A method for sorting stations based on signal parameter estimation technique

Abstract

The present application belongs to the technical field of network station sorting, and particularly relates to a network station sorting method based on signal parameter estimation technology. The network station sorting method uses a short-time Fourier transform method to accumulate a time-frequency graph for a period of time, estimates a threshold value by using an adaptive threshold method, separates background noise, then introduces a fast connected region searching method to search for suspected signals, filters out frequency hopping signals by using a preset duration range, acquires signal characteristics by using a high-precision parameter estimation technology, and finally uses time of arrival combined with characteristic clustering technology to complete network station sorting and count network station characteristics. The method provided by the present application solves the key problem of restricting the practicability of the network station sorting method.

Description

Technical Field

[0001] This invention belongs to the field of network station sorting technology, specifically relating to a network station sorting method based on signal parameter estimation technology. Background Technology

[0002] Station selection for multiple frequency-hopping signals in complex electromagnetic environments is one of the key issues in the field of communication countermeasures. Without prior information, when multiple signals such as fixed-frequency signals, interference signals, and frequency-hopping signals coexist, accurately detecting frequency-hopping signals and accurately selecting frequency-hopping stations are the two main challenges of this problem.

[0003] Traditional network station sorting methods consist of two parts: signal parameter estimation technology and signal feature clustering technology. Existing technologies focus on in-depth innovation and improvement of signal feature clustering technology, which is relatively mature and effective. However, when the electromagnetic environment is complex and the acquisition bandwidth is large, the effectiveness of signal parameter estimation technology becomes the main factor restricting the practicality of network station sorting.

[0004] Current network station sorting methods based on signal parameter estimation technology include: acquiring data streams; obtaining time-frequency maps using the STFT method; setting threshold values ​​using the histogram method to obtain binarized images; filtering noise using duration ranges to extract signal parameter streams; and sorting the signal parameter streams based on feature clustering technology to obtain network station frequency sets, hopping speeds, and other features.

[0005] Existing network-based sorting technologies encounter practical problems during engineering implementation, such as low execution efficiency, difficulty in obtaining adaptive threshold values, and poor signal parameter estimation accuracy. These problems are not easily exposed in simple electromagnetic environments, but they severely limit the effectiveness of the algorithms when the electromagnetic environment becomes more complex. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a network station sorting method based on signal parameter estimation technology; the signal parameter estimation technology has been improved, and the factors restricting the practicality of the network station sorting method have been resolved.

[0007] This invention is achieved through the following technical solution:

[0008] A network station sorting method based on signal parameter estimation technology, the network station sorting method comprising:

[0009] Accumulate a time-frequency graph over a period of time using the short-time Fourier transform method;

[0010] An adaptive thresholding method is used to estimate the threshold value and separate background noise;

[0011] A fast connected region search method is introduced to locate suspected signals;

[0012] Frequency hopping signals are filtered out using a preset duration range;

[0013] High-precision parameter estimation techniques are used to obtain signal characteristics;

[0014] Finally, by combining arrival time with feature clustering technology, network station sorting was completed and network station characteristics were statistically analyzed.

[0015] Furthermore, the method includes:

[0016] (1) Spectrum accumulation: The spectrum is accumulated using the short-time Fourier transform method to obtain a time-frequency diagram over a period of time;

[0017] (2) Signal detection: Set an energy threshold value to separate background noise and suspected signals from the time-frequency graph, and use the maximum inter-class method to find the threshold value according to the image processing method;

[0018] The time-frequency image is binarized according to the threshold value. Time-frequency points with energy values ​​greater than the threshold value are set as category A, and time-frequency points with energy values ​​less than or equal to the threshold value are set as category B. All connected regions of category B in the binarized image are searched, and each connected region is a suspected signal.

[0019] Set the signal duration range (based on experience, the duration of a frequency hopping network station signal is approximately in the range of 0.5ms-50ms), remove noise and continuous signals, and obtain the frequency hopping signal;

[0020] (3) Parameter estimation: Based on the time-frequency diagram, the estimated positions of the start frequency, cutoff frequency, start time, and cutoff time of the frequency hopping signal are obtained;

[0021] Based on the estimated position of the frequency-hopping signal in the time and frequency domains, a narrowband bandpass filter is used to obtain the signal's time-domain data to avoid the inherent contradiction between time resolution and frequency resolution. The mathematical expression for the narrowband bandpass filter is:

[0022] y(t)=F^(-1)[H(jω)*X(jω)]

[0023] Where y(t) is the filtered time-domain data, F^(-1) represents the inverse Fourier transform, H(jω) is the frequency-domain filter type, * represents the convolution operation, and X(jω) is the Fourier transform of the input signal.

[0024] Obtain the signal feature set A = {X1, X2, ..., X...} i , ..., X N}, where N is the total number of signals in the signal feature set; each element represents a frequency hopping signal, and the i-th element is X. i ={bf i , ef i ,bti et i}, bf i For the starting frequency, ef i For the end frequency, bt i For the start time, et i End time;

[0025] (4) Signal fusion: The signals interrupted in the spectrum accumulation step are fused together by utilizing the overlap of the frequency ranges of the signals and the continuity of the corresponding time.

[0026] Determine the result A of the j-th iteration. j A certain signal X in n and the result A of the (j-1)th iteration j-1 A certain signal X in m The condition for them to be the same signal is: X n The start time and X m As the end time approaches, X n Frequency range (bf) n , ef n ) and X m Frequency range (bf) m , ef m ) overlap, X n and X m Merging into a new signal X nm :

[0027] X nm ={bf nm , ef nm ,bt nm et nm};

[0028] Among them, bt nm =bt m et nm =bt n bf nm =(bf n +bf m ) / 2, ef nm =(ef n +ef m ) / 2;

[0029] (5) Signal accumulation: Obtain the signal feature stream after processing in step (4), accumulate the signal from the signal feature stream for a period of time, and use it to restore the frequency hopping sequence for subsequent network station sorting;

[0030] (6) Network station sorting: Network station sorting is performed using a two-stage clustering method. The first clustering uses duration, and the second clustering uses arrival time. Both clustering methods use the K-Means clustering method. The mathematical expression for K-Means clustering is:

[0031]

[0032] Where D is the sum of the squared distances between all data points and the cluster centers where the data points are located; C i It is the i-th cluster, u i is the center of the i-th cluster, and x is a cluster element;

[0033] The signals accumulated in step (5) are processed into a set of network stations B = {Y1, Y2, ..., Y}. i , ..., Y M}, M is the total number of network stations in the centralized network station; the i-th element is Y. i ={X1, X2, ..., X j , ..., X N};

[0034] (7) Network-TV integration: Determine the result B of the k-th iteration. k A certain online platform Y n and the result B of the (k-1)th iteration k-1 A certain online platform Y m The condition for being on the same network platform is: Y n Y m The same signal exists in them;

[0035] If the same signal exists, Y n Y m Merging into a single network platform Y nm On the online platform Y nm Only one copy of Y is retained. n Y m The same signal in the middle.

[0036] Furthermore, the formula for accumulating the spectrum using the short-time Fourier transform method is as follows:

[0037]

[0038] Where τ is the time variable of the signal being analyzed, t is the time variable of the time-frequency plot, f is the frequency, x is the signal to be analyzed, and ω is the window function.

[0039] Furthermore, in step (1), the frequency resolution and time resolution of the obtained time-frequency diagram can be adjusted.

[0040] Further, in step (2), the method of setting an energy threshold value to separate the background and suspected signals from the time-frequency graph, and using the maximum inter-class method to find the threshold value according to image processing methods, is as follows:

[0041] Based on the grayscale characteristics of the image, the image is divided into two categories. The average grayscale value of the image is the initial threshold k. The part less than the threshold k is background noise, and the part greater than the threshold k is a suspected signal.

[0042] The formula for calculating the threshold value is:

[0043] σ 2 =p A (k)p B (k)(m A (k)-m B (k)) 2

[0044] In the formula, σ represents the inter-class variance between the background noise and suspected signal images; p A (k) represents the time-frequency proportion of background noise, p B (k) represents the proportion of suspected signal points in time and frequency; m A (k) represents the average energy value of the background noise, m B (k) represents the average energy value of the suspected signal;

[0045] Make σ 2 The threshold value is the threshold k corresponding to the maximum value.

[0046] Beneficial technical effects of the present invention:

[0047] The network station sorting method provided by this invention, based on an improved signal parameter estimation technique, improves the signal parameter estimation technique and can estimate signal parameters quickly, adaptively and accurately. At the same time, it combines feature clustering technology to enhance the practicality of the network station sorting algorithm and solves the key problem that restricts the practicality of the network station sorting method. Attached Figure Description

[0048] Figure 1 This is a flowchart of frequency hopping signal detection in an embodiment of the present invention;

[0049] Figure 2 This is a diagram of a frequency hopping communication model in an embodiment of the present invention;

[0050] Figure 3 This is a flowchart of the network station sorting process in an embodiment of the present invention;

[0051] Figure 4 This is a time-frequency image obtained from the accumulated spectrum in an embodiment of the present invention;

[0052] Figure 5This is a binarized image obtained after signal detection and signal fusion processing in an embodiment of the present invention;

[0053] Figure 6 This is a scatter plot of the distribution of network station signals in the parameter space in an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0055] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0056] This invention provides a network station sorting method based on signal parameter estimation technology, the method comprising:

[0057] Accumulate a time-frequency graph over a period of time using the short-time Fourier transform method;

[0058] An adaptive thresholding method is used to estimate the threshold value and separate background noise;

[0059] A fast connected region search method is introduced to locate suspected signals;

[0060] Frequency hopping signals are filtered out using a preset duration range;

[0061] High-precision parameter estimation techniques are used to obtain signal characteristics;

[0062] Finally, by combining arrival time with feature clustering technology, network station sorting was completed and network station characteristics were statistically analyzed.

[0063] The method includes the following steps:

[0064] (1) Spectrum Accumulation: The spectrum is accumulated using the short-time Fourier transform method to obtain a time-frequency graph over a period of time; specifically, the frequency resolution and time resolution of the obtained time-frequency graph can be adjusted; wherein, the formula for accumulating the spectrum using the short-time Fourier transform method is:

[0065]

[0066] Where τ is the time variable of the analyzed signal, t is the time variable of the time-frequency plot; f is the frequency, x is the signal to be analyzed, and ω is the window function. The main advantages of the STFT method are its simplicity, speed, and ability to obtain the time-frequency representation of the signal. The short-time Fourier transform method is used to accumulate the spectrum, and compared to other time-frequency analysis methods such as wavelet transform, the short-time Fourier transform is easier to implement in engineering.

[0067] In step (1), the frequency resolution and time resolution of the obtained time-frequency diagram can be adjusted.

[0068] (2) Signal detection: Set an energy threshold value to separate background noise and suspected signals from the time-frequency graph, and use the maximum inter-class method to find the threshold value according to the image processing method;

[0069] The time-frequency image is binarized according to the threshold value. Time-frequency points with energy values ​​greater than the threshold value are set as category A, and time-frequency points with energy values ​​less than or equal to the threshold value are set as category B. All connected regions of category B in the binarized image are searched, and each connected region is a suspected signal.

[0070] Set the signal duration range (based on experience, the duration of a frequency hopping network station signal is approximately in the range of 0.5ms-50ms), remove noise and continuous signals, and obtain the frequency hopping signal;

[0071] The method for setting an energy threshold to separate background and suspected signals from the time-frequency graph, and using the maximum inter-class method to find the threshold according to image processing methods, is as follows:

[0072] Based on the image's grayscale characteristics, the image is divided into two categories. The average grayscale value is the initial threshold k. Values ​​below threshold k are considered background noise, while values ​​above threshold k are considered potential signals. A larger inter-class variance indicates a greater difference between background noise and potential signals, and a lower probability of misclassification. The threshold value is calculated using the following formula:

[0073] σ 2 =p A (k)p B (k)(m A (k)-m B (k)) 2

[0074] In the formula, σ represents the inter-class variance between the background noise and suspected signal images; p A (k) represents the time-frequency proportion of background noise, p B (k) represents the proportion of suspected signal points in time and frequency; m A (k) represents the average energy value of the background noise, m B (k) represents the average energy value of the suspected signal;

[0075] Make σ 2 The threshold value is the threshold k corresponding to the maximum value.

[0076] (3) Parameter estimation: Based on the time-frequency diagram, the estimated positions of the start frequency, cutoff frequency, start time, and cutoff time of the frequency hopping signal are obtained;

[0077] Since the accuracy of network station sorting depends on the accuracy of signal time parameter estimation, it is necessary to further improve the accuracy of parameter estimation. The solution of this invention is to detect the time parameter in the time domain and obtain the estimated position of the time domain data frequency hopping signal by narrowband bandpass filtering.

[0078] Based on the estimated position of the frequency-hopping signal in the time and frequency domains, a narrowband bandpass filter is used to obtain the signal's time-domain data to avoid the inherent contradiction between time resolution and frequency resolution. The mathematical expression for the narrowband bandpass filter is:

[0079] y(t)=F^(-1)[H(jω)*X(jω)]

[0080] Where y(t) is the filtered time-domain data, F^(-1) represents the inverse Fourier transform, H(jω) is the frequency-domain filter type, * represents the convolution operation, and X(jω) is the Fourier transform of the input signal.

[0081] Obtain the signal feature set A = {X1, X2, ..., X...} i , ..., X N}, where N is the total number of signals in the signal feature set; each element represents a frequency hopping signal, and the i-th element is X. i ={bf i , ef i ,bt i et i}, bf i For the starting frequency, ef i For the end frequency, bt i For the start time, et i End time;

[0082] (4) Signal fusion: The signals interrupted in the spectrum accumulation step are fused together by utilizing the overlap of the frequency ranges of the signals and the continuity of the corresponding time.

[0083] Because the cumulative spectrum segmentation process divides the continuous signal into segments, the continuous signal may be interrupted. Therefore, after processing each segment, the interrupted signals must be fused together. The frequency hopping signal detection process is as follows: Figure 1 As shown. Figure 1 This is an explanatory diagram of the signal detection process. Signal parameter estimation is performed cyclically, so the result A of the j-th iteration is...j and the result A of the (j-1)th iteration j-1 There may be the same interrupted signal in the middle.

[0084] Determine the result A of the j-th iteration. j A certain signal X in n and the result A of the (j-1)th iteration j-1 A certain signal X in m The condition for them to be the same signal is: X n The start time and X m As the end time approaches, X n Frequency range (bf) n , ef n ) and X m Frequency range (bf) m , ef m ) overlap, X n and X m Merging into a new signal X m :

[0085] X nm ={bf nm , ef nm ,bt nm et nm};

[0086] Among them, bt nm =bt m et nm =bt n bf nm =(bf n +bf m ) / 2, ef nm =(ef n +ef m ) / 2;

[0087] The signal feature stream after step (4) is obtained, and the signal accumulated from the signal feature stream for a period of time is used to restore the frequency hopping sequence and perform subsequent network station sorting.

[0088] Frequency hopping communication model such as Figure 2 As shown, in the receiver, the local frequency hopping sequence, consistent with the transmitter's frequency hopping sequence, retrieves the frequency control code from the frequency hopping table to control the frequency synthesizer, causing the output local oscillator signal frequency to jump accordingly according to the frequency hopping sequence. Each network station has a pseudo-random frequency hopping sequence, and network station sorting is essentially a process of restoring the frequency hopping sequence. Therefore, after... Figure 1 The signal processing procedure shown can acquire the signal feature stream. At this time, the signal accumulated from the signal feature stream for a period of time can be used to restore the frequency hopping sequence and perform network station sorting.

[0089] (6) Network Station Sorting: Network station sorting is performed using a two-stage clustering method. The first clustering is based on duration, and the second clustering is based on arrival time. Both clustering methods use the K-Means clustering method, an unsupervised clustering algorithm. Its purpose is to divide n data points into K clusters, each with a centroid. These centroids minimize the distance between the data points within them and the centroid. The mathematical expression for K-Means clustering is:

[0090]

[0091] Where D is the sum of the squared distances between all data points and the cluster centers where the data points are located; C i It is the i-th cluster, u i is the center of the i-th cluster, and x is a cluster element;

[0092] The signals accumulated in step (5) are processed into a set of network stations B = {Y1, Y2, ..., Y}. i , ..., Y M}, M is the total number of network stations in the centralized network station; the i-th element is Y. i ={X1, X2, ..., X j , ..., X N};

[0093] (7) Network-TV Integration: Due to the real-time requirements of network-TV sorting, data is processed in segments. This can potentially interrupt the continuous operation of a network of active stations. Therefore, network-TV integration is necessary to ensure the continuity of the network. The network-TV sorting process is as follows: Figure 3 As shown. Figure 3 This is a diagram illustrating the network station sorting process. Network station sorting is performed cyclically, so the result B of the k-th cycle... k and the result B of the (k-1)th iteration k-1 There may be the same interrupted network station within the network. Determine the result B of the k-th iteration. k A certain online platform Y n and the result B of the (k-1)th iteration k-1 A certain online platform Y m The condition for being on the same network platform is: Y n Y m The same signal exists in them;

[0094] If the same signal exists, Y n Y m Merging into a single network platform Y nm On the online platform Y nm Only one copy of Y is retained. n Y m The same signal in the middle.

[0095] Algorithm Testing: Two network stations were used to simulate a real electromagnetic environment to test the sorting effect of the stations. The frequency hopping range of both stations was between 902-930MHz. Figure 4 It is a time-frequency image obtained through accumulated spectrum. From the time-frequency image, you can intuitively see that the signals of the two network stations are mixed together. Figure 5 It is a binarized image obtained after signal detection and signal fusion processing, at which point background noise and signal have been separated. Figure 6 The table shows a scatter plot of the network station signals in the parameter space. The scatter plot clearly shows two signal clusters. By using clustering, all signals from both network stations can be obtained. Table 1 shows the frequency sets of the two network stations obtained statistically. The frequency distribution of the two network stations shows a high degree of overlap, further demonstrating the effectiveness of the network station sorting method provided by this invention in complex electromagnetic environments.

[0096] Table 1 Frequency sets of the two network stations

[0097]

[0098] The network station sorting method provided by this invention utilizes the short-time Fourier transform method to accumulate time-frequency graphs over a period of time, employs an adaptive threshold method to estimate threshold values, and separates background noise. Then, a fast connected region search method is introduced to find suspected signals. Using a preset duration range, frequency-hopping signals are filtered out, and high-precision parameter estimation technology is used to obtain signal characteristics. Finally, arrival time combined with feature clustering technology is used to complete network station sorting and statistically analyze network station characteristics. This method, based on improved signal parameter estimation technology, solves the key problem restricting the practicality of network station sorting methods. Actual test results show that the network station sorting method provided by this invention has advantages such as stable time-frequency threshold values, fast execution speed, and high signal parameter accuracy, improving the practicality of network station sorting algorithms. Furthermore, the advantages of the network station sorting method based on improved signal parameter estimation technology provided by this invention include fast algorithm execution speed, strong applicability, and high network station sorting accuracy.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A network station sorting method based on signal parameter estimation technology, characterized in that, The network station sorting method includes: Accumulate a time-frequency graph over a period of time using the short-time Fourier transform method; An adaptive thresholding method is used to estimate the threshold value and separate background noise; A fast connected region search method is introduced to locate suspected signals; Frequency hopping signals are filtered out using a preset duration range; High-precision parameter estimation techniques are used to obtain signal characteristics; Finally, arrival time combined with feature clustering technology is used to complete the network station sorting and statistical analysis of network station characteristics; Specifically, it includes: (1) Spectrum accumulation: The spectrum is accumulated using the short-time Fourier transform method to obtain a time-frequency diagram over a period of time; (2) Signal detection: Set an energy threshold value to separate background noise and suspected signals from the time-frequency graph, and use the maximum inter-class method to find the threshold value according to the image processing method; The time-frequency image is binarized according to the threshold value. Time-frequency points with energy values ​​greater than the threshold value are set as category A, and time-frequency points with energy values ​​less than or equal to the threshold value are set as category B. All connected regions of category B in the binarized image are searched, and each connected region is a suspected signal. Set the signal duration range, remove noise and continuous signals, and obtain the frequency hopping signal; (3) Parameter estimation: Based on the time-frequency diagram, the estimated positions of the start frequency, cutoff frequency, start time, and cutoff time of the frequency hopping signal are obtained; Based on the estimated position of the frequency-hopping signal in the time and frequency domains, a narrowband bandpass filter is used to obtain the signal's time-domain data to avoid the inherent contradiction between time resolution and frequency resolution. The mathematical expression for the narrowband bandpass filter is: y(t)=F^(-1)[H(jω)*X(jω)], Where y(t) is the filtered time-domain data, F^(-1) represents the inverse Fourier transform, H(jω) is the frequency-domain filter type, * represents the convolution operation, and X(jω) is the Fourier transform of the input signal. Obtain the signal feature set A={x1,x2,…,x i ,…,x N }, where N is the total number of signals in the signal feature set; each element represents a frequency hopping signal, and the i-th element is x. i ={bf i ,ef i ,bt i ,et i }, bf i For the starting frequency, ef i For the end frequency, bt i For the start time, et i End time; (4) Signal fusion: The signals interrupted in the spectrum accumulation step are fused together by utilizing the overlap of the frequency ranges of the signals and the continuity of the corresponding time. Determine the result A of the j-th iteration. j A certain signal x in n and the result A of the (j-1)th iteration j-1 A certain signal x in m The condition for them to be the same signal is: x n The start time and x m The end time is approaching, x n Frequency range (bf) n ,ef n ) and x m Frequency range (bf) m ,ef m ) overlap, and x n and x m Merging into a new signal x nm : x nm ={bf nm ,if nm ,bt nm ,and nm }; wherein bt nm =bt m , et nm =et n , bf nm =(bf n +bf m ) / 2, ef nm =(ef n +ef m ) / 2; (5) Signal accumulation: Obtain the signal feature stream after processing in step (4), accumulate the signal from the signal feature stream for a period of time, and use it to restore the frequency hopping sequence for subsequent network station sorting; (6) Network station sorting: Network station sorting is performed using a two-stage clustering method. The first clustering uses duration, and the second clustering uses arrival time. Both clustering methods use the K-Means clustering method. The mathematical expression for K-Means clustering is: ， Where D is the sum of the squared distances between all data points and the cluster centers where the data points are located; C i It is the i-th cluster, u i is the center of the i-th cluster, x is a cluster element, and K is the number of clusters; The signals accumulated in step (5) are processed into a network set B = {Y1, Y2, ..., Y}. i ,…,Y M }, M is the total number of network stations in the centralized network station; the i-th element is Y. i ={X1,X2,…,X j ,…,X N }; (7) Network-TV integration: Determine the result B of the k-th iteration. k A certain online platform Y n and the result B of the (k-1)th iteration k-1 A certain online platform Y m The condition for being on the same network platform is: Y n Y m The same signal exists in them; If the same signal exists, Y n Y m Merging into a single network platform Y nm On the online platform Y nm Only one copy of Y is retained. n Y m The same signal in the middle.

2. The network station sorting method based on signal parameter estimation technology according to claim 1, characterized in that, The formula for accumulating the spectrum using the short-time Fourier transform method is: ， Where τ is the time variable of the signal being analyzed, t is the time variable of the time-frequency plot, f is the frequency, x is the signal to be analyzed, and ω is the window function.

3. The network station sorting method based on signal parameter estimation technology according to claim 1, characterized in that, In step (1), the frequency resolution and time resolution of the obtained time-frequency diagram can be adjusted.

4. The network station sorting method based on signal parameter estimation technology according to claim 1, characterized in that, In step (2), the method of setting an energy threshold value to separate the background and suspected signals from the time-frequency graph, and using the maximum inter-class method to find the threshold value according to image processing methods, is as follows: Based on the grayscale characteristics of the image, the image is divided into two categories. The average grayscale value of the image is the initial threshold k. The part less than the threshold k is background noise, and the part greater than the threshold k is a suspected signal. The formula for calculating the threshold value is: σ 2 =p A (k)p B (k)(m) A (k)-m B (k)) 2 , In the formula, σ represents the inter-class variance between the background noise and suspected signal images; p A (k) represents the time-frequency proportion of background noise, p B (k) represents the proportion of suspected signal points in time and frequency; m A (k) represents the average energy value of the background noise, m B (k) represents the average energy value of the suspected signal; Make σ 2 The threshold value is the threshold k corresponding to the maximum value.

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