Aircraft space-time probability envelope determination method and system

Abstract

The invention provides an aircraft space-time probability envelope determination method and system, and belongs to the technical field of trajectory prediction, and the method comprises the steps: inputting a data set of an aircraft into a Gaussian process regression model, and obtaining a prediction mean value and a prediction covariance of each prediction space position of the aircraft after a future moment; wherein the data set comprises a plurality of current flight data and a plurality of current environment data; based on each prediction mean value and each prediction covariance, calculating the probability that the aircraft appears at each prediction space position after the future moment; and gathering all the predicted spatial positions of which the probabilities are greater than a preset probability threshold to obtain a space-time probability envelope of the aircraft. According to the method, the spatial position and the uncertainty of the aircraft at the future moment are predicted based on the Gaussian process regression model by using the current flight data and the environmental data, and the high-probability region is screened out by setting the probability threshold value to form the spatial-temporal probability envelope of the aircraft, so that the spatial position of the aircraft at the future moment is accurately predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of trajectory prediction, and in particular to a method and system for determining a space-time probability envelope of an aircraft. Background Art

[0002] As the demand for air transportation grows, the number of aircraft continues to increase, and the complexity and density of air traffic have also increased significantly. In order to ensure flight safety and improve the efficiency of air traffic management, it is crucial to accurately predict the future position of aircraft during flight. Aircraft usually operate in a changing weather environment and dynamic air traffic flow, which makes it difficult to accurately predict their flight trajectory.

[0003] In the current technical scenario, the future position prediction methods of aircraft rely on approaches based on deterministic models. These methods usually use the current state of the aircraft (such as position, velocity, acceleration) and flight dynamics equations for prediction. For example, the commonly used Kalman filter method assumes that the system is linear and observable, and makes the best estimate of the future state based on the current state. However, Kalman filters and similar deterministic methods perform poorly when dealing with complex nonlinear aircraft motion, especially when encountering complex environmental factors (such as airflow changes and sudden weather conditions). Such methods have difficulty dealing with nonlinear characteristics in aircraft trajectories. In addition, many existing path prediction algorithms usually cannot provide the uncertainty of the prediction results, which means that even if the prediction results seem accurate, it is impossible to give a confidence interval for the future position of the aircraft. This lack of uncertainty estimation makes it impossible to accurately predict the spatial position of the aircraft at future times, thereby increasing the possibility of flight accidents.

[0004] Therefore, how to accurately predict the spatial position of an aircraft at a future moment, thereby reducing the possibility of flight accidents, has become a technical problem that needs to be solved urgently. Summary of the invention

[0005] The present invention provides a method, system, electronic device and storage medium for determining the space-time probability envelope of an aircraft, which are used to solve the defects in the prior art and achieve accurate prediction of the spatial position of an aircraft at a future time, thereby reducing the possibility of flight accidents.

[0006] The present invention provides a method for determining a space-time probability envelope of an aircraft, comprising the following steps: inputting an aircraft data set into a Gaussian process regression model to obtain a predicted mean and a predicted covariance of each predicted spatial position of the aircraft at a future time; wherein the data set includes a plurality of current flight data and a plurality of current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future time, and the spatial point corresponds to any point in a spatial geometric body formed by velocity vectors in various directions of the aircraft at a future time; Calculating the probability of the aircraft appearing at each of the predicted spatial positions after a future time based on each of the predicted means and each of the predicted covariances; All predicted spatial positions whose probabilities are greater than a preset probability threshold are collected to obtain the spatiotemporal probability envelope of the aircraft.

[0007] According to a method for determining a space-time probability envelope of an aircraft provided by the present invention, the Gaussian process regression model is trained by the following method: Constructing a plurality of training samples, each of the training samples comprising a flight data sample and an environment data sample; Determine Gaussian process and kernel function; Constructing a log-marginal likelihood function based on all the training samples, the Gaussian process and the kernel function; By maximizing the log-marginal likelihood function, initial hyperparameters of the Gaussian process regression model are obtained; The initial hyperparameters are optimized to obtain optimized hyperparameters, and the initial model is trained based on the optimized hyperparameters to obtain the Gaussian process regression model.

[0008] According to a method for determining a space-time probability envelope of an aircraft provided by the present invention, the Gaussian process is represented by the following formula: ; Among them, x is the input feature vector of the training sample, is the observed value of the training sample, is the correlation function of the training samples, is Gaussian noise, is the variance of the noise, and n is the number of training samples.

[0009] According to a method for determining a space-time probability envelope of an aircraft provided by the present invention, the kernel function is expressed by the following formula: ; in, is the kernel function, is the input feature vector of the i-th training sample, is the input feature vector of the jth training sample, and l is the length scale parameter.

[0010] According to a method for determining a space-time probability envelope of an aircraft provided by the present invention, the logarithmic marginal likelihood function is expressed by the following formula: ; Among them, y is the observation value vector of all training samples, X is the feature matrix containing all training samples, is the transpose of the observation vector, K is the covariance matrix containing all kernel functions, is the variance of the noise, n is the number of training samples, and I is the identity matrix.

[0011] According to a method for determining a space-time probability envelope of an aircraft provided by the present invention, the data set includes a plurality of input units, each of which includes a current flight data and a current environment data; the method is characterized in that the data set of the aircraft is input into a Gaussian process regression model to obtain a predicted mean and a predicted covariance of each predicted spatial position of the aircraft at a future time, specifically including: Based on all the input units, a plurality of current input feature vectors are obtained; Based on each of the current input feature vectors, obtaining an observation value of each input unit; Constructing the observation values ​​of all the input units into an observation value vector of all the input units; Based on all the current input feature vectors, a plurality of kernel functions are calculated, and based on all the kernel functions, a covariance matrix is ​​constructed; Based on each of the input units, construct a feature matrix containing all the input units; Based on the feature matrix containing all input units, the observation value vectors of all input units and the covariance matrix, the predicted mean and predicted covariance of each predicted spatial position of the aircraft after a future moment are calculated.

[0012] The present invention also provides an aircraft space-time probability envelope determination system, comprising: a first processing module and a second processing module; The first processing module is used to input the data set of the aircraft into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future time; wherein the data set includes a plurality of current flight data and a plurality of current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future time, and the spatial point corresponds to any point in the spatial geometric body formed by the velocity vectors in all directions of the aircraft at a future time; The second processing module is used to calculate the probability of the aircraft appearing at each of the predicted spatial positions after a future moment based on each of the predicted means and each of the predicted covariances; The second processing module is further used to collect all the predicted spatial positions whose probabilities are greater than a preset probability threshold to obtain the spatiotemporal probability envelope of the aircraft.

[0013] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements any of the above-described methods for determining the space-time probability envelope of an aircraft.

[0014] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for determining the space-time probability envelope of an aircraft as described in any one of the above is implemented.

[0015] The present invention also provides a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the method for determining the space-time probability envelope of an aircraft as described above is implemented.

[0016] In summary, one or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages: By inputting the aircraft data set into the Gaussian process regression model, the model can accurately predict the mean and covariance of each spatial position that the aircraft may reach in the future based on the current flight data and environmental data. The effect of this approach is that it utilizes the complex nonlinear relationship between historical flight data and environmental characteristics, thereby improving the accuracy of the aircraft's future position prediction. Based on the mean and covariance of each predicted spatial position, the probability of the aircraft appearing at these positions in the future is further calculated. In this way, the model can not only provide the most likely prediction results, but also quantify the uncertainty of these prediction results. Through the Gaussian process regression model, the prediction results can be expressed as a normal distribution. The model accurately describes the probability distribution of future positions through the mean and covariance, so that managers can evaluate the confidence interval of the aircraft's future position based on these probabilities. By setting a preset probability threshold, all predicted spatial positions with probabilities greater than the threshold are collected to form the aircraft's spatiotemporal probability envelope. This scheme ensures that the spatiotemporal envelope only includes high-probability areas, thereby accurately predicting the aircraft's spatial position in the future, thereby reducing the possibility of flight accidents. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 It is one of the flow charts of the method for determining the space-time probability envelope of an aircraft provided by the present invention.

[0019] Figure 2 This is the second flow chart of the method for determining the space-time probability envelope of an aircraft provided by the present invention.

[0020] Figure 3 It is a structural schematic diagram of the aircraft space-time probability envelope determination system provided by the present invention.

[0021] Figure 4 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are 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.

[0023] It should be noted that, in the description of the present invention, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "include one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements. The orientation or positional relationship indicated by the terms "upper", "lower", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the system or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0024] The terms "first", "second", etc. in the present invention are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present invention can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" means at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0025] Combine the following Figure 1-Figure 4The invention describes the method, system, electronic device and storage medium for determining the space-time probability envelope of an aircraft.

[0026] Figure 1 FIG. 1 is one of the flow charts of the method for determining the space-time probability envelope of an aircraft provided by the present invention, such as Figure 1 As shown, including but not limited to the following steps: Step 11: Input the aircraft data set into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future moment; wherein the data set includes multiple current flight data and multiple current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future moment, and the spatial point corresponds to any point in the spatial geometry formed by the velocity vectors in all directions of the aircraft at a future moment.

[0027] When implementing step 11, the aircraft data set is input into the Gaussian process regression model to accurately predict each predicted spatial position that the aircraft may reach in the future, and based on this, its predicted mean and predicted covariance are calculated. The core of this step is to build a model with high-precision prediction capabilities by making full use of current flight data and environmental data, thereby improving the reliability and accuracy of the aircraft's future position prediction.

[0028] The data set includes multiple input units, each of which includes a current flight data and a current environmental data. The current flight data includes but is not limited to predicted track, position, speed, acceleration, flight altitude and other flight parameters; the current environmental data includes but is not limited to meteorological conditions, wind speed, air pressure, electromagnetic intensity, etc.

[0029] The process of inputting the aircraft data set into the Gaussian process regression model includes obtaining the current velocity vector of the aircraft and its possible trajectory at future moments. Specifically, the model will calculate any spatial point that the aircraft may reach at future moments based on the current velocity vector of the aircraft in all directions. Each predicted spatial position corresponds to any point in the spatial geometry formed at this future moment. The core of this step is to use the ability of the Gaussian process regression model to handle nonlinear dynamic systems. By capturing the complex nonlinear relationship between the aircraft velocity and the environment, the future trajectory of the aircraft can be accurately modeled.

[0030] In the Gaussian process regression model, the key prediction outputs include the mean and covariance of each predicted spatial position. The predicted mean represents the spatial position where the aircraft is most likely to appear in the future, while the predicted covariance quantifies the model's confidence or uncertainty in the predicted value. In this process, the model uses known flight data and environmental data to calculate the possible future flight space and generates the corresponding predicted mean and predicted covariance for each possible location point.

[0031] In subsequent embodiments, the specific training method of the Gaussian process regression model and the specific implementation method of inputting the aircraft data set into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future moment will be described in detail.

[0032] In one possible implementation, refer to Figure 2 , Figure 2 This is the second flow chart of the method for determining the space-time probability envelope of an aircraft provided by the present invention. The specific training method of the Gaussian process regression model includes the following steps: Step 21: Construct multiple training samples, each training sample includes a flight data sample and an environment data sample.

[0033] When implementing step 21, multiple training samples are constructed to provide sufficient historical data for the Gaussian process regression model to predict the spatial position of the aircraft at future moments. Since the dynamic characteristics of the aircraft and environmental changes have a complex nonlinear relationship, these changes cannot be captured by relying on a single data source. Therefore, by combining flight data and environmental data, multiple training samples are constructed so that the model can fully understand the flight laws of the aircraft under different conditions.

[0034] The specific process of constructing training samples is as follows: First, collect the historical flight data of the aircraft, including key information such as historical position, historical speed, historical acceleration, etc., and ensure that these data are dense enough to reflect the dynamic changes of the aircraft. Then, obtain the historical environmental data corresponding to each historical flight data point, including historical real-time meteorological conditions, wind speed, air pressure, electromagnetic intensity, etc. At each time step, combine a flight data sample with the environmental data sample at the corresponding time point to form a training sample. Constructing multiple training samples in this way enables the model to simultaneously learn the interaction between the internal state of the aircraft and the external environment.

[0035] Step 22: Determine the Gaussian process and kernel function.

[0036] In one possible implementation, the Gaussian process is represented by the following formula: ; Among them, x is the input feature vector of the training sample, is the observed value of the training sample, is the correlation function of the training samples, is Gaussian noise, is the variance of the noise, and n is the number of training samples.

[0037] The kernel function is expressed by the following formula: ; in, is the kernel function, is the input feature vector of the i-th training sample, is the input feature vector of the jth training sample, and l is the length scale parameter.

[0038] When implementing step 22, determining the Gaussian process and kernel function is one of the core steps of the Gaussian process regression model, which determines how the model learns and predicts based on flight data and environmental data. Selecting the appropriate Gaussian process and kernel function is crucial to capturing the complex nonlinear relationship in the aircraft trajectory and improving the prediction accuracy of the model.

[0039] First, the core of determining the Gaussian process is to define how the model views the relationship between data. The Gaussian process assumes that the observed output y(x) is a combination of a potential function f(x) about the input feature x plus noise ϵ, that is, . The noise term ϵ is independent and normally distributed, indicating that the observations of the aircraft may be affected by sensor errors or external interference. Therefore, through this assumption, the Gaussian process can well handle the uncertainty and noise problems in the flight path of the aircraft.

[0040] The choice of kernel function is crucial because it directly affects the model's similarity measurement of input data. The kernel function is used to measure the similarity between flight data and environmental data samples. The commonly used kernel function is the radial basis function (RBF), and its mathematical expression is: ; in, is the kernel function, is the input feature vector of the i-th training sample, is the input feature vector of the jth training sample, and l is the length scale parameter.

[0041] By using the RBF kernel function, we can capture the smooth, continuous, nonlinear relationship between the aircraft state and environmental changes. The characteristic of the RBF kernel function is that it can give higher similarity to samples that are close to each other, thereby generating smoother predictions in the model. In other words, if the flight state and environmental conditions of the aircraft at two points in time are close, the kernel function will consider the similarity between these states to be high, making the model prediction more stable.

[0042] In order for the model to work effectively under different flight conditions, it is also necessary to optimize the hyperparameters in the kernel function. For example, the length scale l controls the smoothness of the kernel function. By adjusting l, you can determine how sensitive the model is to changes in the aircraft state. Smaller l values ​​mean that the model is more sensitive to input changes and is better suited to handling rapidly changing flight conditions, while larger l values ​​produce smoother predictions and are suitable for handling stable flight conditions. Therefore, choosing the right kernel function and hyperparameters can ensure that the model remains robust in complex flight environments.

[0043] Step 23: Construct a log-marginal likelihood function based on all training samples, Gaussian process and kernel function.

[0044] In one possible implementation, the log marginal likelihood function is expressed by the following formula: ; Among them, y is the observation value vector of all training samples, X is the feature matrix containing all training samples, is the transpose of the observation vector, K is the covariance matrix containing all kernel functions, is the variance of the noise, n is the number of training samples, and I is the identity matrix.

[0045] When implementing step 23, the log-marginal likelihood function is constructed based on all training samples, Gaussian processes, and kernel functions to evaluate the degree of fit of the model to the training data and provide a basis for optimizing the model's hyperparameters. By maximizing the log-marginal likelihood function, the model can be effectively adjusted to accurately capture the inherent structure in the aircraft trajectory data and improve the prediction performance.

[0046] First, through steps 21 and 22, multiple training samples have been constructed, and the Gaussian process model and kernel function have been determined. These training samples include the flight data and environmental data of the aircraft, and the model uses these data to understand the movement law of the aircraft. However, in order to further improve the accuracy and reliability of the model, a logarithmic marginal likelihood function must be constructed to measure the model's fitting effect on these data.

[0047] Specifically, the log-marginal likelihood function is an indicator of how well the Gaussian process regression model models the observed data. It determines whether the model effectively captures the trend of the future position of the aircraft by calculating the difference between the observed values ​​of the training data and the predicted values ​​of the model, as well as the model's treatment of noise. The formula for the log-marginal likelihood function is as follows: ; Among them, y is the observation value vector of all training samples, X is the feature matrix containing all training samples, is the transpose of the observation vector, K is the covariance matrix containing all kernel functions, is the variance of the noise, n is the number of training samples, and I is the identity matrix.

[0048] In this formula, the first term It reflects the degree of fit of the model to the observed value, that is, the deviation between the model prediction value and the actual observed value. By maximizing this term, the model can better fit the data and reduce the prediction error. Reflects the complexity of the model. This item penalizes the complexity of the model to prevent overfitting, so that the model still has good generalization ability in scenarios outside the training data. is a constant term that does not affect the fit of the model, but must be included in the formula to ensure correct calculation of the log marginal likelihood.

[0049] By constructing a log-marginal likelihood function, the model can balance prediction accuracy and model complexity and find the optimal hyperparameter configuration to ensure that it can effectively fit existing data when processing the prediction of the future trajectory of the aircraft and will not perform abnormally in future scenarios.

[0050] Step 24: Obtain the initial hyperparameters of the Gaussian process regression model by maximizing the log marginal likelihood function.

[0051] When implementing step 24, maximizing the logarithmic marginal likelihood function to obtain the initial hyperparameters of the Gaussian process regression model is to ensure the optimal fit of the model on the training data, thereby providing a solid foundation for the model's accurate prediction. Through this step, the model can dynamically adjust its parameters based on flight data and environmental data, so that it can better capture the changing trend of the aircraft's future position.

[0052] In the previous step, the logarithmic marginal likelihood function has been constructed, the core of which is to quantify the degree of fit of the model to the training data. In the Gaussian process regression model, the most critical hyperparameters include the length scale parameter l in the kernel function and the noise variance These parameters directly affect the smoothness of the model, its sensitivity to data, and its ability to handle noise and abnormal data.

[0053] In order to make the model have the best predictive ability, the optimal values ​​of these hyperparameters must be found by maximizing the log marginal likelihood function. Specifically, the length scale l in the kernel function controls how quickly the model responds to changes in the input features. A smaller length scale l makes the model very sensitive to slight changes in the state of the aircraft, while a larger length scale makes the model smoother to input changes. In addition, the noise variance Controls the model's ability to handle noise and uncertainty. By adjusting the noise variance, you can balance the model's signal and noise components in the aircraft data so that it neither overfits the noise nor ignores the useful signal.

[0054] In practice, maximizing the log-marginal likelihood function is usually achieved through some numerical optimization methods. These methods include gradient descent, conjugate gradient method, Bayesian optimization, etc. Through these optimization algorithms, the system can search in the parameter space so that the log-marginal likelihood function reaches the maximum value. The maximization process dynamically adjusts the model parameters until the optimal kernel function parameters and noise variance are found to ensure that the model can best fit the motion law of the aircraft in the training data.

[0055] By maximizing the log-marginal likelihood function, the model obtains the best hyperparameter configuration. These hyperparameters enable the model to more flexibly cope with nonlinear changes in flight data while reducing the interference of noise and abnormal data on the prediction results. Finally, after this process, the model obtains the initial optimal hyperparameter configuration, laying the foundation for subsequent training and optimization.

[0056] Step 25: Optimize the initial hyperparameters to obtain optimized hyperparameters, and train the initial model based on the optimized hyperparameters to obtain a Gaussian process regression model.

[0057] When implementing step 25, the initial hyperparameters are optimized to further improve the performance of the Gaussian process regression model, so that it has stronger generalization ability and prediction accuracy in complex flight data and environmental data. Although the initial hyperparameters have been obtained by maximizing the logarithmic marginal likelihood function in step 24, these hyperparameters usually need to be further optimized to ensure that the model can show better adaptability and robustness in practical applications.

[0058] In practice, hyperparameter optimization usually uses optimization techniques such as Bayesian optimization, grid search, and random search. These methods can search for the optimal solution in a complex high-dimensional parameter space. Bayesian optimization is particularly suitable for hyperparameter tuning of Gaussian process regression models. It avoids too much invalid search in the parameter space by gradually exploring and utilizing previous optimization results. Through these optimization techniques, the model can maintain prediction accuracy while ensuring better robustness to changes in the trajectory of the aircraft.

[0059] Next, the initial model is retrained based on the optimized hyperparameters. The purpose of retraining is to allow the model to refit the training data using the newly optimized hyperparameters, thereby further improving the fit of the flight data and environmental data. During retraining, the model will recalculate the weight of each training sample based on the adjusted hyperparameters and regenerate the covariance matrix. Ultimately, the model will achieve the best prediction capability for the aircraft at future moments based on the optimized kernel function and noise processing mechanism.

[0060] In a possible implementation, step 11 specifically includes the following steps: Based on all input units, multiple current input feature vectors are obtained; Based on each current input feature vector, obtain the observation value of each input unit; Construct the observation values ​​of all input units into the observation value vector of all input units; Based on all current input feature vectors, multiple kernel functions are calculated, and based on all kernel functions, a covariance matrix is ​​constructed; Based on each input unit, construct a feature matrix of all input units; Based on the feature matrix of all input units, the observation value vector of all input units and the covariance matrix, the predicted mean and predicted covariance of each predicted spatial position of the aircraft at the future moment are calculated.

[0061] Specifically, when implementing step 11, first, based on the current flight data and environmental data of the aircraft, multiple input feature vectors are extracted. The construction of the input feature vector is the basis of the entire prediction process because it represents the state of the aircraft at the current moment and the environment in which it is located.

[0062] Next, by processing each input feature vector, we get the observation value of each input unit. Each observation value reflects the state or position information of the aircraft at a specific point in time. The significance of this step is to provide clear observation values ​​for each input unit so that the Gaussian process regression model can learn and predict the future flight trajectory based on these observation values.

[0063] After the observations are generated, the observations of all input units need to be constructed into a complete observation vector. This step ensures that all flight data and environmental data can be fully utilized by the model and provides a basis for the calculation of the covariance matrix. The observation vector is a centralized representation of the data, which integrates all input data points into a compact structure that can be used for kernel function calculation.

[0064] After obtaining the observation vector, the model uses the kernel function to calculate the similarity between different inputs based on all current input feature vectors. The kernel function is a tool used to capture the relationship between data in Gaussian process regression, and can effectively reflect the correlation between input feature vectors. Through the calculation of the kernel function, the covariance matrix between the input data can be obtained, which represents the correlation between different data points and is further used for model prediction.

[0065] With the covariance matrix constructed, the next step is to construct all input units into a feature matrix containing all input units. Finally, based on the feature matrix containing all input units, the observation vector of all input units, and the covariance matrix, the model calculates the predicted mean and predicted covariance of each predicted spatial position of the aircraft at the future moment. The specific formulas for calculating the predicted mean and predicted covariance are as follows: ; ; in, is the predicted mean, is the feature matrix containing all input units, X is the feature matrix containing all training samples, K is the covariance matrix, y is the observation value vector of all input units, is the noise variance, I is the identity matrix, represents the covariance between the input unit and the training samples, Represents the covariance between the input units.

[0066] Step 12: Based on each prediction mean and each prediction covariance, calculate the probability that the aircraft will appear at each predicted spatial position after the future time.

[0067] When implementing step 12, the probability of the aircraft appearing at each predicted spatial position at a future time is calculated based on each predicted mean and each predicted covariance in order to quantify the uncertainty of the aircraft's future trajectory. By calculating the probability of each predicted spatial position, the model can not only give the best prediction of the aircraft's possible location, but also provide the confidence level of the prediction. The purpose of this step is to allow the model to more fully reflect the potential flight path and risks when processing the aircraft's future trajectory.

[0068] First, after the previous steps, the model has generated the mean and covariance of each predicted spatial position that the aircraft may arrive at in the future. The mean represents the most likely position of the aircraft, while the covariance quantifies the uncertainty of the model about this prediction. Based on this information, the probability of the aircraft appearing at each predicted spatial position can be calculated through the probability density function of the Gaussian distribution. Specifically, the predicted mean and covariance define a normal distribution, and the probability of the aircraft appearing at a specific position in the future can be estimated by the probability density function of this distribution.

[0069] To calculate this probability, each predicted spatial location is considered as a random variable whose distribution is controlled by the predicted mean and covariance of that location. Based on the characteristics of Gaussian process regression, the model assumes that these locations follow a normal distribution, so the probability density function of the normal distribution can be used to calculate the probability. The formula is as follows: ; in, is the probability that the aircraft will appear at position x at the future time t, is the predicted mean, is the prediction covariance.

[0070] The above method can not only provide a predicted trajectory for the aircraft, but also provide a probability estimate for each trajectory point. This probability estimate is very important because it provides a quantitative basis for the subsequent decision-making process. For example, in air traffic management, the predicted position of the aircraft and its corresponding probability can help managers judge future risks and take necessary countermeasures. By quantifying uncertainty, managers can better plan flight paths and ensure flight safety.

[0071] Finally, by calculating the probability of the aircraft at each location based on the predicted mean and covariance, the model is able to generate a comprehensive probability distribution that reflects the possible locations of the aircraft at future moments and their probability of appearing. This lays the foundation for the subsequent construction of spatiotemporal probability envelopes and the formulation of more accurate flight plans.

[0072] Step 13: Collect all predicted spatial positions whose probabilities are greater than a preset probability threshold to obtain the space-time probability envelope of the aircraft.

[0073] When implementing step 13, all predicted spatial positions with probabilities greater than the preset probability threshold are combined to obtain the space-time probability envelope of the aircraft. The purpose of this step is to screen out the spatial region where the aircraft is most likely to appear in the future by setting a probability threshold. In this way, an area where an aircraft is likely to appear with a high probability can be constructed to provide decision support for air traffic management and flight path planning.

[0074] In the previous step, the probability of each predicted spatial position has been calculated based on the predicted mean and covariance of the aircraft. These probabilities reflect the possibility of the aircraft appearing at different locations at a specific moment in the future. However, in order to ensure the flight safety and path optimization of the aircraft in a complex environment, it is necessary to further screen out those spatial positions with higher probabilities and combine these positions into an overall area, namely the space-time probability envelope. This envelope area is the area where the aircraft is most likely to appear. By setting a preset probability threshold θ, it can be ensured that the envelope only contains those spatial positions whose probability of appearance is greater than or equal to the threshold.

[0075] Specifically, the model calculates the probability of the aircraft at each predicted position and compares these positions with a preset threshold θ. Any position with a probability greater than or equal to θ at a future moment will be retained, while other positions are excluded. This process ensures that the spatiotemporal probability envelope only contains areas where the probability of the aircraft appearing is high. The setting of the threshold is usually determined by the specific application scenario. For example, in flight safety management, a higher threshold may be set to ensure that the aircraft has a high probability of staying in the safe area, while in some application scenarios with a higher tolerance rate, a lower threshold may be allowed.

[0076] In practice, by selecting a reasonable probability threshold θ, the aircraft spatiotemporal probability envelope can include all locations where the aircraft is likely to appear in the future. This process not only reduces the spatial scope that needs to be monitored, but also provides an accurate reference for subsequent flight route planning, airspace management, and risk assessment. The spatiotemporal probability envelope can help the air traffic management system monitor the flight status of aircraft in real time, predict the trajectory that the aircraft may deviate from in advance, and take timely countermeasures to reduce potential risks.

[0077] Refer to,3, Figure 3 It is a structural schematic diagram of the aircraft space-time probability envelope determination system provided by the present invention, the system comprises: a first processing module and a second processing module; The first processing module is used to input the data set of the aircraft into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future time; wherein the data set includes a plurality of current flight data and a plurality of current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future time, and the spatial point corresponds to any point in the spatial geometric body formed by the velocity vectors in all directions of the aircraft at a future time; A second processing module is used to calculate the probability of the aircraft appearing at each predicted spatial position after a future time based on each predicted mean and each predicted covariance; The second processing module is also used to collect all predicted spatial positions whose probabilities are greater than a preset probability threshold to obtain a spatiotemporal probability envelope of the aircraft.

[0078] In a possible implementation, the system further includes: a training module; the training module is used to construct a plurality of training samples, each training sample including a flight data sample and an environment data sample; The training module is also used to determine the Gaussian process and kernel functions; The training module is also used to construct the log-marginal likelihood function based on all training samples, Gaussian processes and kernel functions; The training module is also used to obtain the initial hyperparameters of the Gaussian process regression model by maximizing the log marginal likelihood function; The training module is also used to optimize the initial hyperparameters to obtain optimized hyperparameters, and to train the initial model based on the optimized hyperparameters to obtain a Gaussian process regression model.

[0079] In a possible implementation, the first processing module is further configured to obtain a plurality of current input feature vectors based on all input units; The first processing module is further used to obtain an observation value of each input unit based on each current input feature vector; The first processing module is further used to construct the observation values ​​of all input units into the observation value vectors of all input units; The first processing module is further used to calculate multiple kernel functions based on all current input feature vectors, and construct a covariance matrix based on all kernel functions; The first processing module is further used to construct a feature matrix including all input units based on each input unit; The first processing module is also used to calculate the predicted mean and predicted covariance of each predicted spatial position of the aircraft after a future moment based on the feature matrix containing all input units, the observation value vectors of all input units and the covariance matrix.

[0080] It should be noted that the aircraft space-time probability envelope determination system provided by the present invention can execute the aircraft space-time probability envelope determination method of any of the above-mentioned embodiments during specific operation, which will not be elaborated in this embodiment.

[0081] Figure 4 is a schematic diagram of the structure of the electronic device provided by the present invention, such as Figure 4As shown, the electronic device may include: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus. The processor may call the logic instructions in the memory to execute the method for determining the space-time probability envelope of the aircraft, which includes: inputting the data set of the aircraft into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future time; wherein the data set includes a plurality of current flight data and a plurality of current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future time, and the spatial point corresponds to any point in the spatial geometry formed by the velocity vectors in all directions of the aircraft at a future time; based on each predicted mean and each predicted covariance, the probability of the aircraft appearing at each predicted spatial position at a future time is calculated; and all predicted spatial positions with probabilities greater than a preset probability threshold are collected to obtain the space-time probability envelope of the aircraft.

[0082] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0083] On the other hand, the present invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the aircraft space-time probability envelope determination method provided by the above-mentioned embodiments, the method including: inputting a data set of the aircraft into a Gaussian process regression model to obtain a predicted mean and predicted covariance of each predicted spatial position of the aircraft after a future moment; wherein the data set includes a plurality of current flight data and a plurality of current environmental data; the predicted spatial position is any spatial point that the aircraft may reach at a future moment, and the spatial point corresponds to any point in a spatial geometry formed by the velocity vectors in all directions of the aircraft at a future moment; based on each predicted mean and each predicted covariance, the probability of the aircraft appearing at each predicted spatial position after the future moment is calculated; and all predicted spatial positions whose probabilities are greater than a preset probability threshold are set to obtain the aircraft's space-time probability envelope.

[0084] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the method for determining the space-time probability envelope of an aircraft provided in the above-mentioned embodiments, the method comprising: inputting a data set of the aircraft into a Gaussian process regression model to obtain a predicted mean and a predicted covariance of each predicted spatial position of the aircraft at a future moment; wherein the data set comprises a plurality of current flight data and a plurality of current environmental data; the predicted spatial position is any spatial point that the aircraft may reach at a future moment, and the spatial point corresponds to any point in a spatial geometry formed by the velocity vectors in all directions of the aircraft at a future moment; based on each predicted mean and each predicted covariance, the probability of the aircraft appearing at each predicted spatial position at a future moment is calculated; and all predicted spatial positions whose probabilities are greater than a preset probability threshold are grouped together to obtain the space-time probability envelope of the aircraft.

[0085] The system embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, i.e., they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Those of ordinary skill in the art may understand and implement it without creative effort.

[0086] Through the description of the above implementation modes, those skilled in the art can clearly understand that each implementation mode can be implemented by means of software plus a necessary general hardware platform, or of course by hardware. Based on such an understanding, the above technical solution can essentially or in other words be embodied in the form of a software product that contributes to the prior art. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiment.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining a space-time probability envelope of an aircraft, characterized in that: include: Inputting the data set of the aircraft into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future time; wherein the data set includes a plurality of current flight data and a plurality of current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future time, and the spatial point corresponds to any point in the spatial geometric body formed by the velocity vectors in all directions of the aircraft at a future time; Calculating the probability of the aircraft appearing at each of the predicted spatial positions after a future time based on each of the predicted means and each of the predicted covariances; All predicted spatial positions whose probabilities are greater than a preset probability threshold are collected to obtain the spatiotemporal probability envelope of the aircraft.

2. The method for determining the space-time probability envelope of an aircraft according to claim 1, characterized in that: The Gaussian process regression model is trained by the following method: Constructing a plurality of training samples, each of the training samples comprising a flight data sample and an environment data sample; Determine Gaussian process and kernel function; Constructing a log-marginal likelihood function based on all the training samples, the Gaussian process and the kernel function; By maximizing the log-marginal likelihood function, initial hyperparameters of the Gaussian process regression model are obtained; The initial hyperparameters are optimized to obtain optimized hyperparameters, and the initial model is trained based on the optimized hyperparameters to obtain the Gaussian process regression model.

3. The method for determining the space-time probability envelope of an aircraft according to claim 2, characterized in that: The Gaussian process is expressed by the following formula: ； Among them, x is the input feature vector of the training sample, is the observed value of the training sample, is the correlation function of the training samples, is Gaussian noise, is the variance of the noise, and n is the number of training samples.

4. The method for determining the space-time probability envelope of an aircraft according to claim 2, characterized in that: The kernel function is expressed by the following formula: ； in, is the kernel function, is the input feature vector of the i-th training sample, is the input feature vector of the jth training sample, and l is the length scale parameter.

5. The method for determining the space-time probability envelope of an aircraft according to claim 2, characterized in that: The log marginal likelihood function is expressed by the following formula: ； Among them, y is the observation value vector of all training samples, X is the feature matrix containing all training samples, is the transpose of the observation vector, K is the covariance matrix containing all kernel functions, is the variance of the noise, n is the number of training samples, and I is the identity matrix.

6. The method for determining the space-time probability envelope of an aircraft according to claim 1, wherein the data set comprises a plurality of input units, each of which comprises a current flight data and a current environment data; The aircraft data set is input into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future time, specifically including: Based on all the input units, a plurality of current input feature vectors are obtained; Based on each of the current input feature vectors, obtaining an observation value of each input unit; Constructing the observation values ​​of all the input units into an observation value vector of all the input units; Based on all the current input feature vectors, a plurality of kernel functions are calculated, and based on all the kernel functions, a covariance matrix is ​​constructed; Based on each of the input units, construct a feature matrix containing all the input units; Based on the feature matrix containing all input units, the observation value vectors of all input units and the covariance matrix, the predicted mean and predicted covariance of each predicted spatial position of the aircraft after a future moment are calculated.

7. A system for determining the space-time probability envelope of an aircraft, characterized in that: include: a first processing module and a second processing module; The first processing module is used to input the data set of the aircraft into the Gaussian process regression model to obtain the predicted mean and predicted covariance of each predicted spatial position of the aircraft at a future time; wherein the data set includes a plurality of current flight data and a plurality of current environment data; the predicted spatial position is any spatial point that the aircraft may reach at a future time, and the spatial point corresponds to any point in the spatial geometric body formed by the velocity vectors in all directions of the aircraft at a future time; The second processing module is used to calculate the probability of the aircraft appearing at each of the predicted spatial positions after a future moment based on each of the predicted means and each of the predicted covariances; The second processing module is further used to collect all the predicted spatial positions whose probabilities are greater than a preset probability threshold to obtain the spatiotemporal probability envelope of the aircraft.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method for determining the space-time probability envelope of an aircraft as described in any one of claims 1-6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for determining the space-time probability envelope of an aircraft as described in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method for determining the space-time probability envelope of an aircraft as described in any one of claims 1 to 6 is implemented.

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