GNSS interference identification method based on spatial transformation, multi-scale feature fusion and KAN

Abstract

The invention discloses a GNSS interference identification method based on spatial transformation, multi-scale feature fusion and KAN. The method comprises the steps of forming an interference signal data set; obtaining a time-frequency image training set and a time-frequency image test set; constructing a GNSS interference identification classifier composed of a spatial transformation module, a multi-scale feature fusion module and a KAN module; a trained GNSS interference identification classifier is obtained; and obtaining a final GNSS interference identification classifier. And finally, outputting the category of the GNSS interference signal acquired in real time by the GNSS interference identification classifier. According to the invention, the spatial transformation module is used to carry out translation, scaling and other operations on the interference signal time-frequency image, and the number of training samples is increased. And the multi-scale feature fusion module adopts parallel convolution kernels of different scales to extract multi-scale spatial features of the time-frequency graph, so that the richness of feature representation is increased, and the recognition accuracy is further improved. The KAN module uses a KAN to replace a traditional multi-layer perceptron to execute a final classification task, and a more complex nonlinear function can be fitted by using fewer parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite navigation anti-interference, and in particular relates to a GNSS (Global Navigation Satellite System) interference identification method based on space transformation, multi-scale feature fusion and KAN (Kolmogorov-Arnold Network). Background Art

[0002] GNSS can provide precise positioning, navigation and timing services, and plays a key role in electronic warfare. However, due to the long distance between navigation satellites and the ground, GNSS signals are very weak when they reach the ground, and are therefore very susceptible to interference signals. In order to improve the navigation performance of GNSS in interference environments, previous studies have mainly focused on studying effective anti-interference methods for specific types of interference. However, the actual working environment of GNSS receivers is complex and changeable, and interference identification can provide a basis for the targeted selection of anti-interference measures.

[0003] Existing GNSS interference identification methods mainly rely on deep learning technology. Although deep learning-based methods can accurately identify GNSS interference signals, they usually require enough samples to train the classifier model. However, in a complex battlefield environment, it is extremely difficult to obtain enough interference signal samples, and there is currently a lack of research on the problem of GNSS interference identification under small sample conditions. In addition, the existing GNSS interference identification methods have too many parameters, which is not conducive to deploying the model on resource-constrained devices such as portable GNSS receivers. Summary of the invention

[0004] In order to solve the above problems, the object of the present invention is to provide a GNSS interference identification method based on spatial transformation, multi-scale feature fusion and KAN.

[0005] In order to achieve the above object, the GNSS interference identification method based on spatial transformation, multi-scale feature fusion and KAN provided by the present invention comprises the following steps performed in sequence:

[0006] 1) Generate 7 types of GNSS interference signals and form an interference signal dataset, and then divide the interference signal dataset into a training set and a test set;

[0007] 2) Perform time-frequency conversion on all interference signals in the training set and the test set to obtain the corresponding time-frequency image training set and time-frequency image test set;

[0008] 3) Construct a GNSS interference identification classifier consisting of a spatial transformation module, a multi-scale feature fusion module and a KAN module;

[0009] 4) using the time-frequency image training set obtained in step 2) to train the GNSS interference recognition classifier constructed in step 3) to obtain a trained GNSS interference recognition classifier;

[0010] 5) Inputting the time-frequency image test set obtained in step 2) into the trained GNSS interference identification classifier obtained in step 3) for testing and verification, and obtaining the final GNSS interference identification classifier;

[0011] 6) The real-time collected GNSS interference signal is input into the final GNSS interference identification classifier obtained in step 5), and the final GNSS interference identification classifier outputs the category of the GNSS interference signal.

[0012] In step 1), the 7 types of GNSS interference signals are single-tone interference signals, multi-tone interference signals, linear chirp interference signals, sinusoidal chirp interference signals, pulse interference signals, narrowband noise frequency modulation interference signals and non-interference signals; all the above GNSS interference signals constitute an interference signal data set, and then 1 sample, 5 samples and 10 samples are extracted from each type of GNSS interference signal in the interference signal data set to form three training sets with different sample numbers; the remaining GNSS interference signals are used to construct a test set;

[0013] The power of each GNSS interference signal is in the range of [-110,-101]dBm, the initial phase of the carrier is in the range of [0,2π], and other parameters are set as follows: the carrier frequency of the single-tone interference signal is in the range of [0,2]MHz; the multi-tone interference signal contains 2 single-tone interference signals, and the carrier frequency of each single-tone interference signal is in the range of [0,2]MHz; the sweep bandwidth of the linear chirp interference signal and the sinusoidal chirp interference signal is in the range of [0.5,2]MHz, and the sweep period is in the range of [20,50]μs; the bandwidth of the narrowband noise FM interference signal is in the range of [0.1,2]MHz; the repetition period of the pulse interference signal is in the range of [0.02,0.2]ms.

[0014] In step 2), the time-frequency conversion uses short-time Fourier transform, and the formula is as follows:

[0015]

[0016] Where y(n(is the GNSS interference signal, n is the time variable, h(n-m0 is the window function centered at time m, m = 0, 1, ..., M y -1, k is a discrete frequency point, k=0,1,...,N y -1, j is the imaginary unit, STFT(m,k) is the time-frequency transformation result of the GNSS interference signal, N yis the number of fast Fourier transform points, M y is the number of times the window function slides, w = 2π / N y .

[0017] In step 3), the spatial transformation module is mainly composed of a grid generator and a sampler; wherein the grid generator generates an affine transformation parameter θ=[θ1, θ2, θ3, θ4] according to the size of the input interference signal time-frequency image, and then constructs an affine transformation matrix T based on the affine transformation parameter θ, and the affine transformation matrix T changes the pixel coordinates of the input time-frequency image through translation and scaling operations; the affine transformation matrix T is composed of the translation matrix T t With the scaling matrix T s Multiply them together and we get:

[0018]

[0019] The affine transformation matrix T maps the coordinates of all pixels in the input interference signal time-frequency image to new coordinates. The calculation formula is as follows:

[0020]

[0021] in, Represents the original coordinates of the i-th pixel in the input interference signal time-frequency image, represents the new coordinates of the i-th pixel in the input interference signal time-frequency image after spatial transformation; all new coordinates will be stored in the sampling grid G(T)={G i}, specifically expressed as Then the sampler extracts pixel values ​​from the input interference signal time-frequency image according to the sampling grid G(T) generated above, and maps them to the corresponding positions of the output interference signal time-frequency image to obtain the interference signal time-frequency image after spatial transformation, so as to expand the number of samples in the time-frequency image training set.

[0022] In step 3), the multi-scale feature fusion module includes a first Inception layer, a second Inception layer, a third Inception layer, a convolution layer, a maximum pooling layer and an average pooling layer; the Inception layer has 3×3, 5×5 and 11×11 convolution kernel branches, and these three branches are used to perform convolution operations of different sizes in parallel to extract multi-scale features from the input data; the 3×3 convolution kernel branch is used to capture local details, the 5×5 convolution kernel branch is used to extract medium-scale features, and the 11×11 convolution kernel branch is used to obtain global information; after each branch is compressed by the maximum pooling layer and the average pooling layer, the output feature map is spliced ​​in the channel dimension to finally obtain a fused multi-scale feature map.

[0023] In step 3), the KAN module includes a first KAN layer and a second KAN layer; the input of the first KAN layer is a feature vector of 1×768 pixels, and the output of the first KAN layer is a feature vector of 1×64 pixels; the input of the second KAN layer is a feature vector of 1×64 pixels, and the output of the second KAN layer is a feature vector of 1×7 pixels p=[p1, p2, p3, p4, p5, p6, p7], where

[0024] In step 4), the specific method of using the time-frequency image training set obtained in step 2) to train the GNSS interference recognition classifier constructed in step 3) to obtain the trained GNSS interference recognition classifier is as follows:

[0025] Input the time-frequency image training set obtained in step 2) into the GNSS interference recognition classifier constructed in step 3), train the GNSS interference recognition classifier, set the initial learning rate to 0.0001, select the Adam algorithm as the optimization algorithm, and select the cross entropy loss function as the loss function;

[0026] Firstly, the short-time Fourier transform is used to perform time-frequency transformation on the GNSS interference signals in the time-frequency image training set to obtain the time-frequency images of all GNSS interference signals in the training set; then, the spatial transformation module is used to perform spatial transformation on the above time-frequency images to generate a large number of interference signal time-frequency images with different parameters; finally, the above interference signal time-frequency images are sequentially passed through the multi-scale feature fusion module and the KAN module to predict the type of interference signal;

[0027] When the rate of change of the cross entropy loss function is less than 0.1%, a trained hierarchical recognition classifier is obtained.

[0028] The GNSS interference identification method based on spatial transformation, multi-scale feature fusion and KAN provided by the present invention has the following advantages:

[0029] 1) By introducing the spatial transformation module, a large number of interference signal time-frequency images with different parameters can be generated, which greatly increases the diversity of the training data set, improves the generalization ability of the model, and reduces the risk of overfitting.

[0030] 2) By introducing a multi-scale feature fusion module, information of different scales of the time-frequency graph is extracted and fused, so that the module can capture the details and features of the time-frequency image at different scales and provide rich feature representation for subsequent category judgment.

[0031] 3) Use KAN to replace the traditional multi-layer perceptron to design the classification network. Compared with the multi-layer perceptron, KAN has a learnable activation function, which fundamentally eliminates the dependence on the linear weight matrix, can fit more complex nonlinear functions with fewer parameters, effectively improves the recognition performance, and reduces the number of parameters required for the model.

[0032] 4) Even when there is only one training sample for each type of interference signal, an interference recognition accuracy of 80.93% is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A flow chart of the GNSS interference identification method based on spatial variation, multi-scale feature fusion and KAN provided by the present invention.

[0034] Figure 2 This is a structural diagram of the space transformation module in the present invention.

[0035] Figure 3 This is a structural diagram of the multi-scale feature fusion module in the present invention.

[0036] Figure 4 This is a structural diagram of the KAN module in the present invention.

[0037] Figure 5 This is the confusion matrix of the method of the present invention when there are only 10 training samples for each type of interference signal.

[0038] Figure 6 This is the confusion matrix of the method of the present invention when there are only 5 training samples for each type of interference signal.

[0039] Figure 7 It is the confusion matrix of the method of the present invention when there is only one training sample for each type of interference signal. DETAILED DESCRIPTION

[0040] The GNSS interference identification method based on spatial variation, multi-scale feature fusion and KAN provided by the present invention is described in detail below in conjunction with the accompanying drawings and embodiments.

[0041] like Figure 1 As shown, the GNSS interference identification method based on spatial variation, multi-scale feature fusion and KAN provided by the present invention includes the following steps performed in sequence:

[0042] 1) Generate 7 types of GNSS interference signals and form an interference signal dataset, and then divide the interference signal dataset into a training set and a test set;

[0043] The seven types of GNSS interference signals are single-tone interference signals, multi-tone interference signals, linear chirp interference signals, sinusoidal chirp interference signals, pulse interference signals, narrowband noise frequency modulation interference signals and non-interference signals; all the above GNSS interference signals constitute an interference signal data set, and then 1 sample, 5 samples and 10 samples are extracted from each type of GNSS interference signal in the interference signal data set to form three training sets with different sample numbers; the remaining GNSS interference signals are used to construct a test set;

[0044] The power of each GNSS interference signal is in the range of [-110,-101]dBm, the initial phase of the carrier is in the range of [0,2π], and other parameters are set as follows: the carrier frequency of the single-tone interference signal is in the range of [0,2]MHz; the multi-tone interference signal contains 2 single-tone interference signals, and the carrier frequency of each single-tone interference signal is in the range of [0,2]MHz; the sweep bandwidth of the linear chirp interference signal and the sinusoidal chirp interference signal is in the range of [0.5,2]MHz, and the sweep period is in the range of [20,50]μs; the bandwidth of the narrowband noise FM interference signal is in the range of [0.1,2]MHz; the repetition period of the pulse interference signal is in the range of [0.02,0.2]ms.

[0045] In this embodiment, according to the parameters of the 7 types of GNSS interference signals described above, SIGLENT's RF signal generator SSG3032X and arbitrary waveform generator SDG6052X-E are used to generate and transmit different types of GNSS interference signals in the L1 frequency band, and then a software receiver based on BladeRF design is used to receive and process them, and the L1 frequency band satellite signal generated by the GPS signal simulator is superimposed. The receiver front-end filter bandwidth and sampling frequency are fixed to 2.2MHz and 10MHz respectively. The training set is divided into three cases according to the number of interference samples of each type, namely, each type of interference signal contains 1 sample, 5 samples and 10 samples. The test set contains a total of 14,000 samples, of which each type of interference signal has 2,000 samples.

[0046] 2) Perform time-frequency conversion on all interference signals in the training set and the test set to obtain the corresponding time-frequency image training set and time-frequency image test set;

[0047] The time-frequency conversion uses short-time Fourier transform, and the formula is as follows:

[0048]

[0049] Where y(n) is the GNSS interference signal, n is the time variable, h(nm) is the window function centered at time m, m = 0, 1, ..., M y-1, k is a discrete frequency point, k=0,1,...,N y -1, j is the imaginary unit, STFT(m,k) is the time-frequency transformation result of the GNSS interference signal, N y is the number of fast Fourier transform points, M y is the number of times the window function slides, w = 2π / N y .

[0050] 3) Construct a GNSS interference identification classifier consisting of a spatial transformation module, a multi-scale feature fusion module and a KAN module;

[0051] like Figure 2 As shown in FIG. 1 , the spatial transformation module is mainly composed of a grid generator and a sampler; wherein the grid generator generates an affine transformation parameter θ=[θ1,θ2,θ3,θ4] according to the size of the input interference signal time-frequency image, and then constructs an affine transformation matrix T based on the affine transformation parameter θ, and the affine transformation matrix T changes the pixel coordinates of the input time-frequency image through translation and scaling operations; the affine transformation matrix T is composed of the translation matrix T t With the scaling matrix T s Multiply them together and we get:

[0052]

[0053] The affine transformation matrix T maps the coordinates of all pixels in the input interference signal time-frequency image to new coordinates. The calculation formula is as follows:

[0054]

[0055] in, Represents the original coordinates of the i-th pixel in the input interference signal time-frequency image, represents the new coordinates of the i-th pixel in the input interference signal time-frequency image after spatial transformation; all new coordinates will be stored in the sampling grid G(T)={G i}, specifically expressed as Then the sampler extracts pixel values ​​from the input interference signal time-frequency image according to the sampling grid G(T) generated above, and maps them to the corresponding positions of the output interference signal time-frequency image to obtain the interference signal time-frequency image after spatial transformation, so as to expand the number of samples in the time-frequency image training set.

[0056] like Figure 3As shown in the figure, the multi-scale feature fusion module includes a first Inception layer, a second Inception layer, a third Inception layer, a convolution layer, a maximum pooling layer and an average pooling layer; the Inception layer has 3×3, 5×5 and 11×11 convolution kernel branches, and these three branches are used to perform convolution operations of different sizes in parallel to extract multi-scale features from the input data; the 3×3 convolution kernel branch is used to capture local details, the 5×5 convolution kernel branch is used to extract medium-scale features, and the 11×11 convolution kernel branch is used to obtain global information; after each branch is compressed by the maximum pooling layer and the average pooling layer, the output feature map is spliced ​​in the channel dimension to finally obtain a fused multi-scale feature map.

[0057] like Figure 4 As shown, the KAN module includes a first KAN layer and a second KAN layer; the input of the first KAN layer is a feature vector of 1×768 pixels, and the output of the first KAN layer is a feature vector of 1×64 pixels; the input of the second KAN layer is a feature vector of 1×64 pixels, and the output of the second KAN layer is a feature vector of 1×7 pixels p=[p1,p2,p3,p4,p5,p6,p7], where

[0058] The design of KAN is derived from the Kolmogorov-Arnold representation theorem, which states that any multivariate continuous function f defined on a bounded domain can be represented by a two-layer nested superposition of a finite number of univariate continuous functions. Its mathematical expression is as follows:

[0059]

[0060] Among them, φ q,p (·) is an internal one-variable continuous function, Φ q (·) is an external one-dimensional continuous function; the internal one-dimensional continuous function forms a KAN layer with an input of n dimensions and an output of 2n+1 dimensions, and the external one-dimensional continuous function forms a KAN layer with an input of 2n+1 dimensions and an output of 1 dimension; KAN does not rely on a fixed activation function, but expresses complex nonlinear functions more flexibly through a learnable activation function, thereby improving the nonlinear fitting ability of the model; by stacking multiple KAN layers, a deeper KAN network structure can be obtained, further enhancing the nonlinear fitting ability of the model;

[0061] After the input x is processed by L layers of KAN, the output is expressed as:

[0062]

[0063] Among them, H lis the activation function matrix of the l-th layer KAN; (l,i) represents the i-th neuron in the l-th layer, (l+1,j) represents the j-th neuron in the i+1-th layer, and the activation function connecting the i-th neuron (l,i) in the l-th layer and the j-th neuron (l+1,j) in the i+1-th layer can be expressed as h l,j,i ,l=0,1,…,L-1,i=1,2,…,n l ,j=1,2,…,n l+1 , n l , n l+1 are the number of nodes of the l-th layer and the l+1-th layer of KAN respectively; the input of the l+1-th layer of KAN is expressed as follows:

[0064]

[0065] In the above formula, the activation function h(x) can be expressed as:

[0066] h(x)=w b b(x)+w s spline(x)(10)

[0067] Among them, w b and w s are the trainable weights corresponding to the basis function b(x) and the spline function spline(x), which are used to better control the overall size of the activation function h(x); the basis function b(x) is expressed as:

[0068]

[0069] The spline function spline(x) is a B-spline curve, expressed as:

[0070]

[0071] Among them, the control point c i is a trainable parameter, I is the number of control points, B i,k (x) is the k-order B-spline basis function, which can be obtained by the deBoor-cox recursive algorithm. The specific calculation formula is as follows:

[0072]

[0073] 4) using the time-frequency image training set obtained in step 2) to train the GNSS interference recognition classifier constructed in step 3) to obtain a trained GNSS interference recognition classifier;

[0074] Input the time-frequency image training set obtained in step 2) into the GNSS interference recognition classifier constructed in step 3), train the GNSS interference recognition classifier, set the initial learning rate to 0.0001, select the Adam algorithm as the optimization algorithm, and select the cross entropy loss function as the loss function;

[0075] Firstly, the short-time Fourier transform is used to perform time-frequency transformation on the GNSS interference signals in the time-frequency image training set to obtain the time-frequency images of all GNSS interference signals in the training set; then, the spatial transformation module is used to perform spatial transformation on the above time-frequency images to generate a large number of interference signal time-frequency images with different parameters; finally, the above interference signal time-frequency images are sequentially passed through the multi-scale feature fusion module and the KAN module to predict the type of interference signal;

[0076] When the rate of change of the cross entropy loss function is less than 0.1%, a trained hierarchical recognition classifier is obtained.

[0077] 5) Inputting the time-frequency image test set obtained in step 2) into the trained GNSS interference identification classifier obtained in step 3) for testing and verification, and obtaining the final GNSS interference identification classifier;

[0078] 6) The real-time collected GNSS interference signal is input into the final GNSS interference identification classifier obtained in step 5), and the final GNSS interference identification classifier outputs the category of the GNSS interference signal.

[0079] The effect of the present invention can be further verified through the following experiments.

[0080] 1. Experimental conditions:

[0081] The hardware platform of the experiment of the present invention is: Intel Core i9-13900K 3.00GHz processor, 128GB memory, NVIDIA Geforce RTX 4090D GPU.

[0082] The software platform of the experiment of the present invention is: Windows 11 operating system, Matlab R2022a, python3.7, PyTorch 2.4.0 (CUDA12.5).

[0083] 2. Experimental content and results analysis:

[0084] The present invention uses a training set to train a GNSS interference identification classifier, and uses a test set to test the performance of the GNSS interference identification classifier.

[0085] The confusion matrix is ​​used to plot the identification results of each interference type when there are only 10 training samples for each type of interference signal, as shown in the figure below: Figure 5 shown.

[0086] The confusion matrix is ​​used to plot the identification results of each interference type when there are only 5 training samples for each type of interference signal, as shown in the figure below: Figure 6 shown.

[0087] The confusion matrix is ​​used to plot the identification results of each interference type when there is only one training sample for each type of interference signal, as shown in the figure below. Figure 7 shown.

[0088] Combine the following Figure 5 , Figure 6 , Figure 7 The experimental result diagram of the present invention is further described.

[0089] Figure 5 , Figure 6 , Figure 7 The STI, MTI, LCI, SCI, Pulse, NFMI, and NIF labels correspond to the single-tone interference signal, multi-tone interference signal, linear chirp interference signal, sinusoidal chirp interference signal, pulse interference signal, narrowband noise FM interference signal and non-interference signal among the seven GNSS interference signals respectively; each column of the confusion matrix is ​​the true category of the GNSS interference signal, and each row is the predicted category of the GNSS interference signal.

[0090] from Figure 5 It can be seen that when there are 10 training samples for each type of interference signal, except for Pulse, the recognition accuracy of the method of the present invention for the other six types of interference signals is above 87%, achieving a relatively high recognition accuracy.

[0091] from Figure 6 It can be seen that when there are 5 training samples for each type of interference signal, except for Pulse, the recognition accuracy of the method of the present invention for the other six types of interference signals is above 85%, achieving a relatively high recognition accuracy.

[0092] from Figure 7 It can be seen that when there is one training sample for each type of interference signal, except for Pulse and NFMI, the recognition accuracy of the method of the present invention for the other five types of interference signals is above 84%, achieving a relatively high recognition accuracy.

[0093] Combination Figure 5 , Figure 6 , Figure 7The experimental results show that the method of the present invention will misidentify some NFMI as STI, because the time-frequency images of NFMI and STI both show the characteristics of narrowband spectrum, especially when the interference frequency of STI is close to 0Hz, the time-frequency image of STI is very similar to the time-frequency image of NFMI. In addition, some pulses are misidentified as NIF, which may be because the repetition period of the defined pulse is 0.02ms to 0.2ms, while the duration of the collected signal is only 100μs, so it is possible that the collected pulse does not have a pulse pair, resulting in a small amount of pulse interference being misidentified as NIF.

Claims

1. A GNSS interference identification method based on spatial transformation, multi-scale feature fusion and KAN, characterized by: The GNSS interference identification method comprises the following steps performed in sequence: 1) Generate 7 types of GNSS interference signals and form an interference signal dataset, and then divide the interference signal dataset into a training set and a test set; 2) Perform time-frequency conversion on all interference signals in the training set and the test set to obtain the corresponding time-frequency image training set and time-frequency image test set; 3) Construct a GNSS interference identification classifier consisting of a spatial transformation module, a multi-scale feature fusion module and a KAN module; 4) using the time-frequency image training set obtained in step 2) to train the GNSS interference recognition classifier constructed in step 3) to obtain a trained GNSS interference recognition classifier; 5) Inputting the time-frequency image test set obtained in step 2) into the trained GNSS interference identification classifier obtained in step 3) for testing and verification, and obtaining the final GNSS interference identification classifier; 6) The real-time collected GNSS interference signal is input into the final GNSS interference identification classifier obtained in step 5), and the final GNSS interference identification classifier outputs the category of the GNSS interference signal.

2. The GNSS interference identification method according to claim 1, characterized in that: In step 1), the seven types of GNSS interference signals are single-tone interference signal, multi-tone interference signal, linear chirp interference signal, sinusoidal chirp interference signal, pulse interference signal, narrowband noise frequency modulation interference signal and non-interference signal; The interference signal dataset is composed of all the above GNSS interference signals. Then, 1 sample, 5 samples, and 10 samples are extracted from each type of GNSS interference signal in the interference signal dataset to form three training sets with different sample numbers. The remaining GNSS interference signals are used to construct the test set. The power of each GNSS interference signal is in the range of [-110,-101]dBm, the initial phase of the carrier is in the range of [0,2π], and other parameters are set as follows: the carrier frequency of the single-tone interference signal is in the range of [0,2]MHz; the multi-tone interference signal contains 2 single-tone interference signals, and the carrier frequency of each single-tone interference signal is in the range of [0,2]MHz; the sweep bandwidth of the linear chirp interference signal and the sinusoidal chirp interference signal is in the range of [0.5,2]MHz, and the sweep period is in the range of [20,50]μs; the bandwidth of the narrowband noise FM interference signal is in the range of [0.1,2]MHz; the repetition period of the pulse interference signal is in the range of [0.02,0.2]ms.

3. The GNSS interference identification method according to claim 1, characterized in that: In step 2), the time-frequency conversion uses short-time Fourier transform, and the formula is as follows: Where y(n) is the GNSS interference signal, n is the time variable, h(nm) is the window function centered at time m, m = 0, 1, ..., M y -1, k is a discrete frequency point, k=0,1,...,N y -1, j is the imaginary unit, STFT(m,k) is the time-frequency transformation result of the GNSS interference signal, N y is the number of fast Fourier transform points, M y is the number of times the window function slides, w = 2π / N y .

4. The GNSS interference identification method according to claim 1, characterized in that: In step 3), the spatial transformation module is mainly composed of a grid generator and a sampler; wherein the grid generator generates an affine transformation parameter θ=[θ1, θ2, θ3, θ4] according to the size of the input interference signal time-frequency image, and then constructs an affine transformation matrix T based on the affine transformation parameter θ, and the affine transformation matrix T changes the pixel coordinates of the input time-frequency image through translation and scaling operations; the affine transformation matrix T is composed of the translation matrix T t With the scaling matrix T s Multiply them together and we get: The affine transformation matrix T maps the coordinates of all pixels in the input interference signal time-frequency image to new coordinates. The calculation formula is as follows: in, Represents the original coordinates of the i-th pixel in the input interference signal time-frequency image, represents the new coordinates of the i-th pixel in the input interference signal time-frequency image after spatial transformation; all new coordinates will be stored in the sampling grid G(T)={G i }, specifically expressed as Then the sampler extracts pixel values ​​from the input interference signal time-frequency image according to the sampling grid G(T) generated above, and maps them to the corresponding positions of the output interference signal time-frequency image to obtain the interference signal time-frequency image after spatial transformation, so as to expand the number of samples in the time-frequency image training set.

5. The GNSS interference identification method according to claim 1, characterized in that: In step 3), the multi-scale feature fusion module includes a first Inception layer, a second Inception layer, a third Inception layer, a convolution layer, a maximum pooling layer, and an average pooling layer; the Inception layer has 3×3, 5×5, and 11×11 convolution kernel branches, and these three branches are used to perform convolution operations of different sizes in parallel to extract multi-scale features from the input data; The 3×3 convolution kernel branch is used to capture local details, the 5×5 convolution kernel branch is used to extract medium-scale features, and the 11×11 convolution kernel branch is used to obtain global information. After each branch is compressed by the maximum pooling layer and the average pooling layer, the output feature map is spliced ​​in the channel dimension to finally obtain a fused multi-scale feature map.

6. The GNSS interference identification method according to claim 1, characterized in that: In step 3), the KAN module includes a first KAN layer and a second KAN layer; the input of the first KAN layer is a feature vector of 1×768 pixels, and the output of the first KAN layer is a feature vector of 1×64 pixels; the input of the second KAN layer is a feature vector of 1×64 pixels, and the output of the second KAN layer is a feature vector of 1×7 pixels p=[p1, p2, p3, p4, p5, p6, p7], where 7. The GNSS interference identification method according to claim 1, characterized in that: In step 4), the specific method of using the time-frequency image training set obtained in step 2) to train the GNSS interference recognition classifier constructed in step 3) to obtain the trained GNSS interference recognition classifier is as follows: Input the time-frequency image training set obtained in step 2) into the GNSS interference recognition classifier constructed in step 3), train the GNSS interference recognition classifier, set the initial learning rate to 0.0001, select the Adam algorithm as the optimization algorithm, and select the cross entropy loss function as the loss function; Firstly, the short-time Fourier transform is used to perform time-frequency transformation on the GNSS interference signals in the time-frequency image training set to obtain the time-frequency images of all GNSS interference signals in the training set; then, the spatial transformation module is used to perform spatial transformation on the above time-frequency images to generate a large number of interference signal time-frequency images with different parameters; finally, the above interference signal time-frequency images are sequentially passed through the multi-scale feature fusion module and the KAN module to predict the type of interference signal; When the rate of change of the cross entropy loss function is less than 0.1%, a trained hierarchical recognition classifier is obtained.

Images