Vehicle lane changing track high-precision redrawing and key parameter accelerated extrapolation method

Abstract

The invention discloses a vehicle lane changing track high-precision redrawing and key parameter accelerated extrapolation method. The method comprises the following steps: acquiring a sampling data set of a real-time dynamic driving scene; screening a complete lane changing scene of multi-vehicle interaction; filtering preprocessing is carried out on the original noisy data; a lane changing track model is constructed based on a midpoint step-by-step lane changing hypothesis, a lane changing process is modeled in a segmented manner by taking a lane line crossing moment as a node, track characteristic parameter identification is carried out based on the lane changing track model of transverse and longitudinal decoupling, a track characteristic parameter distribution rule is mined, and lane changing scene parameter distribution characteristics are condensed; extracting parameter distribution characteristics of the lane changing scene based on a Gaussian mixture model, and proposing a joint probability model of scene multi-dimensional parameters; extracting lane changing scene distribution gradient information; carrying out Hamilton Monte Carlo sampling; and forming a lane changing acceleration test scene library. According to the invention, dimensionality reduction and high-precision redrawing of the lane changing track are realized, and extrapolation of key scene parameters and construction of a high-precision and high-efficiency lane changing acceleration test scene library are completed.

Description

Technical Field

[0001] The present invention relates to the field of intelligent driving simulation technology, and in particular to a method for high-precision redrawing of a vehicle lane-changing trajectory and accelerated extrapolation of key parameters. Background Art

[0002] Building a high-precision and efficient accelerated simulation test scenario library is of great significance to the development and application of intelligent driving systems. In recent years, in order to further improve test efficiency, the concept of accelerated testing has gradually been applied to virtual simulation testing of intelligent driving systems. In addition to making full use of 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 scenario, using a small number of highly representative scenarios for testing to reduce the number of scenarios required for testing, etc. However, while reducing the parameter dimension, it also reduces the data accuracy, which inevitably leads to deviations in the test results. It is also difficult to balance between reducing the number of scenarios and ensuring scenario coverage.

[0003] Lane changing is one of the most basic driving conditions. Compared with the following condition, it has a higher risk and is the focus of simulation testing. To build a lane changing acceleration simulation test scenario library, first, it is necessary to reduce the parameter dimension. The traditional lateral and longitudinal decoupling planning assumes that the longitudinal speed is constant, and it is applicable to few conditions. It can maintain a certain accuracy when fitting the lane changing trajectory in natural driving data, but it loses the characteristics of the actual lane changing trajectory. The integrated trajectory planning method assumes a lane changing trajectory model, in which the lateral speed, longitudinal speed, and lane changing time are coupled. The trajectory generally meets the driver's expectations for safety and comfort, that is, it retains certain driving style characteristics, but the accuracy loss is large; second, it is necessary to use a small number of scenes to achieve the characterization of natural driving data, that is, the distribution of the scenario 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 assumes a uniform longitudinal speed or uniform acceleration, and assumes that the longitudinal speed remains unchanged during the cut-in process or that the vehicle moves with uniform acceleration. The lane-changing time and the entire process are determined, and it is further believed that whether a collision event occurs is also determined accordingly. Since the longitudinal motion is greatly simplified, the constructed lane-changing scenario is close to the vehicle-following scenario to a certain 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 speed or uniform acceleration, this lane-changing trajectory model is difficult to restore the driver's behavior in the lane-changing process to ensure his safety or comfort, and the redrawn trajectory cannot reflect the driving behavior of the actual lane-changing trajectory. Although this type of technology uses various proxy models in the subsequent sampling process to ensure the unbiasedness of the test results through accelerated testing methods, the loss of trust in specific scenarios will lead to unreliable single test results, and also seriously restrict the efficiency of accelerated testing and reduce the credibility of test results.

[0005] The traditional integrated lane-changing trajectory model is fitted according to the real trajectory by presetting the lane-changing trajectory model, such as a quintic polynomial, a Bezier curve, or a piecewise function composed of multiple curves, and the redrawn lane-changing trajectory is obtained by taking the lane-changing time or lateral acceleration as the model input. The use of curve functions to fit the real trajectory leads to the coupling of the lateral and longitudinal motions of the lane-changing trajectory, that is, the longitudinal speed, the lateral speed and the lane-changing time are coupled, and the generalization ability of the trajectory model is weak; and because the lane-changing trajectory is a certain curve set in advance, the lateral speed, the longitudinal speed and the lane-changing time of the vehicle during the lane-changing process are coupled with each other. When used for trajectory planning, this type of method can simply and efficiently output a suitable lane-changing curve, but when used for trajectory redrawing, facing edge scenes, especially dangerous scenes, the lane-changing trajectory often has the characteristics of rapid acceleration and deceleration in the lateral or longitudinal direction, and large errors will be generated when using curve fitting. Therefore, when this type of technology is used for scene library construction, the fitting accuracy is low, the generalization ability is weak, and it is not convenient to perform edge scene extrapolation.

[0006] Therefore, how to reduce the dimension of scene parameters while improving the accuracy of lane change trajectory redrawing and improving test efficiency while ensuring scene representativeness is an urgent problem to be solved. Summary of the invention

[0007] In order to overcome the defects and shortcomings of the prior art, the present invention provides a method for high-precision redrawing of vehicle lane changing trajectories and accelerated extrapolation of key parameters. The present invention first establishes a lane changing trajectory model based on the midpoint step-by-step hypothesis, performs segmented modeling on the lane changing trajectory, and establishes a high-precision lane changing trajectory. The data accuracy is ensured while the dimension of the data set is reduced, and further proposes the use of a Gaussian mixture model to fit the distribution characteristics of scene samples, and uses a Monte Carlo sampling method considering Hamiltonian dynamics to establish a lane changing scenario library that conforms to real driving scenarios. The scenario coverage is guaranteed while the number of scenarios required for the test is reduced, and the method can well serve the accelerated simulation test of the intelligent driving system and the development, training, and deployment of the intelligent driving system, and realize the high-precision redrawing of the lane changing trajectory of the target vehicle in complex dynamic traffic scenarios and the use of relevant key parameters for scene accelerated extrapolation.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] The present invention provides a method for high-precision redrawing of a vehicle lane-changing trajectory and accelerated extrapolation of key parameters, comprising the following steps:

[0010] Obtain scene parameters under natural driving conditions and obtain a sampling data set of driving scenes;

[0011] Screening the complete lane-changing scenarios under complex dynamic traffic scenarios in the sampled dataset;

[0012] Perform data preprocessing on the screened sampling data set;

[0013] The lane-changing trajectory model is constructed based on the step-by-step assumption of the lane-changing midpoint, and the lane-changing process is segmented and modeled with the moment of crossing the lane line as the node;

[0014] Acquire real trajectory data, fit the real lane-changing trajectory that meets the set accuracy requirements based on the lane-changing trajectory model to obtain trajectory characteristic parameters, and calculate the distribution law of the trajectory characteristic parameters to obtain the lane-changing scenario parameter distribution characteristics;

[0015] 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 maximum expectation, so as to obtain the joint probability distribution of multi-dimensional parameters.

[0016] Extracting lane-changing scene distribution gradient information;

[0017] Construct Hamiltonian dynamics models and perform Hamiltonian Monte Carlo sampling;

[0018] The MH acceptance condition is used to determine whether to accept the sample of Hamilton Monte Carlo sampling. If the sampling is accepted, the scenario parameters of the accepted sample are stored as the acceleration test scenario library. The parameter distribution characteristics of the acceleration test scenario library are statistically analyzed and compared to construct the final lane change acceleration test scenario library.

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

[0020] Decouple the lateral and longitudinal motion of the vehicle during the lane-changing process and model it. Set the driving direction of the road as the longitudinal direction and the direction perpendicular to it as the lateral direction, and build the longitudinal motion model and lateral motion model of the vehicle during the lane-changing process.

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

[0022]

[0023] Where x(t) is the vertical coordinate of the vehicle at time t, v x0 is the longitudinal speed of the vehicle at the start of lane change, a x1 、a x2 are the longitudinal acceleration of the vehicle before and after crossing the lane line, T cross is the lane-changing time of the vehicle, T is the total lane-changing time of the vehicle;

[0024] The lateral motion model of the vehicle in the lane changing process adopts a piecewise quintic polynomial model. The lane changing starting point, the coordinate point of crossing the lane line, and the lane changing end point are used as boundary conditions, and quintic polynomial interpolation is performed on the two trajectories before and after crossing the lane line.

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

[0026]

[0027] Where h = y1-y0, y0, v y0 、a y0 are the vehicle's horizontal coordinate, lateral velocity, lateral acceleration, y1, v at the start time respectively y1 、a y1 They are the vehicle's horizontal coordinate, lateral speed, and lateral acceleration at the end point, and T is the duration.

[0028] As a preferred technical solution, the trajectory characteristic parameters are obtained based on the lane-changing trajectory model fitting the real lane-changing trajectory with set accuracy requirements, specifically including:

[0029] Real trajectory data is obtained, and a random feature number is used as an iterative starting point of an optimization algorithm. After iteration, characteristic parameters for characterizing the lane changing trajectory are obtained. The optimization algorithm adopts any one of a linear least squares method, a nonlinear least squares method, and a robust regression algorithm. The characteristic parameters for characterizing the lane changing trajectory include the longitudinal velocity of the vehicle at the start of the lane changing, the longitudinal acceleration before and after crossing the lane line, the coefficients of a quintic polynomial, and the lane changing duration.

[0030] As a preferred technical solution, the statistical trajectory characteristic parameter distribution law is used to obtain the lane change scene parameter distribution characteristics, which specifically includes:

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

[0032] Calculate scenario safety proxy indicators, including expected collision time, headway, reverse collision time, and corrected collision time;

[0033] Statistical distribution characteristics of scenario parameters except lane-changing trajectory characteristic parameters, including maximum value, minimum value, average value, median, 25% quantile, 75% quantile, 3σ value, and frequency of each value;

[0034] The trajectory characteristic parameters of changing lanes to the left and changing lanes to the right are counted separately.

[0035] As a preferred technical solution, 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 maximum expected value as the goal. The specific steps include:

[0036] Based on the Bayesian information criterion, the optimal Gaussian mixture model parameters are obtained as the parameters of the final model by comparing the number of model parameters, the number of samples, and the likelihood function. The calculation formula of the Bayesian information criterion is expressed as:

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

[0038] Among them, 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;

[0039] The Gaussian mixture model is a linear combination of multiple normal distribution functions. The expression of a single multidimensional normal is:

[0040]

[0041] The Gaussian mixture model is composed of multiple multidimensional normal distribution weights and is expressed as:

[0042]

[0043] Among them, α j It means that after the j-th multidimensional fitting is completed, the BIC is used to determine the optimal GMM model;

[0044] The likelihood function for a single normal distribution is expressed as:

[0045]

[0046] Corresponding Gaussian mixture models are established for the left lane change data and the right lane change data respectively.

[0047] As a preferred technical solution, extracting the lane change scene distribution gradient information specifically includes:

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

[0049]

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

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

[0052] The system dynamics equation consisting of kinetic energy and potential energy is constructed as:

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

[0054] Among them, 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 about the momentum p. In the absence of external energy input, H(x,p) remains unchanged, that is:

[0055]

[0056] The continuous Hamiltonian system is discretized and expressed as:

[0057]

[0058] Among them, ε is the step size, is the gradient of the potential energy function U of sample x at time t, and the sample point is sampled after L cycles.

[0059] As a preferred technical solution, the MH acceptance condition is used to determine whether to accept the sample of Hamiltonian Monte Carlo sampling, specifically including:

[0060] The Metropolis-Hasting method is used to decide whether to accept or reject the sample point obtained after each L cycles, which is expressed as:

[0061]

[0062] in, is the updated sample point, H(x n-1 ,p n-1 ) is the sample point of the last sampling, and the acceptance rate ρ is adjusted by adjusting the step size ε and the number of steps L.

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

[0064]

[0065] Among them, f(x) is the objective function, θ is its integral on the interval, p(x) is the probability distribution of the variable x in the interval, n is the number of samples, and the samples are obtained by sampling using Markov chain.

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

[0067] (1) The present invention uses the lane changing midpoint as the dividing point, divides the lane changing process into two sections and models them separately, uses the proposed model to fit the lane changing trajectory and characterizes the lane changing trajectory with model parameters, thereby achieving dimensionality reduction and high-precision redrawing of the lane changing trajectory, solving the problem that the traditional lane changing trajectory model has low redrawing accuracy and weak generalization ability and cannot meet the high-precision requirements of scene parameters for virtual simulation testing.

[0068] (2) The present invention uses a Gaussian mixture model to fit the sample distribution of natural driving data according to the lane changing trajectory characteristic parameters and surrounding vehicle information in the lane changing scenario, and introduces a Monte Carlo sampling method based on Hamiltonian dynamics on the basis of the distribution characteristics. A small number of high-precision samples are used to characterize the lane changing scene characteristics under natural driving conditions, thereby realizing the extrapolation of key scenes and the construction of a high-precision and efficient lane changing acceleration test scenario library, thereby solving the problem that the natural driving data set has sparse dangerous scenes and lacks collision scenes, and it is difficult to consider the extrapolation of edge scenes while ensuring the authenticity of the scene library when constructing the scene library. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a flow chart of the high-precision redrawing of vehicle lane-changing trajectory and the accelerated extrapolation method of key parameters of the present invention;

[0070] Figure 2 This is a schematic diagram of a lane changing scenario of the present invention;

[0071] Figure 3 A schematic diagram of a sample lane-changing trajectory of a vehicle according to the present invention;

[0072] Figure 4 (a) is the longitudinal velocity statistical histogram of the lane-changing vehicle Car0 at the initial moment of lane-changing;

[0073] Figure 4 (b) is the longitudinal relative speed statistical histogram of the lane-changing vehicle Car0 and the front vehicle Car3 in the target lane at the initial moment of lane-changing;

[0074] Figure 4 (c) is the statistical histogram of the longitudinal relative distance between the lane-changing vehicle Car0 and the front vehicle Car3 in the target lane at the initial moment of lane changing;

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

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

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

[0078] Figure 5 (a) is a schematic diagram showing the comparison between the original trajectory and the modeled trajectory based on the implementation method of the present invention;

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

[0080] Figure 6This is a schematic diagram of data comparison of the Bayesian Information Criterion of the Gaussian mixture model of the present invention;

[0081] Figure 7 A schematic diagram of Gaussian mixture model parameters selected for the present invention;

[0082] Figure 8 A schematic diagram of the marginal distribution of some parameters of the Gaussian mixture model selected for the present invention;

[0083] Fig. 9 (a) is a comparison diagram of the longitudinal velocity sample distribution, sampling distribution, and model distribution of the lane-changing vehicle Car0 at the initial moment of lane changing;

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

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

[0086] Fig. 9 (d) is a comparison diagram of the lane-changing time sample distribution, sampling distribution, and model distribution of the lane-changing vehicle Car0;

[0087] Fig. 9 (e) is a comparison diagram of the sample distribution, sampling distribution, and model distribution of the lane-changing vehicle Car0;

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

[0089] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0090] Example

[0091] This embodiment provides a method for high-precision redrawing of a vehicle lane-changing trajectory and accelerated extrapolation of key parameters, including the following steps:

[0092] The first step is to collect scene-related parameters under natural driving conditions through on-board sensors or roadside sensors. This embodiment is preferably a two-lane four-vehicle scene, with the lane-changing vehicle as the target vehicle, i.e., the ego vehicle, and other vehicles as background vehicles. The target recognition algorithm and related modules are used to obtain information including the lateral and longitudinal speeds, acceleration, head-to-head distance, vehicle length and width, and lane width of the ego vehicle and surrounding vehicles.

[0093] The second step is to filter the lane-changing scenarios in the dataset. A lane change is defined as the vehicle changing from the current lane to the target lane and keeping the lane unchanged for 5 seconds after the lane change. The surrounding vehicles include the front vehicle in the original lane and the front and rear vehicles in the target lane. The sensing range is 200m, and the time window is a certain period of time before the start of the lane change to the end of the lane change.

[0094] The third step is to preprocess the filtered data to reduce noise and exclude outliers. Noise reduction 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 of logarithmic exponential moving filter, symmetric exponential moving filter, etc., and finally the scene data can be smoothed. The logarithmic exponential moving filter expression is shown in formula (1):

[0095]

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

[0097] The fourth step is to establish a lane-changing trajectory model based on the midpoint step-by-step hypothesis. Due to the wide variety of driving scenarios and the variable lane-changing duration, the size of the lane-changing trajectory data is not consistent, which brings difficulties to data processing. By establishing a lane-changing trajectory model, it is possible to use a small number of parameters to characterize the lane-changing trajectory, reduce the data dimension, and facilitate the establishment of a scenario library and subsequent research. Aiming at the lane-changing characteristics of highway scenarios, the present invention decouples and models the lateral and longitudinal motions of the vehicle during the lane-changing process, defines the road's driving direction as the longitudinal direction, and the direction perpendicular to it as the lateral direction, such as Figure 2As shown in the figure, the scene of the lane changing process is simulated. The moment when the lane changing vehicle Car0 crosses the lane line is taken as the initial lane changing moment, and the lane changing process is divided into two sections. In the first lane changing process, the driver needs to adjust the longitudinal speed of the vehicle to control the distance with Car1 and Car2 so as to obtain sufficient longitudinal distance to achieve safe lane changing; in the second process, the main attention is paid to the distance with Car2 and Car3 to ensure safety. Therefore, the driver has different control targets for the vehicle in the two lane changing processes, and the lateral and longitudinal accelerations of the vehicle are different. Segmented modeling is required to better restore the driver's operation in the driving data set.

[0098] For the longitudinal motion of the lane-changing vehicle, the present invention proposes to use a segmented uniform acceleration model. Assuming that the vehicle performs uniform acceleration (deceleration) motion at different accelerations (decelerations) before and after the lane change, the model parameters are fitted using the nonlinear least squares method to obtain a model that characterizes the longitudinal motion of the vehicle during lane change. The longitudinal motion model of the vehicle during lane change is shown in formula (2):

[0099]

[0100] Where x(t) is the vertical coordinate of the vehicle at time t, v x0 is the longitudinal speed of the vehicle at the start of lane change, a x1 、a x2 are the longitudinal acceleration of the vehicle before and after crossing the lane line, T cross is the defined lane changing time of the vehicle, and T is the total lane changing time of the vehicle.

[0101] For the lateral motion of the lane-changing vehicle, the present invention uses a piecewise quintic polynomial model. Taking the lane-changing starting point, the lane-crossing line coordinate point, and the lane-changing end point as boundary conditions, quintic polynomial interpolation is performed on the two trajectories before and after crossing the lane line. The coefficients of the quintic polynomial are calculated as shown in formula (3).

[0102]

[0103] Where h = y1-y0, y0, v y0 、a y0 are the vehicle's horizontal coordinate, lateral velocity, lateral acceleration, y1, v at the start time respectively y1 、a y1 They are the vehicle's horizontal coordinate, lateral speed, and lateral acceleration at the end point, and T is the duration.

[0104] The fifth step is to obtain the trajectory characteristic parameters and verify the trajectory accuracy by fitting the real lane-changing trajectory according to the model. First, obtain the real trajectory data and use the random feature number as the iterative starting point of the algorithm. The algorithm can be an optimization algorithm such as linear least squares, nonlinear least squares, and robust regression. After iteration, the characteristic parameters used to characterize the lane-changing trajectory are obtained, including the longitudinal speed of the vehicle at the start of the lane change, the longitudinal acceleration before and after crossing the lane line, the fifth-order polynomial coefficient, and the lane-changing time. After completing the fitting, compare the longitudinal, lateral, and comprehensive root mean square errors (RMSE) of the obtained trajectory with the real trajectory to see if they are within the acceptable range. The calculation method of the lateral and longitudinal root mean square errors is shown in formula (4).

[0105]

[0106] Where m is the total number of samples, x i is the true value of the i-th longitudinal coordinate, is the predicted value of the i-th vertical coordinate, y i is the true value of the i-th horizontal coordinate, is the predicted value of the ith lateral coordinate. If the fitting result is accepted, proceed to step 4, otherwise return to step 4 and replace the lane-changing time T defined in equation (2) with cross Change to a time before or after the originally defined lane-changing time and refit.

[0107] Step 6: Statistics on the distribution of trajectory characteristic parameters. Statistics on the distribution of lane-changing trajectory characteristic parameters obtained in step 5 include maximum value, minimum value, mean value, median, 25% quantile, 75% quantile, 3σ value, frequency of each value, etc. The data of lane changes to the left and lane changes to the right are counted separately to avoid the sampling difficulty caused by bimodal distribution.

[0108] Step 7: Statistics of distribution characteristics of other scene features. Statistics of distribution characteristics of scene parameters other than lane change trajectory characteristic parameters obtained in step 5, including maximum value, minimum value, mean value, median, 25% quantile, 75% quantile, 3σ value, frequency of each value, etc.; at the same time, scene safety proxy indicators are calculated based on the parameters in step 6, including but not limited to expected collision time, headway, reverse collision time, enhanced collision time, etc. The data of lane change to the left and lane change to the right are counted separately to avoid sampling difficulties caused by bimodal distribution.

[0109] In the eighth step, the Gaussian mixture model for the key parameter distribution of the lane changing scenario is built. The parameters of the sixth and seventh steps are combined to obtain the parameter distribution characteristics of the lane changing scenario. The Gaussian mixture model is used to fit the statistical characteristics of the lane changing scenario parameters. The parameters of the Gaussian mixture model are estimated with the maximum expectation as the goal to obtain the joint probability distribution of the multi-dimensional parameters. Using the Bayesian Information Criterion (BIC), the optimal Gaussian mixture model parameters are obtained as the parameters of the final model based on the comparison of the number of model parameters, the number of samples, and the likelihood function. The calculation method of the Bayesian Information Criterion is shown in formula (5).

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

[0111] Among them, 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, and theoretically has the ability to fit any type of distribution. The expression of a single multidimensional normal is shown in formula (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 a plurality of weighted multidimensional normal distributions represented by equation (6), as shown in equation (7):

[0116]

[0117] Among them, α j It means that after the j-th multidimensional model is fitted, BIC is used to determine the optimal GMM model.

[0118] The calculation formula of the likelihood function of a single normal distribution is shown in formula (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 lane changing to the left and to the right, the data is divided into left lane changing data and right lane changing data, and corresponding Gaussian mixture models are established respectively.

[0122] Step 9: Extract scene distribution gradient information. Before performing edge parameter extrapolation, it is necessary to obtain the gradient information of the model distribution. Based on the Gaussian mixture model obtained in step 8, the potential energy and gradient calculation formula of the distribution model are derived. Using the negative log-likelihood function as the potential energy function of the model, the model potential energy calculation formula 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 methods of formula (11) to formula (13) can also be replaced by the Markov Monte Carlo sampling method, as shown in the following formula:

[0126]

[0127] The tenth step is to establish a Hamiltonian dynamics model and perform Hamiltonian Monte Carlo sampling. The Gaussian mixture model of the scene parameters established in the eighth step is sampled to obtain multiple sets of scene parameters. The sampling method is Hamiltonian Monte Carlo sampling. The HMC method is an improved Markov Chain Monte Carlo method. The motion process of the sampling point is described by the constructed Hamiltonian dynamics equation, so that the sampling process converges to the target distribution faster. First, the system dynamics equation composed of kinetic energy and potential energy is constructed, as shown in formula (11):

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

[0129] Among them, 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 about 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 using the “Leapfrog” method. The complete step is shown in equation (13):

[0132]

[0133] Among them, ε is the step size, is the gradient of the potential energy function U of sample x at time t. After looping this step L times, the sample point is sampled. Combining equations (9), (10), (11), (12), and (13), it can be seen that when the sampling point is in the high probability region of the probability distribution function, the potential energy is large and the kinetic energy is small. It moves in the high probability region with a small step to sample. When it is in the low probability region, the potential energy is small and the kinetic energy is large. It moves with a large step and gradually returns to the high probability region, thus approximating the probability distribution function with a small number of samples.

[0134] In the eleventh step, the MH acceptance condition is used to determine whether to accept the sample sampled in the tenth step. The rejection-acceptance sampling method is the key to building an acceleration test scenario library and conducting acceleration tests. By rejecting samples with a high degree of similarity to existing samples, the scenario library only needs to use fewer samples to represent the real driving environment, thereby improving the test efficiency while ensuring the authenticity of the test results and the scenario coverage. The Metropolis-Hasting method is used to decide whether to accept or reject the sample point obtained after each L cycle, as shown in formula (14).

[0135]

[0136] in, is the updated sample point, H(x n-1 ,p n-1 ) is the sample point of the last sampling. The acceptance rate ρ can be adjusted by adjusting the step length ε and the number of steps L. If the sampling result is accepted, move forward, otherwise return to the tenth step to continue sampling.

[0137] Step 12: Statistics and comparison of distribution characteristics of the scene library. The scene parameters of the samples accepted in step 11 are stored as the accelerated test scene library, and the parameter distribution characteristics of the accelerated test scene library are statistically analyzed to form the accelerated test scene library. Compare the original number of scenes, the number of scenes of the traditional Monte Carlo sampling method under different sampling times, the number of scenes of the Markov Monte Carlo sampling method and the number of valid scenes of the method proposed in the present invention, and compare them with the Gaussian mixture distribution model obtained in step 8. The comparison parameters include but are not limited to KL divergence, JS divergence, mean, peak value, etc. The formulas of KL divergence and JS divergence are shown in equations (15) and (16).

[0138]

[0139] Among them, p(x) is the original scene distribution, and q(x) is the sampled scene library distribution.

[0140] Step 13: Establish a lane-changing acceleration test scenario library. After proving the effectiveness of this method in building a lane-changing acceleration test scenario library in step 12, further compare the divergence and number of valid scenarios of the scenario library obtained under different sampling times, so as to select the sampling times that are most suitable for the data input in step 1 and establish the most efficient lane-changing acceleration test scenario library.

[0141] This embodiment uses the natural driving data of German highways collected by the highD dataset as the original data as an example to illustrate the effectiveness and accuracy of the high-precision redrawing of lane change trajectories and the accelerated extrapolation of key parameters in complex dynamic traffic scenarios proposed by the present invention, as follows:

[0142] First, the lane-changing data is filtered in the data set. The filtering rule is that the target vehicle only changes lanes once continuously, and the surrounding vehicles include the front vehicle in the original lane of the target vehicle and the front vehicle and the rear vehicle in the target lane, and the distance is within 200m. Figure 3 As shown, the lane change trajectory samples are obtained after screening from the data set and preprocessing using the average moving filter.

[0143] Statistics are collected on some scene feature parameters of all lane-changing scene samples in the HighD dataset, such as Figure 4 As shown, the histogram distribution is obtained.

[0144] Figure 5 As shown, the fourth and fifth steps are performed to obtain the modeled trajectory. It can be seen that when the original data trajectory has a certain change, the traditional method is difficult to ensure the accuracy of the redrawn trajectory. The method proposed in the present invention redraws the original trajectory with high precision while using a similar number of parameters, ensuring 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 within 1 m accounts for 99.89%, and the data with an error within 0.2 m accounts for 95.12%. It can be considered that the lane changing trajectory redrawing method proposed in the present invention can effectively characterize the lane changing trajectory in the highway scenario, and achieves high-precision expression of the lane changing trajectory using less data, which is conducive to the establishment of a high-precision and efficient lane changing acceleration simulation test scenario library.

[0146] Table 1 Trajectory redrawing error table

[0147]

[0148] Based on the data obtained in steps 6 and 7, z-score normalization is performed and the Gaussian mixture distribution fitting function fitgmdist of Matlab is used for fitting. The component k is set to 1 to 20, the regularization coefficient is 0.01, and four combinations of covariance type and shared covariance are set respectively. 80 sets of fitting results are obtained, as shown in the figure. Figure 6 As shown, the Bayesian Information Criterion (BIC) data comparison of 80 sets of fitting results was obtained.

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

[0150] like Figure 8 As shown, the marginal distribution of the model is plotted according to the model parameters. It can be seen that the distribution of the model fitting basically conforms to the data characteristics of the HighD highway natural driving dataset.

[0151] Use programming software to write the HMC sampling algorithm. First, according to the Gaussian mixture model used in the eighth step, construct the corresponding Hamiltonian dynamic equation function, namely H(x), U(x), dU(x). Then construct the "frog jump" algorithm, use the random number generation function to select the sampling starting point, and use a variable step length for "frog jump" sampling under a fixed step length. Finally, construct the MH acceptance condition algorithm required for the eleventh step. If the sample sampled in the tenth step is similar to the previously sampled sample, that is, it meets the existing sample distribution, then reject the sample and continue sampling with the sample as the starting point, and repeat until the set number of samplings is reached.

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

[0153] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in 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: The steps include: Obtain scene parameters under natural driving conditions and obtain a sampling data set of driving scenes; Screening the complete lane-changing scenarios under complex dynamic traffic scenarios in the sampled dataset; Perform data preprocessing on the screened sampling data set; The lane-changing trajectory model is constructed based on the step-by-step assumption of the lane-changing midpoint, and the lane-changing process is segmented and modeled with the moment of crossing the lane line as the node; Acquire real trajectory data, fit the real lane-changing trajectory that meets the set accuracy requirements based on the lane-changing trajectory model to obtain trajectory characteristic parameters, and calculate the distribution law of the trajectory characteristic parameters to obtain the lane-changing scenario parameter distribution characteristics; 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 maximum expectation, so as to obtain the joint probability distribution of multi-dimensional parameters. Extracting lane-changing scene distribution gradient information; Construct Hamiltonian dynamics models and perform Hamiltonian Monte Carlo sampling; The MH acceptance condition is used to determine whether to accept the sample of Hamiltonian Monte Carlo sampling. If the sampling is accepted, the scenario parameters of the accepted sample are stored as the acceleration test scenario library. The parameter distribution characteristics of the acceleration test scenario library are statistically analyzed and compared to construct the final lane change acceleration test scenario library.

2. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1 is characterized in that: The lane-changing trajectory model is constructed based on the step-by-step assumption of the lane-changing midpoint, including: Decouple the lateral and longitudinal motion of the vehicle during the lane-changing process and model it. Set the driving direction of the road as the longitudinal direction and the direction perpendicular to it as the lateral direction, and build the longitudinal motion model and lateral motion model of the vehicle during the lane-changing process. The longitudinal motion model of the vehicle lane changing process is expressed as: Where x(t) is the vertical coordinate of the vehicle at time t, v x0 is the longitudinal speed of the vehicle at the start of lane change, a x1 、a x2 are the longitudinal acceleration of the vehicle before and after crossing the lane line, T cross is the lane-changing time of the vehicle, T is the total lane-changing time of the vehicle; The lateral motion model of the vehicle in the lane changing process adopts a piecewise quintic polynomial model. The lane changing starting point, the coordinate point of crossing the lane line, and the lane changing end point are used as boundary conditions, and quintic polynomial interpolation is performed on the two trajectories before and after crossing the lane line.

3. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 2 is characterized in that: The coefficients of the fifth-order polynomial in the fifth-order polynomial interpolation are expressed as: Where h = y1-y0, y0, v y0 、a y0 are the vehicle's horizontal coordinate, lateral velocity, lateral acceleration, y1, v at the start time respectively y1 、a y1 They are the vehicle's horizontal coordinate, lateral speed, and lateral acceleration at the end point, and T is the 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 lane-changing trajectory model is used to fit the actual lane-changing trajectory with set accuracy requirements to obtain trajectory characteristic parameters, including: Real trajectory data is obtained, and a random feature number is used as an iterative starting point of an optimization algorithm. After iteration, characteristic parameters for characterizing the lane changing trajectory are obtained. The optimization algorithm adopts any one of a linear least squares method, a nonlinear least squares method, and a robust regression algorithm. The characteristic parameters for characterizing the lane changing trajectory include the longitudinal velocity of the vehicle at the start of the lane changing, the longitudinal acceleration before and after crossing the lane line, the coefficients of a quintic polynomial, and the lane changing duration.

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 statistical trajectory characteristic parameter distribution law is used to obtain the lane change scene parameter distribution characteristics, which specifically includes: Statistical distribution characteristics of lane-changing trajectory characteristic parameters, including maximum value, minimum value, average value, median, 25% quantile, 75% quantile, 3σ value, and the frequency of each value; Calculate scenario safety proxy indicators, including expected collision time, headway, reverse collision time, and corrected collision time; Statistical distribution characteristics of scenario parameters except lane-changing trajectory characteristic parameters, including maximum value, minimum value, average value, median, 25% quantile, 75% quantile, 3σ value, and frequency of each value; The trajectory characteristic parameters of changing lanes to the left and changing lanes to the right are counted 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 scenario are fitted based on the Gaussian mixture model, and the parameters of the Gaussian mixture model are estimated with the goal of maximum expectation. The specific steps include: Based on the Bayesian information criterion, the optimal Gaussian mixture model parameters are obtained as the parameters of the final model by comparing the number of model parameters, the number of samples, and the likelihood function. The calculation formula of the Bayesian information criterion is expressed as: BIC=-2log(l)+klog(n) Among them, 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; The Gaussian mixture model is a linear combination of multiple normal distribution functions. The expression of a single multidimensional normal is: The Gaussian mixture model is composed of multiple multidimensional normal distribution weights and is expressed as: Among them, α j It means that after the j-th multidimensional fitting is completed, the BIC is used to determine the optimal GMM model; The likelihood function for a single normal distribution is expressed as: Corresponding Gaussian mixture models are established for the left lane change data and the 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: Extract the lane-changing scene distribution gradient information, including: Based on the Gaussian mixture model, the potential energy and gradient calculation formula of the distribution model are derived, and the negative log-likelihood function is used as the potential energy function of the model, which is expressed as: Where y is the probability density function of x in the Gaussian mixture distribution model.

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: Construct a Hamiltonian dynamics model and perform Hamiltonian Monte Carlo sampling, including: The system dynamics equation consisting of kinetic energy and potential energy is constructed as: H(x,p)=U(x)+K(p) Among them, 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 about the momentum p. In the absence of external energy input, H(x,p) remains unchanged, that is: The continuous Hamiltonian system is discretized and expressed as: Among them, ε is the step size, ▽U(x(t)) is the gradient of the potential energy function U of sample x at time t, and the sample point is sampled after L cycles.

9. The method for high-precision redrawing of vehicle lane-changing trajectories and accelerated extrapolation of key parameters according to claim 1, characterized in that: Use the MH acceptance condition to determine whether to accept the sample of Hamilton Monte Carlo sampling, including: The Metropolis-Hasting method is used to decide whether to accept or reject the sample point obtained after each L cycles, which is expressed as: in, is the updated sample point, H(x n-1 ,p n-1 ) is the sample point of the last sampling, and the acceptance rate ρ is adjusted by adjusting the step size ε and the number of steps L.

10. 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, which is expressed as: Among them, f(x) is the objective function, θ is its integral on the interval, p(x) is the probability distribution of the variable x in the interval, n is the number of samples, and the samples are obtained by sampling using Markov chain.

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