A method for constructing optimal features for GNSS spoofing detection based on PCA and genetic algorithm

Abstract

This invention relates to a method for constructing optimal features for GNSS spoofing detection based on PCA and a genetic algorithm. The method includes: acquiring satellite navigation signals; extracting correlation domain features from the satellite navigation signals; performing dimensionality reduction on the correlation domain features to generate high-expressive features; inputting the high-expressive features into a genetic algorithm model to obtain optimal joint features; wherein, the optimal joint features are used for GNSS spoofing detection; the genetic algorithm model is trained using a training set; during the training process, an objective function is set, with minimizing the objective function as the training objective, and the weight parameters are updated through a selection process using the genetic algorithm. This invention has higher spoofing detection efficiency and is expected to protect critical communication infrastructure from spoofing attacks.

Description

Technical Field

[0001] This invention relates to the fields of satellite navigation signal processing and machine learning technology, and in particular to a method for constructing optimal features for GNSS spoofing detection based on PCA and genetic algorithms. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) serve as the core infrastructure of modern communication networks, providing a wide range of navigation, positioning, and precise timing services, such as location services for Internet of Things (IoT) devices and high-precision synchronization for future 6G communication systems. However, GNSS signals exhibit significant vulnerabilities during propagation: their low signal power and publicly available structure make them highly susceptible to malicious interference attacks. Deception jamming, by forging navigation signals that closely resemble genuine signals, induces receivers to output false position, velocity, and time (PVT) information. This highly covert and destructive method has become a major challenge in the field of GNSS security.

[0003] Existing technologies for detecting spoofing interference can be categorized into three types: external aids, signal encryption, and signal feature-based detection. External aids rely on inertial navigation systems, high-precision clocks, or 5G signals to provide additional information. While offering excellent detection performance, they are costly and difficult to deploy on a large scale. Signal encryption technologies improve signal integrity to resist spoofing, requiring global coordination to update infrastructure, making implementation challenging. Therefore, signal feature-based detection methods have become a research hotspot due to their advantages of requiring no additional hardware support and offering high algorithmic flexibility. These methods identify anomalies by analyzing signal characteristics in the time, frequency, or correlation domains of the tracking loop (such as signal power, Doppler shift, and correlation peak distortion). Among these, the latest research based on Signal Quality Monitoring (SQM) designs features that characterize spoofing interference by weighting multiple raw observations, represented by Q-channel monitoring (Qmetric), weighted second-order central moment (WSCM), and three-dimensional correlation peak volume difference (VSQM). However, these methods require the use of uniform weights (such as Qmetric, VSQM) or weights that are inversely proportional to the correlator spacing (such as WSCM) when designing weights. Therefore, the existing feature designs mentioned above mostly rely on expert experience and obtain weights through heuristic thinking to weight and combine the original features, lacking a rigorous theoretical optimization basis, which leads to limited detection performance.

[0004] In recent years, machine learning methods have provided new approaches to deception detection. Detectors based on models such as convolutional neural networks (CNNs) and support vector machines (SVMs) have significantly improved detection accuracy by uncovering the nonlinear relationships between high-dimensional features. However, in pursuit of higher performance, these methods often directly input a large number of raw features (such as the output of a multi-channel correlator), leading to the "curse of dimensionality" problem. For example, the time complexity of a one-dimensional convolutional neural network increases linearly with the number of input features, while multi-dimensional feature inputs result in a dramatic increase in computational complexity.

[0005] Existing technical solutions also disclose a joint feature construction method based on XGBoost and logistic regression. Although it can build joint features, its detection performance is low and it requires a large number of original features to construct joint features.

[0006] In summary, existing signal feature-based detection methods face a dual challenge: traditional manual feature design lacks theoretical optimality, while machine learning methods are limited by the computational burden of high-dimensional features. Therefore, how to construct low-dimensional, highly discriminative optimal features while preserving key signal information has become the core issue for improving the efficiency and reliability of GNSS spoofing detection. Summary of the Invention

[0007] To address the problems of existing technologies, this invention proposes an optimal feature construction method for GNSS spoofing detection based on PCA and genetic algorithms. PCA is used to generate basic features, and a genetic algorithm is employed to calculate the weights assigned to each feature. Finally, these generated features are constructed into a single feature, namely Principal Component Regression (PCR). A one-dimensional convolutional neural network is then used to compare and evaluate the PCR method with traditional composite features. Results show that the PCR method consistently outperforms traditional features, achieving higher spoofing detection performance and possessing the potential to protect critical communication infrastructure from spoofing attacks.

[0008] To achieve the above objectives, the present invention provides the following solution:

[0009] A method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithms includes:

[0010] Collect satellite navigation signals, extract the correlation domain features of the satellite navigation signals, perform dimensionality reduction processing on the correlation domain features, and generate highly expressive features;

[0011] The high-expressive features are input into the genetic algorithm model to obtain the optimal joint features; wherein, the optimal joint features are used for GNSS deception detection; the genetic algorithm model is obtained by training on the training set; during the training process on the training set, an objective function is set, and the minimum of the objective function is used as the training objective, and the weight parameters of the model are updated using the genetic algorithm.

[0012] Optionally, generating the high-expressiveness features includes:

[0013] The relevant domain features are standardized and preprocessed, the covariance matrix of the preprocessed result is calculated, and the covariance matrix is ​​decomposed to obtain the eigenvalues ​​and corresponding eigenvectors.

[0014] The eigenvectors are arranged in descending order according to their eigenvalues, and the first K eigenvectors are selected to form the principal component matrix;

[0015] The original data is projected onto the subspace defined by the principal component matrix to generate the high-expressive features; wherein the original data is a target matrix composed of relevant domain features.

[0016] Optionally, updating the model's weight parameters includes:

[0017] Calculate the conditional probability of all samples in the training set, construct the loss function, and add a regularization term;

[0018] The objective function is set according to the loss function with added regularization term, the fitness of each candidate weight parameter is calculated and the best performers are eliminated, and the genetic algorithm is used to find the weight parameters that minimize the objective function.

[0019] Optionally, calculating the conditional probability of all samples in the training set includes:

[0020]

[0021] in, , These are the probability values ​​for binary classification as 1 and 0, respectively. For binary classification labels, For the i-th sample, It is a natural constant. For each feature weight parameter, This is the transpose operator.

[0022] Optionally, setting the objective function includes:

[0023]

[0024] in, Let be the objective function. For the number of samples, The label representing sample i. The value represents the predicted probability of sample i, K is the total number of features, and k represents the kth feature.

[0025] Optionally, calculating fitness and retaining candidate solutions with smaller objective functions includes:

[0026] Define fitness as , It is a local minimum value, used to prevent division by zero, employing a roulette wheel strategy, based on probability. Select individuals to enter the mating pool ;in, Let be the fitness of the i-th candidate solution. Let be the loss function for the i-th candidate solution.

[0027] Optionally, generating offspring candidate solutions includes:

[0028] Randomly pair parents, with probability Perform arithmetic crossover and generate child solutions according to the following formula:

[0029]

[0030] in, The mixing factor is uniformly sampled within [0,1]. and For the paired parent generation solution, and For the offspring solution, the mutation stage uses probability. Apply Gaussian perturbation to each dimension of the offspring , Let V be the variance of the Gaussian perturbation.

[0031] Optionally, obtaining the optimal joint features includes:

[0032]

[0033] in, The k-th feature generated by PCA It is the transpose operator. This is the intercept.

[0034] Optionally, the method further includes: inputting the optimal joint features into a one-dimensional convolutional neural network to obtain a deception detection performance evaluation result.

[0035] The beneficial effects of this invention are as follows:

[0036] This invention proposes an optimal feature construction method for spoofing interference detection. The method uses PCA to generate highly expressive features and then employs a genetic algorithm to weight and construct the optimal feature set. This invention offers higher spoofing detection efficiency and holds promise for protecting critical communication infrastructure from spoofing attacks.

[0037] This invention uses PCA dimensionality reduction and genetic algorithm weighting to compress the original features into a single PCR feature, which greatly reduces the complexity while maintaining performance comparable to the input multidimensional features.

[0038] This invention constructs an objective function based on the maximum likelihood method and optimizes the weights by minimizing the objective function, overcoming the limitations of traditional heuristic design methods and improving the deceptive representation ability of the designed features. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart of an optimal feature construction method for GNSS deception detection based on PCA and genetic algorithm according to an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the time evolution curves of IE2, IE4, QE2, and QE4 in an embodiment of the present invention.

[0042] Figure 3 The results of the visualization comparison between PCA and three other feature ranking methods in this embodiment of the invention are shown below; (a) is the visualization result of PCA, (b) is the visualization result of random forest regression, (c) is the visualization result of randomized Lasso, and (d) is the visualization result of Pearson correlation coefficient.

[0043] Figure 4 This is a schematic diagram illustrating the PCR detection performance of different principal component feature numbers K under a 10% false alarm rate according to an embodiment of the present invention.

[0044] Figure 5 This is a schematic diagram comparing the deception detection rates of various features under a 10% false alarm rate, according to an embodiment of the present invention.

[0045] Figure 6 The graph shows the performance of the method of this invention and the feature XLR built based on XGBoost under the same scenario conditions as the K value. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] like Figure 1 As shown, this embodiment discloses an optimal feature construction method for GNSS deception detection based on PCA and genetic algorithm, including: acquiring satellite navigation signals, extracting relevant domain features of the satellite navigation signals, performing dimensionality reduction processing on the relevant domain features to generate high expressive features; inputting the high expressive features into a genetic algorithm model to obtain the optimal joint features; wherein, the optimal joint features are used for GNSS deception detection; the genetic algorithm model is obtained by training using a training set; during the training process on the training set, an objective function is set, with the minimum objective function as the training objective, and the weight parameters of the model are updated according to the principle of survival of the fittest using a genetic algorithm.

[0049] Specifically, this embodiment discloses an optimal feature construction method for GNSS deception detection based on PCA and genetic algorithm, including: using a software receiver to receive satellite navigation signals and extract relevant domain features; using PCA to perform dimensionality reduction processing on the original features of the satellite navigation signals to generate high-expressive features; constructing a genetic algorithm model; inputting the high-expressive features into the genetic algorithm model for weighted combination to generate the optimal joint features; and inputting the optimal joint features into a one-dimensional convolutional neural network (1D-CNN) for deception detection performance evaluation.

[0050] Furthermore, generating high-expressive features includes: performing standardized preprocessing on the relevant domain features, calculating the covariance matrix of the preprocessing result, performing eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors; arranging the eigenvectors in descending order of eigenvalues, and selecting the top K eigenvectors to form a principal component matrix; projecting the original data onto the subspace defined by the principal component matrix to generate high-expressive features; wherein the original data is a target matrix composed of relevant domain features.

[0051] Specifically, the dimensionality reduction processing of the original features of satellite navigation signals using PCA includes: performing standardization preprocessing on the original feature data and calculating the standardized covariance matrix; performing eigenvalue decomposition on the covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors; arranging the eigenvectors in descending order of eigenvalues ​​and selecting the top K eigenvectors to form the principal component matrix; projecting the original data onto the subspace defined by the principal component matrix to generate highly expressive features; the original data is a matrix composed of features in the relevant domain, with each column representing a different feature, each row representing different times of the navigation signal, and the values ​​in the matrix being the eigenvalues ​​of a specific feature at a specific time.

[0052] K opl The method for determining the value includes: using different numbers of K principal components as input to the genetic algorithm, gradually increasing the K value and evaluating and recording the detection performance; when the change in detection accuracy is less than a preset threshold, the current K value is determined to be the optimal number of principal components K. opl .

[0053] Furthermore, updating the model's weight parameters according to the principle of survival of the fittest includes: calculating the conditional probability of all samples in the training set, constructing a loss function, and adding a regularization term; setting the objective function based on the loss function with the added regularization term; iteratively updating the weight parameters while calculating the objective function of each candidate solution in each iteration, and using the minimum objective function as the training objective; continuously retaining candidate solutions with smaller objective functions according to the principle of survival of the fittest and generating new candidate solutions based on them; iteratively performing the above steps until the maximum number of iterations is reached or the objective function reaches its minimum.

[0054] Specifically, generating the optimal joint features involves: obtaining high-expressive features using the PCA method, obtaining the optimal weights corresponding to these features using a genetic algorithm, and then linearly combining these high-expressive features into a single optimal feature using weight parameters.

[0055] Calculating the conditional probability of all samples in a given training set includes:

[0056]

[0057] in, , These are the probability values ​​for binary classification as 1 and 0, respectively. For binary classification labels, For the i-th sample, It is a natural constant. For each feature weight parameter, This is the transpose operator.

[0058] The objective function expression is:

[0059]

[0060] in, Let be the objective function. For the number of samples, The label representing sample i. The value represents the predicted probability of sample i, K is the total number of features, and k represents the kth feature.

[0061] The method for calculating fitness and retaining candidate solutions with smaller objective functions is as follows:

[0062] according to Calculate the fitness of candidate solutions. Let i be the objective function for candidate solution i. This is to prevent division by zero. A roulette wheel selection strategy is then used, specifically based on probability. Individuals are randomly selected to enter the mating pool. ,in, Let be the fitness of the i-th candidate solution. Let be the loss function for the i-th candidate solution.

[0063] The method for generating candidate solutions for offspring until the optimal weights are obtained is as follows:

[0064] Randomly pair parents, with probability Perform an arithmetic crossover operation to generate a child solution, as shown in the following formula.

[0065]

[0066] in, Let be the mixing factor uniformly sampled within [0,1], where and For the paired parent generation solution, and For offspring solutions. The mutation phase uses probability. Apply Gaussian perturbation to each dimension of the offspring , Let be the variance of the Gaussian perturbation. Iteratively perform the steps of retaining candidate solutions and generating offspring candidate solutions until the maximum number of rounds is reached or the objective function is minimized.

[0067] The method for constructing a single optimal feature is as follows:

[0068]

[0069] in, The k-th feature generated by PCA It is the transpose operator. This is the intercept.

[0070] like Figure 1As shown, this embodiment discloses an optimal feature construction method for GNSS deception detection based on PCA and genetic algorithms, including: acquiring the original features of satellite navigation signals and standardizing the features; constructing a PCA model, inputting the standardized features into the model for principal component extraction to obtain a low-dimensional feature representation; optimizing the principal component selection through variance contribution rate to obtain the optimal feature subset, specifically:

[0071] PCA-based feature dimensionality reduction and optimization involves: using PCA to perform linear transformation on high-dimensional features, mapping the original features to a low-dimensional space through orthogonal projection, and maximizing the variance of the projected features. After processing satellite navigation signals using SQM technology, a series of features are obtained. These features are high-dimensional and redundant. Directly using them for deception detection would not only increase the computational burden but also introduce noise interference due to the redundancy. Therefore, dimensionality reduction and optimization of features are necessary before constructing the detection model. Considering the physical characteristics of navigation signal features, the dimensionality reduction method must retain the main information and eliminate correlations between features. This invention proposes a PCA-based feature dimensionality reduction process for satellite navigation signals, generating low-dimensional features through linear combination. This reduces dimensionality while improving feature discriminative power, thus providing efficient input for subsequent detection models.

[0072] The core advantage of PCA lies in capturing the linear relationships between features through covariance matrix analysis and extracting principal components based on the variance maximization criterion. The variance contribution rate of the principal components can quantify their information representation ability; the larger the variance, the stronger the component's ability to represent the original data distribution.

[0073] The PCA dimensionality reduction process can be divided into the following four steps:

[0074] Step 1: Standardize the original features so that the mean of each dimension is 0 and the variance is 1;

[0075] Step 2: Calculate the covariance matrix of the standardized features;

[0076] Step 3: Perform eigenvalue decomposition on the covariance matrix, arrange the corresponding eigenvectors in descending order of eigenvalues, and obtain the principal component directions;

[0077] Step 4: Select the top k principal components (that meet the cumulative variance contribution rate threshold), project the original data onto the principal component space, and generate a low-dimensional feature representation.

[0078] Then, a genetic algorithm is used to combine the K features generated by PCA to create a single optimal feature. Genetic algorithms are a statistical method widely used in classification problems. Through genetic algorithms, the optimal feature combination can be found, enabling the joint feature to integrate the advantages of various features from different aspects and improve its expressiveness.

[0079] Linear regression is commonly used to analyze linear relationships between variables. In linear regression, the model can be represented as... ,in The dependent variable representing the prediction. It is the input feature matrix. It is a parameter vector. This represents the bias term. For simplicity, the intercept... It can be viewed as a feature with a constant value of 1, and its corresponding weight is also... Unlike linear regression, LR (Genetic Algorithm) applies the sigmoid activation function to map the output to the range [0,1], thus obtaining a predictive probability that facilitates classification. The difference between the predicted and actual values ​​is used to calculate the loss, which is then used to construct the objective function. Through iterative training, the parameter vector w is optimized by minimizing the objective function to achieve a suitable solution.

[0080] The derivation of the scaling function is as follows. For a given training dataset... In this embodiment, the conditional probability distribution of each data item is first calculated. In a binary classification problem, Y∈{0,1}, the conditional probability distribution of LR can be expressed as:

[0081]

[0082] The maximum likelihood function is obtained by multiplying the conditional probabilities of all samples in a given training set and then taking the negative logarithm.

[0083] Considering that small sample size and imbalanced sample distribution are common problems in practical applications and can lead to overfitting, this embodiment adds a... Regularization terms are used to overcome this. Therefore, the objective function can be written as:

[0084]

[0085] in, Let be the objective function. For the number of samples, The label representing sample i. The value represents the predicted probability of sample i, K is the total number of features, and k represents the kth feature.

[0086] In obtaining Then, a genetic algorithm is further applied to solve for the globally optimal weight parameter w. opt The optimal weights are calculated iteratively. The algorithm aims to minimize the objective function.

[0087]

[0088] in, Given the preset feasible region of parameters, minimize using the above formula. This leads to the construction of the optimal joint features.

[0089] By simulating the process of biological evolution, it is possible to achieve this within the parameter feasible region. Internal Search The algorithm begins with randomly generating the global optimal solution. The candidate solutions (individuals) constitute the initial population. Each parameter component Uniform sampling is performed within the initialization range. In each iteration, the objective function value for all individuals is first calculated. And dynamically update the global optimal solution. and its target value If the optimal solution is continuous The generation has not been improved or has reached the maximum number of generations. The algorithm terminates and outputs the current optimal solution.

[0090] The selection phase employs a roulette wheel strategy, defining fitness as... , To prevent division by zero for the minimum value, based on probability... Select individuals to enter the mating pool .in, Let be the fitness of the i-th candidate solution. Let be the loss function for the i-th candidate solution.

[0091] During the crossover phase, parents are randomly paired with each other based on probability. Performing arithmetic crossover generates the following child solutions:

[0092]

[0093] in, The mixing factor is uniformly sampled within [0,1]. The mutation phase is based on probability. Apply Gaussian perturbation to each dimension of the offspring And through projection operation Ensure the solution satisfies the boundary constraints. Among them, Let the variance be the Gaussian perturbation. These represent the minimum and maximum boundaries of the weight values. The new generation of the population consists of offspring generated by crossover mutation and the optimal values ​​of the current generation. It is composed of a group of elite individuals, and the process continues to iterate until the termination condition is met.

[0094] This method establishes an objective function based on minimum cross-entropy and iteratively updates the weights to minimize the objective function. Therefore, the constructed features are mathematically guaranteed to be optimal.

[0095] Joint feature optimization involves using genetic algorithms to find the optimal feature combination, enabling the joint features to integrate the advantages of various features from different aspects and improve their expressiveness. The difference between predicted and actual values ​​is used to calculate the cross-entropy loss, which is then used to construct the objective function. Through iterative training, the parameter vector is optimized by minimizing the objective function to achieve a suitable solution.

[0096] The evaluation of spoofing detection methods included comparing and evaluating the PCR method with traditional composite features using a one-dimensional convolutional neural network. The results showed that the PCR method consistently outperformed traditional features, demonstrating its superior spoofing detection performance and potential to protect critical communication infrastructure from spoofing attacks.

[0097] Table 1

[0098]

[0099] This invention uses the Texas Deception Test Battery (TEXBAT) dataset for performance evaluation. The invention uses raw data from TEXBAT scenarios 2, 3, and 6 and processes it using a SoftGNSS receiver, as shown in Table 1. Scenario 2 simulates a scenario where the deception interference is suppressed power and the receiver remains stationary. Compared to scenario 2, scenario 3 uses a matched power attack for deception interference. Scenario 6 represents a scenario where the receiver is under deception attack while in dynamic motion. The receiver configuration parameters are as follows: sampling frequency 2.5 MHz, coherent integration time 4 ms. During the tracking phase, 54 custom correlators are deployed to extract features, with 27 correlators each allocated to the in-phase (I-phase) and quadrature (Q-phase) branches. The correlators are evenly distributed within the range of -2.6 to 2.6 chips at 0.2 chip intervals (the spacing between adjacent correlators is fixed at 0.2 chips). The 54-dimensional features include lead (E), lag (L), and instantaneous (P) correlator output values: in-phase branch features are labeled IE. n IP and IL n (The subscript n represents the chip offset, for example, the lead correlator at -2.6 chips for IE13); the quadrature branch features are labeled QEn, QLn, and QP. It should be noted that the chip offset of the TEXBAT spoofing signal is approximately 2 chips (equivalent distance 600 meters), therefore the maximum offset of the correlator is set to 2.6 chips to ensure complete capture of the correlation peak deformation information.

[0100] Furthermore, the proposed method is universally applicable to features in the correlation domain, frequency domain, and power domain. To ensure a fair comparison with traditional SQM methods, this experiment uniformly uses correlation domain features for deception detection and performance evaluation.

[0101] Figure 2The temporal evolution curves of four typical features (IE2, IE4, QE2, and QE4) during the entire spoofing attack were plotted. Taking IE2 as an example, its curve shows an upward trend between 75 and 95 seconds, indicating that the power of the spoofing signal gradually increases; between 95 and 190 seconds, the curve exhibits significant oscillations and deviates severely from the normal value, suggesting that the correlation peaks of the spoofing signal and the real signal separate. Obviously, the spoofing signal is most easily detected during the separation phase, so the data in this period is ultimately labeled as spoofing samples. The correlator outputs with different chip intervals carry differentiated signal information, resulting in temporal differences in the spoofing characterization. Figure 2 In the data analysis, the QE2 feature was generated using a narrow-spacing correlator (0.4 chips), with fluctuations appearing in the earlier stage between 100 and 140 seconds; the QE4 feature was extracted using a wide-spacing correlator (0.8 chips), with significant fluctuations appearing delayed until 140 to 220 seconds. Therefore, the different features reflect a shift in the timeframe during which spoofing occurs. After comprehensive analysis, data from 100 to 200 seconds was ultimately selected as the spoofing sample for all features.

[0102] Figure 3 A direct comparison of the performance differences between PCA and three other feature ranking methods (random forest, randomized Lasso, and Pearson correlation coefficient) is presented: Figure 3 (a) Displaying the results of the PCA method, with the coordinate axes representing the projection values ​​of the original data onto the first two principal components; Figure 3 (b)-(d) show the scatter plots of the first two features after sorting by random forest, randomized Lasso, and Pearson correlation coefficient, respectively. The axes correspond to the first two features generated or sorted by each method. To evaluate the classification performance after dimensionality reduction, all features were normalized to the [-1,1] interval. The figures contain data samples of real and deceptive signals and their centroid positions. It can be observed that not only is the overlap between the distribution areas of the two types of signals minimal, but the centroid distance between the real and deceptive signals is also improved by more than 32% compared to other methods. The features generated by PCA exhibit better inter-class separability, indicating that PCA has a stronger representational ability in preserving deceptive sensitive information.

[0103] After obtaining the principal components, the optimal number of principal components K is determined through simulation experiments. opl The specific process is as follows:

[0104] 1. Feature generation based on different principal component numbers: The principal components are sorted according to their variance contribution rate, and then the number of principal components K is changed as the input of the genetic algorithm to generate multiple PCR features;

[0105] 2. Detection performance evaluation: PCR features are input into a one-dimensional convolutional neural network for deception detection. The network structure includes: input layer (receiving feature vectors), 1D convolutional layer (64 filters, convolutional kernel size = 3, stride = 1), 1D max pooling layer (pooling kernel size = 2, stride = 2), two fully connected layers (extracting high-order nonlinear features), and Softmax output layer (outputting the classification probability of deception / real signal).

[0106] Figure 4 The detection performance of the proposed PCR feature in Scenario 2 is demonstrated as the number of principal components K varies. Performance metrics include accuracy, detection rate, and false alarm rate. Accuracy refers to the proportion of correctly classified samples, detection rate represents the proportion of fraudulent samples correctly identified as fraudulent, and false alarm rate represents the percentage of genuine samples incorrectly identified as fraudulent. In this embodiment, for ease of comparison, the false alarm rate is uniformly set to 10%. Figure 4 The upper part shows that as K increases, the detection rate and accuracy initially improve, but eventually reach a saturation point. Beyond this point, the performance gain from adding new features becomes negligible. Therefore, K opl Defined as the minimum number of features required to reach the saturation point where performance is stable.

[0107] To determine K opl Gradually increase the K value and record the change in detection rate corresponding to each increase (e.g., ...). Figure 4 (As shown in the lower half). Based on experience, the decision threshold is set at ±0.5%: if the accuracy change caused by the addition of new features remains within this range, the method's performance is considered to be stable. Based on this criterion, from... Figure 4 As can be seen, the accuracy reaches a saturation point when the 13th feature is included, at which point the accuracy is 99.2%. Therefore, in subsequent simulations, K is set... opl =13, meaning the first 13 principal components generated by PCA are selected as the input for the genetic algorithm to construct PCR. Similarly, K in scenarios 5 and 6... opl They were determined to be 17 and 9 respectively.

[0108] To evaluate the performance of the proposed PCR features, the proposed features, along with five other features, were used as input to a one-dimensional convolutional neural network for deception detection. Qmetric, WSCM, VSQM, and ELP are manually designed SQM features, while AllFeature represents the case where all 54 original features are directly used as detection input. Specifically: Qmetric achieves detection by measuring the signal energy of orthogonal branches; WSCM calculates the weighted second-order central moment based on the values ​​at the left and right peaks of the correlation peak; VSQM constructs features by quantifying the volume differences between the early and late portions of the correlation peak; and ELP characterizes signal anomalies using the phase difference between the leading and lagging correlators.

[0109] Figure 5 The detection rates of different features in scenarios 2, 5, and 6 were compared under a false alarm rate of 10%. The results show that the detection performance of traditional manually designed features is relatively poor. Taking TEXBAT scenario 2 as an example, although WSCM outperforms other traditional features, its detection rate is only 80.2%. In contrast, the proposed PCR feature achieves the highest detection rate of 99.2% among these features, an improvement of over 23.7% over WSCM. Although AllFeature achieves the highest performance, its computational complexity is extremely high, making it unsuitable for real-time detection. Furthermore, the performance of the PCR feature is comparable to AllFeature. This confirms that the PCR feature integrates the effective information from 54 original features into a single feature, thereby significantly improving detection performance without increasing computational complexity.

[0110] Finally, to illustrate the superiority of this method over existing XLR features built on XGBoost, the performance curves of both methods as a function of K are plotted under scenario 6. Figure 6 As shown in the figure, the XLR method requires 21 features to achieve its highest accuracy, while the PCR method reaches its maximum accuracy with only 9 features. This means that compared to the XLR method, the PCR method requires fewer features to construct the optimal feature set, making it computationally simpler. Furthermore, at optimal performance, the XLR method achieves an accuracy of 95.7%, while the PCR method achieves 97.3%, an improvement of over 1.67%. This is because the PCR method generates high-quality features rather than simply ranking existing features, thus constructing an optimal feature set with improved performance compared to XLR, and a stronger ability to characterize deception.

[0111] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithms, characterized in that, include: Collect satellite navigation signals, extract the correlation domain features of the satellite navigation signals, perform dimensionality reduction processing on the correlation domain features, and generate highly expressive features; The high-expressive features are input into the genetic algorithm model to obtain the optimal joint features; wherein, the optimal joint features are used for GNSS deception detection; the genetic algorithm model is obtained by training on the training set; during the training process on the training set, an objective function is set, and the minimum of the objective function is used as the training objective, and the weight parameters of the model are updated using the genetic algorithm.

2. The method for constructing optimal features for GNSS spoofing detection based on PCA and genetic algorithm according to claim 1, characterized in that, Generating the high-expressiveness features includes: The relevant domain features are standardized and preprocessed, the covariance matrix of the preprocessed result is calculated, and the covariance matrix is ​​decomposed to obtain the eigenvalues ​​and corresponding eigenvectors. The eigenvectors are arranged in descending order according to their eigenvalues, and the first K eigenvectors are selected to form the principal component matrix; The original data is projected onto the subspace defined by the principal component matrix to generate the high expressive features; wherein the original data is a target matrix composed of relevant domain features.

3. The method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithm according to claim 1, characterized in that, Updating the model's weight parameters includes: Calculate the conditional probability of all samples in the training set, construct the loss function, and add a regularization term; The objective function is set according to the loss function with added regularization term, the fitness of each candidate weight parameter is calculated and the best performers are eliminated, and the genetic algorithm is used to find the weight parameters that minimize the objective function.

4. The method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithm according to claim 3, characterized in that, Calculating the conditional probability of all samples in the training set includes: in, , These are the probability values ​​for binary classification as 1 and 0, respectively. For binary classification labels, For the i-th sample, It is a natural constant. For each feature weight parameter, This is the transpose operator.

5. The method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithm according to claim 3, characterized in that, Setting the objective function includes: in, Let be the objective function. For the number of samples, The label representing sample i. The value represents the predicted probability of sample i, K is the total number of features, and k represents the kth feature.

6. The method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithm according to claim 3, characterized in that, Calculating fitness and retaining candidate solutions with smaller objective functions includes: Define fitness as , It is a local minimum value, used to prevent division by zero, employing a roulette wheel strategy, based on probability. Select individuals to enter the mating pool ;in, Let be the fitness of the i-th candidate solution. Let be the loss function for the i-th candidate solution.

7. The method for constructing optimal features for GNSS deception detection based on PCA and genetic algorithm according to claim 3, characterized in that, The generated offspring candidate solutions include: Randomly pair parents, with probability Perform arithmetic crossover and generate child solutions according to the following formula: in, The mixing factor is uniformly sampled within [0,1]. and For the paired parent generation solution, and For the offspring solution, the mutation stage uses probability. Apply Gaussian perturbation to each dimension of the offspring , Let V be the variance of the Gaussian perturbation.

8. The method for constructing optimal features for GNSS spoofing detection based on PCA and genetic algorithm according to claim 1, characterized in that, Obtaining the optimal joint features includes: in, The k-th feature generated by PCA It is the transpose operator. This is the intercept.

9. The method for constructing optimal features for GNSS spoofing detection based on PCA and genetic algorithm according to claim 1, characterized in that, The method further includes: inputting the optimal joint features into a one-dimensional convolutional neural network to obtain the deception detection performance evaluation result.

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