How to determine correct antenna placement by radiation pattern prediction

Abstract

The present invention describes a method for determining the correct placement of an antenna, for example on a vehicle's support structure. The technique disclosed herein uses Bayesian optimization to optimize the location of an antenna mounted on a fixed platform, in combination with an electromagnetic solver and a fully convolutional neural network (U-Net), which determines a fitness function through electromagnetic simulation of the behavior of the antenna at a given location.

Description

Detailed Description of the Invention

[0001] [Technical field] The present application describes a method for determining the correct placement of an antenna on a support structure.

[0002] [Background technology] For proper use of Global Navigation Satellite Systems (GNSS) in a vehicle, the antennas must be placed in locations where their radiation patterns are optimal and where there is the least possible interference.

[0003] Since there are an infinite number of possible points in the space, manually analyzing the behavior of the antenna in all possible positions can be computationally and time-consuming. Applying an optimization model with evolutionary algorithms improves the accuracy of the search path and guides the solver to the area with the best radiation pattern. These algorithms require many evaluation functions in the space, which can limit their use if the time required for each evaluation is large.

[0004] Since the placement of antennas directly affects the accuracy of the vehicle's positioning system [1]-[2], it is necessary to find ways to minimize the interference between antennas and optimize their performance. A comparison of four stochastic models for searching the optimal position of antennas on a platform was carried out in [3], and it was shown that the evolutionary model, although slower, has a higher accuracy of the optimal position. Also, in [4], a genetic algorithm was used to optimize the position of several antennas on a ship's platform, comparing chromosomal fitness functions to reduce the total amount of time required to simulate the position according to the dominance of some positions at the expense of others. In the case of antennas, a characteristic model was applied to determine the position of a monopole antenna to be installed on the metal roof of the vehicle, achieving the highest gain in the horizontal plane [5-6].

[0005] However, evolutionary optimization algorithms are usually used in problems where there is enough time for many model evaluations. However, if there is no closed form for the objective function (black box), the optimization of the objective function takes a long time, i.e., minutes, hours or even days, for each position evaluation. The determination of the correct position depends on two steps. One is to calculate the radiation pattern at each guess position. The other is to determine at which test positions the calculations should be performed to reach the desired position. When we want to avoid many iterations, when we do not have access to derivatives, and when the search space is not too large, as in this antenna placement problem, Bayesian optimization methods are more suitable [7-8].

[0006] This technique has already been used in [9-11] for antenna array design as an alternative to other techniques, but not yet for antenna placement problems.

[0007] In [6], the location of the antenna is considered using a genetic algorithm and the Finite Difference Time Domain (FDTD) solver XFdtd software. To avoid the extensive and time-consuming calculations to determine the radiation diagram at each position of the full vehicle model, a calculation based on the prediction of such radiation patterns and a vehicle subset model is used. The calculation is supported by a database of historical radiation patterns, allowing to predict the radiation diagram of the full model.

[0008] [overview] The present invention describes a method for determining the correct placement of an antenna on a support structure, said placement providing the best radiation pattern for said antenna, said method comprising the following steps: - Including random initialization of antenna placement optimization for antenna placement (Pn), The antenna arrangement optimization includes: - determining ideal candidate solutions based on said antenna arrangements (Pn); - determining the simplified realized gain and axial ratio of said antenna arrangement (Pn), - predicting realized gain and axial ratio; - obtaining a fitness function; -If a positive solution is found, an output result is provided; If the results are not satisfactory, the search for ideal candidate solutions is repeated.

[0009] In a proposed embodiment of the present invention, the radiation pattern prediction comprises the following steps: Obtaining a model fitting result based on the segmentation map obtained from the U-Net convolutional neural network; - obtaining an embedding output training based on the obtained model fitting; - Obtaining predicted realized gain (RG) and axial ratio (AR).

[0010] Furthermore, in another embodiment proposed in the present invention, the model fitting is configured to determine a generalization rate of a machine learning model on similar data trained based on at least one of a kernel filter, a regularized linear unit activation function, a max pooling operation with stride, and a feature map.

[0011] Furthermore, in another embodiment proposed in the present invention, the embedded output training includes the initial data set used to train the U-Net convolutional neural network.

[0012] Furthermore, in another embodiment proposed in the present invention, the predicted realized gain (RG) and axial ratio (AR) include simplified data (SD) as input and precise data (PD) as output for each point determined by said antenna placement optimization.

[0013] Furthermore, in another embodiment proposed in the present invention, the segmentation map includes data derived from the elevation angle value (θ) and / or azimuth angle (φ) for each antenna arrangement (Pn).

[0014] Furthermore, in another embodiment proposed in the present invention, the U-Net convolutional neural network includes the input radiation pattern of the antenna arrangement (Pn).

[0015] Furthermore, in another embodiment proposed in the present invention, the input radiation pattern includes at least one set of quantitative data points characterizing the antennas in each antenna arrangement (Pn).

[0016] Furthermore, in another embodiment proposed in the present invention, a U-Net convolutional neural network is trained using the input radiation patterns.

[0017] Furthermore, in another proposed embodiment proposed in the present invention, prediction of realized gain and axial ratio is obtained from the predicted realized gain (RG) and axial ratio (AR) of the embedded input / output training and radiation pattern prediction.

[0018] [General Description] The present invention describes a method for determining the correct placement of an antenna, for example on a vehicle's support structure, including a methodology for reducing the time required to calculate the radiation pattern at each test location, and a methodology for determining an antenna location that satisfies antenna radiation requirements.

[0019] Besides the antenna characteristics, the radiation pattern of the antenna also depends on the antenna position and the material of the platform / support structure. This behavior can be determined by solving Maxwell's equations in an electromagnetic solver. In this case, simulation models can be created that are as close as possible to the real thing. The accuracy of these models depends on many factors, such as the details and material composition of the structure on which the antenna is installed. To achieve the most accurate representation, the simulation models must be complex and representative of the real thing. This requires more computation time to perform the simulation. The correct placement of the antenna on the support structure may also be supported by the simulation tool. However, the electromagnetic simulation of a full vehicle model or related vehicle models can be very time-consuming and may take weeks or months to complete a full simulation.

[0020] To overcome these limitations, we simulate a simplified vehicle model and use the simulation data as input for a convolutional neural network (U-Net) with a certain accuracy to estimate an accurate radiation diagram of the full model vehicle and analyze many positions and radiation patterns in a much shorter time than if we were to use a solver alone. Further optimization techniques are added later along with this methodology so that the search for the optimal position is done in as few steps as possible.

[0021] The technique disclosed herein optimizes antenna positions on a fixed platform / support structure using Bayesian Optimization (BO) as a solution to the problem of maximizing realized gain and minimizing axial ratio in GNSS antenna placement, in combination with an electromagnetic solver and a fully convolutional neural network (U-Net). A fitness function is determined through an electromagnetic simulation of the antenna's behavior at a given position. Correctly determining the fitness function is important for the optimization algorithm to work efficiently. This means that the response provided by the electromagnetic simulator should reflect the desired radiation pattern of the antenna as closely as possible to ensure the effectiveness of the search algorithm.

[0022] Bayesian optimization methods based on Bayes' theorem provide a conditional probabilistic method for drawing conclusions with incomplete information, providing a relationship between data / points (P) and a fitness model / function (F). When the objective fitness function F is unknown, a common approach is to create a surrogate model F' that creates an image of the objective function F as more samples are observed. This can be done by a variety of approaches, but the most common is to apply general Bayesian inference principles to a Gaussian Process (GP).

[0023] The method proposed herein ensures the required accuracy of the calculation results without spending a huge amount of time on electromagnetic simulations in a full car model. This approach allows the antenna behavior in some specific configurations to be obtained for full and simplified vehicle models, based on which machine learning tools can be used to predict the exact radiation pattern of the full model from a given simplified input, such as a roof model.

[0024] The biggest challenge in simulating the electromagnetic behavior of an antenna inside a vehicle is to model the geometry of the vehicle and the antenna and determine the materials. This modeling may involve simplifying the geometry (removing, modifying, combining components), repairing the geometry (an automated process that removes CAD inconsistencies), changing the spatial orientation and position (moving or rotating the model as needed), and determining the materials of each element (defining appropriate and realistic materials for each component).

[0025] Testing the antenna behavior at all possible positions on the vehicle roof is, if not impossible, hardly practical due to the time required. Therefore, to obtain the antenna behavior at some specific positions for the full and simplified vehicle models, the proposed method uses machine learning tools to predict the exact (full model) radiation pattern given a simplified input (only the roof model). Thus, using a search optimization algorithm and a simplified model of the vehicle geometry, it is possible to reduce the response time and obtain a more accurate solution by approximating the radiation pattern using machine learning.

[0026] Therefore, the antenna arrangement on the roof of the car is input to the U-Net convolutional neural network in both the case of the full vehicle model and the simplified vehicle model, and the realized gain (RG) and axial ratio (AR) are obtained depending on the value of the elevation angle θ and the azimuth angle φ. RG and AR are denoted as dBi and dB, respectively. The architecture of the U-Net convolutional neural network used in this specification has been modified to reduce the number of image data and extend the work on more accurate image segmentation. Using the U-Net convolutional neural network, an accurate simulation of the full vehicle model can be predicted using a partial model together with information from data obtained from the full model obtained from simulation or measurement. As the methodology is performed, the accuracy of the simulation of the sub-model tends to improve as the database from the simulation or measurement of the full model is expanded. In the proposed embodiment, U-Net is used to obtain accurate simulation results from the simplified model, but other algorithms can be used as long as a combination of results from the simplified model and data from the full model or measurement can be used.

[0027] [Brief description of the drawings] For a better understanding of the present application, drawings illustrating preferred embodiments are attached, which are, however, not intended to limit the technology disclosed herein.

[0028] FIG. 1 shows an initial data set that includes a set of 13 sampled antenna placement points P1 to P13 (i.e., Pn) located at different distances within a limited area of ​​the vehicle (1600 × 1200 centimeters in this particular case).

[0029] Figure 2 shows an overview of the stages involved in antenna prediction and position optimization.

[0030] FIG. 3 shows the multiple stages of the Bayesian optimization method, illustrated by the unknown function and prior mean function (a), the acquisition function and mean update (b), algorithm evaluation 1 (c), and algorithm evaluation 2 (d).

[0031] [Description of the embodiment] Some embodiments will now be described in more detail with reference to the drawings, which are not intended to limit the scope of the present patent application.

[0032] The present invention discloses a methodology for predicting the radiation diagram of an antenna on a fixed surface of a vehicle using machine learning techniques. The proposed model is able to solve magnetic simulation problems in both small and large areas and is particularly suitable for vehicles. Vehicles require a lot of simulation time and resources, especially when combining radiation pattern calculation with the search for the optimal antenna position. While an optimization model can find the optimal point by the minimum number of calls of the objective function, U-Net helps to further reduce this time by predicting a precise model from a simplified model faster than the precise model of the simulator. The prediction is made based on a simplified vehicle model to reduce the calculation time, and after the prediction, a precise position for the placement of the antenna on the vehicle is determined to meet the predetermined radiation characteristics.

[0033] The steps of the preferred embodiment include an electromagnetic simulation, an algorithmic control stage, and an artificial intelligence algorithm stage to find the correct position. In this embodiment, a 3D vehicle model and a 3D antenna model can also be used. Using supervised machine learning methods aimed at speeding up the calculation of the antenna radiation pattern, the power at the remaining points can be inferred in a more accurate and faster way than the results of a frequency solver.

[0034] A Bayesian optimization model is added onto U-Net as a way to find the optimal position of the antenna. In this way, the U-Net convolutional neural network aims to replace the electromagnetic simulation of the antenna with a full model, which requires a lot of time, and instead make predictions from a simplified model. The simplified simulation results are fed into U-Net. The prediction results are fed into the Bayesian optimization model to calculate the objective function.

[0035] The accurate radiation pattern prediction model (full vehicle model) is integrated into a Bayesian optimization (BO) model. This strategy allows to speed up the simulation using a less accurate antenna model and get closer to the results of a more accurate model (longer simulation time) by predicting the radiation pattern using a convolutional neural network. The criterion selected to determine the optimal antenna placement is: for all azimuth angles predicted by the neural network, at position i with elevation angle θ<θmax, Average Realized Gain

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[0036] An example of an initial data set is shown in Figure 1. The initial data set includes a set of sampled antenna placement points located at different distances within a limited area of ​​the vehicle. In this particular illustration, there are 13 possible antenna placement points P1-P13, i.e. Pn, located at different distances within a 1600x1200 limited area of ​​the vehicle.

[0037] A general overview of the stages involved in antenna placement optimization is supported by Figure 2. The example in Figure 2 includes two main stages: radiation pattern prediction (200) and antenna placement optimization (300).

[0038] Generally speaking, the method for determining the correct placement of antennas includes three stages: a training stage, a prediction stage (200), and an optimization stage (300).

[0039] The radiation pattern prediction stage (200) makes it possible to predict from simplified values ​​all the exact values ​​of realized gain (RG) and axial ratio (AR) at all possible points on the search plane.

[0040] Finally, in an optimization stage (300), the resulting RG and AR values ​​can be included in an optimization model (eg, Bayesian optimization) to search for optimal antenna positions.

[0041] The proposed method for determining the correct placement of the antenna simulates a simplified vehicle model with less computation time and predicts a more complex vehicle model, and the method shows a simulation computation time that is much shorter than simulating the most accurate vehicle model at each search point.

[0042] Radiation pattern prediction (200) includes three stages: model fitting (201), embedded input-output training (202), and prediction of realized gain (RG) and axial ratio (AR) (203).

[0043] In the initial stage, which may be interpreted as the training stage, the U-Net convolutional neural network included in the radiation pattern prediction (200) is fed with input radiation patterns (101) of antenna position arrangements (Pn). For the full vehicle model and the simplified vehicle model, the radiation patterns (101) of the training input antennas Pn on the rooftop of the vehicle are provided to the U-Net convolutional neural network (e.g., an electromagnetic simulator). This allows for a resulting output segmentation map based on elevation angle values ​​(θ) from 0 to 180 and azimuth angles (φ) from 0 to 360 in 1° increments for each position point (Pn).

[0044] The U-Net network is an end-to-end fully convolutional network that contains only two separate convolutional training layers and no dense layers, allowing it to accept images of any size.

[0045] When a sufficient amount of data (101) is not available to train and test the U-Net convolutional neural network, a possible alternative is to use data augmentation techniques to generate new data for the original images using simple techniques such as rotation, reflection, displacement, and magnification to increase the set of initial samples and avoid overfitting. This technique contributes to using the model when a large enough database cannot be obtained for training and testing. After obtaining RG and AR data for both the simplified and precise vehicle models at the points described in Figure 2, the data augmentation technique is applied. In the metrics of the U-Net learning process, unlike RG, AR has little correlation between the simplified and precise models. This has little impact on the prediction and accuracy of the model.

[0046] The model fitting (201) for the radiation pattern prediction (200) is configured to determine the generalization rate of similar data on which the machine learning model was trained. The settings of the model fitting (201) vary depending on the machine learning model used, and in the proposed U-Net model, it is configured to involve a 3x3 kernel filter, a Rectified Linear Unit (ReLU) activation function, a 2x2 max pooling operation with stride 2 at the end of each step, and feature maps equal to [32, 64, 128]. Thus, the model fitting (201) allows tuning the model parameters to improve accuracy.

[0047] The embedded input-output training (202) of radiation pattern prediction (200) includes an initial data set used for training, as shown in Figure 1. In the proposed example, the data set includes 13 sampled antenna placement points P1-P13, i.e. Pn, located at different distances within a limited area of ​​the vehicle (1600 x 1200 in this particular example), and is configured according to the proposed machine learning model. In this particular case, U-Net is defined as follows:

[0048] Number of channels = 2 (corresponding to the realized gain and axial ratio) Number of outputs = 2 (corresponding to the realized gain and axial ratio) Batch size = 32 (the number of training examples used in one iteration) Number of epochs = 0 (number of complete passes through the training dataset).

[0049] Therefore, embedded input-output training (202) is configured to train and test a model that predicts the next step.

[0050] The predicted realized gain (RG) and axial ratio (AR) (203) of the radiation pattern prediction (200) includes simplified data (SD) as input and precise data (PD) as output for each point determined by a Bayesian optimization technique that is configured to take electromagnetic simulator results for the simplified vehicle model and predict values ​​for the precise vehicle model.

[0051] The proposed method for predicting the radiation pattern (200) on the surface of a vehicle allows to reduce the electromagnetic simulation time, which can be very time consuming depending on the complexity of the vehicle model or simulation parameters used. Thus, the simplified model is simulated in less computational time to obtain predictions for the complex model. If the complex model were to be completely solved for all position points (Pn), it would require a huge computational simulation time.

[0052] The antenna placement optimization (300), i.e., the optimization model, includes a random initialization step (303), a candidate solution step (304), a simplified realized gain and axial ratio step (305), a full realized gain and axial ratio step (306), a fitness function step (307), and a solution finding test step (308). The test (308) step has two possible outcomes: if a positive solution is found (309), an output result is provided (310). If the result is not suitable (311), the process returns to the procedure (304) to search for candidate solutions again.

[0053] The random initialization step (303) includes the determination of the necessary parameters. The solution candidate step (304) includes the determination of the new point (Pn) to be analyzed. The simplified realized gain and axial ratio step (305) is a simulation step, in which the obtained simplified vehicle model is simulated for the determined new point (Pn). The complete realized gain and axial ratio step (306) includes the resulting exact values ​​of RG and AR predicted by the radiation pattern prediction (200) for the new point (Pn). The fitness function step (307), or objective function (F), includes the maximization of RG and the minimization of AR. Finally, the solution finding test step (308) provides the best solution (310) based on the best position if the performed test is positive (309). Otherwise (311), the optimization process (300) performs a new analysis (304) based on said point (Pn).

[0054] For the optimization model (300), Bayesian optimization is proposed. It works by constructing a probabilistic model of the objective function (F) using a Bayesian machine learning technique called surrogate function. As shown in FIG. 3, the optimization includes at least an unknown function and a priori mean function (a), an acquisition function and mean update (b), algorithm evaluation 1 (c), and algorithm evaluation 2 (d). In the unknown function and a priori mean function (a) of the input point or antenna configuration, the unknown function F(ρ) (400) is shown for ρn=(x,y) and n=0. Also shown are the mean value (401) of the Gaussian process (GP) and the standard deviation (404) of the Gaussian process. In the acquisition function and mean update (b), the antenna configuration ρ1 and the minimum acquisition function (402) for n=1 are shown. In a similar approach, in algorithm evaluation 1 (c) and algorithm evaluation 2 (d), ρ2 and ρ3 for n=2 and n=3 are shown, respectively. Also shown is the acquisition minimum (403). Then, before a candidate sample (402) is selected for evaluation with the actual objective function (F), it is efficiently explored by the acquisition function using a Gaussian regression process. This is the most efficient approach in terms of the number of function evaluations required.

[0055] Everything the user knows about the objective function (F) can be used to estimate the cost of various candidate samples (304) that may be needed to evaluate the search. This estimation of the objective function is done using a surrogate function. To select the next sample from the search space, the Bayesian antenna placement optimization (300) uses an acquisition function. The acquisition function measures the value that would be generated by evaluating the objective function (F) at a new point (Pn) based on the current posterior distribution for fitness. These estimates and confidence intervals are obtained using Gaussian process regression. This optimization technique has the property of minimizing the number of evaluations of the objective function, and also works well in settings where the objective function has multiple local maxima.

[0056] The improvements made by using BO (Bayesian Optimization) are mainly related to finding the optimal location with fewer iterations compared to evolutionary algorithms (GA and PSO), but it also succeeds in being more accurate in location prediction.

[0057] The method described below shows how Bayesian optimization (300) evaluates the objective function in an initial space and allocates the remainder of the budget for N function evaluations.

[0058] The basic Bayesian optimization method (300) includes the following steps:

[0059] - Set a Gaussian Process (GP) prior for the antenna placement objective function F'(P). By default, we take the mean μ(P)=0 (deterministic); -Based on the current prior distribution, observe the objective function F at location n, and continue the following process while n≦N, where N is the total number of n locations: -Update the posterior probability distribution of the objective function F using all available data; -Let Pn be the maximizing point of the acquisition function for P, where the acquisition function is calculated using the current posterior distribution; - Obtaining a radiation pattern set by the realized gain (RG) and axial ratio (AR) from the simplified model and sending the radiation pattern to U-Net; -U-Net predicts the exact values ​​of radiation pattern, RG, and AR and sends them back to BO (Bayesian Optimization); - Observe F(Pn); - Update the Gaussian Process (GP) prior distribution with the new data to generate a posterior distribution, which will become the prior distribution for the next step; -Increase n; -Return either the point assessed by the best F(Pn) or the point with the largest posterior mean.

[0060] [References] [1] E. Adegoke, J. Zidane, E. Kampert, P. A. Jennings, C. R. Ford, S. A. Birrell, and M. D. Higgins, “Evaluating machine learning & antenna placement for enhanced gnss accuracy for cavs,” in 2019 IEEE Intelligent Vehicles Symposium (IV) . IEEE, 2019, pp. 1007-1012. [2] M. Kirkko- Jaakkola, S. Feng, Y. Xue, X. Zhang, S. Honkala, S. S“oderholm, L. Ruotsalainen, W. Ochieng, and H. Kuusniemi, ”Effect of antenna location on gnss positioning for its applications,” in 2016 European Navigation Conference (ENC) . IEEE, 2016, pp. 1-7. [3] A. Jauhri, J. D. Lohn, and D. S. Linden, “A comparison of antenna placement algorithms,” in Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation, 2014, pp. 1223-1230. [4] T. H. O’Donnell, R. Haupt, K. Lysiak, and D. J. Jacavanco, “Issues involved in developing a genetic algorithm methodology for optimizing the position of shipboard antennas,” in Evolutionary and Bio-Inspired Computation: Theory and Applications III, vol. 7347. International Society for Optics and Photonics, 2009, p. 73470U. [5] J. Yang, J. Li, and S. Zhou, “Study of antenna position on vehicle by using a characteristic modes theory, ” IEEE Antennas and Wireless Propagation Letters, vol. 17, no. 7, pp. 1132-1135, 2018. [6] J. M. K. Infantolino, M. J. Barney, and R. L. Haupt, “Using a genetic algorithm to determine an optimal position for an antenna mounted on a platform,” in MILCOM 2009-2009 IEEE Military Communications Conference. IEEE, 2009, pp. 1- 6. [7] Frazier, Peter I. “A tutorial on Bayesian optimization.” arXiv preprint arXiv : 1807.02811 (2018) . [8] Brochu, Eric, Vlad M. Cora, and Nando De Freitas. “A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning.” arXiv preprint arXiv: 1012.2599 (2010). [9] M. J. Inman, J. M. Earwood, A. Z. Elsherbeni, and C. E. Smith, “Bayesian optimization techniques for antenna design,” Progress In Electromagnetics Research, vol. 49, pp. 71-86, 2004.

[10] H. Gazzah and J.-P. Delmas, “Optimization of the antenna array geometry based on a bayesian doa estimation criterion, ” in 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2011, pp. 2544-2547.

[11] A. Ghani, F. Keyvani, and S. H. Sedighy, “Antenna array placement on limited bound for isotropic and optimal direction-of-arrival estimation, ” IET Signal Processing, vol. 12, no. 3, pp. 277-283, 2018.

Brief Description of the Drawings

[0061] [Figure 1] An initial data set is shown, which includes a set of 13 sampled antenna placement points P1 to P13 (i.e., Pn) located at different distances within a limited area of ​​the vehicle (1600 × 1200 centimeters in this particular case). [Diagram 2] 1 shows an overview of the stages including antenna prediction and position optimization. [Diagram 3] The multiple stages of the Bayesian optimization method are shown, illustrated by the unknown function and the prior mean function (a), the acquisition function and the mean update (b), algorithm evaluation 1 (c), and algorithm evaluation 2 (d).

Claims

1. 1. A method for determining correct placement of an antenna on a support structure, comprising: said arrangement providing the best radiation pattern for said antenna; The method comprises: A random initialization (303) of an antenna placement optimization (300) for an antenna placement (Pn), The antenna arrangement optimization (300) includes: determining (304) an ideal candidate solution based on the antenna configuration (Pn); determining (305) a simplified realized gain and axial ratio of said antenna arrangement (Pn); Predicting realized gain and axial ratio (306); Obtaining a fitness function (307); If a positive solution is found (309), an output result is provided (310); If the results are not satisfactory (311), the search for ideal candidate solutions (304) is repeated; A method for determining proper placement of an antenna, comprising:

2. The radiation pattern prediction (200) is Obtaining a result of model fitting (201) based on the segmentation map obtained from the U-Net convolutional neural network; Obtaining an embedded output training (202) based on the obtained model fitting (201); Obtaining predicted realized gain (RG) and axial ratio (AR) (203); 2. The method of claim 1, further comprising:

3. 3. The method for determining a correct placement of an antenna according to claim 1 or 2, wherein the model fitting (201) is configured to determine a generalization rate of a machine learning model on similar data trained based on at least one of a kernel filter, a regularized linear unit activation function, a max pooling operation with strides, and a feature map.

4. The method for determining a correct placement of an antenna according to any one of claims 1 to 3, wherein the embedded output training (202) includes an initial data set used to train the U-Net convolutional neural network.

5. 5. The method for determining the correct placement of an antenna according to claim 1, wherein the predicted realized gain (RG) and axial ratio (AR) (203) includes simplified data (SD) as input and precise data (PD) as output for each point defined by the antenna placement optimization (300).

6. 6. The method for determining the correct placement of antennas according to claim 1, wherein the segmentation map contains data derived from at least one of an elevation angle value (θ) and an azimuth angle (φ) for each antenna placement (Pn).

7. The method for determining the correct placement of antennas according to any one of claims 1 to 6, wherein the U-Net convolutional neural network includes an input radiation pattern (101) of an antenna placement (Pn).

8. 8. The method for determining the correct placement of antennas according to claim 1, wherein the input radiation pattern (101) comprises at least one set of quantitative data points characterizing the antennas at each antenna placement (Pn).

9. The method for determining the correct placement of an antenna according to any one of claims 1 to 8, wherein the U-Net convolutional neural network is trained using the input radiation pattern (101).

10. 10. The method for determining the correct placement of an antenna according to any one of claims 1 to 9, wherein the prediction (306) of realized gain and axial ratio is obtained from the predicted realized gain (RG) and axial ratio (AR) (203) of the embedded input-output training (202) and the radiation pattern prediction (200).

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