A multi-target line spectrum feature distinguishing method based on single-link hierarchical clustering

Abstract

The application discloses a kind of multi-target line spectrum feature distinguishing methods based on Single-link hierarchical clustering, comprising step one: short-time frequency-modulated Fourier transform;Step two: line spectrum frequency-modulated slope identifiable feature extraction;Step three: outlier removal;Step four: Single-link clustering analysis and result output.The application is aimed at the problem that multi-target line spectrum feature is difficult to identify under the complex environment of underwater sound, extracts the frequency-modulated slope matrix of different frequency and different time by short-time frequency-modulated Fourier transform and uses it as line spectrum identifiable feature, processes different frequency identifiable feature set using Single-link hierarchical clustering method, finally obtains the line spectrum set of different targets, realizes multi-target line spectrum feature distinguishing.Data analysis results show that the method can effectively distinguish the line spectrum feature from different targets, lays a foundation for subsequent extraction of target motion feature and realization of multi-target positioning, and has good engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustics and underwater acoustic signal processing, specifically relating to the discrimination of multi-target line spectrum features in complex underwater acoustic environments, and in particular, a method for the discrimination of multi-target line spectrum features based on Single-link hierarchical clustering. Background Technology

[0002] Sound waves are currently the only effective way to propagate long distances underwater. The complex and variable underwater acoustic environment can significantly impact sound propagation, leading to severe interference between multiple target features on small-aperture sonar receiving platforms such as buoys, posing a serious challenge to target identification. Based on the characteristic that the same moving target line spectrum group follows the same Doppler variation law, cluster analysis can effectively distinguish the line spectrum features of multiple targets and achieve classification of line spectra from different sources. The Single-link hierarchical clustering method can effectively handle non-spherical clusters and discover chain-like structures in the data. It uses the distance between the two closest points in two clusters as the standard, giving it a significant advantage in identifying irregularly shaped clusters. Simultaneously, it tends to connect clusters with closer proximity, making it highly effective in discovering chain-like or extended structures in the data.

[0003] Furthermore, selecting effective discriminative features is one of the challenges in multi-target line spectrum resolution. Short-Time Fourier Transform (STFT) is widely used in target feature analysis and extraction because it reflects the local spectral characteristics of a target. However, this method requires that the data be stationary within each time window. Doppler signals are time-varying within a time window. Although stationarity can be maintained using short-segment Doppler signals, STFT cannot achieve a high signal-to-noise ratio. Therefore, this invention utilizes Short-Time Chirp Fourier Transform (STCFT) to extract discriminative features of targets. STCFT treats segmented data as linear frequency modulation (LFM) signals. Without the STFT stationarity assumption, longer time windows can still maintain higher frequency resolution. Approximating segmented data as LFM signals is more accurate than treating them as stationary signals.

[0004] In view of the problem that the line spectrum characteristics of multiple targets are difficult to identify in a complex underwater acoustic environment, the application first extracts a frequency-modulation slope matrix of different frequencies and different times by short-time frequency-modulated Fourier transform and uses the matrix as a line spectrum identifiable feature, processes a set of different frequency identifiable features by using a Single-link hierarchical clustering method, and finally obtains a line spectrum set of different targets to realize the identification of multiple target line spectrum characteristics. SUMMARY

[0005] Based on the deficiencies of the prior art, the application provides a multiple target line spectrum feature identification method based on Single-link hierarchical clustering, which extracts target identifiable features by short-time frequency-modulated Fourier transform in a complex underwater acoustic environment, processes a set of identifiable features by using Single-link hierarchical clustering, and finally realizes the identification of multiple target line spectrum features.

[0006] The technical scheme of the application is as follows:

[0007] A multiple target line spectrum feature identification method based on Single-link hierarchical clustering, comprising:

[0008] Step one: short-time frequency-modulated Fourier transform: receiving time-domain data s(t) of a space low-resolution sonar platform, and performing short-time frequency-modulated Fourier transform on the data to obtain a frequency-modulated Fourier transform spectrum

[0009] Step two: line spectrum frequency-modulation slope identifiable feature extraction: extracting a frequency-modulation slope corresponding to a peak value of each frequency of a short-time frequency-modulated Fourier transform result of each time period k i to obtain a frequency-modulation slope matrix of different frequencies and different times , wherein i represents a corresponding spectrum line frequency;

[0010] Step three: outlier removal: removing outliers in the frequency-modulation slope matrix caused by noise or interference by using a hampel function

[0011] Step four: Single-link clustering analysis and result output: performing clustering analysis on a set of different frequencies by using a Single-link hierarchical clustering method to obtain a clustering result, and if the cluster numbers of the line spectrums are the same, it is indicated that the line spectrums belong to the same target. The application has the following beneficial effects:

[0012]

[0013] ​​​​Aiming at the prominent problem that multi-target line spectrum is difficult to identify in complex underwater acoustic environment, a multi-target identification method based on Single-link hierarchical clustering is given, which processes the time domain data of spatial low resolution sonar platform through short time chirp Fourier transform (STCFT), extracts the chirp slope matrix of different frequencies and different times, takes it as the identifiable feature of line spectrum, processes the different frequency identifiable feature set through Single-link hierarchical clustering method, and finally obtains the line spectrum set of different targets, so as to realize multi-target line spectrum identification.

[0014] Data analysis results show that the multi-target line spectrum identification method based on Single-link hierarchical clustering can successfully cluster the same target line spectrum features and separate different target line spectrum features, effectively solve the multi-target line spectrum feature identification problem, and lay a foundation for subsequent extraction of target motion features and realization of multi-target positioning. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 The figure is a flow chart of the implementation process of the multi-target line spectrum feature identification method based on Single-link hierarchical clustering;

[0016] Fig. 2 (a) is a simulation target line spectrum time-frequency diagram of line spectrum 1 when the signal-to-noise ratio is-20dB, Fig. 2 (b) is a simulation target line spectrum time-frequency diagram of line spectrum 2 when the signal-to-noise ratio is-20dB, and Fig. 2 (c) is a simulation target line spectrum time-frequency diagram of line spectrum 3 when the signal-to-noise ratio is-20dB;

[0017] Fig. 3 (a) is a line spectrum chirp slope and outlier removal comparison of line spectrum 1 when the signal-to-noise ratio is-20dB, Fig. 3 (b) is a line spectrum chirp slope and outlier removal comparison of line spectrum 2 when the signal-to-noise ratio is-20dB, and Fig. 3 (c) is a line spectrum chirp slope and outlier removal comparison of line spectrum 3 when the signal-to-noise ratio is-20dB;

[0018] Fig. 4 (a) is a chirp slope feature clustering result when the signal-to-noise ratio is-20dB, and Fig. 4 (b) is an instantaneous frequency feature clustering result when the signal-to-noise ratio is-20dB;

[0019] Fig. 5 (a) is a simulation target line spectrum time-frequency diagram of line spectrum 1 when the signal-to-noise ratio is-30dB, Fig. 5 (b) is a simulation target line spectrum time-frequency diagram of line spectrum 2 when the signal-to-noise ratio is-30dB, and Fig. 5 (c) is a simulation target line spectrum time-frequency diagram of line spectrum 3 when the signal-to-noise ratio is-30dB;

[0020] Fig. 6 (a) is a line spectrum chirp slope and outlier removal comparison of line spectrum 1 when the signal-to-noise ratio is-30dB, Fig. 6 (b) is a line spectrum chirp slope Figure 6 (c) is a comparison of line spectrum 3 of the line spectrum chirp rate at a signal-to-noise ratio of -30 dB and outlier removal;

[0021] Figure 7 (a) is a clustering result of the chirp rate feature at a signal-to-noise ratio of -30 dB, and figure 7 (b) is a clustering result of the instantaneous frequency feature at a signal-to-noise ratio of -30 dB. DETAILED DESCRIPTION

[0022] The application will be further described below in combination with specific embodiments and the accompanying drawings:

[0023] The application aims at the problem of difficult identification of multi-target line spectrum in a complex underwater acoustic environment, uses a short-time chirp Fourier transform to extract a chirp rate matrix of different frequencies and different times to obtain identifiable features of the line spectrum, traverses all frequency points, processes different frequency identifiable feature sets by a Single-link hierarchical clustering method, and finally obtains a line spectrum set of different targets to realize multi-target line spectrum identification. Actual data analysis results show that the method can effectively identify different target line spectrums and has good engineering practical value.

[0024] (I) Implementation process:

[0025] The application provides a multi-target line spectrum feature identification method based on Single-link hierarchical clustering, and a flowchart of the implementation process is shown in figure Figure 1 , and the specific implementation process is as follows:

[0026] (1) Short-time chirp Fourier transform:

[0027] Receive the time-domain data s (t) of a low-resolution sonar platform in space, and perform a short-time chirp Fourier transform on the time-domain data to obtain:

[0028] ,

[0029] Wherein, STCFT is a chirp Fourier transform spectrum, s (t) is the time-domain data of the sonar platform, g (t) is a window function, f is an instantaneous frequency, k is a chirp rate, is a time delay, j is an imaginary unit, and t is time.

[0030] (2) Extracting identifiable features of the line spectrum chirp rate:

[0031] Extract the peak value corresponding to the chirp rate k of each frequency of the short-time chirp Fourier transform result of each time period i , so as to obtain a chirp rate matrix of different frequencies and different times , , and i represents the corresponding spectral line frequency.

[0032] ,

[0033] where, is the frequency modulation slope of a time period, s(t) is the sonar platform time domain data, g(t) is the window function, f is the instantaneous frequency, k is the frequency modulation slope, is the time delay, j is the imaginary unit, t is the time.

[0034] (3) Outlier removal:

[0035] Use the hampel function to remove outliers in and interference, the Hample function improves the accuracy of outlier detection by using the median and median absolute deviation MAD, the median represents the median value of the data, and the median absolute deviation MAD measures the dispersion between the data points and the median, the Hample filter outlier determination standard is as follows:

[0036] If the data point is identified as an outlier, that is, the absolute deviation divided by MAD exceeds the threshold, then it is replaced by the median of , otherwise, the original value of the data point is kept, the expression is:

[0037] ,

[0038] where, represents the median calculation, MAD represents the median absolute deviation, .

[0039] (4) Single-link clustering analysis and result output:

[0040] Use the Single-link clustering method to cluster the set of different frequencies, get the clustering result, the specific process is as follows:

[0041] 1) Take the frequency modulation slope matrix as the target line spectrum identifiable feature, calculate the distance matrix :

[0042] ,

[0043] ,

[0044] where, d ij is the distance between and , var represents the variance, is the covariance of and ;

[0045] 2) Select the two closest clusters k i、 k j , merge them into ;

[0046] 3) Delete the rows and columns of k i and k j in the distance matrix, add , and update the distance;

[0047] Let k a , k b , k c represent three groups of data, i.e. three clusters, then the distance between k c and can be represented by the Lance-Williams formula:

[0048] ,

[0049] Where D(・) represents the distance between clusters, k a , k b , k c represent three different clusters, and |・| represents the absolute value calculation.

[0050] 4) Repeat steps 2) and 3) until the number of clusters is ≤2.

[0051] 5) Merge the remaining clusters.

[0052] If the line spectrum belongs to the same cluster number, it indicates that it belongs to the same target.

[0053] (II) Data test results

[0054] On the basis of "(I) Implementation process", the processing results of the present application are given by analyzing and processing simulation data:

[0055] With a signal sampling rate of 1000Hz, a signal length of 2000s, 3 groups of moving targets are constructed, the target moving speed is v, the closest distance between the receiving hydrophone and the sound source motion trajectory is R0, the time when the sound source reaches the closest point between the two is t0, white noise is added, and the signal-to-noise ratio is set to -20dB and -30dB. The signal parameters of each group are as follows:

[0056] Target 1: v=10m / s, R0=5000m, t0=1000s, set target radiation 5 line spectrum, frequency is 100Hz, 115Hz, 130Hz, 145Hz, 160Hz;

[0057] Target 2: v=7m / s, R0=1000m, t0=1900s, set the target to emit 5 spectral lines with frequencies of 105Hz, 120Hz, 135Hz, 150Hz and 165Hz respectively;

[0058] Target 3: v=5m / s, R0=3000m, t0=500s, set the target to emit 5 spectral lines with frequencies of 110Hz, 125Hz, 140Hz, 155Hz and 170Hz respectively.

[0059] Figures 2(a), 2(b), and 2(c) show the instantaneous frequencies of the first line spectrum of the three moving targets when the signal-to-noise ratio is -20dB. The time-frequency diagrams show that the line spectra of the three groups of targets are relatively clear at this point, with a high signal-to-noise ratio, and the changes in the instantaneous line spectra over time can be clearly observed. Figures 5(a), 5(b), and 5(c) show the instantaneous frequencies of the first line spectra of the three groups of moving targets when the signal-to-noise ratio is -30dB. The time-frequency plots, when compared with Figures 2(a), 2(b), and 2(c), show that the instantaneous frequency trajectory is significantly weaker and is about to be obscured by the background, making it difficult to identify and classify the subsequent line spectrum.

[0060] Figures 3(a), 3(b), and 3(c) show the frequency modulation slope of the first line spectrum of the three moving targets when the signal-to-noise ratio is -20dB. The comparison of data changes over time and outlier removal shows that the Hampel filter effectively removes outliers caused by noise or interference, thus smoothing the data. Figures 6(a), 6(b), and 6(c) show the frequency modulation slope of the first line spectrum of three moving targets at a signal-to-noise ratio of -30dB. The changes over time and the removal of outliers were compared with Figures 3(a), 3(b), and 3(c). It was found that as the signal-to-noise ratio decreased, the number of outliers in the frequency modulation slope increased. Although the Hampel filter could still remove outliers, it could not effectively filter some individual points.

[0061] In summary, as the signal-to-noise ratio decreases, the number of outliers in the frequency modulation slope increases. The Hampel filter can effectively remove outliers caused by noise or interference and smooth the data. However, it cannot effectively filter individual points at lower signal-to-noise ratios.

[0062] Fig. 4(a), Fig. 4(b) are Single-link clustering results when the signal-to-noise ratio is -20dB, Fig. 7(a), Fig. 7(b) are Single-link clustering results when the signal-to-noise ratio is -30dB. Here, the line spectrum of the clustering result for target 1 is highlighted by a red line, the line spectrum of the clustering result for target 2 is highlighted by a green line, the line spectrum of the clustering result for target 3 is highlighted by a blue line, in addition, to highlight the correctness of the clustering result, a solid line indicates a correct judgment, and a dashed line indicates an incorrect judgment. As can be seen from Fig. 4(a), Fig. 4(b), at this time, the clustering results of the three groups of moving targets taking the frequency modulation slope and the instantaneous frequency as distinguishable features are all correct. In Fig. 7(a), it can be seen that: the Single-link clustering results based on the frequency modulation slope feature are all correct, while in Fig. 7(b), the Single-link clustering results based on the instantaneous slope feature incorrectly classify the first line spectrum of target 1 as target 3.

[0063] Therefore, when the signal-to-noise ratio is high, taking the frequency modulation slope and the instantaneous frequency as distinguishable features, both can effectively distinguish the target line spectrum, and when the signal-to-noise ratio is low, taking the instantaneous frequency as a distinguishable feature for multi-target resolution, the first line spectrum of target 1 is incorrectly classified, while the Single-link clustering result based on the frequency modulation slope feature of the present application is still correct.

[0064] Taking the frequency modulation slope and the instantaneous frequency as distinguishable features of the line spectrum for clustering, the Single-link clustering algorithm is used to distinguish the simulation moving target line spectrum features, and the data is shown in Table 1:

[0065] Table 1 Clustering results of simulation signals

[0066]

[0067] The data processing results show that: the short-time frequency modulation Fourier transform can effectively extract the target frequency modulation slope and other line spectrum distinguishable features, on this basis, the Singles-link hierarchical clustering analysis can effectively realize the multi-target line spectrum resolution in a complex underwater acoustic environment, and has good engineering application prospect.

[0068] It should be noted that the above embodiments are only the preferred embodiments of the present application, not to limit the protection scope of the present application, and the equivalent transformations made on the basis of the above embodiments all belong to the protection scope of the present application.

Claims

1. A method for resolving multi-target line spectrum features based on Single-link hierarchical clustering, characterized in that, include: Step 1: Short-time frequency-modulated Fourier transform: Receive time-domain data s(t) from the low-resolution space sonar platform and perform a short-time frequency-modulated Fourier transform on it to obtain the frequency-modulated Fourier transform spectrum. f is the instantaneous frequency. For time delay; Step 2: Extracting Distinguishing Features from Line Spectrum Frequency Modulation Slope: Extract the frequency modulation slope k corresponding to the peak value at each frequency from the short-time frequency modulation Fourier transform results for each time period. i Thus, the frequency modulation slope matrix at different frequencies and times can be obtained. , , where i represents the corresponding spectral line frequency; Step 3: Outlier Removal: Use the hampel function to remove outliers individually. Outliers caused by noise or interference; Step 4: Single-link clustering analysis and result output: Use the Single-link hierarchical clustering method to analyze clusters of different frequencies. Cluster analysis is performed on the set to obtain the clustering results. If the line spectra belong to the same cluster number, it indicates that they belong to the same target. The specific process for obtaining the clustering results in step four is as follows: 1) Modulate the frequency modulation slope matrix As a distinguishable feature of the target line spectrum, the distance matrix is ​​calculated. : ， ； Where, d ij for and The distance between them Represents variance. for and covariance; 2) Select the two closest clusters k i、 k j merge the two into ; 3) Remove k from the distance matrix i and k j Add rows and columns and update the distance; Let k a k b k c This represents three sets of data, i.e., three clusters, where k c and The distance between them can be expressed using the Lance-Williams formula: ， Where D(・) represents the distance between clusters, k a k b k c This represents three different clusters, and |・| represents absolute value calculation; 4) Repeat steps 2) and 3) until the number of clusters is ≤2; 5) Merge the remaining clusters.

2. The method for resolving multi-target line spectrum features based on Single-link hierarchical clustering according to claim 1, characterized in that: In step one, the frequency-modulated Fourier transform spectrum The expression is: ， Where STCFT is the frequency-modulated Fourier transform spectrum, s(t) is the time-domain data of the sonar platform, g(t) is the window function, f is the instantaneous frequency, and k is the frequency modulation slope. The delay is represented by j, where j is the imaginary unit and t is the time.

3. The method for resolving multi-target line spectrum features based on Single-link hierarchical clustering according to claim 2, characterized in that: In step two, for the frequency modulation slope matrix , , The expression is: ， in, Let s(t) be the frequency modulation slope over a time period, g(t) be the time-domain data of the sonar platform, f be the instantaneous frequency, and k be the frequency modulation slope. The delay is represented by j, where j is the imaginary unit and t is the time.

4. The method for resolving multi-target line spectrum features based on Single-link hierarchical clustering according to claim 3, characterized in that: In step three, the Hample function improves the accuracy of outlier detection by using the median and the median absolute deviation (MAD). The median represents the middle value of the data, while the MAD measures the dispersion of the data points from the median. The outlier determination criteria of the Hample filter are as follows: For data points If data point x i If a value is identified as an outlier, meaning the absolute deviation divided by MAD exceeds a threshold, then it is replaced with... If the median is found, otherwise, keep the original values ​​of the data points. The expression is: ， in, This indicates the median calculation, and MAD represents the absolute deviation of the median. .

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