Multi-target line spectrum feature distinguishing method based on Single-link hierarchical clustering

Abstract

The invention discloses a multi-target line spectrum feature distinguishing method based on Single-link hierarchical clustering. The multi-target line spectrum feature distinguishing method comprises the following steps: step 1, performing short-time frequency modulation Fourier transform; step 2, extracting line spectrum frequency modulation slope identifiable features; step 3, outliers are removed; and step 4, Single-link clustering analysis and result output are carried out. In order to solve the problem that multi-target line spectrum features are difficult to identify in an underwater acoustic complex environment, frequency modulation slope matrixes of different frequencies and different time are extracted through short-time frequency modulation Fourier transform and serve as line spectrum identifiable features, and a Single-link hierarchical clustering method is utilized to process different-frequency identifiable feature sets. Finally, a line spectrum set of different targets is obtained, and multi-target line spectrum feature resolution is realized. A data analysis result shows that the method can effectively distinguish line spectrum features from different targets, lays a foundation for subsequent extraction of target motion features 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] To address the challenge of identifying the line spectrum features of multiple targets in complex underwater acoustic environments, this invention first extracts the frequency modulation slope matrices at different frequencies and times using short-time frequency-modulated Fourier transform and uses these as discriminative line spectrum features. Then, a Single-link hierarchical clustering method is employed to process the sets of discriminative features at different frequencies, ultimately yielding a set of line spectra for different targets, thus achieving multi-target line spectrum feature differentiation. Data analysis results demonstrate that this method can effectively distinguish line spectrum features from different targets, laying the foundation for subsequent multi-target identification and possessing significant engineering practical value. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a multi-target line spectrum feature discrimination method based on Single-link hierarchical clustering. In complex underwater acoustic environments, the method extracts identifiable features of targets through short-time frequency-modulated Fourier transform, processes the identifiable feature set using Single-link hierarchical clustering, and ultimately achieves multi-target line spectrum feature discrimination.

[0006] The technical solution of this invention is as follows:

[0007] A multi-target line spectral feature discrimination method based on Single-link hierarchical clustering includes:

[0008] Step 1: Short-time frequency modulated Fourier transform: Receive time-domain data from a low-resolution space sonar platform. The frequency-modulated Fourier transform spectrum is obtained by performing a short-time frequency-modulated Fourier transform on it. ;

[0009] Step 2: Identifiable Feature Extraction of Line Spectrum Frequency Modulation Slope: Extract the frequency modulation slope corresponding to the peak value at each frequency from the short-time frequency modulation Fourier transform results of each time period. Thus, the frequency modulation slope matrix at different frequencies and times can be obtained. , , where i represents the corresponding spectral line frequency;

[0010] Step 3: Outlier Removal: Use the hampel function to remove outliers individually. Outliers caused by noise or interference;

[0011] 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.

[0012] The beneficial effects of this invention are as follows:

[0013] To address the prominent problem of difficulty in identifying the line spectra of multiple targets in complex underwater acoustic environments, a multi-target resolution method based on Single-link hierarchical clustering is proposed. This method processes the time-domain data of a low-resolution sonar platform using Short-Time Modulated Fourier Transform (STCFT) to extract the frequency modulation slope matrices at different frequencies and times, which are then used as distinguishable features of the line spectra. The Single-link hierarchical clustering method is then used to process the sets of distinguishable features at different frequencies, ultimately obtaining the line spectra sets of different targets, thus achieving multi-target line spectra resolution.

[0014] Data analysis results show that the multi-target line spectrum resolution method based on Single-link hierarchical clustering proposed in this invention can successfully cluster the same target line spectrum features and separate different target line spectrum features, effectively solving the problem of multi-target line spectrum feature resolution and laying the foundation for subsequent extraction of target motion features and multi-target localization. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the implementation of a multi-target line spectrum feature discrimination method based on Single-link hierarchical clustering according to the present invention. Figure 2(a) is the time-frequency diagram of the simulated target line spectrum 1 when the signal-to-noise ratio is -20dB; Figure 2(b) is the time-frequency diagram of the simulated target line spectrum 2 when the signal-to-noise ratio is -20dB; Figure 2(c) is the time-frequency diagram of the simulated target line spectrum 3 when the signal-to-noise ratio is -20dB. Figure 3(a) shows the frequency modulation slope of line spectrum 1 when the signal-to-noise ratio is -20dB. And outlier removal comparison, Figure 3(b) shows the frequency modulation slope of line spectrum 2 when the signal-to-noise ratio is -20dB. And outlier removal comparison, Figure 3(c) shows the frequency modulation slope of line spectrum 3 when the signal-to-noise ratio is -20dB. And comparison of outlier removal; Figure 4(a) shows the clustering results of the frequency modulation slope features at a signal-to-noise ratio of -20dB, and Figure 4(b) shows the clustering results of the instantaneous frequency features at a signal-to-noise ratio of -20dB. Figure 5(a) is the time-frequency diagram of the simulated target line spectrum 1 at a signal-to-noise ratio of -30dB; Figure 5(b) is the time-frequency diagram of the simulated target line spectrum 2 at a signal-to-noise ratio of -30dB; and Figure 5(c) is the time-frequency diagram of the simulated target line spectrum 3 at a signal-to-noise ratio of -30dB. Figure 6(a) shows the frequency modulation slope of line spectrum 1 when the signal-to-noise ratio is -30dB. And outlier removal comparison, Figure 6(b) shows the frequency modulation slope of line spectrum 2 when the signal-to-noise ratio is -30dB. And outlier removal comparison, Figure 6(c) shows the frequency modulation slope of line spectrum 3 when the signal-to-noise ratio is -30dB. And comparison of outlier removal; Figure 7(a) shows the clustering results of the frequency modulation slope features when the signal-to-noise ratio is -30dB, and Figure 7(b) shows the clustering results of the instantaneous frequency features when the signal-to-noise ratio is -30dB. Detailed Implementation

[0016] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0017] This invention addresses the challenge of distinguishing line spectra from multiple targets in complex underwater acoustic environments. It utilizes short-time frequency-modulated Fourier transform to extract frequency modulation slope matrices at different frequencies and times, obtaining distinguishable features of the line spectra. By traversing all frequency points and processing the distinguishable feature sets at different frequencies using a single-link hierarchical clustering method, a set of line spectra for different targets is finally obtained, achieving multi-target line spectrum resolution. Actual data analysis results demonstrate that this method can effectively distinguish line spectra from different targets and has significant engineering practical value.

[0018] (I) Implementation process:

[0019] This invention provides a multi-target line spectrum feature discrimination method based on Single-link hierarchical clustering, and the implementation flowchart is as follows: Figure 1 As shown, the specific implementation process is as follows:

[0020] (1) Short-time frequency modulation Fourier transform:

[0021] Receive time-domain data from space low-resolution sonar platform Perform a short-time frequency modulated Fourier transform on it to obtain

[0022]

[0023] Wherein, STCFT is the frequency-modulated Fourier transform spectrum. For time-domain data of the sonar platform, For window functions, Instantaneous frequency, For frequency modulation slope, For time delay, The imaginary unit is t, where t is time.

[0024] (2) Identifiable feature extraction based on line spectrum frequency modulation slope:

[0025] For each time period, the frequency modulation slope corresponding to the peak value is extracted from the short-time frequency modulation Fourier transform results at each frequency. This allows us to obtain the frequency modulation slope matrix at different frequencies and times. , , where i represents the corresponding spectral line frequency.

[0026]

[0027] in, ( () represents the frequency modulation slope over a time period. For time-domain data of the sonar platform, For window functions, Instantaneous frequency, For frequency modulation slope, For time delay, The imaginary unit is t, where t is time.

[0028] (3) Wild point removal:

[0029] Use the Hampel function to remove respectively Outliers caused by noise or interference are detected by the Hample function, which improves outlier detection accuracy by using the median and median absolute deviation (MAD). The median represents the middle value of the data, while MAD measures the dispersion of data points from the median. The outlier detection criteria of the Hample filter are as follows:

[0030] If data points 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:

[0031]

[0032] in, This indicates the median calculation, and MAD represents the absolute deviation of the median. .

[0033] (4) Single-link clustering analysis and result output:

[0034] Using the Single-link clustering method to cluster different frequencies Cluster analysis is performed on the set to obtain the clustering results. The specific process is as follows:

[0035] 1) Modulate the frequency modulation slope matrix As a distinguishable feature of the target line spectrum, the distance matrix is ​​calculated. :

[0036] , ,

[0037] in, for and The distance between them Represents variance. for and covariance;

[0038] 2) Select the two clusters that are closest to each other. , merge the two into ;

[0039] 3) Delete from the distance matrix and Add rows and columns and update the distance;

[0040] set up , , If we represent three sets of data, that is, three clusters, then... and The distance between them can be expressed using the Lance-Williams formula:

[0041]

[0042] Where D(・) represents the distance between clusters, , , This represents three different clusters, and |・| represents absolute value calculation.

[0043] 4) Repeat steps 2) and 3) until the number of clusters reaches a certain threshold. 2.

[0044] 5) Merge the remaining clusters.

[0045] If the line spectra belong to the same cluster number, it indicates that they belong to the same target.

[0046] (II) Data Test Results

[0047] Based on the "(I) Implementation Process", the processing results of this invention are presented through analysis and processing of simulation data:

[0048] With a signal sampling rate of 1000Hz and a signal length of 2000s, three sets of moving targets are constructed, and the target speed is assumed to be... The closest distance between the receiving hydrophone and the trajectory of the sound source is The moment when the sound source reaches the point where the two are closest is White noise was added, with the signal-to-noise ratio set to -20dB and -30dB respectively. The parameters for each signal group are as follows:

[0049] Objective 1: =10m / s, =5000m, =1000s, set the target radiation to 5 line spectra with frequencies of 100Hz, 115Hz, 130Hz, 145Hz and 160Hz respectively;

[0050] Objective 2: =7m / s, =1000m, =1900s, set the target radiation to 5 line spectra with frequencies of 105Hz, 120Hz, 135Hz, 150Hz and 165Hz respectively;

[0051] Objective 3: =5m / s, =3000m, =500s, set the target radiation to 5 lines with frequencies of 110Hz, 125Hz, 140Hz, 155Hz and 170Hz respectively.

[0052] 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.

[0053] 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. By comparing the changes over time and the removal of outliers with Figures 3(a), 3(b), and 3(c), it was found that as the signal-to-noise ratio decreases, the number of outliers in the frequency modulation slope increases. Although the Hampel filter can still remove outliers, it cannot effectively filter individual points.

[0054] 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.

[0055] Figures 4(a) and 4(b) show the Single-link clustering results at a signal-to-noise ratio of -20dB, and Figures 7(a) and 7(b) show the Single-link clustering results at a signal-to-noise ratio of -30dB. Here, the spectrum of target 1 is highlighted with a red line, the spectrum of target 2 with a green line, and the spectrum of target 3 with a blue line. Furthermore, to highlight the correctness of the clustering results, solid lines indicate correct judgments, and dashed lines indicate incorrect judgments. As can be seen from Figures 4(a) and 4(b), the clustering results for the three groups of moving targets using frequency modulation slope and instantaneous frequency as distinguishable features are all correct. In Figure 7(a), it can be seen that the Single-link clustering results based on the frequency modulation slope feature are all correct. However, in Figure 7(b), the Single-link clustering results based on the instantaneous slope feature incorrectly classify the first spectrum line of target 1 as target 3.

[0056] Therefore, when the signal-to-noise ratio is high, both the frequency modulation slope and the instantaneous frequency can effectively distinguish the target line spectrum. When the signal-to-noise ratio is low, the instantaneous frequency is used as the distinguishable feature for multi-target discrimination, but the first line spectrum of target 1 will be classified incorrectly. However, the Single-link clustering result based on the frequency modulation slope feature of this invention is still correct.

[0057] The modulation slope and instantaneous frequency were used as distinguishable features of the line spectrum for clustering. The Single-link clustering algorithm was used to distinguish the line spectrum features of the simulated moving target. The data are shown in Table 1. Table 1. Simulated signal clustering results

[0058] The data processing results above show that short-time frequency modulation Fourier transform can effectively extract distinguishable line spectrum features such as the target frequency modulation slope. Based on this, Singles-link hierarchical clustering analysis can effectively achieve multi-target line spectrum resolution in complex underwater acoustic environments, which has good engineering application prospects.

[0059] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent modifications made based on the above embodiments are all within the scope of protection of the present invention.

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 from a low-resolution space sonar platform. The frequency-modulated Fourier transform spectrum is obtained by performing a short-time frequency-modulated Fourier transform on it. ; Step 2: Identifiable Feature Extraction of Line Spectrum Frequency Modulation Slope: Extract the frequency modulation slope corresponding to the peak value at each frequency from the short-time frequency modulation Fourier transform results of each time period. 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.

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: ； Wherein, STCFT is the frequency-modulated Fourier transform spectrum. For time-domain data of the sonar platform, For window functions, Instantaneous frequency, For frequency modulation slope, For time delay, The imaginary unit is t, where t is 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 for ) is: ； in, ( () represents the frequency modulation slope over a time period. For time-domain data of the sonar platform, For window functions, Instantaneous frequency, For frequency modulation slope, For time delay, The imaginary unit is t, where t is 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: If data points 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. .

5. The method for resolving multi-target line spectrum features based on Single-link hierarchical clustering according to claim 4, characterized in that: 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. : ， ； in, for and The distance between them Represents variance. for and covariance; 2) Select the two clusters that are closest to each other. , merge the two into ; 3) Delete from the distance matrix and Add rows and columns and update the distance; set up , , This represents three sets of data, i.e., three clusters. and The distance between them can be expressed using the Lance-Williams formula: ； Where D(・) represents the distance between clusters, , , This represents three different clusters, and |・| represents absolute value calculation; 4) Repeat steps 2) and 3) until the number of clusters reaches a certain threshold. 2; 5) Merge the remaining clusters.

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