A Link16 frequency hopping signal denoising and reconnaissance recognition algorithm

Abstract

The present invention specifically relates to a Link16 frequency hopping signal denoising reconnaissance and identification algorithm, comprising the following steps: S1: sampling the intercepted frequency hopping signal to obtain baseband original IQ path data; S2: performing spectrogram time-frequency analysis on the frequency hopping signal to obtain a time-frequency graph; S3: performing a comprehensive denoising algorithm based on FCME on the time-frequency graph; S4: performing MeanShift clustering on the denoised time-frequency image to extract feature parameters; and S5: drawing time-frequency ridges based on the clustered time-frequency features, and obtaining frequency hopping parameter estimates through first-order differences of the time-frequency ridges. The Link16 frequency hopping signal denoising reconnaissance and identification algorithm of the present invention improves reconnaissance accuracy, reduces hopping period and hopping frequency estimation errors, reduces complexity, improves algorithm efficiency, and ensures reconnaissance timeliness.

Description

Technical Field

[0001] The present invention belongs to the technical field of data link signal communication countermeasure signal reconnaissance and identification, and in particular relates to a Link16 frequency hopping signal denoising reconnaissance and identification algorithm. Background Art

[0002] Frequency hopping (FH) communication is a common method in spread-spectrum communication systems. It boasts numerous advantages, including being difficult to intercept, difficult to decipher, and resistant to interference. It is widely used in both military and civilian communications, with research on the Link 16 tactical data link being a key area of research. Signal interception technology is relatively mature, but identifying and efficiently processing intercepted signals remains a key research priority.

[0003] In a complex shortwave channel environment, in order to reduce the impact of various interference signals and noise on frequency hopping signals and realize blind detection of frequency hopping signals under low signal-to-noise ratio, it is crucial to propose a fast blind detection technology for Link16 frequency hopping signals based on FCME denoising combined with MeanShift clustering algorithm. Summary of the Invention

[0004] To address the problems of low computational cost, time efficiency, and weak denoising capabilities in existing algorithms, the present invention provides a Link16 frequency-hopping signal denoising reconnaissance and recognition algorithm. This algorithm improves the purity of the frequency-hopping recognition signal by performing comprehensive denoising on the data. It also combines the Meanshift clustering algorithm for time-frequency analysis, thereby improving recognition accuracy while reducing the complexity of the algorithm calculation.

[0005] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] A Link16 frequency hopping signal denoising reconnaissance and recognition algorithm includes the following steps:

[0007] S1: Sample the intercepted frequency hopping signal to obtain the original baseband IQ path data;

[0008] S2: Perform spectrogram time-frequency analysis on the frequency hopping signal to obtain a time-frequency graph;

[0009] S3: Perform FCME-based comprehensive denoising algorithm on the time-frequency graph;

[0010] S4: Perform MeanShift clustering on the denoised time-frequency image to extract feature parameters;

[0011] S5: Draw the time-frequency ridge line according to the clustered time-frequency characteristics, and obtain the frequency hopping parameter estimation through the first-order difference of the time-frequency ridge line.

[0012] Furthermore, the above S3 is specifically as follows: before identifying the signal, secondary denoising is performed on the spectrum line value of each time slot of the current time-frequency matrix. By classifying and identifying the signal frequency points, the FCME algorithm selects an iterative update method, performs binary discrimination on the frequency point set that meets the false alarm probability threshold, removes the noise frequency points below the threshold, and repeatedly performs threshold adaptive calculation for multiple iterations until all frequency point sets are iterated, obtains the signal after the maximum iteration, and realizes noise adaptive threshold elimination.

[0013] Furthermore, the false alarm probability factor u in the iterative process of the above FCME algorithm is fcme and adaptive threshold T fcme The calculation formula is:

[0014] u fcme =-ln(p f ) (1-1)

[0015] T fcme =E(M noise (k))·u fcme (1-2)

[0016] In formula (1-1), P f is the false alarm probability, in formula (1-2), M noise is the noise frequency point set, E(M noise (k)) represents the mean value of the noise frequency spectrum, and k represents the number of noise frequency points divided into the noise frequency set after threshold screening.

[0017] Furthermore, the above S3 implementation steps are:

[0018] Step 1: False alarm probability P f Perform statistics on the detection frequency distribution and determine the number of iterations D;

[0019] Step 2: Sort the N frequency spectrum values, using the set {A1, A2, A3, ..., A N} indicates that the first N / 8 frequencies in the set are assumed to be noise frequencies, and the set M noise Mark, average the noise spectrum power and variance Calculation of

[0020] Step 3: According to the mean and variance Substitute into the formula Get the threshold value T of the false alarm probability factor adaptive fcme ;

[0021] Step 4: For the frequency point set {A1, A2, A3, ..., A N}, and perform iterative threshold judgment on the next N / 8 frequency points in the set. If the frequency power is greater than the threshold value, it is considered to be a useful frequency hopping component; if it is less than the threshold value, it is considered to be a noise frequency point and is assigned to the set M. noise middle;

[0022] Step 5: Perform FCME iteration and average the updated noise frequency set and variance The next iteration is completed until all N frequency point sets {A1, A2, A3, ..., A N}All iterations are completed or the maximum iteration value is reached, and the FCME noise suppression optimization is completed.

[0023] Furthermore, the above S4 is specifically as follows: based on the MeanShift clustering algorithm, for the denoised time-frequency matrix, according to the different probability density distributions of the data, the time-frequency signal is shifted to the most concentrated area, so that the data converges to the local density extreme value and clusters.

[0024] Furthermore, the above S4 includes:

[0025] The MeanShift algorithm assumes that data sets of different clusters conform to different probability density distributions. It finds the direction with the densest sample concentration and continuously shifts to the point with the highest density. As the samples converge to the local maximum density, it assumes that the points that converge to the same maximum value during the iteration process are members of the same cluster.

[0026] The MeanShift clustering vector is defined as:

[0027]

[0028] Use A k represents a high-dimensional ball with a radius of r, α i Represents the centroid of the current i-th region, satisfying the β point set:

[0029] A k (α) = {β: (β-α i ) T (β-α i )≤r 2} (1-4)

[0030] In formula (1-4), A k Represents the sample point α i There are k points falling in the region. Starting from the center of the region, the distance vectors are added along different gradient directions to obtain the MeanShift vector. r (α) Mark the offset mean vector for iterative update to move the data to a higher density collection point;

[0031] The Gaussian kernel function is added to MeanShift to expand the scope of application of the MeanShift algorithm. The improved MeanShift clustering vector is defined as follows:

[0032]

[0033]

[0034] Where S(·) represents the Gaussian kernel function, ω(α i ) represents the sample weight and estimates the kernel function:

[0035]

[0036] In formula (1-7), n represents the d-dimensional dataset {α i}Numerical size, r d Represents the volume of the d-dimensional high-dimensional ball region, Q represents the kernel function, and the derivative of the probability density function (1-7) is:

[0037]

[0038] definition:

[0039]

[0040] Combining equations (1-8) and (1-9), we get:

[0041]

[0042]

[0043]

[0044] Imperative Form (1-10) Find local extrema of a probability density:

[0045]

[0046] Extract feature parameters.

[0047] Furthermore, the above S5 includes:

[0048] According to the clustered time-frequency features SPEC(n,k), find the matrix peak at each moment and draw the time-frequency ridge line according to the matrix peak:

[0049] loc(n)=arg{max f [SPEC(n,k)]} (1-14)

[0050] Through the first-order difference of the time-frequency ridge line, the time-frequency ridge line difference sequence is obtained:

[0051] d(n)=abs{diff[loc(n)]} (1-15)

[0052] The sequence interval calculation is performed on the time-frequency ridge difference sequence. Since the interval between two adjacent frequency hopping points is the frequency hopping interval, the parameter estimation of the frequency hopping signal hopping period can be obtained by averaging all intervals:

[0053] T h =mean{diff[d(n)]} (1-16)

[0054] The frequency range of the frequency point can be obtained by calculating the mean value of the frequency range of the time-frequency ridge difference sequence. The frequency value of the i-th frequency hopping point is:

[0055] f(i)=mean{loc(d(i-1):d(i))} (1-17)

[0056] Obtain frequency hopping parameter estimates.

[0057] The beneficial effects of the present invention are:

[0058] 1. Based on the FCME secondary denoising combined with the MeanShift clustering algorithm, this paper designs a method that can adaptively optimize and suppress Link 16 data link noise. At the same time, MeanShift clustering is used to reduce the algorithm complexity, achieving accurate and timely detection of Link 16 data link frequency hopping signals.

[0059] 2. The present invention achieves good performance in estimating the period and frequency of frequency-hopping signals in an environment with a signal-to-noise ratio (SNR) of (-10dB, 10dB). This means that the present invention is suitable for accurate and timely detection of Link 16 frequency-hopping signals in complex channel environments.

[0060] 3. This invention improves the purity of the received signal by performing comprehensive denoising optimization based on FCME on the time-frequency graph. The received signal bit error rate is improved before and after denoising, which improves the reconnaissance accuracy and reduces the hopping period and frequency estimation errors.

[0061] 4. The present invention performs MeanShift clustering on the time-frequency graph to improve the time-frequency aggregation of the frequency-hopping signal components. The accuracy of time-frequency ridge parameter extraction after clustering is improved, and the computational complexity of the MeanShift algorithm is lower than that of the K-Means algorithm, which can improve the computational efficiency of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic diagram of the overall flow of the algorithm of this embodiment;

[0063] Figure 2This is a schematic diagram of the FCME-based denoising algorithm used in this embodiment;

[0064] Figure 3 Schematic diagram of the structure of the MeanShift clustering algorithm used in this embodiment;

[0065] Figure 4 This is a simulation diagram of the clustering effect based on the MeanShift clustering algorithm in this embodiment;

[0066] Figure 5 3. It is a schematic diagram of simulation of frequency hopping signal hopping period estimation before and after optimization in this embodiment;

[0067] Figure 6 3 is a schematic diagram of simulation of frequency hopping frequency estimation of a frequency hopping signal before and after optimization in this embodiment. DETAILED DESCRIPTION

[0068] To further illustrate the technical means and effectiveness of this invention in achieving its intended purpose, the following detailed description of a Link16 frequency-hopping signal denoising and reconnaissance identification algorithm, in conjunction with the accompanying drawings and specific embodiments, is provided. The aforementioned and other technical aspects, features, and effectiveness of this invention are clearly presented in the following detailed description of the specific embodiments, accompanied by the accompanying drawings.

[0069] Refer to the attached Figure 1 This embodiment provides a Link16 frequency hopping signal denoising and reconnaissance identification algorithm, including the following steps:

[0070] S1: Sampling the intercepted frequency hopping signal to obtain baseband original IQ data. In this embodiment, the intercepted frequency hopping signal is first sampled by a digital receiver, with a sampling bandwidth set to 240 MHz, to obtain baseband original IQ data.

[0071] S2: Perform spectrogram-based time-frequency analysis on the frequency-hopping signal to obtain a time-frequency diagram. Before signal recognition, perform spectrogram-based time-frequency analysis on the current signal to obtain a time-frequency matrix with better time-frequency aggregation, thereby improving the purity of the required reconnaissance frequency-hopping signal components.

[0072] S3: Apply an FCME-based integrated denoising algorithm to the time-frequency graph to eliminate background noise and fixed-frequency interference. Before signal recognition, secondary denoising is performed on the spectral line values of each time slot in the current time-frequency matrix. By classifying and identifying signal frequencies, the FCME algorithm selects an iterative update method for frequency points that meet the false alarm probability threshold, performs a binary discrimination, and removes noise frequencies below the threshold. Threshold adaptive calculations are repeated and repeated multiple times until all frequency points have been iterated. The maximum iterated signal is obtained, achieving adaptive threshold noise removal. In this embodiment, FCME is forward continuous mean denoising.

[0073] False alarm probability factor u during the iteration of the FCME algorithm fcme and adaptive threshold T fcme The calculation formula is:

[0074] u fcme =-ln(p f ) (1-1)

[0075] T fcme =E(M noise (k))·u fcme (1-2)

[0076] In formula (1-1), P f is the false alarm probability, in formula (1-2), M noise is the noise frequency point set, E(M noise (k)) represents the mean value of the noise frequency spectrum, and k represents the number of noise frequency points divided into the noise frequency set after threshold screening.

[0077] The implementation steps are:

[0078] Step 1: False alarm probability P f Perform statistics on the detection frequency distribution and determine the number of iterations D;

[0079] Step 2: Sort the N frequency spectrum values, using the set {A1, A2, A3, ..., A N} indicates that the first N / 8 frequencies in the set are assumed to be noise frequencies, and the set M noise Mark, average the noise spectrum power and variance Calculation,

[0080] Step 3: According to the mean and variance Substitute into the formula Get the threshold value T of the false alarm probability factor adaptive fcme ;

[0081] Step 4: For the frequency point set {A1, A2, A3, ..., A N}, and perform iterative threshold judgment on the next N / 8 frequency points in the set. If the frequency power is greater than the threshold value, it is considered to be a useful frequency hopping component; if it is less than the threshold value, it is considered to be a noise frequency point and is assigned to the set M. noise middle;

[0082] Step 5: Perform FCME iteration and average the updated noise frequency set and variance The next iteration is completed until all N frequency point sets {A1, A2, A3, ..., A N}All iterations are completed or the maximum iteration value is reached, and the FCME noise suppression optimization is completed.

[0083] Refer to the attached Figure 2 First, the denoised frequencies are classified using an initial threshold. The N / 8 frequency points preceding the denoised frequencies are then classified. If the sample point exceeds the noise threshold, it is considered a valid frequency hopping signal; otherwise, it is considered noise. Through iterative optimization, clustering and denoising are completed for all frequencies, ensuring simulation accuracy.

[0084] S4: MeanShift clustering is performed on the denoised time-frequency image to improve the clustering of the signal time-frequency graph and extract characteristic parameters. Based on the MeanShift clustering algorithm, the time-frequency signal is shifted to the most concentrated area according to the different probability density distributions of the data after denoising, so that the data converges to the local density extreme value and clustering is performed.

[0085] The MeanShift algorithm assumes that data sets of different clusters conform to different probability density distributions. It finds the direction in which the samples are most densely concentrated and continuously shifts to the point with the highest density. As the samples converge to the local density maximum, it assumes that the points that converge to the same maximum during the iteration process are members of the same cluster.

[0086] The MeanShift clustering vector is defined as:

[0087]

[0088] Use A k represents a high-dimensional ball with a radius of r, α i Represents the centroid of the current i-th region, satisfying the β point set:

[0089] A k (α) = {β: (β-α i ) T (β-α i )≤r 2} (1-4)

[0090] In formula (1-4), A k Represents the sample point α i There are k points falling in the region. Starting from the center of the region, the distance vectors are added along different gradient directions to obtain the MeanShift vector. r (α) Mark the offset mean vector for iterative update to move the data to a higher density collection point;

[0091] The Gaussian kernel function is added to MeanShift to expand the scope of application of the MeanShift algorithm. The improved MeanShift clustering vector is defined as follows:

[0092]

[0093]

[0094] Where S(·) represents the Gaussian kernel function, ω(α i ) represents the sample weight and estimates the kernel function:

[0095]

[0096] In formula (1-7), n represents the d-dimensional dataset {α i}Numerical size, r d Represents the volume of the d-dimensional high-dimensional ball region, Q represents the kernel function, and the derivative of the probability density function (1-7) is:

[0097]

[0098] definition:

[0099]

[0100] Combining equations (1-8) and (1-9), we get:

[0101]

[0102]

[0103]

[0104] Imperative Form (1-10) Find local extrema of a probability density:

[0105]

[0106] Extract feature parameters.

[0107] Refer to the attached Figure 3 In this embodiment, the Meanshift clustering algorithm randomly selects a frequency point as the center of the iterative optimization circle and rewrites the derived probability density function as follows: make The local extreme value of the probability density can be found. The MeanShift clustering algorithm targets the target through the local maximum value iteration reward, realizing the MeanShift clustering iteration of the target. The clustering effect simulation diagram based on the MeanShift clustering algorithm is shown in the attached figure. Figure 4 .

[0108] S5: Draw the time-frequency ridge line according to the clustered time-frequency characteristics, and obtain the frequency hopping parameter estimation through the first-order difference of the time-frequency ridge line.

[0109] According to the clustered time-frequency features SPEC(n,k), find the matrix peak at each moment and draw the time-frequency ridge line according to the matrix peak:

[0110] loc(n)=arg{max f [SPEC(n,k)]} (1-14)

[0111] Through the first-order difference of the time-frequency ridge line, the time-frequency ridge line difference sequence is obtained:

[0112] d(n)=abs{diff[loc(n)]} (1-15)

[0113] The sequence interval calculation is performed on the time-frequency ridge difference sequence. Since the interval between two adjacent frequency hopping points is the frequency hopping interval, the parameter estimation of the frequency hopping signal hopping period can be obtained by averaging all intervals.

[0114] T h =mean{diff[d(n)]} (1-16)

[0115] The frequency range of the frequency point can be obtained by calculating the mean value of the frequency range of the time-frequency ridge difference sequence. The frequency value of the i-th frequency hopping point is:

[0116] f(i)=mean{loc(d(i-1):d(i))} (1-17)

[0117] Obtain frequency hopping parameter estimates.

[0118] This embodiment optimizes the Link16 frequency hopping signal denoising and reconnaissance identification algorithm. The simulation diagram of the frequency hopping signal hopping period estimation before and after optimization is shown in the attached figure. Figure 5 . The simulation diagram of frequency hopping signal frequency estimation before and after optimization is shown in the attached figure. Figure 6 .

[0119] The process of the Link16 frequency hopping signal denoising reconnaissance and identification algorithm of the present invention can be referred to the attached Figure 1 First, the signal received by the receiver is sampled to obtain the baseband IQ data. The data is subjected to spectrogram time-frequency analysis to obtain the time-frequency image of the signal. The spectrum values of N frequency points are sorted and the set {A1, A2, A3, ..., A N}. Assume the first N / 8 frequency points in the set as noise frequency points, and use the set M noise Mark, average the noise spectrum power and variance Calculation, and then get the threshold value T of the false alarm probability factor adaptivefcme For the frequency point set {A1,A2,A3,…,A N}, and perform iterative threshold judgment on the next N / 8 frequency points in the set. If the frequency power is greater than the threshold value, it is considered to be a useful frequency hopping component; if it is less than the threshold value, it is considered to be a noise frequency point and is assigned to the set M. noise Perform FCME iteration and average the updated noise frequency set and variance The next iteration is completed until all N frequency point sets {A1, A2, A3, ..., A N} are all iterated or the maximum iteration value is reached, and the FCME optimization is completed. The optimized image is output as a time-frequency graph, and a frequency point in the time-frequency matrix is randomly selected as the clustering center. Assuming that the initial frequency point cluster radius is r, the meanshift vector is calculated, and by taking the derivative of the probability density function, the density extreme value in the direction of the vector is obtained to achieve the first shift to the extreme point. The new density extreme point is used as the new clustering center and repeated iterations are performed until all frequency points are clustered. The maximum density value after clustering is output as the extreme value element and the time-frequency ridge line is drawn. The time-frequency ridge line is processed by first-order difference to obtain the differenced sequence. The corresponding frequency hopping signal parameter estimation can be obtained by analyzing the difference sequence.

[0120] Through the description of the specific implementation methods, a deeper and more specific understanding can be obtained of the technical means and effects adopted by the present invention to achieve the predetermined purpose. However, the accompanying drawings are only provided for reference and illustration purposes and are not used to limit the technical solutions of the present invention.

Claims

1. A Link16 frequency hopping signal denoising and reconnaissance identification algorithm, characterized in that: The steps include: S1: Sample the intercepted frequency hopping signal to obtain the original baseband IQ path data; S2: Perform spectrogram time-frequency analysis on the frequency hopping signal to obtain a time-frequency graph; S3: Perform FCME-based comprehensive denoising algorithm on the time-frequency graph; S4: Perform MeanShift clustering on the denoised time-frequency image to extract feature parameters; S5: Draw the time-frequency ridge according to the clustered time-frequency characteristics, and obtain the frequency hopping parameter estimation through the first-order difference of the time-frequency ridge; The S3 is specifically as follows: before identifying the signal, performing secondary denoising on the spectrum line value of each time slot of the current time-frequency matrix, classifying and identifying the signal frequency points, and selecting the frequency point set that meets the false alarm probability threshold by the FCME algorithm in an iterative update manner, performing binary discrimination, removing the noise frequency points below the threshold, and repeatedly performing threshold adaptive calculation for multiple iterations until all frequency point sets are iterated to obtain the maximum iterated signal, thereby achieving noise adaptive threshold elimination; The S4 is specifically as follows: based on the MeanShift clustering algorithm, for the denoised time-frequency matrix, according to the different probability density distributions of the data, the time-frequency signal is shifted to the most concentrated area, so that the data converges to the local density extreme value and clusters.

2. The Link16 frequency hopping signal denoising and reconnaissance identification algorithm according to claim 1 is characterized in that: The false alarm probability factor u in the FCME algorithm iteration process fcme and adaptive threshold T fcme The calculation formula is: u fcme =-ln(p f ) (1-1) T fcme =E(M noise (k))·u fcme (1-2) In formula (1-1), P f is the false alarm probability, in formula (1-2), M noise is the noise frequency point set, E(M noise (k)) represents the mean value of the noise frequency spectrum, and k represents the number of noise frequency points divided into the noise frequency set after threshold screening.

3. The Link16 frequency hopping signal denoising and reconnaissance identification algorithm according to claim 2 is characterized in that: The S3 implementation steps are: Step 1: False alarm probability P f Perform statistics on the detection frequency distribution and determine the number of iterations D; Step 2: Sort the N frequency spectrum values, using the set {A1, A2, A3, ..., A N } indicates that the first N / 8 frequency points in the set are assumed to be noise frequency points, and the set M noise Mark, average the noise spectrum power and variance Calculation of Step 3: According to the mean and variance Substitute into the formula Get the threshold value T of the false alarm probability factor adaptive fcme ; Step 4: For the frequency point set {A1, A2, A3, ..., A N }, and perform iterative threshold judgment on the next N / 8 frequency points in the frequency hopping process. If the frequency power is greater than the threshold value, it is considered to be a useful frequency hopping component. If it is less than the threshold value, it is considered as a noise frequency point and is assigned to the set M noise middle; Step 5: Perform FCME iteration and average the updated noise frequency set and variance The next iteration is completed until all N frequency point sets {A1, A2, A3, ..., A N }All iterations are completed or the maximum iteration value is reached, and the FCME noise suppression optimization is completed.

4. The Link16 frequency hopping signal denoising and reconnaissance identification algorithm according to claim 1, characterized in that: The S4 includes: The MeanShift algorithm assumes that data sets of different clusters conform to different probability density distributions. It finds the direction with the densest sample concentration and continuously shifts to the point with the highest density. As the samples converge to the local maximum density, it assumes that the points that converge to the same maximum value during the iteration process are members of the same cluster. The MeanShift clustering vector is defined as: Use A k represents a high-dimensional ball with a radius of r, α i Represents the centroid of the current i-th region, satisfying the β point set: A k (α)＝{β:(β-α i ) T (β-α i )≤r 2} (1-4) In formula (1-4), A k Represents the sample point α i There are k points falling in the region. Starting from the center of the region, the distance vectors are added along different gradient directions to obtain the MeanShift vector. r (α) Mark the offset mean vector for iterative update to move the data to a higher density collection point; The Gaussian kernel function is added to MeanShift to expand the scope of application of the MeanShift algorithm. The improved MeanShift clustering vector is defined as follows: Where S(·) represents the Gaussian kernel function, ω(α i ) represents the sample weight and estimates the kernel function: In formula (1-7), n represents the d-dimensional dataset {α i }Numerical size, r d Represents the volume of the d-dimensional high-dimensional ball region, Q represents the kernel function, and the derivative of the probability density function (1-7) is: definition: Combining equations (1-8) and (1-9), we get: Imperative Form (1-10) Find local extrema of a probability density: Extract feature parameters.

5. The Link16 frequency hopping signal denoising and reconnaissance identification algorithm according to claim 1, characterized in that: The S5 includes: According to the clustered time-frequency features SPEC(n,k), find the matrix peak at each moment and draw the time-frequency ridge line according to the matrix peak: loc(n)=arg{max f [SPEC(n,k)]} (1-14) Through the first-order difference of the time-frequency ridge line, the time-frequency ridge line difference sequence is obtained: d(n)=abs{diff[loc(n)]} (1-15) The sequence interval calculation is performed on the time-frequency ridge difference sequence. Since the interval between two adjacent frequency hopping points is the frequency hopping interval, the parameter estimation of the frequency hopping signal hopping period can be obtained by averaging all intervals: T h =mean{diff[d(n)]} (1-16) The frequency range of the frequency point can be obtained by calculating the mean value of the frequency range of the time-frequency ridge difference sequence. The frequency value of the i-th frequency hopping point is: f(i)=mean{loc(d(i-1):d(i))} (1-17) Obtain frequency hopping parameter estimates.

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