Track prediction method for line-surface fitting based on machine learning
Through the line-plane fitting method based on machine learning, the trajectory prediction function is adaptively constructed, which solves the problem that existing methods rely on specific assumptions and are sensitive to outliers, and achieves more accurate and efficient trajectory prediction.
Patent Information
- Application Number
- CN202411870801.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-18
- Publication Date
- 2025-04-04
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Existing trajectory prediction methods rely on specific assumptions, such as Gaussian functions or linear regression, resulting in inaccurate or biased fitting results when the data does not meet these assumptions, and are sensitive to outliers, resulting in poor prediction results.
Using machine learning-based line-plane fitting method, the target trajectory prediction function is adaptively constructed through the initial function generation model and optimization degree data calculation, avoid relying on specific assumptions, and optimized parameters of the reference set by forward and reverse adjustment.
It improves the accuracy and robustness of trajectory prediction, reduces iteration time and computing power requirements, and achieves faster and more efficient trajectory prediction.
Smart Images
Figure CN119762535A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of machine learning, and in particular to a trajectory prediction method for line-surface fitting based on machine learning. Background Art
[0002] Curve fitting has broad and far-reaching importance in the real world, and its applications cover multiple fields, affecting scientific research, engineering technology, business decisions and social development. Scientists collect data in experiments and observations, and can identify the relationship between variables and verify hypotheses through curve fitting; in engineering design, curve fitting is used to optimize product performance and evaluate the impact of different variables on results; in public health and epidemiology, curve fitting is used to model disease transmission, vaccine effectiveness evaluation, etc. Economists use curve fitting technology to analyze market data and predict economic trends, such as inflation rate, unemployment rate and market demand changes; by fitting data on temperature, sea level rise, etc., scientists can identify trends in climate change and evaluate the impact of human activities on the environment. Conventional curve fitting methods are based on Gaussian functions, which are a special form of function that is mainly used to fit data that exhibits specific characteristics, such as data with peaks and symmetrical distribution.
[0003] Trajectory prediction is an important process for achieving autonomous driving and optimal path prediction. However, the use of Gaussian functions for trajectory prediction has too many limitations, because Gaussian functions are less effective for distributions such as exponential growth, periodic fluctuations, and piecewise linear distributions. In addition to using Gaussian functions, many existing methods also mostly use specific assumptions, such as linear regression. If the data does not meet these assumptions, the fitting results may be inaccurate or biased, resulting in poor trajectory prediction results. In addition, existing prediction methods are usually sensitive to outliers or outliers in the data, which may cause the model to deviate from the actual trend of the data. Summary of the invention
[0004] In order to overcome the shortcomings of the prior art, the purpose of the present invention is to provide a trajectory prediction method based on machine learning for line-surface fitting, so as to realize trajectory prediction using a trajectory prediction function that is not based on specific assumptions.
[0005] To achieve the above object, the present invention provides the following solutions:
[0006] Collecting a target environment image, and converting the target environment image into an HSV space for Gaussian filtering to obtain a preprocessed image;
[0007] Using the Canny edge detection algorithm to perform line and surface extraction on the preprocessed image to obtain the line and surface to be fitted, and extracting coordinate data of the line and surface to be fitted to obtain the coordinate set to be fitted;
[0008] Input the coordinate set of the line and surface to be fitted into the pre-trained initial function generation model to obtain the original function to be fitted;
[0009] Determining a parameter value range of a sub-function within the original function to be fitted according to the coordinate set to be fitted;
[0010] Within the parameter value range, the parameters of each sub-function in the original function to be fitted are randomly assigned separately to obtain a single parameter adjustment function set;
[0011] Simulating each function in the single parameter adjustment function set separately to obtain a plurality of simulation coordinate sets, and simulating the original function to be fitted to obtain a control coordinate set;
[0012] Calculating the difference between the reference coordinate set and the coordinate set to be fitted to obtain a reference coordinate difference set, and calculating the difference between all the simulation coordinate sets and the coordinate set to be fitted to obtain several groups of simulation coordinate difference sets;
[0013] The optimization degree data of each function in the single parameter adjustment function set is calculated according to the control coordinate difference set and the simulation coordinate difference set; the calculation formula of the optimization degree data is: Among them, O p is the optimization degree data corresponding to the pth function in the single parameter adjustment function set; pi is the ith difference data in the pth simulation coordinate difference set; f 0i is the ith difference data in the reference coordinate difference set; n is the number of coordinates in the coordinate set to be fitted;
[0014] Updating the adjusted sub-function in the function whose optimization degree data is less than 0 to the original function to be fitted, and calculating the error between the updated original function to be fitted and the coordinate set to be fitted to obtain a loss value;
[0015] When the loss value is greater than the target expectation, the adjustment direction of the sub-function adjusted in the function whose optimization degree data is less than 0 is extracted to obtain a forward adjustment reference set, and the adjustment direction of the sub-function adjusted in the function whose optimization degree data is greater than or equal to 0 is extracted to obtain a reverse adjustment reference set;
[0016] According to the direction of the forward adjustment reference set and the opposite direction of the reverse adjustment reference set, the parameters of each sub-function in the updated original function to be fitted are randomly assigned separately to obtain the updated single-parameter adjustment function set, and return to the step of "simulating each function in the single-parameter adjustment function set separately to obtain several groups of simulation coordinate sets, simulating the original function to be fitted to obtain a control coordinate set" to iterate until the number of iterations reaches the target number of times or the loss value is less than the target expectation, stop the iteration, and output the original function to be fitted obtained by the last iteration to obtain the target trajectory prediction function;
[0017] The target trajectory prediction function is used to perform trajectory prediction to obtain target prediction trajectory data.
[0018] Preferably, the pre-training process of the initial function generation model includes:
[0019] Constructing a basic function library, randomly selecting functions and setting parameters based on the basic function library to obtain a constructed function set;
[0020] Simulating the construction function set to obtain multiple sets of construction coordinate data sets and construction line-surface image sets;
[0021] Using a VGG feature extraction network to perform feature extraction on the constructed line-surface image set to obtain an image feature set, using a one-dimensional CNN to perform feature extraction on the constructed coordinate data set to obtain a coordinate feature set, and fusing the image feature set and the coordinate feature set to obtain a fused feature vector;
[0022] Constructing a function type recognition model based on a neural network, taking the fused feature vector as a model input and the function type of the constructed function set as a target output, training the function type recognition model to obtain the trained function type recognition model;
[0023] A preset parameter library is added to the trained function type recognition model to obtain the initial function generation model.
[0024] Preferably, determining the parameter value range of the sub-function within the original function to be fitted according to the coordinate set to be fitted includes:
[0025] Determine the maximum value, minimum value and interval range of the coordinate set to be fitted;
[0026] Taking the maximum value and the minimum value as the upper boundary and the lower boundary, calculate the minimum parameter value of each sub-function in the original function to be fitted that traverses the lower boundary and the range of the lower boundary within the interval, construct a value interval from 0 to the minimum parameter value, and obtain the parameter value range.
[0027] Preferably, when the number of the coordinate sets to be fitted exceeds a preset upper limit of the number of coordinates, the coordinate sets to be fitted are divided into a plurality of coordinate subsets to be fitted according to the upper limit of the number of coordinates.
[0028] Preferably, the calculation formula of the loss value is:
[0029]
[0030] Among them, Loss is the loss value; β 1 is the first weight; β 2 is the second weight; β 3 is the third weight; y′ m is the updated m-th coordinate value of the original function simulation to be fitted; 0m is the mth coordinate value of the coordinate set to be fitted; y′ max , y′ min are respectively the maximum and minimum values of the simulation results of the original function to be fitted after update; 0max ,y 0min are respectively the maximum and minimum values of the coordinate set to be fitted.
[0031] Preferably, the one-dimensional CNN includes: a first input layer, a first output layer, first to fourth convolutional layers with a stride of 1, and first to third fully connected layers with a stride of 2; all convolutional layers and connection layers in the one-dimensional CNN adopt batch normalization and rectified linear unit activation function; the first convolutional layer to the fourth convolutional layer each contain a number of convolutional kernels of size 1×1; the first convolutional layer to the fourth convolutional layer are each followed by a maximum pooling layer; the number of neuronal units from the first fully connected layer to the third fully connected layer are 2048, 1024, and 1024, respectively; the first output layer is a softmax layer.
[0032] Preferably, the VGG feature extraction network includes: a second input layer, a second output layer, the fifth to twenty-first convolutional layers with a stride of 1 and a ReLU activation function, and the fourth to sixth fully connected layers with a stride of 2 and a ReLU activation function; the fifth to twenty-first convolutional layers contain 3×3 convolution kernels of size 64, 64, 128, 128, 256, 256, 512, and 512, respectively; the sixth convolutional layer, the eighth convolutional layer, the eleventh convolutional layer, the fourteenth convolutional layer, and the twenty-first convolutional layer are all followed by a maximum pooling layer of size 2×2 and a stride of 2; the fourth to sixth fully connected layers each include 4096 neurons.
[0033] The present invention discloses the following technical effects:
[0034] The present invention provides a trajectory prediction method based on line-surface fitting of machine learning. By generating a model with an initial function, the defect that a single function structure is adopted in a traditional method resulting in poor trajectory prediction effect is solved, and trajectory prediction is performed using a target trajectory prediction function adaptively constructed according to a target environment image. By designing optimization data and a forward adjustment reference set and a reverse adjustment reference set, the problems of a long iteration time and a high computing power requirement of the traditional method are solved, and the trajectory prediction time is reduced. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.
[0036] Figure 1 A schematic diagram of a trajectory prediction and fitting process for line-surface fitting based on machine learning provided in an embodiment of the present invention;
[0037] Figure 2 A flowchart for obtaining the original function to be fitted provided by an embodiment of the present invention;
[0038] Figure 3 A flow chart for determining a parameter value range provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0040] The purpose of the present invention is to provide a trajectory prediction method for line-surface fitting based on machine learning, so as to realize trajectory prediction using a trajectory prediction function not based on specific assumptions.
[0041] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.
[0042] Figure 1 A schematic diagram of a trajectory prediction process for line-surface fitting based on machine learning provided in an embodiment of the present invention is shown in FIG. Figure 1 As shown, the present invention provides a trajectory prediction method based on machine learning for line-surface fitting, comprising:
[0043] Step 100: Collect a target environment image, and convert the target environment image into an HSV space for Gaussian filtering to obtain a preprocessed image;
[0044] Step 200: using the Canny edge detection algorithm to perform line-surface extraction on the preprocessed image to obtain the line-surface to be fitted, and extracting coordinate data of the line-surface to be fitted to obtain the coordinate set to be fitted;
[0045] Step 300: inputting the coordinate set to be fitted of the line and surface to be fitted into the pre-trained initial function generation model to obtain the original function to be fitted;
[0046] Step 400: determining the parameter value range of the sub-function within the original function to be fitted according to the coordinate set to be fitted;
[0047] Step 500: within the parameter value range, individually and randomly assigning the parameters of each sub-function in the original function to be fitted to obtain a single-parameter adjustment function set;
[0048] Step 600: Simulate each function in the single parameter adjustment function set separately to obtain a plurality of simulation coordinate sets, and simulate the original function to be fitted to obtain a control coordinate set;
[0049] Step 700: Calculate the difference between the reference coordinate set and the coordinate set to be fitted to obtain a reference coordinate difference set, calculate the difference between all the simulation coordinate sets and the coordinate set to be fitted to obtain a plurality of simulation coordinate difference sets;
[0050] Step 800: Calculate the optimization degree data of each function in the single parameter adjustment function set according to the control coordinate difference set and the simulation coordinate difference set; the calculation formula of the optimization degree data is: Among them, O p is the optimization degree data corresponding to the pth function in the single parameter adjustment function set; pi is the ith difference data in the pth simulation coordinate difference set; f 0i is the ith difference data in the reference coordinate difference set; n is the number of coordinates in the coordinate set to be fitted;
[0051] Step 900: updating the adjusted sub-function in the function whose optimization degree data is less than 0 to the original function to be fitted, and calculating the error between the updated original function to be fitted and the coordinate set to be fitted to obtain a loss value;
[0052] Step 1000: When the loss value is greater than the target expectation, the adjustment direction of the sub-function adjusted in the function whose optimization degree data is less than 0 is extracted to obtain a positive adjustment reference set, and the adjustment direction of the sub-function adjusted in the function whose optimization degree data is greater than or equal to 0 is extracted to obtain a negative adjustment reference set;
[0053] Step 1100: according to the direction of the forward adjustment reference set and the opposite direction of the reverse adjustment reference set, the parameters of each sub-function in the updated original function to be fitted are randomly assigned separately to obtain the updated single-parameter adjustment function set, and return to the step of "simulating each function in the single-parameter adjustment function set separately to obtain several groups of simulation coordinate sets, simulating the original function to be fitted to obtain a control coordinate set" to iterate until the number of iterations reaches the target number of times or the loss value is less than the target expectation, stop the iteration, and output the original function to be fitted obtained by the last iteration to obtain the target trajectory prediction function;
[0054] Step 1200: Use the target trajectory prediction function to perform trajectory prediction to obtain target predicted trajectory data.
[0055] refer to Figure 2 , the pre-training process of the initial function generation model includes:
[0056] Step 301: construct a basic function library, randomly select functions and set parameters based on the basic function library to obtain a constructed function set;
[0057] Step 302: simulating the construction function set to obtain multiple sets of construction coordinate data sets and construction line-surface image sets;
[0058] Step 303: using a VGG feature extraction network to perform feature extraction on the constructed line-surface image set to obtain an image feature set, using a one-dimensional CNN to perform feature extraction on the constructed coordinate data set to obtain a coordinate feature set, and fusing the image feature set and the coordinate feature set to obtain a fused feature vector;
[0059] Step 304: constructing a function type recognition model based on a neural network, taking the fused feature vector as a model input and the function type of the constructed function set as a target output, training the function type recognition model to obtain the trained function type recognition model;
[0060] Step 305: adding a preset parameter library to the trained function type recognition model to obtain the initial function generation model.
[0061] refer to Figure 3, determining the parameter value range of the sub-function within the original function to be fitted according to the coordinate set to be fitted, including:
[0062] Step 401: Determine the maximum value, minimum value and interval range of the coordinate set to be fitted;
[0063] Step 402: With the maximum value and the minimum value as the upper boundary and the lower boundary, calculate the minimum parameter value of each sub-function in the original function to be fitted that traverses the lower boundary and the range of the lower boundary within the interval, construct a value interval from 0 to the minimum parameter value, and obtain the parameter value range.
[0064] Preferably, when the number of the coordinate sets to be fitted exceeds a preset upper limit of the number of coordinates, the coordinate sets to be fitted are divided into a plurality of coordinate subsets to be fitted according to the upper limit of the number of coordinates.
[0065] Specifically, the calculation formula of the loss value is:
[0066]
[0067] Among them, Loss is the loss value; β 1 is the first weight; β 2 is the second weight; β 3 is the third weight; y′ m is the updated m-th coordinate value of the original function simulation to be fitted; 0m is the mth coordinate value of the coordinate set to be fitted; y′ max , y′ min are respectively the maximum and minimum values of the simulation results of the original function to be fitted after update; 0max ,y 0min are respectively the maximum and minimum values of the coordinate set to be fitted.
[0068] Specifically, the one-dimensional CNN includes: a first input layer, a first output layer, first to fourth convolutional layers with a stride of 1, and first to third fully connected layers with a stride of 2; all convolutional layers and connection layers in the one-dimensional CNN use batch normalization and rectified linear unit activation functions; the first convolutional layer to the fourth convolutional layer each contain a number of convolutional kernels of size 1×1; the first convolutional layer to the fourth convolutional layer are each followed by a maximum pooling layer; the number of neuron units in the first fully connected layer to the third fully connected layer are 2048, 1024, and 1024, respectively; the first output layer is a softmax layer.
[0069] Preferably, the VGG feature extraction network includes: a second input layer, a second output layer, the fifth to twenty-first convolutional layers with a stride of 1 and a ReLU activation function, and the fourth to sixth fully connected layers with a stride of 2 and a ReLU activation function; the fifth to twenty-first convolutional layers contain 3×3 convolution kernels of size 64, 64, 128, 128, 256, 256, 512, and 512, respectively; the sixth convolutional layer, the eighth convolutional layer, the eleventh convolutional layer, the fourteenth convolutional layer, and the twenty-first convolutional layer are all followed by a maximum pooling layer of size 2×2 and a stride of 2; the fourth to sixth fully connected layers each include 4096 neurons.
[0070] Specifically, the idea of loss control is as follows: based on the parameter update in the previous step, if the parameters of multiple functions change, a single function parameter change formula is constructed to calculate the fitting result of the formula and the positive improvement degree of the target coordinate point, as well as the degree of proximity between the coordinates calculated by the formula and the coordinate points calculated by the formula before the update relative to the target coordinate point; using the cumulative formula, close is negative, far is positive, and a negative cumulative result indicates that the function parameter modification is optimized, otherwise the modification should be abandoned.
[0071] Preferably, for a two-dimensional curve, the basic function library includes: exponential function, logarithmic function, trigonometric function, inverse trigonometric function, transcendental function, power function, etc. This embodiment provides a parameter design method: for an exponential function, the coefficient and the exponent are parameters, and the coefficient and the exponent can also be any function in the basic function library, and the other functions are set similarly. In order to limit the complexity of the constructor and reduce the amount of data in the calculation process, this embodiment limits the number of nested layers of functions to within 5 layers.
[0072] Specifically, this embodiment has a set of adaptive setting methods for simulation. First, if the line-surface image is extracted, a local dense grid division method will be adopted in the extraction process, that is, a denser grid will be used for extraction in the area with larger curvature. The staff can set the minimum size and change method of the grid according to their needs; before the function is simulated, the grid distribution of the line-surface image is first extracted, and the simulation is performed according to the grid distribution points to reduce unnecessary calculation workload. For fine simulation requirements, the staff can use a uniform simulation method to meet the accuracy requirements.
[0073] Preferably, the VGG feature extraction network is often used as a feature extractor due to its good feature representation ability. The VGG feature extraction network explores the relationship between the depth of the convolutional neural network and its performance, and successfully constructs a 16- to 19-layer deep convolutional neural network, proving that increasing the depth of the network can affect the final performance of the network to a certain extent, significantly reducing the error rate, while also having strong scalability and good generalization when migrated to other image data.
[0074] Optionally, the loss function used in this embodiment combines mean square error, mean absolute error and extreme error. Mean square error is particularly sensitive to large deviations because the square of the error increases the weight of larger deviations. Mean absolute error gives the same weight to all deviations and is therefore more robust to outliers. Extreme error is more sensitive to span intervals, so this embodiment sets their weights to 0.7, 0.2, and 0.1 respectively.
[0075] The beneficial effects of the present invention are as follows:
[0076] The present invention uses an initial function generation model to eliminate the traditional method of using a single function structure, thereby improving the accuracy of trajectory prediction; by designing optimization data and a forward adjustment reference set and a reverse adjustment reference set, a fast random parameter optimization solution is provided, which reduces the time and computing power cost required for trajectory prediction.
[0077] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.
[0078] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of the present invention. At the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.
Claims
1. A trajectory prediction method based on line-surface fitting based on machine learning, characterized in that: include: Collecting a target environment image, and converting the target environment image into an HSV space for Gaussian filtering to obtain a preprocessed image; Using the Canny edge detection algorithm to perform line and surface extraction on the preprocessed image to obtain the line and surface to be fitted, and extracting coordinate data of the line and surface to be fitted to obtain the coordinate set to be fitted; Input the coordinate set of the line and surface to be fitted into the pre-trained initial function generation model to obtain the original function to be fitted; Determining a parameter value range of a sub-function within the original function to be fitted according to the coordinate set to be fitted; Within the parameter value range, the parameters of each sub-function in the original function to be fitted are randomly assigned separately to obtain a single parameter adjustment function set; Simulating each function in the single parameter adjustment function set separately to obtain a plurality of simulation coordinate sets, and simulating the original function to be fitted to obtain a control coordinate set; Calculating the difference between the reference coordinate set and the coordinate set to be fitted to obtain a reference coordinate difference set, and calculating the difference between all the simulation coordinate sets and the coordinate set to be fitted to obtain several groups of simulation coordinate difference sets; The optimization degree data of each function in the single parameter adjustment function set is calculated according to the control coordinate difference set and the simulation coordinate difference set; the calculation formula of the optimization degree data is: Among them, O p is the optimization degree data corresponding to the pth function in the single parameter adjustment function set; pi is the ith difference data in the pth simulation coordinate difference set; f 0i is the ith difference data in the reference coordinate difference set; n is the number of coordinates in the coordinate set to be fitted; Updating the adjusted sub-function in the function whose optimization degree data is less than 0 to the original function to be fitted, and calculating the error between the updated original function to be fitted and the coordinate set to be fitted to obtain a loss value; When the loss value is greater than the target expectation, the adjustment direction of the sub-function adjusted in the function whose optimization degree data is less than 0 is extracted to obtain a forward adjustment reference set, and the adjustment direction of the sub-function adjusted in the function whose optimization degree data is greater than or equal to 0 is extracted to obtain a reverse adjustment reference set; According to the direction of the forward adjustment reference set and the opposite direction of the reverse adjustment reference set, the parameters of each sub-function in the updated original function to be fitted are randomly assigned separately to obtain the updated single-parameter adjustment function set, and the step of "simulating each function in the single-parameter adjustment function set separately to obtain several groups of simulation coordinate sets, simulating the original function to be fitted to obtain a control coordinate set" is returned to iterate until the number of iterations reaches the target number of times or the loss value is less than the target expectation, the iteration is stopped, and the original function to be fitted obtained by the last iteration is output to obtain the target trajectory prediction function; The target trajectory prediction function is used to perform trajectory prediction to obtain target prediction trajectory data.
2. The trajectory prediction method based on machine learning for line-surface fitting according to claim 1, characterized in that: The pre-training process of the initial function generation model includes: Constructing a basic function library, randomly selecting functions and setting parameters based on the basic function library to obtain a constructed function set; Simulating the construction function set to obtain multiple sets of construction coordinate data sets and construction line-surface image sets; Using a VGG feature extraction network to perform feature extraction on the constructed line-surface image set to obtain an image feature set, using a one-dimensional CNN to perform feature extraction on the constructed coordinate data set to obtain a coordinate feature set, and fusing the image feature set and the coordinate feature set to obtain a fused feature vector; Constructing a function type recognition model based on a neural network, taking the fused feature vector as a model input and the function type of the constructed function set as a target output, training the function type recognition model to obtain the trained function type recognition model; A preset parameter library is added to the trained function type recognition model to obtain the initial function generation model.
3. The trajectory prediction method based on machine learning for line-surface fitting according to claim 1, characterized in that: Determining the parameter value range of the sub-function within the original function to be fitted according to the coordinate set to be fitted, including: Determine the maximum value, minimum value and interval range of the coordinate set to be fitted; Taking the maximum value and the minimum value as the upper boundary and the lower boundary, calculate the minimum parameter value of each sub-function in the original function to be fitted that traverses the lower boundary and the range of the lower boundary within the interval, construct a value interval from 0 to the minimum parameter value, and obtain the parameter value range.
4. The trajectory prediction method based on machine learning for line-surface fitting according to claim 1, characterized in that: When the number of the coordinate sets to be fitted exceeds a preset upper limit of the number of coordinates, the coordinate sets to be fitted are divided into a plurality of coordinate subsets to be fitted according to the upper limit of the number of coordinates.
5. The trajectory prediction method based on machine learning for line-surface fitting according to claim 1, characterized in that: The calculation formula of the loss value is: Wherein, Loss is the loss value; β1 is the first weight; β2 is the second weight; β3 is the third weight; y′ m is the updated m-th coordinate value of the original function simulation to be fitted; 0m is the mth coordinate value of the coordinate set to be fitted; y′ max , y′ min are respectively the maximum and minimum values of the simulation results of the original function to be fitted after update; 0max ,y 0min are respectively the maximum and minimum values of the coordinate set to be fitted.
6. The trajectory prediction method based on machine learning for line-surface fitting according to claim 2, characterized in that: The one-dimensional CNN includes: a first input layer, a first output layer, first to fourth convolutional layers with a stride of 1, and first to third fully connected layers with a stride of 2; all convolutional layers and connection layers in the one-dimensional CNN adopt batch normalization and rectified linear unit activation functions; the first convolutional layer to the fourth convolutional layer each contain a number of convolutional kernels of size 1×1; the first convolutional layer to the fourth convolutional layer are each followed by a maximum pooling layer; the number of neuron units in the first fully connected layer to the third fully connected layer are 2048, 1024, and 1024, respectively; the first output layer is a softmax layer.
7. The trajectory prediction method based on machine learning for line-surface fitting according to claim 2, characterized in that: The VGG feature extraction network includes: a second input layer, a second output layer, the fifth to twenty-first convolutional layers with a stride of 1 and a ReLU activation function, and the fourth to sixth fully connected layers with a stride of 2 and a ReLU activation function; the fifth to twenty-first convolutional layers contain 3×3 convolution kernels of sizes 64, 64, 128, 128, 256, 256, 512, and 512, respectively; the sixth convolutional layer, the eighth convolutional layer, the eleventh convolutional layer, the fourteenth convolutional layer, and the twenty-first convolutional layer are all followed by a maximum pooling layer of size 2×2 and a stride of 2; the fourth to sixth fully connected layers each include 4096 neurons.