Parabolic Trajectory Prediction Method and System Based on Deep Learning

Abstract

The present invention relates to the field of deep learning technology, specifically a parabolic trajectory prediction method and system based on deep learning, comprising the following steps: collecting parabolic trajectory data under different environmental conditions, subdividing the initial velocity, launch angle, and position of each trajectory data point, performing standardized sorting in timestamp order, and using feature extraction to calculate the optimal matching points between sequences. In the present invention, by refining and rematching the parabolic trajectory data, the timeliness and accuracy of data processing are improved, the prediction error caused by environmental changes is reduced, making the prediction results more in line with the actual situation. The adoption of a bidirectional learning method optimizes the processing of the dependency relationship between data points, enhancing the model's ability to handle complex changing conditions. The introduction of a feedback loop enables the model to self-correct biases during the prediction process, further improving the accuracy of the prediction. These measures significantly improve the data processing efficiency and the accuracy of trajectory prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of deep learning, and particularly to a parabolic trajectory prediction method and system based on deep learning. Background Art

[0002] Deep learning is a technology that realizes machine learning by simulating the working mode of the human brain. It is mainly based on a computational model called an artificial neural network, especially those networks designed with multiple (deep) layers. These models automatically identify complex patterns and features through training with a large amount of data. The applications of deep learning are very extensive, covering multiple fields such as image and speech recognition, natural language processing, and autonomous vehicle technology. Its key advantage lies in the ability to process and learn a large amount of unstructured data, thereby enabling efficient prediction and decision-making on this data without explicit programming instructions.

[0003] Among them, the parabolic trajectory prediction method based on deep learning refers to using deep learning technology to predict the motion trajectory of an object under the action of external forces such as gravity. This prediction technology is usually applied to physics experiments, motion analysis, military and aerospace fields, and other scenarios that require accurate calculation of the trajectory of projectiles. By training a neural network to identify trajectory data under different initial velocities, angles, and environmental conditions, this technology can help scientists and engineers more accurately simulate and predict the motion behavior of objects.

[0004] In the existing deep learning technology for parabolic trajectory prediction, the commonly used network structures and algorithms show insufficient flexibility and adaptability in dealing with complex dynamic environments. Especially in scenarios that require extremely high precision such as physical experiments and aerospace applications, traditional methods may lead to insufficient prediction accuracy due to the failure to fully capture the influence of large-changing initial conditions, such as velocity and angle. This limitation may cause errors in precise tasks, affecting the execution safety and efficiency of tasks. Summary of the Invention

[0005] The purpose of the present invention is to solve the drawbacks existing in the prior art, and to propose a parabolic trajectory prediction method and system based on deep learning.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: A parabolic trajectory prediction method based on deep learning, comprising the following steps:

[0007] S1: Collect parabolic trajectory data under different environmental conditions, subdivide the initial velocity, launch angle, and position of each trajectory data point, perform standardized sorting in the order of time stamps, use feature extraction to calculate the optimal matching points between sequences, and adjust the data point matching time series to generate time-synchronized sequence data;

[0008] S2: Input the time synchronization sequence data into the bidirectional LSTM network, learn from both ends of the sequence simultaneously, convert the dependence between each data point and its adjacent data point into state updates, merge the updated states, and generate a merged feature vector;

[0009] S3: Based on the merged feature vector, analyze the weight influence of the features at each time point, adjust the weight of each feature, correct the model prediction deviation through a feedback loop, and generate optimized weight data;

[0010] S4: Apply the optimized weight data to adjust the time warping parameter in the bidirectional LSTM network, fine-tune the time perception layer in the network structure to adapt to environmental changes, output the predicted trajectory, and establish a predicted trajectory model.

[0011] As a further solution of the present invention, the acquisition steps of the time synchronization sequence data are specifically as follows:

[0012] S111: Collect parabolic trajectory data under multiple environmental conditions, including the initial velocity, launch angle, and position information of each data point, sort the data according to the time stamp, and generate a preliminary trajectory data set;

[0013] S112: Based on the preliminary trajectory data set, analyze the fitting degree between data points through feature extraction, identify and calculate the optimal matching points, and generate a feature matching data set;

[0014] S113: Use the feature matching data set to adjust the time series of data points, using the formula:

[0015]

[0016] Calculate the time offset and generate an adjusted time series data set;

[0017] where, Δt represents the time offset, t obs,i represents the observation data time stamp, t model,i represents the model prediction time stamp, w i represents the weight of the matching point in time adjustment, and n represents the number of data points;

[0018] S114: Use the adjusted time series data set to synchronize the time series of all trajectory data points to ensure that multiple data points are consistent in time, and obtain the time synchronization sequence data.

[0019] As a further solution of the present invention, the acquisition steps of the merged feature vector are specifically as follows:

[0020] S211: Input the time-synchronized sequence data into a bidirectional LSTM network, synchronously process data points from both ends of the sequence, analyze the dependency of each data point with adjacent data points, and generate forward and backward dependency analysis results;

[0021] S212: Calculate the state update of each data point based on the forward and backward dependency analysis results, using the formula:

[0022] u i =α·f i +β·b i

[0023] Generate status update results;

[0024] Among them, u i Indicates the updated state of the i-th data point, f i represents the forward state, b i represents the backward state, α and β are the weight adjustment coefficients of the forward and backward states respectively;

[0025] S213: Using the state update result, merge the updated states and integrate them using a weighted formula:

[0026] s i =γ·(u f,i +u b,i )

[0027] Generate merge status results;

[0028] Among them, s i Represents the merged state vector, u f,i 、u b,i represents the updated forward and backward states, and γ is the state merging weight;

[0029] S214: Extract feature vectors from the merged state result, where each vector comprehensively represents the temporal and spatial characteristics of a group of data points, to generate a merged feature vector set.

[0030] As a further solution of the present invention, the step of obtaining the optimization weight data is specifically as follows:

[0031] S311: Starting from the merged feature vector, analyzing the influence of features at multiple time points, calculating initial weights of multiple features using statistical methods, determining a baseline weight for each feature, and generating an initial weight analysis result;

[0032] S312: Based on the initial weight analysis results, the weight of each feature is refined and adjusted using the formula:

[0033] w i ′ =wi ·(1 + k·(δ i - e i ))

[0034] Calculate the current weight to generate the adjusted weight result;

[0035] where w i ′ represents the adjusted weight, w i represents the original weight, δ i represents the adjustment factor, e i represents the prediction deviation, and k represents the value of the adjustment coefficient;

[0036] S313: Use the adjusted weight result set to correct the deviation in the prediction of the real - time feedback loop correction model, and ensure the accuracy of each feature weight through dynamic adjustment to generate optimized weight data.

[0037] As a further solution of the present invention, the acquisition steps of the prediction trajectory model are specifically as follows:

[0038] S411: Based on the optimized weight data, re - configure the time warping parameters in the bidirectional LSTM network, refine and adjust the processing logic at each time point to generate the time warping parameter adjustment result;

[0039] S412: Use the time warping parameter adjustment result to perform fine - tuning of the time - aware layer in the network structure, using the formula:

[0040] L new = L old ·(1 + η·T adj )

[0041] to obtain the fine - tuned time - aware layer result;

[0042] where L new represents the adjusted layer parameter, L old is the original layer parameter, T adj is the time warping adjustment amount, and η is the fine - tuning coefficient;

[0043] S413: Apply the fine - tuned time - aware layer to process real - time data, and output the prediction trajectory in combination with environmental changes to establish a prediction trajectory model.

[0044] A parabolic trajectory prediction system based on deep learning, which is used to execute the above - mentioned parabolic trajectory prediction method based on deep learning. The system includes:

[0045] The data synchronization module collects parabolic trajectory data under different environmental conditions, sorts the initial velocity, launch angle, and position of each data point by timestamp, synchronizes the time series data, and generates standardized time series data;

[0046] The feature vector synthesis module inputs the standardized time series data into a bidirectional LSTM network, calculates the dependence of each data point on its adjacent data points, updates the state, and merges the state information to obtain a merged feature vector;

[0047] The weight optimization module analyzes and adjusts the feature weights at each time point based on the merged feature vector, corrects the prediction deviation through a feedback mechanism, and generates optimized weight data;

[0048] The time warping adjustment module applies the optimized weight data to adjust the time warping parameters in the bidirectional LSTM network, fine-tunes the time perception layer, matches the environmental changes, and generates adjusted network parameters;

[0049] The trajectory prediction model construction module uses the adjusted network parameters to perform trajectory prediction operations, outputs the predicted trajectory, and establishes a parabolic trajectory prediction model.

[0050] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0051] In the present invention, by refining and rematching the parabolic trajectory data, the timeliness and accuracy of data processing are improved, the prediction error caused by environmental changes is reduced, and the prediction result is more in line with the actual situation. The bidirectional learning method is adopted to optimize the processing of the dependence relationship between data points and enhance the model's response ability under complex changing conditions. The introduction of the feedback loop enables the model to self-correct the deviation during the prediction process and further improves the prediction accuracy. These measures significantly improve the data processing efficiency and the accuracy of trajectory prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the working process of the present invention;

[0053] Figure 2 It is a flowchart of the steps for obtaining the time synchronization sequence data of the present invention;

[0054] Figure 3 It is a flowchart of the steps for obtaining the merged feature vector of the present invention;

[0055] Figure 4 It is a flowchart of the steps for obtaining the optimized weight data of the present invention;

[0056] Figure 5 It is a flowchart of the steps for obtaining the predicted trajectory model of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0057] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0058] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, in the description of the present invention, the meaning of "a plurality of" is two or more unless otherwise specifically defined.

[0059] Embodiment 1

[0060] Please refer to Figure 1 , the present invention provides a technical solution: a parabolic trajectory prediction method based on deep learning, including the following steps:

[0061] S1: Collect parabolic trajectory data under different environmental conditions, subdivide the initial velocity, launch angle and position of each trajectory data point, perform standardized sorting in the order of time stamps, use feature extraction to calculate the optimal matching points between sequences, adjust the data point matching time series, and generate time-synchronized sequence data;

[0062] S2: Input the time-synchronized sequence data into a bidirectional LSTM network, learn from both ends of the sequence simultaneously, convert the dependence of each data point on adjacent data points into state updates, and merge the updated states to generate a merged feature vector;

[0063] S3: Based on the merged feature vector, analyze the weight influence of the features at each time point, adjust the weight of each feature, correct the model prediction deviation through a feedback loop, and generate optimized weight data;

[0064] S4: Apply the optimized weight data, adjust the time warping parameter in the bidirectional LSTM network, fine-tune the time perception layer in the network structure, adapt to environmental changes, output the predicted trajectory, and establish a predicted trajectory model.

[0065] The time-synchronized sequence data includes the initial velocity, launch angle, position and time stamp. The merged feature vector includes the forward feature, backward feature and fusion representation of the bidirectional LSTM. The optimized weight data includes feature weights and feedback adjustment parameters. The predicted trajectory is specifically a sequence of trajectory points and velocity information.

[0066] Please refer to Figure 2 , the steps for obtaining time synchronization sequence data are specifically as follows:

[0067] S111: Collect parabolic trajectory data under multiple environmental conditions, including the initial velocity, launch angle, and position information of each data point, sort the data according to the time stamp, and generate a preliminary trajectory data set;

[0068] Collect parabolic trajectory data under multiple environmental conditions, including the initial velocity, launch angle, and position information of each data point. The data is sorted according to the time stamp. By measuring the data points, including using radar and optical sensors to capture the velocity and angle of each projectile, record the launch point and time information of each projectile, and generate a preliminary trajectory data set. This data set can be used for iterative trajectory analysis and pattern recognition. Through this method, it is possible to ensure that the collected data is both accurate and complete for trajectory matching and feature analysis.

[0069] S112: Based on the preliminary trajectory data set, analyze the fitness between data points through feature extraction, identify and calculate the optimal matching points, and generate a feature matching data set;

[0070] Apply feature extraction technology to the preliminary trajectory data set. By analyzing the fitness between data points, identify and calculate the optimal matching points. Use machine learning algorithms to analyze the trajectory data to identify similar or repeated trajectory patterns, including using clustering algorithms to group trajectory points, calculate the fitness of data points in each group, and determine the trajectory points with the highest matching degree. This process involves the comprehensive application of multiple algorithms, from data cleaning to feature extraction, to ensure that each matching point is the optimal representative based on the actual trajectory data, thereby generating a feature matching data set. This data set provides a basis for subsequent time series adjustment.

[0071] S113: Use the feature matching data set to perform time series adjustment on the data points, using the formula:

[0072]

[0073] Calculate the time offset and generate an adjusted time series data set;

[0074] where, Δt represents the time offset, t obs,i represents the observation data time stamp, t model,i represents the model prediction time stamp, w i represents the weight of the matching point in time adjustment, and n represents the number of data points;

[0075] Formula:

[0076]

[0077] The advantage of the formula is that by introducing the weight factor w i , each data point has a differential influence according to its reliability or precision differentiation, so as to calibrate the time series;

[0078] Detailed explanation of the formula and the derivation process of formula calculation:

[0079] Set the observation timestamps t of three data points obs to be 1.5s, 2.5s, 3.5s respectively, and the model prediction timestamps t model to be 1s, 2s, 3s respectively, and the weights w to be 0.5, 1, 1.5 respectively, and insert them into the formula for calculation:

[0080]

[0081] The results show that the adjusted average time offset is about 0.167s, indicating that the observed time series needs to be adjusted forward by about 0.167 seconds to better align with the model prediction, so as to synchronize the time series.

[0082] S114: Use the adjusted time series dataset to synchronize the time series of all trajectory data points, ensure that multiple data points are consistent in time, and obtain time-synchronized sequence data.

[0083] Use the adjusted time series dataset to synchronize the time series of all trajectory data points, ensure that multiple data points are consistent in time, and obtain time-synchronized sequence data. Align the observed data with the time series of the prediction model by adjusting the timestamps of the data points. This process involves recalculating and correcting the timestamps of each data point to ensure that all data points can be compared and analyzed within the same time frame. This not only improves the usability of the data but also enhances the accuracy of data analysis. The obtained time-synchronized sequence data provides a solid foundation for the next step of analysis.

[0084] Please refer to Figure 3 , and the specific steps for obtaining the combined feature vector are as follows:

[0085] S211: Input the time-synchronized sequence data into a bidirectional LSTM network, synchronously process the data points from both ends of the sequence, analyze the dependence of each data point on adjacent data points, and generate forward and backward dependence analysis results;

[0086] Input the time synchronization sequence data into a bidirectional LSTM network. The network processes data points synchronously from both ends of the sequence, analyzes the dependencies between each data point and its adjacent data points, and uses the forward and backward recurrent neural network structures to capture the long-term dependencies in the time series data. This structure enables the network to learn information from both ends of the sequence towards the center, optimize the parsing of the time dependencies between data points, and improve the model's ability to capture time series features by dynamically adjusting the weights and biases of the network. This method is particularly suitable for scenarios that require extracting time characteristics from sequence data, such as speech recognition and stock price prediction. Through bidirectional learning, the network can more comprehensively analyze the front and back relationships of the data structure, thereby generating more accurate dependency analysis results.

[0087] S212: Calculate the state update for each data point based on the forward and backward dependency analysis results, using the formula:

[0088] u i = α·f i + β·b i

[0089] Generate the state update result;

[0090] where u i represents the updated state of the i-th data point, f i represents the forward state, b i represents the backward state, and α and β are the weight adjustment coefficients for the forward and backward states respectively;

[0091] Formula:

[0092] u i = α·f i + β·b i

[0093] The benefit of the formula is that by introducing the weight parameters α and β, the influence of the forward state f i and the backward state b i can be adjusted, making the model more flexible in matching different data characteristics. This weighting method helps to balance the time dynamics in the sequence data and improve the accuracy of the state update.

[0094] Detailed explanation of the formula and the derivation process of the formula calculation:

[0095] ]Set the value of the forward state f i to 0.6, the value of the backward state b i to 0.4, and the weights α and β to 0.5 and 0.5 respectively. The calculation process is as follows:

[0096] u i = 0.5·0.6 + 0.5·0.4 = 0.3 + 0.2 = 0.5

[0097] The result shows that the state update result u i is 0.5, which indicates that under the given weights, the forward and backward states are evenly referenced, reflecting the average effect of the data point update state. This helps to more accurately merge the states in subsequent steps and improve the prediction performance of the model.

[0098] S213: Use the state update result to merge the updated states and integrate them through a weighted formula:

[0099] s i = γ · (u f,i + u b,i )

[0100] Generate the merged state result;

[0101] where s i represents the merged state vector, u f,i , u b,i represent the updated forward and backward states, and γ is the state merging weight;

[0102] Formula:

[0103] s i = γ · (u f,i + u b,i )

[0104] The benefit of the formula is that by adjusting the merging weight γ, the contributions of the forward and backward update states u f,i and u b,i can be effectively balanced, enabling the state merging to not only refer to the information at both ends of the time series but also cope with time series data with different characteristics by matching and adjusting γ, enhancing the flexibility and accuracy of the model when processing data with different time dependence intensities.

[0105] Detailed explanation of the formula and the derivation process of the formula calculation:

[0106] Set the value of the forward update state u f,i to 0.7, the value of the backward update state u b,i to 0.3, and the merging weight γ to 0.8. The calculation process is as follows:

[0107] s i = 0.8 · (0.7 + 0.3) = 0.8 · 1.0 = 0.8

[0108] The result shows that the merged state vector s i is 0.8, reflecting that under the current weights, the model effectively integrates the state information from both ends of the sequence, improves the integration effect of features, and provides a basis for generating the feature vector set.

[0109] S214: Extract feature vectors from the merged state result. Each vector comprehensively represents the temporal and spatial characteristics of a set of data points, generating merged feature vectors.

[0110] Extract feature vectors from the merged state result. Each vector comprehensively represents the temporal and spatial characteristics of a set of data points. This process involves performing high-dimensional feature transformation on the merged state, which is carried out through the stacking of activation functions and network layers in a machine learning model. The extraction of feature vectors not only includes the temporal information of data points but also incorporates the spatial interrelationships. Such a processing method enables the feature vectors to more comprehensively describe the inherent characteristics of the data, providing richer and more useful input information for subsequent machine learning tasks including classification and prediction. Through the analysis of feature vectors, time series prediction or classification can be carried out more accurately, assisting in improving the accuracy of the decision support system, and thus playing a key role in practical applications.

[0111] Please refer to Figure 4 , and the specific steps for optimizing the acquisition of weight data are as follows:

[0112] S311: Starting from the merged feature vectors, analyze the influence of multi-time point features, calculate the initial weights of multiple features using statistical methods, determine the baseline weight of each feature, and generate the initial weight analysis result;

[0113] During the process of analyzing the merged feature vectors, the influence of each feature's time point is quantified through statistical methods. It not only refers to the performance of multiple features in the model but also adjusts their weights through real-time data feedback to ensure the accuracy and practicality of the analysis. In this way, the influence of each feature on the model output is obtained, and then adjusted one by one according to the actual performance of the model. The statistical method adjusts the weights of multiple features by comparing the deviation between the predicted values and the actual values of multiple features, ensuring that the model after weight adjustment can more accurately predict the trends in future time periods. The implementation effect of this method will directly affect the optimization and accuracy of the model.

[0114] S312: Based on the initial weight analysis result, refine and adjust the weight of each feature, using the formula:

[0115] w ′ i = w i ·(1 + k·(δ i - e i ))

[0116] Calculate the current weight, generating the adjusted weight result;

[0117] where, w ′ i represents the adjusted weight, wi Represents the original weight, δ i Represents the adjustment factor, e i Represents the prediction deviation, and k represents the value of the adjustment coefficient;

[0118] Formula:

[0119] w ′ i = w i ·(1 + k·(δ i - e i ))

[0120] The benefit of the formula is that by introducing the adjustment coefficient k and the dynamic adjustment factor δ i - e i , the weight can be flexibly adjusted according to the deviation of the actual model prediction, enhancing the adaptability of the model to data fluctuations and the prediction accuracy.

[0121] Detailed explanation of the formula and the derivation process of the formula calculation:

[0122] Set the initial weight w i = 0.5, the adjustment coefficient k = 0.1, the adjustment factor δ i = 0.05, the prediction deviation e i = 0.02;

[0123] The calculation process according to the formula is as follows:

[0124] w ′ i = 0.5·(1 + 0.1·(0.05 - 0.02)) = 0.5·(1 + 0.1·0.03) = 0.5·1.003 = 0.5015

[0125] The result shows that by fine-tuning the weight, the model can more precisely adjust the response to the target feature and improve the prediction performance.

[0126] S313: Use the adjusted weight result set to correct the deviation in the model prediction in combination with the real-time feedback loop, and ensure the accuracy of each feature weight through dynamic adjustment to generate optimized weight data.

[0127] Using the adjusted weights, combined with a real-time feedback loop for predictive bias correction of the model, this dynamic correction mechanism enables the adjustment of each feature weight not only based on data but also combined with the feedback of real-time data. By cyclically adjusting and optimizing the weight parameters, it ensures that the model can exhibit higher flexibility and adaptability when facing current data, not only improving the prediction accuracy of the model but also enhancing the model's response ability to emergencies. Real-time optimization of the weights generates optimized weight data that can more accurately reflect the actual impact of each feature on the model output, thus making the model prediction closer to the actual situation.

[0128] Please refer to Figure 5 , the steps for obtaining the prediction trajectory model are specifically as follows:

[0129] S411: Based on the optimized weight data, reconfigure the time warping parameters in the bidirectional LSTM network, refine and adjust the processing logic at each time point, and generate the time warping parameter adjustment result;

[0130] The process of reconfiguring the time warping parameters of the bidirectional LSTM network based on the optimized weight data requires analyzing the adaptability of the dynamic changes of data points. This process involves analyzing and determining the most suitable parameters at each time point through batch real-time monitoring of data. By collecting and analyzing the data fluctuations in different time periods, the adjustment value of the time warping parameters can be calculated. This value reflects the impact of environmental changes on the network performance. Adjusting the time warping parameters can enable the network to better match the changes in future data, and real-time adjustment ensures the flexibility of the network and its ability to respond to emergencies. The generated time warping parameter adjustment result provides the network with more precise time perception ability to match the characteristics of the cyclically changing input data.

[0131] S412: Using the time warping parameter adjustment result, perform fine-tuning of the time perception layer in the network structure, using the formula:

[0132] L new =L old ·(1 + η·T adj )

[0133] Obtain the fine-tuned time perception layer result;

[0134] Among them, L new represents the adjusted layer parameter, L old is the original layer parameter, T adj is the time warping adjustment amount, and η is the fine-tuning coefficient;

[0135] Formula:

[0136] L new =L old ·(1 + η·T adj )

[0137] The advantage of the formula is that by adjusting the coefficient η and the time distortion parameter T adj , the reaction speed and sensitivity of the network layer can be flexibly adjusted to match the differentiated operating environment and data changes, thereby improving the adaptability and accuracy of the model.

[0138] Detailed explanation of the formula and the derivation process of formula calculation:

[0139] Set the original time perception layer parameter L old to 0.5, set the adjustment coefficient η to 0.05, and the adjusted value T of the time distortion parameter adj is determined to be 2 based on data analysis, then adj

[0140] L new = 0.5·(1 + 0.05·2) = 0.5·1.1 = 0.55

[0141] The results show that through fine-tuning, the parameter of the time perception layer increases from 0.5 to 0.55, enhancing the layer's ability to match time distortion and improving the network's sensitivity and reaction speed to time changes.

[0142] S413: Process real-time data using the fine-tuned time perception layer, output a predicted trajectory in combination with environmental changes, and establish a predicted trajectory model.

[0143] The fine-tuned time perception layer processes real-time data. During this process, data on environmental changes is integrated to adjust the network output. First, real-time data is collected by environmental monitoring devices, and then the data is input into the fine-tuned LSTM network. The network calculates the predicted trajectory based on the characteristics and data patterns of the input data, using the newly adjusted time perception layer parameters. This calculation process includes not only the forward propagation of data but also the backpropagation of errors to optimize the prediction for future time periods. Through data processing and network adjustment, it is ensured that the output predicted trajectory fits the actual situation to the greatest extent. The obtained predicted trajectory model will be used for prediction tasks in future similar environments to ensure that the model can continuously provide high-precision output.

[0144] A parabolic trajectory prediction system based on deep learning, which is used to execute the above-mentioned parabolic trajectory prediction method based on deep learning. The system includes:

[0145] The data synchronization module collects parabolic trajectory data under different environmental conditions, sorts the initial velocity, launch angle, and position of each data point by timestamp, and synchronizes the time series data to generate standardized time series data;

[0146] The eigenvector synthesis module inputs the standardized time series data into the bidirectional LSTM network, calculates the dependencies between each data point and its adjacent data points, updates the states and merges the state information to obtain the merged eigenvector;

[0147] The weight optimization module analyzes and adjusts the feature weights at each time point based on the merged eigenvector, corrects the prediction bias through a feedback mechanism, and generates optimized weight data;

[0148] The time warping adjustment module applies the optimized weight data to adjust the time warping parameters in the bidirectional LSTM network, fine-tunes the time perception layer, matches the environmental changes, and generates the adjusted network parameters;

[0149] The trajectory prediction model construction module uses the adjusted network parameters to perform trajectory prediction operations, outputs the predicted trajectory, and establishes a parabolic trajectory prediction model.

[0150] The above are only the preferred embodiments of the present invention, and do not limit the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes and apply them to other fields. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A parabolic trajectory prediction method based on deep learning, characterized in that It includes the following steps: Collect parabolic trajectory data under different environmental conditions, subdivide the initial velocity, launch angle, and position of each trajectory data point, perform standardized sorting in timestamp order, use feature extraction to calculate the optimal matching points between sequences, adjust the data point matching time series, and generate time-synchronized sequence data; Input the time-synchronized sequence data into a bidirectional LSTM network, learn from both ends of the sequence simultaneously, convert the dependence of each data point on adjacent data points into state updates, merge the updated states, and generate a merged feature vector; Based on the merged feature vector, analyze the weight influence of features at each time point, adjust the weight of each feature, correct the model prediction deviation through a feedback loop, and generate optimized weight data; Apply the optimized weight data, adjust the time warping parameter in the bidirectional LSTM network, fine-tune the time perception layer in the network structure, adapt to environmental changes, output the predicted trajectory, and establish a predicted trajectory model; The specific steps for obtaining the merged feature vector are as follows: Input the time-synchronized sequence data into a bidirectional LSTM network, process the data points synchronously from both ends of the sequence, analyze the dependence of each data point on adjacent data points, and generate forward and backward dependence analysis results; According to the forward and backward dependence analysis results, calculate the state update of each data point, using the formula: Generate the state update result; Among them, represents the state after the update of the th data point, represents the forward state, represents the backward state, , are the weight adjustment coefficients for the forward and backward states respectively; Use the state update result, merge the updated states, and integrate them through a weighted formula: Generate the merged state result; Among them, represents the merged state vector, , represent the updated forward and backward states, is the state merging weight; Extract the feature vector from the merged state result, where each vector comprehensively represents the time and space characteristics of a group of data points, and generate a merged feature vector set; The specific steps for obtaining the optimized weight data are as follows: Starting from the merged feature vector, analyze the influence of multi-time point features, use statistical methods to calculate the initial weights of multi-features, determine the baseline weight of each feature, and generate the initial weight analysis result; Based on the initial weight analysis result, refine and adjust the weight of each feature, using the formula: Calculate the current weight and generate the adjusted weight result; Among them, represents the adjusted weight, represents the original weight, represents the adjustment factor, represents the prediction deviation, represents the value of the adjustment coefficient; Use the adjusted weight result set, combine the real-time feedback loop to correct the deviation in model prediction, and ensure the accuracy of each feature weight through dynamic adjustment to generate optimized weight data.

2. The parabolic trajectory prediction method based on deep learning according to claim 1, wherein The specific steps for obtaining the time-synchronized sequence data are as follows: Collect parabolic trajectory data under multiple environmental conditions, including the initial velocity, launch angle, and position information of each data point, sort the data according to the timestamp, and generate a preliminary trajectory data set; Based on the preliminary trajectory data set, analyze the fitting degree between data points through feature extraction, identify and calculate the optimal matching points, and generate a feature matching data set; Using the feature matching data set, adjust the time series of data points, using the formula: Calculate the time offset and generate the adjusted time series data set; wherein, represents the time offset, represents the timestamp of the observed data, represents the timestamp of the model prediction, represents the weight of the matching point in time adjustment, represents the number of data points; Using the adjusted time series data set, synchronize the time series of all trajectory data points to ensure the consistency of multiple data points in time, and obtain the time-synchronized sequence data.

3. The parabolic trajectory prediction method based on deep learning according to claim 2, wherein The specific steps for obtaining the predicted trajectory model are as follows: Based on the optimized weight data, reconfigure the time warping parameters in the bidirectional LSTM network, refine and adjust the processing logic at each time point, and generate the time warping parameter adjustment result; Utilize the time warping parameter adjustment result to perform fine-tuning of the time perception layer in the network structure, using the formula: Obtain the fine-tuned time perception layer result; Among them, represents the adjusted layer parameters, is the original layer parameter, is the time warping adjustment amount, is the fine-tuning coefficient; Apply the fine-tuned time perception layer to process real-time data, combine environmental changes to output a predicted trajectory, and establish a predicted trajectory model.

4. A parabolic trajectory prediction system based on deep learning, characterized in that, According to the deep learning-based parabolic trajectory prediction method according to any one of claims 1-3, the system includes: The data synchronization module collects parabolic trajectory data under different environmental conditions, sorts the initial velocity, launch angle, and position of each data point by timestamp, and synchronizes the time series data to generate standardized time series data; The feature vector synthesis module inputs the standardized time series data into the bidirectional LSTM network, calculates the dependence of each data point on its adjacent data points, updates the state and merges the state information to obtain a merged feature vector; The weight optimization module analyzes and adjusts the feature weights at each time point based on the merged feature vector, corrects the prediction deviation through a feedback mechanism, and generates optimized weight data; The time warping adjustment module applies the optimized weight data to adjust the time warping parameters in the bidirectional LSTM network, fine-tunes the time perception layer, matches the environmental changes, and generates the adjusted network parameters; The trajectory prediction model construction module utilizes the adjusted network parameters to perform trajectory prediction operations, outputs a predicted trajectory, and establishes a parabolic trajectory prediction model.

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