Multi-target track identification method and system based on Grubrum angle field and CNN (Convolutional Neural Network)

Abstract

The invention discloses a multi-target track identification method and system based on a Grubrum angle field and a CNN, and relates to a target identification and machine learning technology, and the method comprises the steps: obtaining the flight data of a target, and carrying out the preprocessing of the flight data; on the basis of the preprocessed flight data, calculating a Grubrum matrix, and converting the time sequence of the flight path into a two-dimensional image by utilizing angular field transformation, so as to represent an angle difference between a flight path point and a reference point at a corresponding moment in the two-dimensional image by utilizing any pixel value; and inputting the two-dimensional image into a pre-trained CNN (Convolutional Neural Network) model so as to output a target track identification result by using the pre-trained CNN model. According to the embodiment of the invention, the time sequence data is converted into the image form through the Grubrum angle field conversion, so that the CNN can conveniently carry out feature learning and pattern recognition, and the automatic recognition of the track is realized.

Description

Technical Field

[0001] The present application relates to the field of target recognition and machine learning, and in particular to a multi-target track recognition method and system based on Gram angular field and CNN. Background Art

[0002] In modern aviation monitoring systems, the track recognition of aerial targets is a key link in ensuring flight safety, optimizing route planning, and improving airspace efficiency. However, existing track recognition technologies mainly rely on traditional signal processing and manual feature extraction methods, which face great challenges in recognition accuracy and real-time performance when facing complex multi-target scenarios.

[0003] Existing technologies face several core problems:

[0004] Limitations of single target recognition: Most methods can only effectively process the track of a single target and have difficulty in dealing with multi-target track recognition, especially when the tracks overlap or intertwine.

[0005] Data quality and quantity: High-quality training data is crucial for the model, but in practical applications, it is difficult to obtain sufficient high-quality track data due to factors such as weather and equipment.

[0006] Real-time and computing resources: Existing methods often ignore real-time requirements, and when computing resources are limited, the model's operating efficiency and response speed are difficult to meet actual operational requirements. Summary of the invention

[0007] An embodiment of the present application provides a multi-target track recognition method and system based on Gram angular field and CNN, which is used to convert time series data into image form through Gram angular field conversion, so as to facilitate CNN to perform feature learning and pattern recognition, thereby realizing automatic recognition of tracks.

[0008] The embodiment of the present application provides a multi-target track recognition method based on Gram angular field and CNN, including:

[0009] Acquiring flight data of the target and preprocessing the flight data;

[0010] Based on the preprocessed flight data, a Gram matrix is ​​calculated, and the time series of the track is converted into a two-dimensional image by using an angular field transform, so that any pixel value in the two-dimensional image represents the angle difference between the track point and the reference point at the corresponding moment;

[0011] The two-dimensional image is input into a pre-trained convolutional neural network (CNN) model to output a target track recognition result using the pre-trained CNN model, wherein the CNN model includes a convolution layer, a pooling layer, a fully connected layer and a Softmax classification layer, wherein the convolution layer is used to extract local features in the two-dimensional image, the pooling layer is used to reduce the spatial dimension and retain important features, the fully connected layer is used to flatten the features extracted by the convolution layer and the pooling layer, and perform feature combination and classification prediction through multiple layers of fully connected neurons, and the Softmax classification layer is used to convert the output of the fully connected layer into a probability distribution.

[0012] Optionally, preprocessing the flight data includes denoising, data smoothing, and normalizing the flight data.

[0013] Optionally, based on the preprocessed flight data, the Gram matrix is ​​calculated and the time series of the track is converted into a two-dimensional image using the angular field transform, including:

[0014] A fixed point on the selected trajectory is used as a reference point;

[0015] Based on the reference point, for any point P on the track i (x i ,y i ), with reference point P ref (x ref ,y ref ) between the angle θ i satisfy:

[0016] θ i =atan2(y i -y ref ,x i -x ref )

[0017] Adjust the calculated θ i Angle range to [0, 2π];

[0018] After the above angle difference calculation is performed for all track points, the Gram matrix is ​​constructed using the NumPy library based on the angle difference array formed;

[0019] The Gram matrix is ​​converted to a two-dimensional image format using a function that maps the matrix values ​​to pixel colors.

[0020] Optionally, using the NumPy library to construct a Gram matrix includes: using the elements of the Gram matrix to represent the similarity of the angle difference, where the element G i,j Represents the cosine similarity of the angle difference between the i-th point and the j-th point on the track:

[0021] Gi,j =cos(θ i -θ j )

[0022] In the formula, θ i and θ j Respectively represent the angle difference between the i-th point and the j-th point and the reference point.

[0023] Optionally, converting the Gram matrix to a two-dimensional image format using a function that maps matrix values ​​to pixel colors includes:

[0024] Using the imshow function, the matrix values ​​are mapped to pixel colors based on a given color spectrum to describe different angle differences.

[0025] Optionally, also include:

[0026] Dynamically adjust the size of the data acquisition time window and the sliding step size according to the instantaneous velocity and acceleration of the identified target; and,

[0027] For each target's track data, Gram angular field transformation is used to obtain a single target's track image, and a transparency weight is assigned to each target's image according to the relative distance and speed difference between the targets.

[0028] Images of a plurality of objects are superimposed, and transparency of the superimposed images is controlled based on the transparency weights.

[0029] An embodiment of the present application also proposes a multi-target track recognition system based on Gram angular field and CNN, including a processor and a memory, wherein a computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the multi-target track recognition method based on Gram angular field and CNN as described above are implemented.

[0030] The embodiment of the present application converts the time series data into image form through Gram angular field conversion, which is convenient for CNN to perform feature learning and pattern recognition, thereby realizing automatic recognition of the track.

[0031] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present application. Also, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0033] Figure 1 The basic process diagram of the multi-target track recognition method based on Gram angular field and CNN in the embodiment of the present application is shown;

[0034] Figure 2 The overall process of the multi-target track recognition method based on Gram angular field and CNN in an embodiment of the present application is schematically illustrated. DETAILED DESCRIPTION

[0035] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0036] The present application embodiment provides a multi-target track recognition method based on Gram angle field and CNN, such as Figure 1 , Figure 2 As shown, the following steps are included:

[0037] In step S101, flight data of a target is acquired and preprocessed.

[0038] In this embodiment, source data acquisition can adopt software-defined radar technology to integrate multiple radar devices, including primary radar, secondary radar and multi-base radar, to ensure all-round and no-dead-angle monitoring. The collaborative work of radar network can be used to achieve data fusion and improve the accuracy of target positioning and anti-interference ability.

[0039] Flight data recorder access: Through a dedicated interface, real-time access to the flight data recorder (black box) is provided to extract flight status data including flight altitude, speed, attitude angle, engine status, etc., to ensure the real-time and integrity of the data.

[0040] Auxiliary sensor data fusion: Integrate data from multiple sensors such as meteorological radar, optical camera, infrared thermal imager, etc., and use data fusion algorithms to improve the reliability and comprehensiveness of data.

[0041] In some embodiments, preprocessing the flight data includes denoising, data smoothing, and normalizing the flight data. Preprocessing the flight data is used to ensure data integrity, redundancy design and fault switching: redundant channels are set at the front end of data acquisition. Once the main channel fails, it will automatically switch to the backup channel to ensure the continuity of the data flow. Anomaly detection mechanism: deploy an anomaly detection model based on machine learning, monitor the data flow in real time, automatically identify abnormal data packets, and mark abnormal time periods. Data verification and repair: use cyclic redundancy check (CRC) checksum technology to regularly check the integrity and consistency of the data. For detected erroneous data packets, try to repair them through historical data interpolation or neighboring data prediction.

[0042] Preprocessing the flight data may include:

[0043] Denoising

[0044] Kalman filter: Construct an extended Kalman filter (EKF) or unscented Kalman filter (UKF) to dynamically update the target's state estimate and suppress the impact of measurement noise. Dynamically adjust the filter parameters based on the real-time evaluated signal-to-noise ratio (SNR) to achieve optimal denoising effect.

[0045] Data smoothing · Moving average filtering: Calculate the average value of the data in the window. The selection of the window size needs to comprehensively consider the frequency of the data and the required smoothing degree. Use the scipy.signal.savgol_filter function in Python's SciPy library to select appropriate parameters based on the number of data points and the polynomial order to achieve the best smoothing effect.

[0046] Data Normalization

[0047] Linear normalization: Use the maximum and minimum normalization formula

[0048]

[0049] x max 、x min are the minimum and maximum values ​​in the data set, respectively.

[0050] Local standardization: The Z-score standardization method is used, that is, x'=\frac{x-\mu}{\sigma}, where \mu and \sigma are the mean and standard deviation of the local data segment, respectively.

[0051] In step S102, based on the preprocessed flight data, the Gram matrix is ​​calculated, and the time series of the track is converted into a two-dimensional image using angular field transformation, so that any pixel value in the two-dimensional image represents the angular difference between the track point and the reference point at the corresponding moment.

[0052] In step S103, the two-dimensional image is input into a pre-trained convolutional neural network (CNN) model to output a target track recognition result using the pre-trained CNN model, wherein the CNN model includes a convolution layer, a pooling layer, a fully connected layer and a Softmax classification layer, wherein the convolution layer is used to extract local features in the two-dimensional image, the pooling layer is used to reduce the spatial dimension and retain important features, the fully connected layer is used to flatten the features extracted by the convolution layer and the pooling layer, and perform feature combination and classification prediction through multiple layers of fully connected neurons, and the Softmax classification layer is used to convert the output of the fully connected layer into a probability distribution.

[0053] In some specific examples, the CNN model architecture includes a convolutional layer, a pooling layer, a fully connected layer, and a Softmax classification layer, where the convolutional layer is used to extract local features in the input image (here, the transformed Gram matrix). In a specific example, the CNN model can contain multiple convolutional layers, each layer using different filters to capture features of different scales and complexities.

[0054] Pooling layer: reduces spatial dimensions and computational complexity while retaining important features. Common pooling operations include maximum pooling and average pooling.

[0055] Fully connected layer: The features extracted by the convolutional layer and the pooling layer are flattened, and then further feature combination and classification prediction are performed through multiple layers of fully connected neurons.

[0056] Softmax classification layer: The output layer is used to convert the output of the previous layer into a probability distribution. The probability of each category indicates the possibility of the category being selected.

[0057] The specific CNN model training can be carried out in the following ways:

[0058] Dataset preparation: Collect and annotate data to ensure that the dataset covers a wide range of track types, including but not limited to different weather conditions, flight altitudes, speed ranges, and target types, to improve the generalization ability of the model.

[0059] Data enhancement increases data diversity through operations such as rotation, flipping, and scaling, making the model more robust when facing unknown data.

[0060] Divide the dataset into training set, validation set and test set, with a typical ratio of 80%, 10%, and 10%, to ensure that the model can be evaluated on independent data. Step 2.3: Model training Step 2.3.1: Train the model using the training set data

[0061] Training process: Step S1031, select the appropriate convolution kernel size, step size and padding method

[0062] Convolution kernel size: Smaller convolution kernels (such as 3x3 or 5x5) can capture local details, while larger convolution kernels (such as 7x7) can capture broader contextual information.

[0063] Step size: controls the distance the convolution kernel moves on the input image. A larger step size can speed up the calculation, but may lose some details.

[0064] Padding method: "same" padding keeps the output size the same as the input size, while "valid" padding does not add extra pixels, resulting in a smaller output size.

[0065] Step S1032: Design residual connection or skip connection

[0066] Residual connections allow the network to directly pass inputs to multiple layers, which helps solve the gradient vanishing problem in deep networks and improves the stability of model training.

[0067] The back-propagation algorithm is used to update the model parameters and minimize the loss function (such as cross entropy) to improve the prediction accuracy of the model.

[0068] Evaluate the model on the validation set, evaluate the model performance regularly, and adjust the model structure or hyperparameters to prevent overfitting by observing the loss and accuracy on the validation set.

[0069] Using training strategies, early stopping can stop training when the performance of the validation set no longer improves to avoid overfitting. The learning rate decay strategy can help the model adjust weights more finely in the later stages of training to improve the final performance.

[0070] Model optimization and testing

[0071] Model performance analysis: evaluate the model on the test set, identify error patterns, and perform targeted optimization.

[0072] Tune hyperparameters, adjust hyperparameters such as learning rate, regularization strength, batch size, etc. to find the optimal configuration to achieve the best model performance.

[0073] Model compression and quantization, model pruning, quantization, and distillation operations are performed to reduce model size and computing requirements, making it more suitable for edge device deployment and improving real-time processing capabilities.

[0074] After completing the CNN model training, the CNN model is applied to convert the track data to be identified into Gram angular field images, input them into the trained CNN model, and output the category probability distribution of the target.

[0075] The embodiment of the present application converts the time series data into image form through Gram angular field conversion, which is convenient for CNN to perform feature learning and pattern recognition, thereby realizing automatic recognition of the track.

[0076] In some embodiments, based on the preprocessed flight data, calculating the Gram matrix and converting the time series of the track into a two-dimensional image using an angular field transform includes:

[0077] Based on the preprocessed flight data, the time series data of the track is organized into an array form, and each track point contains timestamp and coordinate information.

[0078] Select a fixed point on the track as the reference point. This point can be the starting point, end point or a point on the track. The choice of reference point will affect the visual effect of the final image and can be determined according to the actual application scenario.

[0079] Based on the reference point, the vector between it and the reference point is calculated, and the angle difference of the vector relative to the direction of the reference point is calculated using the angle formula of the vector. Specifically, the angle difference is calculated for any point P on the track. i (x i ,y i ), with reference point P ref (x ref ,y ref ) between the angle θ i satisfy:

[0080] θ i =atan2(y i -y ref ,x i -x ref )

[0081] This can be achieved using the atan2 function:

[0082] \theta_i=atan2(y_i-y_{ref},x_i-x_{ref})

[0083] The atan2 function is able to return the correct angle value based on the given (y) and (x) coordinates, taking into account all four quadrants, thus avoiding the problem that the (arctan) function only returns angles in the range of -\frac{\pi}{2} to \frac{\pi}{2}. (y_i-y_{ref}) and (x_i-x_{ref}): These two values ​​represent the vertical and horizontal distances from the reference point (P_{ref}) to the track point (P_i), respectively. By calculating the difference between the two, we can get the direction of the vector pointing to (P_i) relative to (P_{ref}).

[0084] Adjust the calculated θi The angle range is [0, 2π], ensuring the continuity and consistency of the angle.

[0085] After the above angle difference calculation is performed for all track points, the Gram matrix is ​​constructed using the NumPy library based on the formed angle difference array.

[0086] The Gram matrix is ​​converted to a two-dimensional image format using a function that maps the matrix values ​​to pixel colors.

[0087] The Gram matrix is ​​a symmetric matrix whose elements represent the dot product of two vectors. In this embodiment, the elements of the Gram matrix are represented as the similarity of the angle difference to focus on the angle difference rather than the vector length. In some embodiments, using the NumPy library to construct the Gram matrix includes: using the elements of the Gram matrix to represent the similarity of the angle difference, where the element G i,j Represents the cosine similarity of the angle difference between the i-th point and the j-th point on the track:

[0088] G i,j =cos(θ i -θ j )

[0089] In the formula, θ i and θ j Respectively represent the angle difference between the i-th point and the j-th point and the reference point.

[0090] cos: The cosine function is used to calculate the similarity of the angle difference. If the angle difference between two points is small, then θ i -θ j Close to 0, then cos(θ i -θ j ) is close to 1, indicating that the directions of the two points are very similar; conversely, if the angle difference between the two points is large, then cos(θ i -θ j ) is close to 0, indicating that the directions of the two points are quite different.

[0091] In some embodiments, using a function matrix to map values ​​to pixel colors to convert the Gram matrix into a two-dimensional image format includes:

[0092] Use the imshow function to map the matrix values ​​to pixel colors and describe different angle differences based on a given color spectrum. Specifically, you can use the imshow function of libraries such as Matplotlib or OpenCV to map the matrix values ​​to pixel colors. Choose a suitable color spectrum, such as a heat map color spectrum, to represent different angle differences. Warm colors represent small angle differences (i.e., high similarity), and cold colors represent large angle differences (i.e., low similarity).

[0093] Post-processing and optimization: Perform necessary post-processing on the generated images, such as contrast enhancement and sharpening, to improve image quality. The visual effect of the image can be optimized by adjusting the range of the color spectrum and the dynamic range to make the features more obvious.

[0094] Through the above steps, the time series of track data can be converted into a two-dimensional image, in which each pixel value represents the angle difference between the track point and the reference point at a specific moment, which is convenient for subsequent feature extraction and analysis. The method of the embodiment of the present application can not only intuitively display the changing trend of the track, but also provide rich visual features for the deep learning model, which helps to improve the accuracy of target recognition and classification.

[0095] In some embodiments, it also includes:

[0096] Dynamic adjustment strategy, according to the instantaneous speed and acceleration of the identified target, dynamically adjust the size of the data acquisition time window and the sliding step size, so as to ensure that the image contains sufficient time information and maintains good time resolution. Further image enhancement, such as contrast enhancement: you can use the cv2.equalizeHist function in the OpenCV library to perform histogram equalization, or use an adaptive contrast enhancement algorithm, such as CLAHE (Contrast Limited Adaptive Histogram Equalization), to improve the image contrast.

[0097] Sharpening: You can use the difference between Gaussian blur and the original image to enhance the clarity of the image edge. This can be achieved using the cv2.GaussianBlur function and cv2.addWeighted function in the OpenCV library.

[0098] Multi-target image generation, independent conversion: Gram angular field transformation is applied to the track data of each target to obtain the track image of a single target. Gram angular field transformation is applied to the track data of each target to obtain the track image of a single target, and a transparency weight is assigned to the image of each target according to the relative distance and speed difference between the targets to ensure clear information hierarchy when the images are superimposed.

[0099] Layered overlay and dynamic adjustment: Use image processing software (such as GIMP, Photoshop) or programming libraries (such as PIL, OpenCV) to overlay images of multiple targets according to the priority of the targets and the dynamic adjustment strategy, and control the transparency of the overlaid images based on the transparency weight. Overlay the images of multiple targets to ensure that the track features of different targets are clearly visible in the final image.

[0100] Inputting the track data to be identified into the trained CNN model for target track identification also includes:

[0101] Normalize the generated Gram angular field images to ensure that their size and format are consistent with the images used when training the model. Use the trained CNN model to make predictions on these images. In TensorFlow or PyTorch, you can use the model.predict function to input the preprocessed image data and get the output of the model. The output is a vector representing the probability distribution of different categories. Each element corresponds to a category, and its value represents the probability of that category predicted by the model.

[0102] Further, according to the set threshold or maximum probability principle, the target category is determined and the category probability distribution of the model output is analyzed. Two main methods can be used to determine the final category:

[0103] Maximum probability principle: select the category with the highest probability as the prediction result. This is the most commonly used method and is suitable for most situations.

[0104] Setting a threshold: For some specific tasks, a higher confidence level may be required to make a decision. In this case, a threshold can be set, and only when the probability of a certain category exceeds this threshold, it will be used as a prediction result; otherwise, more data or further verification may be required.

[0105] If the maximum probability principle is applied, the category with the highest probability can be directly selected; if a threshold is set, it is necessary to check whether the probabilities of all categories exceed the threshold, and only the categories that meet the conditions can be adopted.

[0106] The identified target categories and their corresponding probability values ​​are fed back to the decision support system or operator in real time. The results can be sent through a graphical user interface (GUI), command line interface (CLI) or other communication protocols (such as TCP / IP) to ensure the timeliness and accuracy of the information.

[0107] In the fields of military, aviation, traffic management, etc., the real-time performance of recognition results is crucial because it directly affects safety and efficiency. Therefore, it is extremely important to ensure that the entire process from model output to result display is efficient and error-free. Through the steps of the embodiments of the present application, not only can the original track data be converted into a format that can be used for CNN model recognition, but also the trained model can be used for efficient track recognition and classification, and finally the recognition results are fed back to decision makers in real time, providing key information support for various application scenarios, which is of great value for improving the effectiveness of aviation monitoring systems and ensuring flight safety.

[0108] An embodiment of the present application also proposes a multi-target track recognition system based on Gram angular field and CNN, including a processor and a memory, wherein a computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the multi-target track recognition method based on Gram angular field and CNN as described above are implemented.

[0109] It should be noted that in the various embodiments of the present application, 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 includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0110] The serial numbers of the above-mentioned embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0111] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, a magnetic disk, or an optical disk), and includes a number of instructions for a terminal (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present application.

[0112] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

Claims

1. A multi-target track recognition method based on Gram angular field and CNN, characterized in that: include: Acquiring flight data of the target and preprocessing the flight data; Based on the preprocessed flight data, a Gram matrix is ​​calculated, and the time series of the track is converted into a two-dimensional image by using an angular field transform, so that any pixel value in the two-dimensional image represents the angle difference between the track point and the reference point at the corresponding moment; The two-dimensional image is input into a pre-trained convolutional neural network (CNN) model to output a target track recognition result using the pre-trained CNN model, wherein the CNN model includes a convolution layer, a pooling layer, a fully connected layer and a Softmax classification layer, wherein the convolution layer is used to extract local features in the two-dimensional image, the pooling layer is used to reduce the spatial dimension and retain important features, the fully connected layer is used to flatten the features extracted by the convolution layer and the pooling layer, and perform feature combination and classification prediction through multiple layers of fully connected neurons, and the Softmax classification layer is used to convert the output of the fully connected layer into a probability distribution.

2. The multi-target track recognition method based on Gram angle field and CNN as claimed in claim 1, characterized in that: The preprocessing of the flight data includes denoising, data smoothing and normalization of the flight data.

3. The multi-target track recognition method based on Gram angle field and CNN as claimed in claim 1, characterized in that: Based on the preprocessed flight data, the Gram matrix is ​​calculated and the time series of the track is converted into a two-dimensional image using the angular field transform, including: A fixed point on the trajectory is selected as a reference point; Based on the reference point, for any point P on the track i (x i ,y i ), with reference point P ref (x ref ,y ref ) between the angle θ i satisfy: θ i =atan2(y i -y ref ,x i -x ref ) Adjust the calculated θ i Angle range to [0, 2π]; After the above angle difference calculation is performed for all track points, the Gram matrix is ​​constructed using the NumPy library based on the angle difference array formed; The Gram matrix is ​​converted to a two-dimensional image format using a function that maps the matrix values ​​to pixel colors.

4. The multi-target track recognition method based on Gram angle field and CNN as claimed in claim 3, characterized in that: Using the NumPy library to construct the Gram matrix includes: using the elements of the Gram matrix to represent the similarity of the angle difference, where the element G i,j Represents the cosine similarity of the angle difference between the i-th point and the j-th point on the track: G i,j =cos(θ i -θ j ) In the formula, θ i and θ j Respectively represent the angle difference between the i-th point and the j-th point and the reference point.

5. The multi-target track recognition method based on Gram angle field and CNN as claimed in claim 4, characterized in that: The function that maps the values ​​of the matrix to the colors of the pixels to convert the Gram matrix to a two-dimensional image format includes: Using the imshow function, the matrix values ​​are mapped to pixel colors based on a given color spectrum to describe different angle differences.

6. The multi-target track recognition method based on Gram angle field and CNN as claimed in claim 1, characterized in that: Also includes: Dynamically adjust the size of the data acquisition time window and the sliding step size according to the instantaneous speed and acceleration of the identified target; as well as, For each target's track data, Gram angular field transformation is used to obtain a single target's track image, and a transparency weight is assigned to each target's image according to the relative distance and speed difference between the targets. Images of a plurality of objects are superimposed, and transparency of the superimposed images is controlled based on the transparency weights.

7. A multi-target track recognition system based on Gram angular field and CNN, characterized in that: The method comprises a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the multi-target track recognition method based on Gram angular field and CNN as described in any one of claims 1 to 6 are implemented.

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