CNN-SVM-based satellite navigation interference detection system and detection method thereof

Abstract

The invention discloses a satellite navigation interference detection system based on CNN-SVM and a detection method thereof, the detection system comprises a time-frequency transformation module, a feature extraction module and an interference detection module, and a time-frequency image processing module comprises a time-frequency standardization module and a normalization processing module; wherein the time-frequency transformation module adopts a time-frequency transformation mode of short-time Fourier transform (STFT), the time-frequency transformation module directly takes an intermediate-frequency digital signal as input, and the feature extraction module comprises a convolutional neural network (CNN), carries out feature extraction on a time-frequency spectrogram after time-frequency transformation, adjusts the structure of the CNN according to the features of the input time-frequency spectrogram, and outputs the feature of the CNN. The optimal effect of feature extraction is achieved; the interference detection module comprises a first-class support vector machine (OCSVM), the first-class SVM is one of SVM methods, and the training of the first-class SVM can realize the detection of interference only by a sample of normal data.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS interference signal detection, and in particular relates to a satellite navigation interference detection system and a detection method thereof based on CNN-SVM. Background Art

[0002] Global Navigation Satellite System (GNSS) plays a vital role in all fields of modern society. They not only provide accurate geographic location and time information for individual users, but are also widely used in military, aviation, marine, transportation and other industries. With the increasing application of GNSS in various fields, the space electromagnetic environment faced by GNSS has become more complex and changeable, causing the satellite navigation system to face various intentional or unintentional interference threats. Due to the open requirements of the civil code of satellite navigation signals and the spatial loss of signals over long distances, the navigation system is extremely susceptible to ground radio interference, resulting in reduced positioning and timing accuracy, or even complete inability to locate. Therefore, the interference detection technology of the global satellite navigation system is an issue that urgently needs to be studied and solved.

[0003] According to the processing flow of the receiver, satellite navigation interference detection technology can be divided into pre-correlation and post-correlation detection technology. Pre-correlation detection technology mainly includes interference detection methods in the time domain and transform domain. Time domain detection determines whether interference exists by analyzing the energy of the received signal. There are mainly detection methods based on filtering technology and sample covariance. Transform domain detection mainly includes frequency domain and time-frequency domain detection. This detection method detects based on the difference in the characteristics of the interference signal and the real signal in the transform domain. Frequency domain detection technology mainly includes detection methods based on energy detection, median filtering and weight leakage; time-frequency domain detection methods perform interference detection based on time-frequency transformation. Common time-frequency transformation methods include wavelet transform, short-time Fourier transform and Wigner transform. For GNSS non-stationary signals, it is not enough to analyze only time domain or frequency domain information. Time-frequency domain detection technology integrates the characteristics of time domain and frequency domain, which is more advantageous for GNSS interference detection.

[0004] So far, many experts and scholars have proposed a variety of detection algorithms for various types of interference. Traditional detection methods include interference detection methods based on chi-square detection, maximum likelihood estimation, minimum mean square error, etc. With the increasing power of artificial intelligence, machine learning, as a powerful data analysis tool, provides a new way for GNSS interference detection. The machine learning algorithms used in most current interference detection methods belong to supervised learning, which have extremely high detection performance when the training set samples are sufficient and the sample types are consistent with those of the test set. However, the diversity and complexity of GNSS interference make it very difficult to establish a training set covering all types of interference. In practice, since some interference is sporadic and others may be intentionally hidden, it is also difficult to collect enough GNSS interference samples. The incompleteness of the samples poses a new challenge to these supervised machine learning detection algorithms that require a large number of labeled samples for model training. Therefore, in view of the above problems, the present invention proposes a satellite navigation interference detection technology based on CNN-SVM, which only requires normal data in the model training stage, and the input data is the time-frequency spectrum of the intermediate frequency digital signal of the receiving satellite. Since there is no need to use interference data for training, the present invention is more suitable for interference detection in satellite navigation than supervised learning methods (such as CNN, SVM, etc.). Summary of the invention

[0005] In view of the complex and diverse interferences to the receiver and the limitation of training samples for supervised learning, the present invention provides a satellite navigation interference detection system and a detection method based on CNN-SVM.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] A satellite navigation interference detection system based on CNN-SVM comprises a time-frequency conversion module, a feature extraction module and an interference detection module, wherein the time-frequency image processing module comprises a time-frequency normalization module and a normalization processing module; wherein: the time-frequency conversion module is a time-frequency conversion mode of short-time Fourier transform (STFT), the time-frequency conversion module directly uses an intermediate frequency digital signal as input, and overcomes the defect that input signals are different due to different front ends; the feature extraction module comprises a convolutional neural network (CNN), which extracts features from a time-frequency spectrum after the time-frequency conversion, and the convolutional neural network (CNN) structure can be adjusted according to the features of the input time-frequency spectrum, so that the feature extraction achieves the best effect; the interference detection module comprises a class of support vector machines (OCSVM), the class of SVM is a type of SVM method, and compared with the traditional SVM, the training of the class of SVM only requires samples of normal data to realize the detection of interference.

[0008] Furthermore, the connection structure of each interference signal detection module is as follows: the GNSS intermediate frequency digital signal collected by the front end is used as the input of the time-frequency conversion module, the output of the time-frequency conversion module is connected to the input of the time-frequency image processing module, the output of the time-frequency image processing module is connected to the input of the feature extraction module, the output of the feature extraction module is connected to the input of the interference detection module, and the output of the interference detection module outputs the interference signal detection result.

[0009] Furthermore, the connection structure of each module inside the time-frequency image processing module is as follows: the output end of the time-frequency normalization module is correspondingly connected to the input end of the normalization processing module, and the output end of the normalization processing module serves as the output end of the time-frequency image processing module.

[0010] A satellite navigation interference detection method based on CNN-SVM includes the following steps:

[0011] S1, input the collected and processed intermediate frequency digital signal into the time-frequency conversion module for time-frequency analysis, use short-time Fourier transform to analyze the intermediate frequency digital signal, obtain the joint distribution information of the signal in the time domain and frequency domain, and output the time-frequency spectrum;

[0012] S2. For the time-frequency spectrum output by STFT, the time-frequency normalization module performs time-frequency normalization processing on it respectively, and uses the bicubic difference method to adjust the size of the image to the size of the input layer of the convolutional neural network;

[0013] S3, input the normalized image into the normalization processing module for normalization processing, and process the image data into grayscale data of 0 to 255 through linear function normalization;

[0014] S4, the time-frequency transformed image after processing in steps S1-S3 is input into the feature extraction module. The input layer is consistent with the size and dimension of the image. The feature extraction module contains a series of convolutional layers and pooling layers. After the image undergoes a series of convolutional layer and pooling layer feature extraction processes, the features are mapped to a space with a lower dimension through a fully connected layer and converted into a feature vector of size 1×2048;

[0015] S5. Input the extracted feature vector into the interference detection module. The size and dimension of the input are consistent with the feature vector. The output layer contains 2 nodes. The input feature vector is passed through a class of SVM to obtain a decision result, judging whether the input is normal or abnormal, thereby realizing the detection of interference signals.

[0016] Furthermore, the short-time Fourier transform in step S1 is:

[0017] For a signal s(p) with limited energy, its short-time Fourier transform is defined as:

[0018]

[0019] Where: s(p) is the input signal, p is the index of the sampling point in the signal sequence, h(pm) is the moving window function, which indicates the offset of the window function relative to the central time point m, m is the central position of the window function, f is the frequency of the signal, F s is the sampling frequency, N is the length of the window function, e is the base of the natural logarithm, and j is the imaginary unit; further, the time-frequency energy density spectrum q(f,m) is:

[0020]

[0021] Where A is a real-valued scalar. For the unilateral energy spectral density, the calculation formula is as follows:

[0022]

[0023] Where: h(p) represents a fixed window function, and at the zero frequency and the Nyquist frequency, the factor 2 in the numerator is changed to 1.

[0024] Furthermore, the time-frequency normalization in step S2 is:

[0025] The time-frequency transformed image is normalized, and the bicubic interpolation method is used to enhance the image. The image size is adjusted to 227×227. The bicubic interpolation method is shown in the following formula:

[0026]

[0027] In the formula, (y,z) represents the coordinates of the input sample feature point, f(y,z) represents the value that should be inserted after calculation of the pixel to be interpolated, (y α ,z β ) represents the points in the 4x4 area near the input sample feature point, where: α, β = 0, 1, 2, 3, and the W function is called the BiCubic basis function:

[0028]

[0029] Where: W(k) is the BiCubic basis function, |k| represents the distance between the target point and the surrounding points, and a is the smoothness parameter;

[0030] After calculation, it is concluded that a = -1 / 2, in order to achieve and provide the best interpolation quality, the BiCubic basis function is expressed as:

[0031]

[0032] Cubic convolution interpolation uses the color values ​​of 16 points around the sampling point, combined with other factors, such as the color change rate of adjacent points, and other factors that may affect the interpolation result, to achieve a more accurate interpolation effect, making the adjusted image resolution closer to the original image.

[0033] Furthermore, the normalization process in step S3 is:

[0034] The normalized time-frequency image is normalized by a linear function. The normalized time-frequency image is represented as S(t,ω), where t and ω represent the time and frequency corresponding to the input signal respectively. The normalized image information is represented as:

[0035]

[0036] Where: S norm (t,ω) is the normalized data, S(t,ω) is the original data, S max (t,ω),S min (t,ω) are the maximum and minimum values ​​of the original data set respectively.

[0037] Furthermore, the support vector machine classification is:

[0038] The feature vector X=[x1,x2,...,x k ] T , where: T represents the transpose of the vector, x1,x2,...,x k is the feature point of the time-frequency spectrum, with a total of k feature points. After mapping the sample feature point x to the high-dimensional feature space through nonlinear mapping x→Φ(x), a hyperplane w·Φ(x)-ρ=0 is established. The distance δ from the input sample feature point x to the hyperplane w·Φ(x)-ρ=0 is expressed as:

[0039]

[0040] Where w is the normal vector of the hyperplane, ρ is the intercept of the hyperplane, ||·|| represents the second norm, and Φ(x) is the nonlinear mapping function;

[0041] In order to maximize the distance ρ / ||w|| between the origin and the positive data, it is necessary to find an optimal hyperplane, so the optimization problem of a class of SVM is:

[0042]

[0043] Among them, w T is the transpose of the normal vector w, x i is a slack variable, M is the number of training feature samples, parameter v represents the maximum proportion of training samples that are allowed to be misclassified, and xi Represents the i-th sample feature point in the training set, and the relaxation variable x i Indicates the degree to which the i-th sample is misclassified, and st means "satisfies the following constraints";

[0044] The Lagrange multiplier method is used to construct the Lagrange function, and then the optimal solution of the original problem is obtained by solving its dual problem. The dual problem of the original problem is obtained through Lagrange duality:

[0045]

[0046] Among them, α is the Lagrange multiplier, x u is the u-th sample feature point in the training set, α i , α u are the Lagrange multipliers corresponding to the i-th and u-th sample feature points, respectively, K(x i ,x u ) is the Gaussian kernel function, and its expression is:

[0047]

[0048] Among them, e is the base of the natural logarithm, and σ is the width parameter of the Gaussian kernel function.

[0049] The hyperplane intercept ρ is given by Any α u It is obtained and expressed as:

[0050]

[0051] The decision function is expressed as:

[0052]

[0053] Where sgn() is the sign function and x is the input sample feature point.

[0054] Therefore, for the input new sample feature point x, the decision function projects it onto the normal vector of the hyperplane to obtain the value of f(x), and uses this to determine the category of the feature point. If f(x)>0, the signal is considered to be a normal signal; if f(x)<0, it is considered to be an interference signal.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) The present invention adopts a time-frequency transformation method to obtain the characteristics of the fusion time domain and frequency domain, and analyzes the GNSS non-stationary signal. Compared with only obtaining time domain or frequency domain information, the performance of interference detection can be improved;

[0057] (2) The present invention adopts a convolutional neural network to identify time-frequency feature images. Compared with the traditional analysis method based on signal feature extraction, it overcomes the limitations of different feature signals and greatly improves accuracy and efficiency;

[0058] (3) The present invention adopts a semi-supervised machine learning method. Compared with the supervised learning method, it does not need to obtain interference signal samples. It only needs to input normal signal samples when training the model to complete the detection. It has stronger adaptability to different interferences and better performance in detecting interference.

[0059] (4) The present invention does not need to rely on a large amount of prior knowledge to train the model, and is more suitable for detecting actual satellite navigation interference scenarios;

[0060] (5). The present invention is based on software algorithm and has the advantages of great flexibility and low cost.

[0061] (6) The present invention uses intermediate frequency signal analysis and is not affected by the satellite signal structure. It is suitable for interference signal detection of various GNSS systems such as GPS and Beidou. It has strong versatility and important engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a structural block diagram of the present invention. DETAILED DESCRIPTION

[0063] The present invention will be further described below in conjunction with the embodiments.

[0064] Example 1

[0065] like Figure 1 As shown, a satellite navigation interference detection system based on CNN-SVM includes a time-frequency conversion module, a feature extraction module and an interference detection module, and the time-frequency image processing module includes a time-frequency normalization module and a normalization processing module; wherein: the time-frequency conversion module is a time-frequency conversion mode of short-time Fourier transform (STFT), and the time-frequency conversion module directly uses an intermediate frequency digital signal as input, thereby overcoming the defect that the input signal has differences due to different front ends; the feature extraction module includes a convolutional neural network (CNN), which extracts features from a time-frequency spectrum after the time-frequency conversion, and can adjust the convolutional neural network (CNN) structure according to the features of the input time-frequency spectrum, so that the feature extraction achieves the best effect; the interference detection module includes a class of support vector machines (OCSVM), a class of SVM is a type of SVM method, and compared with the traditional SVM, the training of a class of SVM only requires samples of normal data to achieve interference detection.

[0066] Connection structure of each interference signal detection module: the GNSS intermediate frequency digital signal collected by the front end is used as the input of the time-frequency conversion module, the output of the time-frequency conversion module is connected to the input of the time-frequency image processing module, the output of the time-frequency image processing module is connected to the input of the feature extraction module, the output of the feature extraction module is connected to the input of the interference detection module, and the output of the interference detection module outputs the interference signal detection result.

[0067] The connection structure of each module inside the time-frequency image processing module: the output end of the time-frequency normalization module is connected to the input end of the normalization processing module, and the output end of the normalization processing module serves as the output end of the time-frequency image processing module.

[0068] Example 2

[0069] A satellite navigation interference detection method based on CNN-SVM includes the following steps:

[0070] S1, input the collected and processed intermediate frequency digital signal into the time-frequency conversion module for time-frequency analysis, use short-time Fourier transform to analyze the intermediate frequency digital signal, obtain the joint distribution information of the signal in the time domain and frequency domain, and output the time-frequency spectrum;

[0071] Specifically, the short-time Fourier transform in step S1 is:

[0072] For a signal s(p) with limited energy, its short-time Fourier transform is defined as:

[0073]

[0074] Where: s(p) is the input signal, p is the index of the sampling point in the signal sequence, h(pm) is the moving window function, which indicates the offset of the window function relative to the central time point m, m is the central position of the window function, f is the frequency of the signal, F s is the sampling frequency, N is the length of the window function, e is the base of the natural logarithm, and j is the imaginary unit; further, the time-frequency energy density spectrum q(f,m) is:

[0075]

[0076] Where A is a real-valued scalar. For the unilateral energy spectral density, the calculation formula is as follows:

[0077]

[0078] Where: h(p) represents a fixed window function, and at the zero frequency and the Nyquist frequency, the factor 2 in the numerator is changed to 1.

[0079] S2. For the time-frequency spectrum output by STFT, the time-frequency normalization module performs time-frequency normalization processing on it respectively, and uses the bicubic difference method to adjust the size of the image to the size of the input layer of the convolutional neural network;

[0080] Specifically, the time-frequency normalization in step S2 is:

[0081] The time-frequency transformed image is normalized, and the bicubic interpolation method is used to enhance the image. The image size is adjusted to 227×227. The bicubic interpolation method is shown in the following formula:

[0082]

[0083] In the formula, (y,z) represents the coordinates of the input sample feature point, f(y,z) represents the value that should be inserted after calculation of the pixel to be interpolated, (y α ,z β ) represents the points in the 4x4 area near the input sample feature point, where: α, β = 0, 1, 2, 3, and the W function is called the BiCubic basis function:

[0084]

[0085] Where: W(k) is the BiCubic basis function, |k| represents the distance between the target point and the surrounding points, and a is the smoothness parameter;

[0086] After calculation, it is concluded that a = -1 / 2, in order to achieve and provide the best interpolation quality, the BiCubic basis function is expressed as:

[0087]

[0088] Cubic convolution interpolation uses the color values ​​of 16 points around the sampling point, combined with other factors, such as the color change rate of adjacent points, and other factors that may affect the interpolation result, to achieve a more accurate interpolation effect, making the adjusted image resolution closer to the original image.

[0089] S3, input the normalized image into the normalization processing module for normalization processing, and process the image data into grayscale data of 0 to 255 through linear function normalization;

[0090] Specifically, the normalization process in step S3 is:

[0091] The normalized time-frequency image is normalized by a linear function. The normalized time-frequency image is represented as S(t,ω), where t and ω represent the time and frequency corresponding to the input signal respectively. The normalized image information is represented as:

[0092]

[0093] Where: S norm (t,ω) is the normalized data, S(t,ω) is the original data, S max (t,ω),S min (t,ω) are the maximum and minimum values ​​of the original data set respectively.

[0094] S4, the time-frequency transformed image after processing in steps S1-S3 is input into the feature extraction module. The input layer is consistent with the size and dimension of the image. The feature extraction module contains a series of convolutional layers and pooling layers. After the image undergoes a series of convolutional layer and pooling layer feature extraction processes, the features are mapped to a space with a lower dimension through a fully connected layer and converted into a feature vector of size 1×2048;

[0095] S5. Input the extracted feature vector into the interference detection module. The size and dimension of the input are consistent with the feature vector. The output layer contains 2 nodes. The input feature vector is passed through a class of SVM to obtain a decision result, and the input is judged to be normal or abnormal, so as to realize the detection of interference signals.

[0096] Specifically, the one type of support vector machine classification:

[0097] The feature vector X=[x1,x2,...,x k ] T , where: T represents the transpose of the vector, x1,x2,...,x k is the feature point of the time-frequency spectrum, with a total of k feature points. After mapping the sample feature point x to the high-dimensional feature space through nonlinear mapping x→Φ(x), a hyperplane w·Φ(x)-ρ=0 is established. The distance δ from the input sample feature point x to the hyperplane w·Φ(x)-ρ=0 is expressed as:

[0098]

[0099] Where w is the normal vector of the hyperplane, ρ is the intercept of the hyperplane, ||·|| represents the second norm, and Φ(x) is the nonlinear mapping function;

[0100] In order to maximize the distance ρ / ||w|| between the origin and the positive data, it is necessary to find an optimal hyperplane, so the optimization problem of a class of SVM is:

[0101]

[0102] Among them, w T is the transpose of the normal vector w, x iis a slack variable, M is the number of training feature samples, parameter v represents the maximum proportion of training samples that are allowed to be misclassified, and x i Represents the i-th sample feature point in the training set, and the relaxation variable x i Indicates the degree to which the i-th sample is misclassified, and st means "satisfies the following constraints";

[0103] The Lagrange multiplier method is used to construct the Lagrange function, and then the optimal solution of the original problem is obtained by solving its dual problem. The dual problem of the original problem is obtained through Lagrange duality:

[0104]

[0105] Where α is the Lagrange multiplier, x u is the u-th sample feature point in the training set, α i , α u are the Lagrange multipliers corresponding to the i-th and u-th sample feature points, respectively, K(x i ,x u ) is the Gaussian kernel function, and its expression is:

[0106]

[0107] Among them, e is the base of the natural logarithm, and σ is the width parameter of the Gaussian kernel function.

[0108] The hyperplane intercept ρ is given by Any α u It is obtained and expressed as:

[0109]

[0110] The decision function is expressed as:

[0111]

[0112] Where sgn() is the sign function and x is the input sample feature point.

[0113] Therefore, for the input new sample feature point x, the decision function projects it onto the normal vector of the hyperplane to obtain the value of f(x), and uses this to determine the category of the feature point. If f(x)>0, the signal is considered to be a normal signal; if f(x)<0, it is considered to be an interference signal.

[0114] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A satellite navigation interference detection system based on CNN-SVM, characterized in that: It includes a time-frequency conversion module, a feature extraction module and an interference detection module, and the time-frequency image processing module includes a time-frequency normalization module and a normalization processing module; wherein: the time-frequency conversion module is a time-frequency conversion method of short-time Fourier transform STFT, the time-frequency conversion module directly uses the intermediate frequency digital signal as input, the feature extraction module includes a convolutional neural network CNN, which extracts features from the time-frequency spectrum after the time-frequency conversion, and adjusts the convolutional neural network CNN structure according to the features of the input time-frequency spectrum so that the feature extraction achieves the best effect; the interference detection module includes a class of support vector machines OCSVM.

2. The satellite navigation interference detection system based on CNN-SVM according to claim 1, characterized in that: The GNSS intermediate frequency digital signal collected by the front end is used as the input end of the time-frequency conversion module, the output end of the time-frequency conversion module is connected to the input end of the time-frequency image processing module, the output end of the time-frequency image processing module is connected to the input end of the feature extraction module, the output end of the feature extraction module is connected to the input end of the interference detection module, and the output end of the interference detection module outputs the interference signal detection result.

3. The satellite navigation interference detection system based on CNN-SVM according to claim 2, characterized in that: The connection structure of each module inside the time-frequency image processing module: the output end of the time-frequency normalization module is correspondingly connected to the input end of the normalization processing module, and the output end of the normalization processing module serves as the output end of the time-frequency image processing module.

4. A detection method for a satellite navigation interference detection system based on CNN-SVM according to any one of claims 2-3, characterized in that: The following steps are involved: S1, input the collected and processed intermediate frequency digital signal into the time-frequency conversion module for time-frequency analysis, use short-time Fourier transform to analyze the intermediate frequency digital signal, obtain the joint distribution information of the signal in the time domain and frequency domain, and output the time-frequency spectrum; S2. For the time-frequency spectrum output by STFT, the time-frequency normalization module performs time-frequency normalization processing on it respectively, and uses the bicubic difference method to adjust the size of the image to the size of the input layer of the convolutional neural network; S3, input the normalized image into the normalization processing module for normalization processing, and process the image data into grayscale data of 0 to 255 through linear function normalization; S4, the time-frequency transformed image after processing in steps S1-S3 is input into the feature extraction module. The input layer is consistent with the size and dimension of the image. The feature extraction module contains a series of convolutional layers and pooling layers. After the image undergoes a series of convolutional layer and pooling layer feature extraction processes, the features are mapped to a space with a lower dimension through a fully connected layer and converted into a feature vector of size 1×2048; S5. Input the extracted feature vector into the interference detection module. The size and dimension of the input are consistent with the feature vector. The output layer contains 2 nodes. The input feature vector is passed through a class of SVM to obtain a decision result, judging whether the input is normal or abnormal, thereby realizing the detection of interference signals.

5. The satellite navigation interference detection method based on CNN-SVM according to claim 4 is characterized in that: The short-time Fourier transform in step S1 is: For a signal s(p) with limited energy, its short-time Fourier transform is defined as: Where: s(p) is the input signal, p is the index of the sampling point in the signal sequence, h(pm) is the moving window function, which indicates the offset of the window function relative to the central time point m, m is the central position of the window function, f is the frequency of the signal, F s is the sampling frequency, N is the length of the window function, e is the base of the natural logarithm, and j is the imaginary unit; further, the time-frequency energy density spectrum q(f,m) is: Where A is a real-valued scalar. For the unilateral energy spectral density, the calculation formula is as follows: Where: h(p) represents a fixed window function, and at the zero frequency and the Nyquist frequency, the factor 2 in the numerator is changed to 1.

6. The satellite navigation interference detection method based on CNN-SVM according to claim 4 is characterized in that: The time-frequency normalization in step S2 is: The time-frequency transformed image is normalized, and the bicubic interpolation method is used to enhance the image. The image size is adjusted to 227×227. The bicubic interpolation method is shown in the following formula: In the formula, (y,z) represents the coordinates of the input sample feature point, f(y,z) represents the value that should be inserted after calculation of the pixel to be interpolated, (y α ,z β ) represents the points in the 4x4 area near the input sample feature point, where: α, β = 0, 1, 2, 3, and the W function is called the BiCubic basis function: Where: W(k) is the BiCubic basis function, |k| represents the distance between the target point and the surrounding points, and a is the smoothness parameter; After calculation, it is concluded that a = -1 / 2, in order to achieve and provide the best interpolation quality, the BiCubic basis function is expressed as: Cubic convolution interpolation uses the color values ​​of 16 points around the sampling point to make the adjusted image resolution closer to the original image.

7. The satellite navigation interference detection method based on CNN-SVM according to claim 4 is characterized in that: The normalization process in step S3: The normalized time-frequency image is normalized by a linear function. The normalized time-frequency image is represented as S(t,ω), where t and ω represent the time and frequency corresponding to the input signal respectively. The normalized image information is represented as: Where: S norm (t,ω) is the normalized data, S(t,ω) is the original data, S max (t,ω),S min (t,ω) are the maximum and minimum values ​​of the original data set respectively.

8. The satellite navigation interference detection method based on CNN-SVM according to claim 4 is characterized in that: The one-class support vector machine classification: The feature vector X=[x1,x2,...,x k ] T , where: T represents the transpose of the vector, x1,x2,...,x k is the feature point of the time-frequency spectrum, with a total of k feature points. After mapping the sample feature point x to the high-dimensional feature space through nonlinear mapping x→Φ(x), a hyperplane w·Φ(x)-ρ=0 is established. The distance δ from the input sample feature point x to the hyperplane w·Φ(x)-ρ=0 is expressed as: Where w is the normal vector of the hyperplane, ρ is the intercept of the hyperplane, ||·|| represents the second norm, and Φ(x) is the nonlinear mapping function; In order to maximize the distance ρ / ||w|| between the origin and the positive data, it is necessary to find an optimal hyperplane, so the optimization problem of a class of SVM is: Among them, w T is the transpose of the normal vector w, x i is a slack variable, M is the number of training feature samples, parameter v represents the maximum proportion of training samples that are allowed to be misclassified, and x i represents the i-th sample feature point in the training set, and the relaxation variable x i Indicates the degree to which the i-th sample is misclassified, and st means "satisfies the following constraints"; The Lagrange multiplier method is used to construct the Lagrange function, and then the optimal solution of the original problem is obtained by solving its dual problem. The dual problem of the original problem is obtained through Lagrange duality: Among them, α is the Lagrange multiplier, x u is the u-th sample feature point in the training set, α i , α u are the Lagrange multipliers corresponding to the i-th and u-th sample feature points, respectively, K(x i ,x u ) is the Gaussian kernel function, and its expression is: Among them, e is the base of the natural logarithm, σ is the width parameter of the Gaussian kernel function; The hyperplane intercept ρ is given by Any α u It is obtained and expressed as: The decision function is expressed as: In the formula, sgn() is the symbol function, and x is the input sample feature point; Therefore, for the input new sample feature point x, the decision function projects it onto the normal vector of the hyperplane to obtain the value of f(x), and uses this to determine the category of the feature point. If f(x)>0, the signal is considered to be a normal signal; if f(x)<0, it is considered to be an interference signal.

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