A Beidou B1C signal anomaly monitoring method based on machine learning

Abstract

The present invention provides a Beidou B1C signal anomaly monitoring method based on machine learning, and relates to the technical field of signal anomaly monitoring. A Beidou B1C signal anomaly monitoring method based on machine learning includes the following steps: offline training and online monitoring, using multi-correlator technology to monitor the three distortion types of analog distortion, subcarrier distortion and PN code distortion of Beidou B1C signals. When performing quality monitoring, the discrimination method we use is quadratic discriminant analysis, which makes the discrimination accuracy higher. The QDA method is used for discrimination. The traditional method believes that the distortion part is less than 18.5% and can be considered as a distortion-free signal. Based on supervised learning, the QDA method is used for classification when discriminating the signal, instead of using a simple threshold decision. Experiments show that the method in this article can not only improve the monitoring accuracy, but also discriminate multiple signal distortion types at the same time.

Description

Technical Field

[0001] The present invention relates to the technical field of signal anomaly monitoring, and in particular to a Beidou B1C signal anomaly monitoring method based on machine learning. Background Art

[0002] With the rapid development of the BeiDou Navigation Satellite System (BDS), the requirements of high-precision systems such as civil aviation for navigation systems are also increasing, and one of the most important is the integrity of the service. Therefore, for the third-generation BeiDou navigation system, service integrity has become the most important research direction. The cause of signal distortion or evil waveform (EWF) is usually a failure in satellite signal production, which usually causes distortion of the cross-correlation function of the service signal. This affects the integrity of the navigation signal service.

[0003] At present, some scholars have proposed some models to measure these distortion types, including analog distortion and digital distortion. With the emergence of modern navigation systems, the types of signal distortion are divided more and more finely. For the Beidou-3 navigation system, digital distortion is further subdivided into PN code distortion and subcarrier distortion. For these three types of distortion, analog distortion and subcarrier code distortion will cause the peak of the signal's cross-correlation function to shift to varying degrees, while PN code distortion has little effect on the correlation peak shift. The multi-correlator method is currently a mainstream signal quality monitoring method. By deploying multiple pairs of correlators in each receiving channel, real-time monitoring of the entire correlation peak is achieved. It calculates some indicators through these correlator measurements, and then compares these indicators with the threshold to achieve the purpose of signal quality monitoring. However, the use of a simple threshold judgment is prone to cause large errors, because different distortion types have different sensitivities to indicators.

[0004] High-precision systems such as civil aviation have put forward higher requirements for navigation systems, including indicators such as accuracy and integrity. Signal distortion and evil waveform (EWF) generated by the hardware generating signals on the satellite will seriously affect the cross-correlation function of the signal, thereby affecting the integrity of the navigation system. With the further development of the Beidou Navigation System (BDS), signal distortion types are subdivided into three types: analog distortion, subcarrier distortion and PN code distortion. The traditional multi-correlator method is no longer applicable under the requirements of modern navigation systems. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a Beidou B1C signal anomaly monitoring method based on machine learning, which solves the problem that the traditional multi-correlator method is no longer applicable under the requirements of modern navigation systems.

[0006] To achieve the above objectives, the present invention is implemented by the following technical solutions: A Beidou B1C signal anomaly monitoring method based on machine learning, comprising the following steps:

[0007] Step 1: Offline training

[0008] S1. Generate training data set: The training data set is preprocessed data, including normal and digitally distorted Beidou B1C signals. The feature vector X = [X 1 ,X 2 ,X d ] T , d is the dimension of the feature vector, Xi(i=1,2,…,d) is some feature measure of the detection. The feature measure is composed of simple ratio measure M z and detla metric M z-z The simple ratio can be expressed as follows:

[0009]

[0010] Among them, I 0 represents the measurement value of the instantaneous correlator, and its main function is to normalize the correlation measurement value. Iz is the measurement value of the in-phase correlator at a distance z from the instantaneous correlator. The main function of the Detla metric is to detect the asymmetry of the correlation peak. The Detla metric can be described by the following formula:

[0011]

[0012] When the BOC signal is distorted, not only the main peak is affected, but also the secondary peak. In the above two feature measurements, when z = -0.05-n1m:m:-0.05, 0.05:m:0.05+n1m, M z and M z-z Used to monitor the asymmetry of the main peak, when z = -0.05-n2m:m:-0.05, 0.05:m:0.05+n2m, M z and M z-z It is used to monitor the asymmetry of the correlation peaks of the secondary peaks, where m is a fixed code delay, i.e., the distance between two adjacent correlators, and n1 and n2 represent the number of correlators on the main peak and the secondary peak. Therefore, when the value of z changes, the combination of these characteristic metrics can simultaneously monitor the correlation peak distortion of the main peak and the secondary peak, thereby more comprehensively and accurately monitoring signal distortion.

[0013] The training dataset consists of a set of input instances and the required output. The input instance can be represented as [x 1 ,x 2 ,,x d ]T , where x i (i=1,2,...,d) represents the result of the detection metric, and the output space is expressed as follows:

[0014] Ω={ω 1 ,ω 2 ,ω 3 ,ω 4}

[0015] Among them, ω 1 ,ω 2 ,ω 3 ,ω 4 They represent the input signal without fault, PN code distortion, subcarrier distortion and analog distortion respectively.

[0016] S2. Calculate model parameters: After the training data set of the model is given, the next step is to calculate the model parameters. Thermal noise can be regarded as a Gaussian process with a mean of zero, so the related measurement values ​​can also be regarded as Gaussian variables. Because the ratio of two Gaussian processes is often also a Gaussian process, the monitoring indicators are also Gaussian variables. Therefore, the input composed of the above input signal without fault, PN code distortion, subcarrier distortion and analog distortion, can be regarded as a variable that obeys a multivariate Gaussian distribution. Therefore, our model can use a multivariate Gaussian model, whose parameters are the mean vector and the covariance matrix.

[0017] We use maximum likelihood estimation to calculate the parameters of the model, and the conditional probability of the input data is:

[0018]

[0019] Where d represents the dimension of the input matrix, μ ωi and Σω i Represents a given model parameter, x ij represents the i-th input data corresponding to the j-th distortion. The joint likelihood function can be expressed as:

[0020]

[0021] The model parameters can be estimated by ML:

[0022]

[0023] From the above formula, we can see that our model parameters contain a total of 4 means and 4 covariance matrices;

[0024] Step 2: Online monitoring

[0025] The input data is processed by multiple correlators. Based on the model parameters trained offline, the entire online monitoring module can detect whether the signal is distorted. We use quadratic discriminant analysis to identify the correlation peak distortion of the test data. The quadratic discriminant analysis models the likelihood of each class as a Gaussian distribution, and then uses the posterior distribution to estimate the category to which the test data belongs.

[0026] During online monitoring and recognition, the discriminant function can be calculated from the test data and offline trained parameters, and the Bayesian formula can be used to obtain:

[0027]

[0028] Among them, p(ω i ) represents ω i The prior probability of can be expressed as n i It corresponds to ω i The number of samples, due to p(x′) and ω i The independence between them, p(x′) can be regarded as a constant. The discriminant function in this paper adopts the maximum a posteriori criterion probability, so it can be described as:

[0029]

[0030] Taking the logarithm of the discriminant function yields:

[0031]

[0032] in, is a constant term. For each discriminant function, p(ω i ) is also unchanged. Therefore, the discriminant function It can be further simplified to:

[0033]

[0034] According to the maximum a posteriori probability, the decision of the monitoring signal can be obtained:

[0035]

[0036] Among them, g ωi Represents the corresponding distortion type. Therefore, our model can not only detect whether the signal is distorted, but also identify the type of distortion.

[0037] The present invention provides a Beidou B1C signal anomaly monitoring method based on machine learning. It has the following beneficial effects:

[0038] The present invention proposes a method based on machine learning to monitor the quality of Beidou B1C signal and uses the QDA method to distinguish. The results show that when ΔS ≥0.03μs, Δ C ≥0.03μs and f d When the frequency is ≤10MHz, the classification accuracy of the method proposed in this paper can reach 10%. Not only that, our method greatly reduces the missed detection rate. The traditional method believes that the distortion part less than 18.5% can be considered as a distortion-free signal. In contrast, our method can reduce the missed detection rate to 0.98%. When making distinctions, we use quadratic discriminant analysis (QDA) to replace the traditional threshold discrimination method. QDA models each class as a Gaussian distribution, and then uses the posterior probability distribution to estimate these classes. We use the QDA method to classify signals based on supervised learning instead of using simple threshold decisions. Experiments show that the method in this paper can not only improve the monitoring accuracy, but also distinguish multiple types of signal distortion at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the correlation function diagram of BOC(1,1) under three types of distortion of the present invention;

[0040] Figure 2 This is a Beidou B1C signal structure diagram of the present invention;

[0041] Figure 3 A receiver configuration diagram used in the present invention;

[0042] Figure 4 is a parameter configuration diagram of the feature vector of the present invention;

[0043] Figure 5 is a diagram of the selection process of the training parameters of the present invention;

[0044] Figure 6 The three types of distortions are judged by the present invention;

[0045] Figure 7 is the characteristic vector X of the present invention 5 Confusion matrix diagram of ;

[0046] Figure 8 is a classification accuracy diagram of different feature vectors of the present invention;

[0047] Fig. 9 The figure is a comparison between the algorithm of the present invention and the traditional method. DETAILED DESCRIPTION

[0048] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0049] Embodiment 1:

[0050] In the embodiment of the present invention, the Beidou B1C signal adopts a binary offset carrier (BOC) modulation method, and its signal is composed of a data component and a pilot component. The data component is the carried data, and the pilot component is composed of the product of the ranging code and the subcarrier. The ranging code expression can be described by the following formula.

[0051]

[0052] in,

[0053]

[0054] Among them, the chip width is T c_B1C =1 / 1.023μs, the chip length is N B1C_pilot =10230, the ranging code is represented by C BIC_pilot (t). The subcarrier consists of two orthogonal subcarriers BOC(1,1) and BOC(6,1) with a power ratio of 29:4. sc_B1C_a =1.023MHZ, f sc_B1C_b =6.138MHZ. Reference [6] stipulates that pilot_a is a subcarrier modulation of BOC(1,1), which contains the pseudo-range measurement code of the airborne receiver. The Beidou B1C signal structure is as follows: Figure 2 shown.

[0055] At present, the more reasonable threat model is the two-stage hierarchical threat model proposed by ICAO in 2000. This model divides signal distortion or evil waveform (EWF) into the following three modes:

[0056] 1. Threat Model A (TM-A): This type of threat is represented by each unit code (T C ) block falling edge relative to the normal falling edge (Δ) advance or delay.

[0057] 2. Threat Model B (TM-B): This type of threat is represented by a 2nd-order step ringing response of a code block, f d It represents the oscillation frequency, the unit is MHZ. σ represents the damping coefficient, the unit is MNp / s.

[0058] 3. Threat Model C (TM-C): This type of threat is represented by a combination of digital distortion and analog distortion.

[0059] GPS C / A has defined some types of signal distortion [1]. However, Beidou B1C uses its unique BOC (1,1) modulation, which requires redefinition of signal distortion types [2]. Based on reading a large amount of literature, this paper focuses on the three types of distortion of Beidou B1C signals: analog distortion, PN code distortion and subcarrier distortion.

[0060] Analog distortion is caused by hardware defects in the RF module at the signal generation end, corresponding to the previous TM-A. Common phenomena that produce analog distortion are amplitude modulation or ringing during chip conversion [7]. The reason for the digital distortion phenomenon is due to internal faults in the baseband generator, corresponding to the previous TM-B. For this type of distortion, some experts and scholars have proposed some methods to subdivide the digital distortion types of Beidou B1C signals into PN code distortion and subcarrier distortion. Based on this, it is proved that the distortion of the pilot component pilot_b of the B1C signal does not affect code tracking.

[0061] During the signal transmission process, multiple types of distortion may occur simultaneously. Since these distortions are generated by different payloads on the satellite, the possibility of this phenomenon is small. This paper mainly studies the signal anomaly monitoring under a single distortion. Figure 1 The normalized correlation functions of the BOC(1,1) signal under the above three distortion types are plotted, (a) analog distortion, (b) subcarrier distortion, and (c) PN code distortion.

[0062] Compared with the traditional supervised learning method, we proposed a supervised machine learning method based on QDA. This method uses multi-correlator technology to monitor the three types of distortion of Beidou B1C signal: analog distortion, subcarrier distortion and PN code distortion. When performing quality monitoring, we use the discriminant method of quadratic discriminant analysis, which will make the discrimination more accurate. Our method is divided into two steps: offline training and online monitoring:

[0063] Step 1: Offline training

[0064] S1. Generate training data set: The training data set is preprocessed data, including normal and digitally distorted Beidou B1C signals. The feature vector X = [X 1 ,X 2 ,X d ] T , d is the dimension of the feature vector, Xi(i=1,2,…,d) is some feature measure of the detection. The feature measure is composed of simple ratio measure M z and detla metric M z-zThe simple ratio can be expressed as follows:

[0065]

[0066] Among them, I 0 represents the measurement value of the instantaneous correlator, and its main function is to normalize the correlation measurement value. Iz is the measurement value of the in-phase correlator at a distance z from the instantaneous correlator. The main function of the Detla metric is to detect the asymmetry of the correlation peak. The Detla metric can be described by the following formula:

[0067]

[0068] When the BOC signal is distorted, not only the main peak is affected, but also the secondary peak. In the above two feature measurements, when z = -0.05-n1m:m:-0.05, 0.05:m:0.05+n1m, M z and M z-z Used to monitor the asymmetry of the main peak, when z = -0.05-n2m:m:-0.05, 0.05:m:0.05+n2m, M z and M z-z It is used to monitor the asymmetry of the correlation peaks of the secondary peaks, where m is a fixed code delay, i.e., the distance between two adjacent correlators, and n1 and n2 represent the number of correlators on the main peak and the secondary peak. Therefore, when the value of z changes, the combination of these characteristic metrics can simultaneously monitor the correlation peak distortion of the main peak and the secondary peak, thereby more comprehensively and accurately monitoring signal distortion.

[0069] The training dataset consists of a set of input instances and the required output. The input instance can be represented as [x 1 ,x 2 ,,x d ] T , where x i (i=1,2,...,d) represents the result of the detection metric, and the output space is expressed as follows:

[0070] Ω={ω 1 ,ω 2 ,ω 3 ,ω 4}

[0071] Among them, ω 1 ,ω 2 ,ω 3 ,ω 4 They represent the input signal without fault, PN code distortion, subcarrier distortion and analog distortion respectively.

[0072] S2. Calculate model parameters: After the training data set of the model is given, the next step is to calculate the model parameters. Thermal noise can be regarded as a Gaussian process with a mean of zero, so the related measurement value can also be regarded as a Gaussian variable. Because the ratio of two Gaussian processes is often also a Gaussian process, the monitoring index is also a Gaussian variable. Therefore, the input composed of the above input signal without fault, PN code distortion, subcarrier distortion and analog distortion, can be regarded as a variable that obeys a multivariate Gaussian distribution. Therefore, our model can use a multivariate Gaussian model, whose parameters are the mean vector and the covariance matrix;

[0073] We use maximum likelihood estimation to calculate the parameters of the model, and the conditional probability of the input data is:

[0074]

[0075] Where d represents the dimension of the input matrix. and Σω i Represents a given model parameter, x ij Represents the i-th input data corresponding to the j-th distortion, and the joint likelihood function can be expressed as:

[0076]

[0077] The model parameters can be estimated by ML:

[0078]

[0079] From the above formula, we can see that our model parameters contain a total of 4 means and 4 covariance matrices;

[0080] Step 2: Online monitoring

[0081] The input data is processed by multiple correlators. Based on the model parameters trained offline, the entire online monitoring module can detect whether the signal is distorted. We use quadratic discriminant analysis to identify the correlation peak distortion of the test data. The quadratic discriminant analysis models the likelihood of each class as a Gaussian distribution, and then uses the posterior distribution to estimate the category to which the test data belongs.

[0082] During online monitoring and recognition, the discriminant function can be calculated from the test data and offline trained parameters, and the Bayesian formula can be used to obtain:

[0083]

[0084] Among them, p(ω i ) represents ω i The prior probability of can be expressed as n i It corresponds to ω iThe number of samples, due to p(x′) and ω i The independence between them, p(x′) can be regarded as a constant. The discriminant function in this paper adopts the maximum a posteriori criterion probability, so it can be described as:

[0085]

[0086] Taking the logarithm of the discriminant function yields:

[0087]

[0088] in, is a constant term. For each discriminant function, p(ω i ) is also unchanged. Therefore, the discriminant function It can be further simplified to:

[0089]

[0090] According to the maximum a posteriori probability, the decision of the monitoring signal can be obtained:

[0091]

[0092] in, Represents the corresponding distortion type. Therefore, our model can not only monitor whether the signal is distorted, but also identify the type of distortion. The receiver configuration used in this paper is as follows: Figure 3 As shown:

[0093] The feature vector we use is also composed of multiple indicators, and its composition is affected by the distance m between adjacent correlators and the number of monitoring points n1 and n2. In our experiment, 6 different sets of feature vectors are used, and their specific configurations are as follows: Figure 4 shown.

[0094] For training models, the most important thing is the parameters of the model. The parameters of the model are calculated by the training parameters. The training parameters in this article include and The principle of selecting training parameters is based on the requirement of false alarm. The selection process is as follows: Figure 5 shown.

[0095] During the test, we added some distorted signals and the B1C signal of BeiDou-3 M2 for evaluation. First, we tested the performance of the proposed method for distortion detection, and then we further analyzed the impact of changing the feature vector on the model. Finally, we compared the algorithm in this paper with the traditional method. The results show that under the same conditions, our method has a higher detection probability for all three types of distortion. At a signal-to-noise ratio of 35dB-Hz, our detection probability is almost twice that of the traditional method.

[0096] Embodiment 2:

[0097] In the above embodiment, the classification results of three types of distortion based on the QDA method are shown. The method proposed in this paper uses the maximum value of all faults in the discriminant function to determine the fault type. For the observed data, the discrimination results are as follows: Figure 6 shown.

[0098] like Figure 6 As shown, the blue, green and red points correspond to the discrimination results of PN code distortion, subcarrier distortion and analog distortion respectively. The results show that our discrimination function can accurately discriminate the three types of distortion. For PN code distortion, g ω2 The value of is greater than that of other discriminant functions. Similarly, the discriminant functions g of the other two types of distortion ωi It is also significantly larger than the other discriminant function values, so our model can accurately distinguish these distorted signals.

[0099] Figure 7 is to use the eigenvector X 5 When doing the confusion matrix for classification, the parameters of the model are set as follows, Δ C =0.03μs, Δ S =0.03μs, f d =10MHz,σ d =0.8Mnepers / s. The results show that our model has a 100% classification accuracy for analog distortion and a 98.5% classification accuracy for PN code distortion and subcarrier distortion. Moreover, for these three types of distortion, the missed detection rate and false alarm rate of our model are kept below 1%. In summary, it can be seen that our model has excellent classification results for the three types of distortion, especially for analog distortion, which has achieved a 100% classification result.

[0100] Embodiment three:

[0101] In the above embodiment, the classification performance of different feature vectors is compared. As shown in Table 3, the parameters of the feature vector are related to the distance between the correlators and the size of the monitoring area. 1 , X2 , X 3 and X 4 have the same correlator interval, but the sizes of the areas they monitor are different. The feature vector X 3 , X 5 and X 6 The two have the same monitoring area size, but the intervals between the correlators are different. This will inevitably lead to different classification accuracy. Therefore, we use different feature vectors to monitor the signal to compare their performance. In the following results, we set the signal-to-noise ratio to 40dB-Hz.

[0102] like Figure 8 As shown in (a) and (b), when Δ S or Δ C When the error is large, the classification accuracy of the proposed method for PN code distortion and subcarrier distortion can reach more than 96%. Figure 8 As shown in (c), when the damping frequency f d and the damping factor σ d When the damping frequency f is small, the proposed method can achieve a classification accuracy of more than 99% for the simulated distortion. d More sensitive. d When f is small, our model can easily detect the simulated distortion, but when f d When becomes larger, our model will be less effective in detecting simulated distortions. This phenomenon may be caused by the increase of missed detection rate.

[0103] from Figure 8 We can also see that using vectors X, X 2 and X 3 The classification accuracy is not much different. When the correlator is far away from the main peak, it is not very useful, because the farther away from the main peak, the fewer useful signal features. However, when we use the vector X 4 When it is used as a feature vector, the classification effect will be significantly reduced. This shows that when the monitored area is too small, it is easy to miss some important information of related functions.

[0104] Two methods to reduce the dimension of the feature vector and the complexity of the algorithm are to reduce the monitoring area and increase the interval between the correlators.

[0105] Figure 8 It shows that using the vector X 3 and X 5 As feature vectors, their classification accuracy is not much different, while the feature vector X 6 The performance of is significantly lower than these two vectors. 5 The required correlator ratio feature vector X 3Much fewer correlators are needed, so the eigenvector X is used 5 The complexity of the algorithm is greatly reduced while maintaining high accuracy.

[0106] The traditional multi-correlator method uses threshold decision to detect signal distortion. This method can only detect a single type of distortion. When multiple distortion types exist at the same time, it can only detect a specific type of distortion but cannot distinguish the distortion type. The figure below shows a comparison of the detection performance of the method proposed in this article and the traditional method.

[0107] from Fig. 9 (a) and (b) show that for PN code distortion and subcarrier distortion, when the SNR is 35dB-Hz, the accuracy of our method is almost twice that of the traditional method. When the SNR is lower than 45dB-Hz, the accuracy of our method is significantly improved compared with the traditional method. For analog distortion, our method has a small improvement compared with the traditional method.

[0108] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A Beidou B1C signal anomaly monitoring method based on machine learning, characterized in that: The following steps are involved: Step 1: Offline training S1. Generate training data set: The training data set is preprocessed data, including normal and digitally distorted Beidou B1C signals. The feature vector X = [X1, X2, X d ] T , d is the dimension of the feature vector, Xi (i = 1, 2, ..., d) is a feature metric for some detections, and the feature metric is composed of a simple ratio M z and detla metric M z-z The simple ratio can be expressed as follows: Among them, I0 represents the measurement value of the instantaneous correlator, and its main function is to normalize the correlation measurement value. Iz is the measurement value of the in-phase correlator at a distance z from the instantaneous correlator. The main function of the Detla metric is to detect the asymmetry of the correlation peak. The Detla metric can be described by the following formula: When the BOC signal is distorted, not only the main peak is affected, but also the secondary peak. In the above two feature measurements, when z = -0.05-n1m:m:-0.05, 0.05:m:0.05+n1m, M z and M z-z Used to monitor the asymmetry of the main peak, when z = -0.05-n2m:m:-0.05, 0.05:m:0.05+n2m, M z and M z-z It is used to monitor the asymmetry of the correlation peak of the secondary peak, where m is the fixed code delay, that is, the distance between two adjacent correlators, and n1 and n2 represent the number of correlators on the main peak and the secondary peak. Therefore, when the value of z changes, the combination of these characteristic metrics simultaneously monitors the correlation peak distortion of the main peak and the secondary peak, thereby more comprehensively and accurately monitoring the signal distortion. The training dataset consists of a set of input instances and the required output. The input instance is represented as [x1, x2,, x d ] T , where x i (i=1,2,...,d) represents the result of the detection metric, and the output space is expressed as follows: Ω={ω1,ω2,ω3,ω4} Among them, ω1, ω2, ω3, and ω4 represent the input signal without fault, PN code distortion, subcarrier distortion, and analog distortion, respectively. S2. Calculate model parameters: After the training data set of the model is given, the next step is to calculate the model parameters. Thermal noise is regarded as a Gaussian process with a mean of zero, so the related measurement value is also regarded as a Gaussian variable. Because the ratio of two Gaussian processes is often also a Gaussian process, the monitoring index is also a Gaussian variable. Therefore, the input signal composed of the above input signal without fault, PN code distortion, subcarrier distortion and analog distortion is regarded as a variable that obeys a multivariate Gaussian distribution. Therefore, our model uses a multivariate Gaussian model, whose parameters are the mean vector and the covariance matrix; We use maximum likelihood estimation to calculate the parameters of the model, and the conditional probability of the input data is: Where d represents the dimension of the input matrix, μ ωi and Σω i Represents a given model parameter, x ij Represents the i-th input data corresponding to the j-th distortion, and the joint likelihood function is expressed as: The model parameters are estimated by ML: From the above formula, we can see that our model parameters contain a total of 4 means and 4 covariance matrices; Step 2: Online monitoring The input data is processed by multiple correlators. Based on the model parameters trained offline, the entire online monitoring module detects whether the signal is distorted. We use quadratic discriminant analysis to identify the correlation peak distortion of the test data. The quadratic discriminant analysis models the likelihood of each class as a Gaussian distribution, and then uses the posterior distribution to estimate the category to which the test data belongs. During online monitoring and recognition, the discriminant function can be calculated from the test data and offline trained parameters, and the Bayesian formula can be used to obtain: Among them, p(ω i ) represents ω i The prior probability of is expressed as n i It corresponds to ω i The number of samples, due to p(x′) and ω i The independence between them, p(x′) is regarded as a constant. The discriminant function of this paper adopts the maximum a posteriori criterion probability, so it is described as: Taking the logarithm of the discriminant function yields: in, is a constant term. For each discriminant function, p(ω i ) is also unchanged, so the discriminant function Further simplified to: The decision of the monitoring signal is obtained according to the maximum a posteriori probability: in, Represents the corresponding distortion type. Therefore, our model can not only detect whether the signal is distorted, but also identify the type of distortion.

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