acceleration assumption, which interferes with the test results. Moreover, since the longitudinal motion of the vehicle is assumed to be uniform or uniformly accelerated, this lane-changing trajectory model cannot restore the behavior of the driver in the lane-changing process to ensure safety or comfort. The redrawn trajectory cannot reflect the driving behavior of the actual lane-changing trajectory. Although such technology ensures the unbiasedness of the test results through various proxy models in the subsequent sampling process, the credibility of the specific scene will lead to the unreliability of the single test result, and also seriously restricts the efficiency of the acceleration test and reduces the credibility of the test results.

[0005] The conventional integrated lane-changing trajectory model is fitted according to a real trajectory by presetting a lane-changing trajectory model such as a quintic polynomial, a Bezier curve or a segmented function combined by multiple curves, and obtaining the redrawn lane-changing trajectory by taking the lane-changing duration or lateral acceleration as the model input. The use of a curve function to fit the real trajectory leads to the coupling of the lateral and longitudinal motions of the lane-changing trajectory, that is, the longitudinal velocity, the lateral velocity and the lane-changing duration are coupled, and the trajectory model has weak generalization ability. Moreover, since the lane-changing trajectory is a certain curve set in advance, the lateral velocity, the longitudinal velocity and the lane-changing duration of the vehicle during the lane-changing process are coupled with each other. When used for trajectory planning, this kind of method can simply and efficiently output a suitable lane-changing curve, but when used for trajectory redrawing, the lane-changing trajectory often has the characteristics of sudden acceleration or sudden deceleration in the lateral or longitudinal direction in the face of edge scenarios, especially dangerous scenarios, and a large error will be generated when the curve fitting is used. Therefore, when used for scenario library construction, this kind of technology has low fitting precision and weak generalization ability, and is not convenient for edge scenario extrapolation.

[0006] Therefore, how to reduce the dimension of the scenario parameters while improving the lane-changing trajectory redrawing precision and improving the test efficiency while ensuring the representativeness of the scenario is a problem to be solved. SUMMARY

[0007] In order to overcome the defects and deficiencies existing in the prior art, the present application provides a vehicle lane-changing trajectory high-precision redrawing and key parameter acceleration extrapolation method. The present application first establishes a lane-changing trajectory model based on the midpoint step assumption, segmentally models the lane-changing trajectory, establishes a high-precision lane-changing trajectory, reduces the dimension of the data set while ensuring the data precision, further proposes to use a Gaussian mixture model to fit the distribution characteristics of the scenario samples, and uses a Monte Carlo sampling method considering Hamilton dynamics to establish a lane-changing scenario library conforming to the real driving scenario, reduces the number of scenarios required for testing while ensuring the scenario coverage, can well serve the acceleration simulation test of the intelligent driving system and the development, training and deployment of the intelligent driving system, and realizes high-precision redrawing of the lane-changing trajectory of the target vehicle in a complex dynamic traffic scenario and acceleration extrapolation of the scenario by using related key parameters.

[0008] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0009] The present application provides a vehicle lane-changing trajectory high-precision redrawing and key parameter acceleration extrapolation method, comprising the following steps:

[0010] Obtaining the sampling data set of the driving scenario by acquiring the scenario parameters in the natural driving condition;

[0011] Screening the complete lane-changing scenario in the complex dynamic traffic scenario from the sampling data set;

[0012] Data preprocessing is performed on the screened sampling data set;

[0013] A lane-changing trajectory model is constructed based on a lane-changing midpoint step assumption, a lane-changing process is modeled by taking a lane-crossing moment as a node, and the lane-changing process is segmented;

[0014] Real trajectory data is obtained, real lane-changing trajectory parameters that meet a set accuracy requirement are fitted based on the lane-changing trajectory model, and a lane-changing scene parameter distribution feature is obtained by counting the lane-changing trajectory parameter distribution.

[0015] A Gaussian mixture model is used to fit the lane-changing scene parameter distribution feature, and an expectation maximization is used to estimate the Gaussian mixture model parameters to obtain a joint probability distribution of multi-dimensional parameters.

[0016] The distribution gradient information of the lane-changing scene is extracted.

[0017] A Hamiltonian dynamics model is constructed and Hamiltonian Monte Carlo sampling is performed.

[0018] An MH acceptance condition is used to determine whether to accept the Hamiltonian Monte Carlo sampling sample, if the sampling is accepted, the scene parameters of the accepted sample are stored as an acceleration test scene library, the parameter distribution features of the acceleration test scene library are counted and compared, and a final lane-changing acceleration test scene library is constructed.

[0019] As a preferred technical solution, the lane-changing trajectory model is constructed based on the lane-changing midpoint step assumption, and specifically includes:

[0020] The longitudinal and lateral motion of the vehicle during the lane-changing process is decoupled and modeled, the driving direction of the road is set as the longitudinal direction, and the direction perpendicular to it is set as the lateral direction, a longitudinal motion model and a lateral motion model of the vehicle during the lane-changing process are constructed.

[0021] The longitudinal motion model of the vehicle during the lane-changing process is represented as:

[0022]

[0023] Where x(t) is the longitudinal coordinate of the vehicle at time t, v x0 is the longitudinal speed of the vehicle at the start of the lane-changing process, a x1 , a x2 are the longitudinal accelerations before and after the vehicle crosses the lane line, T cross is the lane-changing time of the vehicle, and T is the total lane-changing time of the vehicle.

[0024] The lateral motion model of the vehicle during the lane-changing process uses a piecewise quintic polynomial model, the lane-changing starting point, the lane-crossing coordinate point, and the lane-changing endpoint are taken as boundary conditions, and quintic polynomial interpolation is performed on the two segments of the trajectory before and after crossing the lane line.

[0025] As a preferred technical solution, the quintic polynomial coefficients in the quintic polynomial interpolation are expressed as:

[0026]

[0027] Wherein, h=y1-y0, y0, v y0 , a y0 are the vehicle transverse coordinates, transverse speed, transverse acceleration at the starting time, respectively, y1, v y1 , a y1 are the vehicle transverse coordinates, transverse speed, transverse acceleration at the end time, respectively, and T is the time length.

[0028] As a preferred technical solution, the real lane-changing trajectory based on the lane-changing trajectory model fitting is set to obtain the trajectory feature parameters, specifically including:

[0029] Real trajectory data is obtained, and a random feature number is used as the iteration starting point of the optimization algorithm, and the feature parameters for representing the lane-changing trajectory are obtained after iteration, the optimization algorithm adopts any one of the linear least square method, the nonlinear least square method and the robust regression algorithm, and the feature parameters for representing the lane-changing trajectory include the longitudinal speed at the starting time of vehicle lane-changing, the longitudinal acceleration before and after crossing the lane line, the quintic polynomial coefficient and the lane-changing time length.

[0030] As a preferred technical solution, the distribution rule of the trajectory feature parameters is obtained by statistics, and the lane-changing scene parameter distribution characteristics are obtained, specifically including:

[0031] The distribution characteristics of the lane-changing trajectory feature parameters are counted, including the maximum value, the minimum value, the average value, the median, the 25% quantile, the 75% quantile, the 3σ value, and the frequency of each value;

[0032] The scene safety agent index is calculated, including the predicted collision time, the vehicle head time, the reverse collision time and the corrected collision time;

[0033] The distribution characteristics of the scene parameters except the lane-changing trajectory feature parameters are counted, including the maximum value, the minimum value, the average value, the median, the 25% quantile, the 75% quantile, the 3σ value, and the frequency of each value;

[0034] The trajectory feature parameters of left lane-changing and right lane-changing are counted respectively.

[0035] As a preferred technical solution, the lane-changing scene parameter distribution characteristics are fitted based on the Gaussian mixture model, the Gaussian mixture model parameters are estimated with the expectation maximization as the target, and the specific steps include:

[0036] Based on the Bayesian information criterion, the optimal Gaussian mixture model parameters are obtained as the final model parameters according to comparison among the number of model parameters, the number of samples and the likelihood function, and the calculation formula of the Bayesian information criterion is represented as:

[0037] BIC = -2log(l) + klog(n)

[0038] Wherein, k is the number of GMM model parameters, n is the number of data points, and l is the likelihood function value of GMM model.

[0039] The Gaussian mixture model is a linear combination of multiple normal distribution functions, and the expression of a single multi-dimensional normal is:

[0040]

[0041] The Gaussian mixture model is composed of multiple multi-dimensional normal distribution weighted, and is represented as:

[0042]

[0043] Wherein, α j After completing the fitting, the optimal GMM model is determined by using BIC.

[0044] The likelihood function of a single normal distribution is represented as:

[0045]

[0046] The corresponding Gaussian mixture model is established for the left lane changing data and the right lane changing data respectively.

[0047] As a preferred technical solution, the lane changing scene distribution gradient information is extracted, specifically including:

[0048] Based on the Gaussian mixture model, the potential energy and gradient calculation formula of the distribution model is derived, and the negative log-likelihood function is used as the potential energy function of the model, which is represented as:

[0049]

[0050] Wherein, y is the probability density function of x in the Gaussian mixture distribution model.

[0051] As a preferred technical solution, the Hamiltonian dynamics model is constructed and Hamiltonian Monte Carlo sampling is performed, specifically including:

[0052] The system dynamics equation composed of kinetic energy and potential energy is constructed, which is represented as:

[0053] H(x, p) = U(x) + K(p)

[0054] Wherein, H is the total energy of the system, U is the sample potential energy determined by the sample point x, K is the sample kinetic energy about momentum p, H(x, p) remains unchanged in the absence of external energy input, namely:

[0055]

[0056] The continuous Hamilton system is discretized and represented as:

[0057]

[0058] Wherein, epsilon is the step size, The gradient of the potential energy function U of the sample x at time t, after L times of circulation, the sample point is sampled.

[0059] As a preferred technical solution, the MH acceptance condition is used to judge whether to accept the Hamilton Monte Carlo sampling sample, and specifically includes:

[0060] The Metropolis-Hasting method is used for each sample point obtained after L times of circulation to determine whether to accept or reject the sample, which is represented as:

[0061]

[0062] Wherein, The updated sample point is H(x n-1 ,p n-1 ) is the last sampled sample point, and the acceptance rate rho is adjusted by adjusting the step size epsilon and the number of steps L.

[0063] As a preferred technical solution, the sampling method is replaced by a Markov Monte Carlo sampling method, which is represented as:

[0064]

[0065] Wherein, f(x) is the target function, theta is the integral on the interval, p(x) is the probability distribution of variable x in the interval, n is the sampling number, and the sample is obtained by using the Markov chain for sampling.

[0066] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0067] (1) The present application divides the lane changing process into two segments and models them respectively with the lane changing midpoint as the dividing point, uses the proposed model to fit the lane changing trajectory and represents the lane changing trajectory with model parameters, realizes dimension reduction and high-precision redrawing of the lane changing trajectory, and solves the problem that the traditional lane changing trajectory model has low redrawing precision, weak generalization ability and cannot meet the high-precision requirement of scene parameters in virtual simulation test.

[0068] (2) The application uses Gaussian mixture model to fit the distribution of natural driving data samples according to the lane-changing trajectory feature parameters and surrounding vehicle information in the lane-changing scene, and introduces a Monte Carlo sampling method based on Hamilton dynamics on the basis of the distribution characteristics, uses a small amount of high-precision samples to represent the lane-changing scene characteristics in the natural driving condition, realizes the extrapolation of key scenes and the construction of a high-precision and efficient lane-changing acceleration test scene library, and solves the problems of sparse dangerous scene and lack of collision scene in the natural driving data set, and the problem that it is difficult to consider the extrapolation of edge scenes and ensure the authenticity of the scene library when constructing the scene library. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 It is a flowchart of the vehicle lane-changing trajectory high-precision redrawing and key parameter acceleration extrapolation method of the application;

[0070] Figure 2 It is a lane-changing scene diagram;

[0071] Figure 3 It is a vehicle lane-changing trajectory sample diagram;

[0072] Figure 4 (a) is a histogram distribution diagram of the longitudinal speed of the lane-changing vehicle Car0 at the initial time of lane-changing;

[0073] Figure 4 (b) is a histogram distribution diagram of the longitudinal relative speed of the lane-changing vehicle Car0 and the front vehicle Car3 of the lane-changing target lane at the initial time of lane-changing;

[0074] Figure 4 (c) is a histogram distribution diagram of the longitudinal relative distance of the lane-changing vehicle Car0 and the front vehicle Car3 of the lane-changing target lane at the initial time of lane-changing;

[0075] Figure 4 (d) is a histogram distribution diagram of the lane-changing time of the lane-changing vehicle Car0;

[0076] Figure 4 (e) is a histogram distribution diagram of the average longitudinal acceleration of the lane-changing vehicle Car0;

[0077] Figure 4 (f) is a histogram distribution diagram of the average lateral acceleration of the lane-changing vehicle Car0;

[0078] Figure 5 (a) is a comparison diagram of the original trajectory and the modeled trajectory based on the implementation method of the application;

[0079] Figure 5 (b) is a comparison diagram of the original trajectory and the modeled trajectory based on the traditional implementation method;

[0080] Figure 6Gaussian mixture model Bayesian information criterion data comparison diagram of the application;

[0081] Figure 7 Gaussian mixture model parameter diagram selected by the application;

[0082] Figure 8 Gaussian mixture model partial parameter edge distribution diagram selected by the application;

[0083] Figure 9 (a) is a longitudinal speed sample distribution, sampling distribution, model distribution comparison diagram of a lane-changing vehicle Car0 at a lane-changing initial moment;

[0084] Figure 9 (b) is a longitudinal relative speed sample distribution, sampling distribution, model distribution comparison diagram of a lane-changing vehicle Car0 and a front vehicle Car3 of a lane-changing target lane at a lane-changing initial moment;

[0085] Figure 9 (c) is a longitudinal relative distance sample distribution, sampling distribution, model distribution comparison diagram of a lane-changing vehicle Car0 and a front vehicle Car3 of a lane-changing target lane at a lane-changing initial moment;

[0086] Figure 9 (d) is a lane-changing duration sample distribution, sampling distribution, model distribution comparison diagram of a lane-changing vehicle Car0;

[0087] Figure 9 (e) is a lane-changing average longitudinal acceleration sample distribution, sampling distribution, model distribution comparison diagram of a lane-changing vehicle Car0;

[0088] Figure 9 (f) is a lane-changing average lateral acceleration sample distribution, sampling distribution, model distribution comparison diagram of a lane-changing vehicle Car0. DETAILED DESCRIPTION

[0089] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application.

[0090] EMBODIMENT

[0091] The embodiment provides a vehicle lane-changing trajectory high-precision redrawing and key parameter acceleration extrapolation method, which comprises the following steps:

[0092] First, the scene-related parameters in natural driving are collected by vehicle-mounted sensors or roadside sensors. In this embodiment, a double-lane four-vehicle scene is preferred, the lane-changing vehicle is the target vehicle, i.e., the ego vehicle, and the other vehicles are background vehicles. The target recognition algorithm and related modules are used to obtain information including the lateral and longitudinal speed, acceleration, vehicle headway, vehicle length and width, lane width, and the like of the ego vehicle and surrounding vehicles.

[0093] Second, the lane-changing scenes in the data set are screened. Defining that the ego vehicle changes lanes from the current lane to the target lane and keeps the lane unchanged for 5s after lane changing as a lane change, the surrounding vehicles include the front vehicle in the original lane and the front and rear vehicles in the target lane, the perception range is 200m, and the time window is a certain period of time before the start of lane changing to the end of lane changing.

[0094] Third, the screened data is preprocessed to reduce noise and exclude outliers. The noise and outliers include but are not limited to noise caused by target recognition or data acquisition modules and data with large errors. After excluding abnormal data, noise reduction can be performed by means such as moving average filtering and symmetric exponential moving filtering, and finally the scene data is smoothed, wherein the logarithmic exponential moving filtering expression is shown in equation (1):

[0095]

[0096] In equation (1), x α (t k ) is the original data of vehicle a at sampling time k, is the smoothed data, N α is the total number of a sample points, T represents the time span of smoothing operation, dt represents the time interval between each frame, and i represents the i-th time of filtered data.

[0097] Fourth, a lane-changing trajectory model based on midpoint step-by-step assumption is established. Since there are various driving scenes and the lane-changing time is variable, the size of the lane-changing trajectory data is not consistent, which brings difficulties to data processing. By establishing a lane-changing trajectory model, the lane-changing trajectory can be represented using a small number of parameters, reducing the data dimension, which is helpful for the establishment of the scene library and subsequent research. The present application is aimed at the lane-changing characteristics of highway scenes, and the lateral and longitudinal motion of the vehicle during lane changing is decoupled and modeled. The driving direction of the road is defined as the longitudinal direction, and the direction perpendicular to it is the lateral direction, such as Figure 2As shown, the scenario of the lane changing process is simulated, the lane changing process is divided into two segments with the moment when Car0 crosses the lane line as the initial lane changing moment, in the first segment of the lane changing process, the driver needs to adjust the longitudinal speed of the vehicle in order to control the distance from Car1 and Car2 so as to obtain sufficient longitudinal distance to realize safe lane changing; in the second segment, the distance from Car2 and Car3 is mainly paid attention to to ensure safety, therefore, the control target of the driver to the vehicle is different in the two segments of the lane changing process, the lateral and longitudinal acceleration of the vehicle is different, and the vehicle needs to be modeled in segments so as to better restore the operation of the driver in the driving data set.

[0098] For the longitudinal motion of the lane changing vehicle, the present application proposes to use a segmented uniform acceleration model. It is assumed that the vehicle moves at different acceleration (deceleration) speeds before and after lane changing, and the nonlinear least squares method is used to fit the model parameters to obtain a model representing the longitudinal motion of the vehicle during lane changing. The longitudinal motion model of the vehicle during lane changing is shown in formula (2):

[0099]

[0100] Wherein, x(t) is the longitudinal coordinate of the vehicle at time t, v x0 is the longitudinal speed of the vehicle at the starting moment of lane changing, a x1 , a x2 are the longitudinal acceleration before and after the vehicle crosses the lane line, T cross is the defined lane changing moment of the vehicle, and T is the total lane changing time length.

[0101] For the lateral motion of the lane changing vehicle, the present application uses a segmented quintic polynomial model. The starting point of lane changing, the coordinate point of crossing the lane line, and the end point of lane changing are taken as boundary conditions, and the trajectories before and after crossing the lane line are respectively interpolated by quintic polynomials. The calculation of the quintic polynomial coefficients is shown in formula (3).

[0102]

[0103] Wherein, h=y1-y0, y0, v y0 , a y0 are the lateral coordinate, lateral speed and lateral acceleration of the vehicle at the starting moment, y1, v y1 , a y1 are the lateral coordinate, lateral speed and lateral acceleration of the vehicle at the end point, and T is the time length.

[0104] Fifth step, according to the model fitting real lane change trajectory to get the trajectory characteristic parameters and verify the trajectory accuracy. First, get the real trajectory data, and use the random characteristic number as the iterative starting point of the algorithm, the algorithm can be linear least square method, nonlinear least square method, robust regression and other optimization algorithms, after iteration, get the characteristic parameters used to represent the lane change trajectory, including the longitudinal velocity at the starting time of lane change, the longitudinal acceleration before and after crossing the lane line, the quintic polynomial coefficient and the lane change duration. After completing the fitting, compare whether the longitudinal, lateral and comprehensive root mean square error (RMSE) of the obtained trajectory and the real trajectory is within the acceptable range. The calculation method of lateral and longitudinal root mean square error is shown in formula (4).

[0105]

[0106] Where m is the total number of samples, x i is the i-th longitudinal coordinate real value, is the i-th longitudinal coordinate predicted value, y i is the i-th lateral coordinate real value, is the i-th lateral coordinate predicted value. If the fitting result is accepted, proceed, otherwise go back to the fourth step, change the lane change time T cross defined in formula (2) to a certain time before or after the originally defined lane change time, and re-fit.

[0107] Sixth step, trajectory characteristic parameter distribution statistics. Statistics of the lane change trajectory characteristic parameters obtained in the fifth step, including maximum value, minimum value, average value, median, 25% quantile, 75% quantile, 3σ value, and the frequency of each value, etc. The data of left lane change and right lane change are counted respectively to avoid the sampling difficulty problem caused by bimodal distribution.

[0108] Seventh step, statistics of the distribution characteristics of the remaining scene parameters. Statistics of the distribution characteristics of the scene parameters other than the lane change trajectory characteristic parameters obtained in the fifth step, including maximum value, minimum value, average value, median, 25% quantile, 75% quantile, 3σ value, and the frequency of each value; at the same time, calculate the scene safety proxy indicators according to the parameters in the sixth step, including but not limited to predicted collision time, vehicle headway, inverse collision time, enhanced collision time, etc. The data of left lane change and right lane change are counted respectively to avoid the sampling difficulty problem caused by bimodal distribution.

[0109] In the eighth step, a Gaussian mixture model is used to model the distribution of the key parameters of the lane-changing scene, and the parameters obtained in the sixth and seventh steps are integrated to obtain the parameter distribution characteristics of the lane-changing scene. The Gaussian mixture model is used to fit the statistical characteristics of the lane-changing scene parameters. The expectation maximization method is used to estimate the parameters of the Gaussian mixture model to obtain the joint probability distribution of the multi-dimensional parameters. The Bayesian information criterion (BIC) is used to compare the number of model parameters, the number of samples, and the likelihood function to obtain the optimal Gaussian mixture model parameters as the final model parameters. The calculation method of the Bayesian information criterion is shown in equation (5).

[0110] BIC = -2log(l) + klog(n) (5)

[0111] where k is the number of GMM model parameters, n is the number of data points, and l is the likelihood function value of the GMM model.

[0112] The Gaussian mixture model is a linear combination of multiple normal distribution functions, which theoretically has the ability to fit any type of distribution. The expression of a single multi-dimensional normal distribution is shown in equation (6).

[0113]

[0114] where X is a vector of length d, μ is a distribution mean vector of length d, and Σ is a d-dimensional covariance matrix.

[0115] The Gaussian mixture model used in this embodiment is composed of multiple multi-dimensional normal distributions represented by equation (6) and weighted as shown in equation (7):

[0116]

[0117] where α j represents the jth multi-dimensional after completing the fitting, the BIC is used to determine the optimal GMM model.

[0118] The likelihood function calculation formula of a single normal distribution is shown in equation (8).

[0119]

[0120] where x i is the ith variable, μ is the mean of the normal distribution, and σ is the variance of the normal distribution.

[0121] In view of the different characteristics of left and right lane changing, the data is divided into left lane changing data and right lane changing data, and corresponding Gaussian mixture models are established.

[0122] Step 9, scene distribution gradient information extraction. Before the edge parameter extrapolation, the gradient information of the model distribution needs to be obtained. According to the Gaussian mixture model obtained in step 8, the potential energy and gradient calculation formula of the distribution model are derived. The negative log-likelihood function is used as the potential energy function of the model, and the model potential energy calculation formula obtained is shown in equations (9) and (10).

[0123]

[0124] where y is the probability density function of x in the Gaussian mixture distribution model.

[0125] In this embodiment, the sampling method of equations (11) to (13) can also be replaced by the Markov Monte Carlo sampling method, as shown in the following formula:

[0126]

[0127] Step 10, establish Hamiltonian dynamics model and perform Hamiltonian Monte Carlo sampling. A plurality of sets of scene parameters are obtained by sampling the scene parameter Gaussian mixture model established in step 8, and the sampling method is Hamiltonian Monte Carlo (HMC) sampling. The HMC method is an improved Markov Chain Monte Carlo (MCMC) method, which describes the motion process of the sampling point by constructing a Hamiltonian dynamics equation, so that the sampling process converges faster to the target distribution. First, the system dynamics equation composed of kinetic energy and potential energy is constructed, as shown in equation (11):

[0128] H(x,p)=U(x)+K(p)(11)

[0129] where H is the total energy of the system, U is the sample potential energy determined by the sample point x, and K is the sample kinetic energy with respect to the momentum p. In the absence of external energy input, H(x,p) remains unchanged, that is:

[0130]

[0131] The continuous Hamiltonian system is discretized by using the "Leapfrog" method, and a complete step is shown in equation (13):

[0132]

[0133] where ε is the step size, The gradient of the potential energy function U of the sample x at time t is sampled after the step is repeated L times. As can be seen from formulas (9), (10), (11), (12), and (13), when the sampling point is in a high-probability region of the probability distribution function, the potential energy is large and the kinetic energy is small, and the sampling is performed in the high-probability region with a small step size. When the sampling point is in a low-probability region, the potential energy is small and the kinetic energy is large, and the sampling is performed with a large step size, so as to gradually return to the high-probability region, and the probability distribution function is approximated with a small number of samples.

[0134] In the tenth step, it is judged whether the sample in the ninth step is accepted or not by using the MH acceptance condition. The rejection-acceptance sampling method is the key to constructing the accelerated test scenario library and carrying out the accelerated test. By rejecting the samples with high similarity to the existing samples, the scenario library only needs to use a small number of samples to represent the real driving environment, so as to improve the test efficiency while ensuring the authenticity of the test results and the scenario coverage. The Metropolis-Hasting method is used to determine whether to accept or reject the sample point obtained after each cycle, as shown in formula (14).

[0135]

[0136] wherein, is the updated sample point, H(x n-1 ,p n-1 is the sample point sampled last time. The acceptance rate p can be adjusted by adjusting the step size e and the number of steps L. If the sampling result is accepted, proceed to the next step, otherwise, return to the tenth step to continue sampling.

[0137] In the twelfth step, the distribution characteristics of the scenario library are counted and compared. The scenario parameters of the sample accepted in the eleventh step are stored as the accelerated test scenario library, the parameter distribution characteristics of the accelerated test scenario library are counted, and the accelerated test scenario library is composed. The original scenario number, the scenario number of the traditional Monte Carlo sampling method under different sampling times, the scenario number of the Markov Monte Carlo sampling method, and the effective scenario number of the method are compared, and the Gaussian mixture distribution model obtained in the eighth step is compared. The comparison parameters include but are not limited to KL divergence, JS divergence, mean, peak value, etc. The formulas of the KL divergence and the JS divergence are shown in formulas (15) and (16).

[0138]

[0139] wherein, p(x) is the original scenario distribution, and q(x) is the scenario library distribution obtained by sampling.

[0140] Thirteenth step, establish the lane change acceleration test scene library. After proving the effectiveness of the method for constructing the lane change acceleration test scene library in the twelfth step, further compare the divergence and effective scene number of the scene library obtained under different sampling times, so as to select the most suitable sampling times of the input data in the first step, and establish the most efficient lane change acceleration test scene library.

[0141] The embodiment takes the natural driving data of German autobahn collected by using the highD data set as the original data as an example to illustrate the effectiveness and accuracy of the lane change trajectory high-precision redrawing and key parameter acceleration extrapolation method proposed in the application in the complex dynamic traffic scene, as follows:

[0142] First, the lane change data in the data set is screened, and the screening rule is that the target vehicle only performs one continuous lane change, and the surrounding vehicles include the front vehicle of the original lane of the target vehicle and the front and rear vehicles of the target lane within a distance of 200 m. As shown in Figure 3 , the lane change trajectory sample obtained after screening from the data set and preprocessed by using the average moving filter is shown.

[0143] The partial scene feature parameters of all lane change scene samples of the HighD data set are counted, and the histogram distribution diagram is obtained as shown in Figure 4 .

[0144] Figure 5 As shown in the figure, the fourth and fifth steps are processed to obtain the modeled trajectory. It can be seen that when there is a certain change in the original data trajectory, the traditional method is difficult to guarantee the accuracy of the redrawing trajectory, while the method proposed in the application redraws the original trajectory with high precision while using similar number of parameters, and guarantees the authenticity of the lane change scene sample.

[0145] As shown in Table 1 below, the longitudinal, lateral and comprehensive root mean square errors (RMSE) of the modeled trajectory are 0.0962, 0.0494 and 0.0814 respectively, the data with an error of less than 1 m accounts for 99.89%, and the data with an error of less than 0.2 m accounts for 95.12%. It can be considered that the lane change trajectory redrawing method proposed in the application can effectively represent the lane change trajectory in the autobahn scene, and the high-precision expression of the lane change trajectory is realized by using less data, which is helpful for the establishment of the high-precision and efficient lane change acceleration simulation test scene library.

[0146] Table 1 Trajectory redrawing error table

[0147]

[0148] Based on the data obtained in steps six and seven, z-score normalization was performed, and the Gaussian mixture distribution fitting function `fitgmdist` in MATLAB was used for fitting. The component k was set to 1 to 20, and the regularization coefficient was 0.01. Four combinations of covariance type and shared covariance were set, resulting in 80 sets of fitting results, as shown below. Figure 6 As shown, the Bayesian Information Criterion (BIC) data comparison yielded 80 sets of fitting results.

[0149] Choose the Full-unshared combination when k=5, such as Figure 7 As shown, the obtained parameter mean and covariance matrix;

[0150] like Figure 8 The marginal distribution of the model is shown in the figure, which is plotted based on the model parameters. It can be seen that the distribution of the model fit basically conforms to the data characteristics of the HighD highway natural driving dataset.

[0151] The HMC sampling algorithm was written using programming software. First, based on the Gaussian mixture model used in step eight, the corresponding Hamiltonian dynamic equations were constructed, namely H(x), U(x), and dU(x). Then, a "frog-jump" algorithm was built, using a random number generation function to select the sampling starting point and performing "frog-jump" sampling with a variable step size under a fixed step size. Finally, the MH acceptance condition algorithm required for step eleven was constructed. If the sample sampled in step ten is similar to the previously sampled samples, i.e., conforms to the existing sample distribution, then the sample is rejected, and sampling continues from that sample as the starting point. This process is repeated until the set number of samplings is reached.

[0152] The accepted samples are stored as a lane-change acceleration test scenario library. For example... Figure 9 As shown, the sample distribution fitted by the Gaussian mixture distribution and the sample distribution obtained by the Hamilton Monte Carlo sampling method are obtained. After 1000 samplings, the number of sampled samples is 561, and the original number of samples in the experiment is 3482. It can be seen that the sampling method used in this invention can well use a small number of samples to characterize the distribution characteristics of real data, and can effectively improve the efficiency of intelligent driving system acceleration testing.

[0153] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters, characterized in that, Includes the following steps: Obtain scene parameters under natural driving conditions to obtain a sampled dataset of driving scenarios; Filter complete lane-changing scenarios under complex dynamic traffic conditions in the sampled dataset; Data preprocessing is performed on the filtered sampled dataset; Based on the assumption of a midpoint in lane change, a lane change trajectory model is constructed, and the lane change process is segmented and modeled with the moment of crossing the lane line as the node. Acquire real trajectory data, fit the real lane change trajectory that meets the set accuracy requirements based on the lane change trajectory model to obtain trajectory feature parameters, and statistically analyze the distribution pattern of trajectory feature parameters to obtain the parameter distribution characteristics of the lane change scenario; The parameter distribution characteristics of the lane-changing scenario are fitted based on the Gaussian mixture model, and the parameters of the Gaussian mixture model are estimated with the goal of maximizing the expectation, so as to obtain the joint probability distribution of the multidimensional parameters. Extract gradient information from lane-changing scenarios; Construct a Hamiltonian dynamics model and perform Hamiltonian Monte Carlo sampling; The Hamilton-Monte Carlo sampling criteria are used to determine whether to accept samples. If the sampling is accepted, the scene parameters of the accepted samples are stored as the accelerated test scene library. The parameter distribution characteristics of the accelerated test scene library are statistically analyzed and compared to construct the final lane-changing accelerated test scene library.

2. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that, A lane-changing trajectory model is constructed based on the step-by-step assumption of the lane-changing midpoint, specifically including: The longitudinal and lateral motion of vehicles during lane changing is decoupled and modeled. The direction of travel of the road is defined as longitudinal, and the direction perpendicular to it is defined as lateral. The longitudinal motion model and the lateral motion model of the vehicle during lane changing are constructed. The longitudinal motion model of the vehicle lane-changing process is represented as follows: ； in, Let be the vehicle's ordinate at time t. The longitudinal velocity of the vehicle at the start of the lane change. , These represent the longitudinal accelerations of the vehicle before and after crossing the lane line. For vehicle lane changing times Total lane-changing time for vehicles; The lateral motion model of the vehicle lane-changing process adopts a piecewise fifth-order polynomial model. The starting point of the lane change, the coordinate point of the lane crossing line, and the ending point of the lane change are used as boundary conditions. The second and third segments of the trajectory before and after crossing the lane line are interpolated by fifth-order polynomials respectively.

3. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 2, characterized in that, The coefficients of the fifth-order polynomial in fifth-order polynomial interpolation are expressed as: ； in, , , , These represent the vehicle's x-coordinate, lateral velocity, and lateral acceleration at the initial moment. , , These represent the vehicle's x-coordinate, lateral velocity, and lateral acceleration at the final moment, respectively. Duration.

4. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that, The trajectory feature parameters are obtained by fitting the actual lane-changing trajectory with a set accuracy requirement based on the lane-changing trajectory model, specifically including: Real trajectory data is obtained, and random feature numbers are used as the starting point for the optimization algorithm iteration. After iteration, feature parameters for characterizing the lane-changing trajectory are obtained. The optimization algorithm adopts any one of linear least squares method, nonlinear least squares method, and robust regression algorithm. The feature parameters for characterizing the lane-changing trajectory include the longitudinal velocity of the vehicle at the start of the lane change, the longitudinal acceleration before and after crossing the lane line, the coefficients of the fifth-order polynomial, and the lane-changing time.

5. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that, The distribution pattern of the statistical trajectory feature parameters yields the parameter distribution characteristics of the lane-changing scenario, specifically including: The distribution characteristics of the lane-changing trajectory parameters were statistically analyzed, including the maximum value, minimum value, average value, median, 25th percentile, 75th percentile, 3σ value, and the frequency of each value. Calculate scenario safety agent metrics, including estimated collision time, headway, reverse collision time, and corrected collision time; The distribution characteristics of scene parameters other than lane change trajectory feature parameters are statistically analyzed, including maximum value, minimum value, average value, median, 25th percentile, 75th percentile, 3σ value, and frequency of each value. The trajectory feature parameters for lane changes to the left and right are statistically analyzed separately.

6. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that, The parameter distribution characteristics of the lane-changing scene are fitted based on a Gaussian mixture model. The parameters of the Gaussian mixture model are estimated with the goal of maximizing the expected value. The specific steps include: Based on the Bayesian information criterion, the optimal Gaussian mixture model parameters are obtained by comparing the number of model parameters, the number of samples, and the likelihood function, and are used as the parameters of the final model. The calculation formula of the Bayesian information criterion is expressed as follows: ； Where k is the number of parameters in the GMM model, n is the number of data points, and l is the likelihood function value of the GMM model; A Gaussian mixture model is a linear combination of multiple normal distribution functions. The expression for a single multidimensional normal distribution is: ； A Gaussian mixture model composed of multiple weighted multidimensional normal distributions is expressed as: ； ； in, This indicates that after the j-th multidimensional model has been fitted, the optimal GMM model is determined using BIC. The likelihood function of a single normal distribution is expressed as: ； Establish corresponding Gaussian mixture models for left lane change data and right lane change data respectively.

7. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that, The Hamilton-Monte Carlo (MH) acceptance criteria are used to determine whether to accept samples from the Hamilton-Monte Carlo sampling method. Specifically, these criteria include: For each sample point obtained after L iterations, the Metropolis-Hasting method is used to determine whether to accept or reject the sample, as shown below: ； in, For the updated sample points, The sample points from the previous sampling are used to adjust the step size. Number of steps L versus acceptance rate Adjustments will be made.

8. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that, The sampling method is replaced by the Markov Monte Carlo sampling method, expressed as: ； in, Let be the objective function. Let its integral over the interval be . For variables The probability distribution within the interval, The sample size is determined by sampling using a Markov chain.

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