Unmanned aerial vehicle track prediction method, device and system based on Bayesian optimization

Abstract

The invention discloses an unmanned aerial vehicle trajectory prediction method, device and system based on Bayesian optimization, and the method comprises the steps: obtaining the historical trajectory data of an unmanned aerial vehicle, including the positions, speeds and accelerations of the unmanned aerial vehicle at different sampling moments; constructing a feedforward neural network, and searching an optimal hyper-parameter of the feedforward neural network by using Bayesian optimization to generate a prediction model; based on the prediction model, predicting the trajectory of the unmanned aerial vehicle to obtain initial prediction trajectory data of the unmanned aerial vehicle; calculating a normalized activation probability between the initial prediction trajectory data and the historical trajectory data; and according to the normalized activation probability, performing adaptive correction on the initial prediction trajectory data to obtain a final prediction trajectory of the unmanned aerial vehicle. According to the method, an adaptive correction mechanism is introduced, the precision and robustness of trajectory prediction are greatly improved, a scientific and reasonable decision basis is provided for autonomous flight of the unmanned aerial vehicle and group cooperation, and the method plays a key role in application scenes such as air traffic control and unmanned aerial vehicle interception.

Description

Technical Field

[0001] The present invention relates to the field of aviation and unmanned aerial vehicles, and in particular to a method, device and system for predicting unmanned aerial vehicle trajectories based on Bayesian optimization. Background Art

[0002] UAV trajectory prediction is one of the key technologies for autonomous flight and group collaboration of UAVs. Accurate trajectory prediction not only helps UAVs navigate and avoid obstacles in complex environments, but also enables UAVs to predict the movement of other UAVs, thereby achieving coordinated flight in formation. Traditional trajectory prediction methods are usually based on model-based methods, but such methods rely on accurate modeling of system dynamics and environmental characteristics, and have high computational complexity, making it difficult to meet the requirements of real-time applications. At the same time, they lack the ability to adapt to new environments or tasks.

[0003] With the development of artificial intelligence technologies such as deep learning and reinforcement learning, data-driven methods have shown significant advantages in drone trajectory prediction. However, since drones are affected by many uncertain factors in actual flight, such as wind speed, airflow changes, and obstacles, how to improve the robustness and accuracy of the prediction model remains a challenge that needs to be solved. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method, device and system for predicting UAV trajectories based on Bayesian optimization. By introducing Bayesian optimization technology, the hyperparameters of the neural network are globally optimized. Through the context sharpness correction method, the activation probability relationship between the prediction result and the historical trajectory is utilized to identify the input sequence that plays a key role in the prediction result. The context sharpness is determined by the entropy measurement method and adaptively adjusted to solve the problems existing in the prior art such as reliance on precise modeling, low prediction accuracy, insufficient robustness and poor real-time performance.

[0005] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0006] In a first aspect, a method for predicting UAV trajectories based on Bayesian optimization is provided, comprising the following steps:

[0007] (1) Obtain the historical trajectory data of the UAV, including the position, speed, and acceleration of the UAV at different sampling times;

[0008] (2) Construct a feedforward neural network and use Bayesian optimization to find the optimal hyperparameters of the feedforward neural network to generate a prediction model;

[0009] (3) Based on the prediction model, the trajectory of the UAV is predicted to obtain the initial predicted trajectory data of the UAV;

[0010] (4) Calculate the normalized activation probability between the initial predicted trajectory data and the historical trajectory data;

[0011] (5) According to the normalized activation probability, the initial predicted trajectory data is adaptively corrected to obtain the final predicted trajectory of the UAV.

[0012] Furthermore, in step (2), the iterative process of the Bayesian optimization to find the optimal hyperparameters is:

[0013]

[0014] Where x next represents a set of settings for hyperparameters, Y is the hybrid design space, P(F(x 1:t )=f(x 1:t )|x) represents the probability of obtaining all observed values ​​when the hyperparameter value is x, F(x 1:t ) is the true value of the objective function, f(x 1:t ) is the target function value approximately predicted by the surrogate model, which uses Gaussian process regression, and t is the observed sequence number.

[0015] x next Substitute it into the surrogate model for prediction. The surrogate model predicts not only the function value f(x), but also its posterior distribution F(x)|F(x 1:t )=f(x 1:t ), that is, given t observation points x 1:t The value of F(x 1:t ), the probability of f(x) taking different values, F(x) is the true value of the target function. Use the expectation of the posterior distribution as the predicted value of the function value f(x):

[0016] f(x)←E[F(x)|F(x 1:t )=f(x 1:t )]

[0017] Where F(x)|F(x 1:t )=f(x 1:t ) is the posterior distribution of f(x), and E[·] represents the expectation.

[0018] Furthermore, in step (5), the normalized activation probability is used as the weight of the corresponding historical flight direction, and all historical flight directions are weighted averaged to obtain a corrected predicted flight direction; the final predicted trajectory of the UAV is obtained based on the position, velocity, acceleration and sampling time of the terminal sampling point in the historical trajectory data.

[0019] Furthermore, in step (4), the calculation formula of the normalized activation probability is as follows:

[0020]

[0021] in, is the normalized activation probability between the initial prediction result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, f(p i ,p t ), g(v i ,v t ), h(a i ,a t ) are mapping functions that characterize position features, velocity features, and acceleration features, respectively. α, β, and γ are weight coefficients of the corresponding feature mapping functions, respectively. i is the sampling time number of the historical trajectory data, i = 1, 2, …, t-1, v t is the initial predicted speed of the UAV at time t, f(p i ,p t )=p i ^·p t ^, g(v i ,v t )=v i ^·v t ^, h(a i ,a t )=a i ^·a t ^, p i ^、v i ^、a i ^ are respectively the normalized historical position, velocity and acceleration of the drone at time i, and p t ^, v t ^, a t ^ are the normalized initial predicted position, velocity and acceleration of the UAV at time t.

[0022] Furthermore, step (5) further includes: adjusting the normalized activation probability, and then adaptively correcting the initial predicted trajectory data based on the adjusted normalized activation probability; wherein the normalized activation probability is adjusted using the following formula:

[0023]

[0024] in, is the normalized activation probability between the initial predicted trajectory number of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, λ i for The adjustment weight, λ i =

[0025]

[0026] and l 2 is the preset threshold used to adjust the cut-off range.

[0027] In a second aspect, a UAV trajectory prediction device based on Bayesian optimization is also provided, comprising:

[0028] The data acquisition module is used to obtain the historical trajectory data of the UAV, including the position, speed and acceleration of the UAV at different sampling times;

[0029] The model generation module is used to build a feedforward neural network and use Bayesian optimization to find the optimal hyperparameters of the feedforward neural network to generate a prediction model;

[0030] The initial prediction module is used to predict the trajectory of the UAV based on the prediction model and obtain the initial predicted trajectory data of the UAV;

[0031] A calculation module, used to calculate the normalized activation probability between the initial predicted trajectory data and the historical trajectory data;

[0032] The trajectory correction module is used to adaptively correct the initial predicted trajectory data according to the normalized activation probability.

[0033] Furthermore, the calculation formula of the normalized activation probability is as follows:

[0034]

[0035] in, is the normalized activation probability between the initial prediction result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, f(p i ,p t ), g(v i ,v t ), h(a i ,a t ) are mapping functions representing position features, velocity features and acceleration features, α, β and γ are weight coefficients of the corresponding feature mapping functions, i is the sampling time number of the historical trajectory data, i = 1, 2, ..., t-1, v t is the initial predicted speed of the UAV at time t, f(p i ,p t )=p i ^·p t ^, g(v i ,v t )=v i ^·v t ^, h(ai ,a t )=a i ^·a t ^, p i ^、v i ^、a i ^ are respectively the normalized historical position, velocity and acceleration of the drone at time i, and p t ^, v t ^, a t ^ are the normalized initial predicted position, velocity and acceleration of the UAV at time t.

[0036] Furthermore, it also includes:

[0037] The adjustment module is used to adjust the normalized activation probability output by the calculation module and then input it into the trajectory correction module; the trajectory correction module adaptively corrects the initial predicted trajectory data according to the adjusted normalized activation probability.

[0038] Furthermore, the normalized activation probability is adjusted using the following formula:

[0039]

[0040] in, is the normalized activation probability between the initial prediction result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, λ i for The adjustment weights, l 1 and l 2 is the preset threshold used to adjust the cut-off range.

[0041] In a third aspect, a computer-readable storage medium storing one or more programs is also provided, wherein the one or more programs include instructions, which, when executed by a computing device, enable the computing device to execute the drone trajectory prediction method as described above.

[0042] In a fourth aspect, an electronic system is also provided, comprising one or more processors, one or more memories and one or more programs, wherein the one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing the UAV trajectory prediction method as described above.

[0043] Beneficial effects: The present invention proposes a UAV trajectory prediction method based on Bayesian optimization. By using Bayesian optimization to perform global optimization on the hyperparameters of the neural network, the optimal model parameters can be found with fewer training and verification times, thereby significantly improving the accuracy of trajectory prediction. At the same time, by calculating the context activation probability between the prediction result and the historical trajectory data, the input sequence that has a key impact on the prediction result can be effectively identified. The preliminary prediction result is corrected by using the part with a more concentrated activation probability in the historical trajectory data, thereby further improving the accuracy of the prediction. The method has accurate prediction results and low computational complexity, meets real-time requirements, greatly improves the accuracy and robustness of trajectory prediction, and thus provides a scientific and reasonable decision-making basis for autonomous flight and group collaboration of UAVs. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a method flow chart of an embodiment of the present invention.

[0045] Figure 2 4 is a Bayesian optimization flow chart of an embodiment of the present invention.

[0046] Figure 3 Schematic diagram of a neural network structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0048] like Figure 1 As shown, a method for predicting UAV trajectories based on Bayesian optimization and context sharpness correction disclosed in an embodiment of the present invention includes the following steps:

[0049] (1) Obtain the historical trajectory data of the UAV, including the position, velocity, and acceleration of the UAV at different sampling times.

[0050] The binocular camera system carried by the drone can capture the spatial position of other drones in real time. The binocular camera uses stereo vision technology and feature point matching to calculate the three-dimensional coordinates of other drones in space and record their historical flight trajectories. In the drone collaborative flight scenario, each drone can also share real-time location information through wireless communication networks (such as Wi-Fi, 5G, V2V, etc.), so that each drone can obtain the complete historical flight data of other drones.

[0051] In order to ensure the validity of the data, the data needs to be preprocessed, including:

[0052] Abnormal data removal: Identify abnormal data points by calculating the first-order difference of the drone's position and remove these abnormal data points;

[0053] Missing data repair: Use Lagrange interpolation and other methods to fill in missing trajectory data.

[0054] (2) Construct a feedforward neural network and use Bayesian optimization to find the optimal hyperparameters of the neural network to generate a prediction model.

[0055] Based on the acquired historical trajectory data, a feedforward neural network is constructed. The structure of the neural network is as follows Figure 2 As shown. The input of the neural network is the historical location information of the drone, and the output is the future predicted location of the drone. In order to improve the prediction performance of the neural network model, the present invention uses Bayesian optimization to optimize the network's hyperparameters (such as the number of nodes in the hidden layer, the learning rate, etc.). Bayesian optimization quickly approximates the optimal solution of the objective function within a limited number of hyperparameter evaluations, thereby finding the most suitable neural network structure and improving the prediction accuracy of the model.

[0056] Specifically, the Bayesian optimization process is as follows Figure 3 As shown, it includes the following steps:

[0057] Step 1: Build a proxy model (Gaussian process regression model) to simulate the performance of the neural network.

[0058] Step 2: Use the acquisition function to select the next hyperparameter evaluation point:

[0059]

[0060] Use the Bayesian formula to convert:

[0061]

[0062] Obviously, the denominator is independent of the parameter, and P(x) is the prior probability of the parameter value, which we assume is equally distributed. Therefore, the most likely parameter value is

[0063]

[0064] Where x next represents a set of settings for hyperparameters, Y is the hybrid design space, P(F(x 1:t )=f(x 1:t )|x) represents the probability of obtaining all observed values ​​when the hyperparameter value is x, F(x 1:t ) is the true value of the objective function, f(x 1:t ) is the target function value approximately predicted by the surrogate model, which uses Gaussian process regression, and t is the observed sequence number.

[0065] x nextSubstitute it into the surrogate model for prediction. The surrogate model predicts not only the function value f(x), but also its posterior distribution F(x)|F(x 1:t )=f(x 1:t ), that is, given t observation points x 1:t The value of F(x 1:t ), the probability of f(x) taking different values, F(x) is the true value of the target function. Use the expectation of the posterior distribution as the predicted value of the function value f(x):

[0066] f(x)←E[F(x)|F(x 1:t )=f(x 1:t )]

[0067] Where F(x)|F(x 1:t )=f(x 1:t ) is the posterior distribution of f(x), and E[·] represents the expectation.

[0068] Step 3: Validate the selected hyperparameter combination in the neural network and update the proxy model based on the validation results;

[0069] Step 4: Repeat the above steps until the optimal hyperparameters are found.

[0070] (3) Based on the Bayesian optimized neural network model, the estimated value of the UAV’s future position is calculated.

[0071] The trajectory prediction is performed using a Bayesian optimized neural network model, with the input being the historical location information of the drone and the output being the predicted future location information. The predicted future location is the three-dimensional coordinates of the drone at the next moment, and these data provide the basis for context sharpness analysis in subsequent steps.

[0072] (4) The normalized activation probability between the historical trajectory and the predicted position is calculated to determine the context sharpness using the entropy metric.

[0073] The prediction result v t The normalized activation probability relative to the historical trajectory is:

[0074]

[0075] in, is the normalized activation probability between the initial prediction result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, f(p i ,p t ), g(v i ,v t ), h(a i ,a t) are mapping functions that characterize position features, velocity features, and acceleration features, respectively. α, β, and γ are weight coefficients of the corresponding feature mapping functions, which are used to adjust the contribution of each feature to the activation probability. i is the sampling time number of the historical trajectory data, i = 1, 2, ..., t-1, v t is the initial predicted speed of the UAV at time t, f(p i ,p t )=p i ^·p t ^, g(v i ,v t )=v i ^·v t ^, h(a i ,a t )=a i ^·a t ^, p i ^、v i ^、a i ^ are respectively the normalized historical position, velocity and acceleration of the drone at time i, and p t ^, v t ^, a t ^ are respectively the normalized initial predicted position, velocity and acceleration of the drone at time t. The activation probability indicates that v t The probability that the UAV flight trend is extracted from the input sequence is large.

[0076] To evaluate the distribution of normalized activation probabilities, use The entropy of is called context entropy, which is used to describe the predicted output v t The expression formula of contextual sharpness and contextual entropy for all historical trajectory data is as follows:

[0077]

[0078] Among them, the correction Represents multiple uncertainty correction functions φ l (v t ,X) to capture the uncertainty or complex dynamics in the local context, v t is the initial prediction result, and X is the historical trajectory data. l (v t ,X) is the position dependency correction function, speed or acceleration correction function. The position dependency correction reflects that certain specific positions may have greater uncertainty in the environment (such as areas with many obstacles), while the speed or acceleration correction reflects the uncertainty caused by sudden changes in speed and acceleration in the trajectory. lis the weight of the correction function, which is used to adjust the impact of different correction functions on context entropy. The correction term needs to be analyzed in combination with the specific environment. If the prediction is based only on historical trajectory data, there is no correction term.

[0079] (5) According to the context sharpness, the preliminary prediction results are adaptively modified to generate the final prediction trajectory.

[0080] Predictions with smaller context entropy are more certain and therefore more likely to be correct. Based on this, it is necessary to increase the weight of context inputs with smaller context entropy, while suppressing those context inputs that increase context entropy. To achieve this, we use the following formula to adjust the normalized activation probability:

[0081]

[0082] in l 1 and l 2 is a threshold used to adjust the cut-off range of context input.

[0083] Based on the adjusted normalized activation probability, we re-predict the flight direction of the drone at the next moment. The normalized activation probability is used as the weight of the corresponding historical flight direction, and all historical flight directions are weighted averaged to obtain the corrected predicted flight direction. Finally, based on the end sampling point of the drone's flight trajectory (that is, the last trajectory point in the historical trajectory data) and its speed, acceleration and sampling time, the predicted position of the drone at the next moment is calculated.

[0084] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the use. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the use methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

[0085] Based on the same technical solution, the present invention also discloses a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, and when the instructions are executed by a computing device, the computing device executes the above-mentioned drone trajectory prediction method.

[0086] Based on the same technical solution, the present invention also discloses a computing device, including one or more processors, one or more memories and one or more programs, wherein the one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing the above-mentioned drone trajectory prediction method.

[0087] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0088] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0089] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0090] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

Claims

1. A UAV trajectory prediction method based on Bayesian optimization, characterized in that: The steps include: (1) Obtain the historical trajectory data of the UAV, including the position, speed, and acceleration of the UAV at different sampling times; (2) Construct a feedforward neural network and use Bayesian optimization to find the optimal hyperparameters of the feedforward neural network to generate a prediction model; (3) Based on the prediction model, the trajectory of the UAV is predicted to obtain the initial predicted trajectory data of the UAV; (4) Calculate the normalized activation probability between the initial predicted trajectory data and the historical trajectory data; (5) According to the normalized activation probability, the initial predicted trajectory data is adaptively corrected to obtain the final predicted trajectory of the UAV.

2. The method for predicting the trajectory of an unmanned aerial vehicle according to claim 1, characterized in that: In step (5), the normalized activation probability is used as the weight of the corresponding historical flight direction, and all historical flight directions are weighted averaged to obtain the corrected predicted flight direction; the final predicted trajectory of the drone is obtained based on the position, speed, acceleration and sampling time of the terminal sampling point in the historical trajectory data.

3. The method for predicting the trajectory of an unmanned aerial vehicle according to claim 1, characterized in that: In step (4), the calculation formula of the normalized activation probability is as follows: in, is the normalized activation probability between the initial prediction result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, f(p i ,p t ), g(v i ,v t ), h(a i ,a t ) are mapping functions that characterize position features, velocity features, and acceleration features, respectively. α, β, and γ are weight coefficients of the corresponding feature mapping functions, respectively. i is the sampling time number of the historical trajectory data, i = 1, 2, …, t-1, v t is the initial predicted speed of the UAV at time t, f(p i ,p t )=p i ^·p t ^, g(v i ,v t )=v i ^·v t ^, h(a i ,a t )=a i ^·a t ^, p i ^、v i ^、a i ^ are respectively the normalized historical position, velocity and acceleration of the drone at time i, and p t ^, v t ^, a t ^ are the normalized initial predicted position, velocity and acceleration of the UAV at time t.

4. The method for predicting the trajectory of an unmanned aerial vehicle according to claim 1, characterized in that: Step (5) also includes: adjusting the normalized activation probability, and then adaptively correcting the initial predicted trajectory data based on the adjusted normalized activation probability; wherein the normalized activation probability is adjusted using the following formula: in, is the normalized activation probability between the initial predicted trajectory number of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, λ i for The adjustment weight of l1 and l2 are preset thresholds for adjusting the cut-off range.

5. A UAV trajectory prediction device based on Bayesian optimization, characterized in that: include: The data acquisition module is used to obtain the historical trajectory data of the UAV, including the position, speed and acceleration of the UAV at different sampling times; The model generation module is used to build a feedforward neural network and use Bayesian optimization to find the optimal hyperparameters of the feedforward neural network to generate a prediction model; The initial prediction module is used to predict the trajectory of the UAV based on the prediction model and obtain the initial predicted trajectory data of the UAV; A calculation module, used to calculate the normalized activation probability between the initial predicted trajectory data and the historical trajectory data; The trajectory correction module is used to adaptively correct the initial predicted trajectory data according to the normalized activation probability.

6. The drone trajectory prediction device according to claim 5, characterized in that: The calculation formula for the normalized activation probability is as follows: in, is the normalized activation probability between the initial prediction j result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, f(p i ,p t ), g(v i ,v t ), h(a i ,a t ) are mapping functions that characterize position features, velocity features, and acceleration features, respectively. α, β, and γ are weight coefficients of the corresponding feature mapping functions, respectively. i is the sampling time number of the historical trajectory data, i = 1, 2, …, t-1, v t is the initial predicted speed of the UAV at time t, f(p i ,p t )=p i ^·p t ^, g(v i ,v t )=v i ^·v t ^, h(a i ,a t )=a i ^·a t ^, p i ^、v i ^、a i ^ are respectively the normalized historical position, velocity and acceleration of the drone at time i, and p t ^, v t ^, a t ^ are the normalized initial predicted position, velocity and acceleration of the UAV at time t.

7. The drone trajectory prediction device according to claim 5, characterized in that: Also includes: An adjustment module, used for adjusting the normalized activation probability output by the calculation module and then inputting it into the trajectory correction module; The trajectory correction module adaptively corrects the initial predicted trajectory data according to the adjusted normalized activation probability.

8. The drone trajectory prediction device according to claim 7, characterized in that: The normalized activation probability is adjusted using the following formula: in, is the normalized activation probability between the initial prediction j result of the drone at time t and the historical trajectory data at time i, v t is the initial prediction result, X is the historical trajectory data, λ i for The adjustment weight of and l2 are preset thresholds used to adjust the cut-off range.

9. A computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, characterized in that: When the instructions are executed by a computing device, the computing device is caused to perform the method according to any one of claims 1 to 4.

10. An electronic system, characterized in that: The method comprises one or more processors, one or more memories and one or more programs, wherein the one or more programs are stored in the one or more memories and are configured to be executed by the one or more processors, and the one or more programs include instructions for executing the method as claimed in any one of claims 1 to 4.

Images