Complex target pole feature extraction method improved by density peak clustering

Abstract

The application provides a complex target pole feature extraction method improved by density peak clustering, including the following steps: S1, obtaining a target time domain response according to scattered frequency domain echo data; S2, obtaining a theoretical late response start time according to a target size and a signal duration, and obtaining a target late response; S3, dynamically setting a mode number, using a sliding window to traverse the late response sequence, and obtaining a series of possible pole sets; and S4, performing density peak clustering on the possible pole sets to obtain final poles, solving the problems that some parameters cannot be determined and false poles are difficult to eliminate in the matrix pencil method, so that the pole features of the complex target are obtained.

Description

Technical Field

[0001] This invention relates to the field of target pole feature extraction technology, and more specifically to a method for extracting complex target pole features using density peak clustering improvement. Background Technology

[0002] When the target's feature size is comparable to the signal wavelength, the radar operates in the resonant region, and poles are the most important features of targets in this region. Poles are insensitive to target attitude and polarization, primarily related to target size, shape, and material; therefore, they can be used to identify radar targets. Accurate extraction of pole features is crucial. Existing extraction methods include the Prony method, E-pulse method, Cauchy method, and matrix-beam method, among which the matrix-beam method is the most widely used. The target's time-domain transient response can be divided into early and late responses. The early response is a forced response, related to the incident pulse signal, while the late response is independent of the incident pulse signal. In practical testing environments, signals with extremely narrow pulse widths are generally used to incident on the target to obtain the target's scattered echo. Narrow pulse widths facilitate the distinction between early and late responses.

[0003] The matrix-bundle method extracts poles from the late-stage transient response of a target in the time domain. It exhibits good noise resistance, high efficiency, and robustness at a given signal-to-noise ratio, making it well-suited for extracting pole features. However, most matrix-bundle methods involve manually truncating the target's transient response in the time domain. For complex targets, issues such as aliasing of early and late responses, difficulty in determining the truncation time, unknown pattern order of complex targets, and difficulty in removing spurious poles commonly exist, making it difficult to apply to the pole extraction problem of practical complex targets. Therefore, the pole extraction problem for complex targets is crucial if pole features are to be used for target recognition. Summary of the Invention

[0004] The purpose of this invention is to address the problems of indeterminate parameters and difficulty in removing spurious poles in the matrix bundle method, thereby obtaining pole features of complex targets. This invention provides a method for extracting pole features of complex targets using density peak clustering, comprising the following steps:

[0005] S1. Obtain the target time domain response based on the scattered radio frequency domain echo data;

[0006] S2. Obtain the theoretical late response start time based on the target size and signal duration to obtain the target's late response;

[0007] S3. Dynamically set the number of modes and use a sliding window to traverse the late response sequence to obtain a set of possible poles;

[0008] S4. Perform density peak clustering on the possible pole set to obtain the final pole.

[0009] In the preferred embodiment, step S1 specifically includes the following steps:

[0010] The target frequency band [f] is obtained using the method of moments. min ,f max The internal frequency interval is δ f Scattered echo data:

[0011]

[0012] H(ω) is the frequency domain impulse response of the target.

[0013] When the incident signal in the time domain is a Singer signal:

[0014] e i (t)=Sa(ω c t),

[0015] ω c If the maximum calculation frequency is given, then the frequency domain expression of the scattered echo signal is:

[0016]

[0017] This equation shows that if the incident signal is a Singer signal, then truncating the frequency domain response will yield the frequency domain scattered signal data. Actual time-domain impulse signals are all real signals, and H(ω) should have a conjugate symmetric form.

[0018]

[0019] The time-domain scattered echo signal is:

[0020]

[0021] in:

[0022]

[0023] Therefore, the time-domain signal obtained by performing conjugate symmetry on the frequency-domain scattered echo data calculated by the method of moments and then performing inverse Fourier transform is equivalent to the time-domain transient response signal obtained by the Singer signal acting on the target.

[0024] A Hamming window function is applied to the frequency domain data to concentrate the signal energy in the main lobe before performing an inverse Fourier transform.

[0025] In the preferred embodiment, step S2 specifically includes the following steps:

[0026] When the signal transmission and reception positions are the same, the early response start time is T1, and the pulse signal width is T. p The time it takes for the signal to travel through the target is T. r The start time of a late response is typically defined as:

[0027] t1 = T1 + 2T r +T p

[0028] Due to the delay in signal propagation, there is a time difference between the responses generated by the target portion that first comes into contact with the signal and the target portion that comes into contact with the signal last. The earlier start time of the late response is defined as:

[0029] t2 = T1 + T r +T p ;

[0030] The calculation of the spatial point where the wavefront of the incident wave just contacts the target includes the distance from the origin and the equivalent signal width T of the incident signal. ep Let L1 be the projected distance from the line connecting the earliest point of contact between the target and the incident signal and the origin to the incident signal's incident direction. Then, the corresponding echo delay T1 = 2L1 / c, where c is the speed of light. The incident signal is used in the equivalent form of a Singer signal, and its equivalent signal width T ep The main lobe width is calculated based on its first zero point:

[0031]

[0032] f m It is the highest frequency corresponding to the incident signal.

[0033] In the preferred embodiment, step S2 further includes the following steps:

[0034] The late-stage transient response of the target is expressed in the form of a sum of decaying exponents on the complex plane:

[0035]

[0036] Where R i =α i +jβ i s i =σ i +jω i ;R i It is a residue, s i It is the pole; σ i and ω i These are the attenuation factor and the attenuation angular frequency, respectively.

[0037] Let the sampled discrete form of the late-time transient response y(t) in the time domain be y(n), expressed as:

[0038]

[0039] Where N is the number of sampling points and M is the number of modes (number of poles);

[0040] Define the Hankel matrix:

[0041]

[0042] Where L is the bundle parameter, in order to overcome noise interference, singular value decomposition is performed on the above equation to remove smaller non-zero singular values:

[0043]

[0044] where Σ=diag{σ1,σ2,...,σ M},σ1,σ2,...,σ M Σ' represents the M largest singular values ​​of Y, and Σ' is a diagonal matrix containing eigenvalues ​​with less noise information.

[0045] Take a lower-rank approximation of Y':

[0046] Y'=UΣV H =[Y1'y0]=[y L Y2']

[0047] Where matrix Y1' is obtained by removing the last column from Y', and Y2' is obtained by removing the first column from Y';

[0048] The target pole z is obtained by solving for the eigenvalues ​​of Y1'+Y2'. i , where Y1'+ is the generalized inverse of Y1';

[0049] The residues corresponding to the poles can be obtained using the least squares method:

[0050] x=(A T A) -1 A T b

[0051] in:

[0052]

[0053] x=[R1,R2,...,R M ] T ,

[0054] b = [y(0), y(1), ..., y(N-1)] T ,

[0055] After extracting the poles using the matrix bundle method, some spurious poles are removed.

[0056] In the preferred scheme, the criteria for spurious pole removal include:

[0057] The poles are conjugate symmetric; considering only the poles in the second quadrant, the attenuation factor σ is... iLess than zero, oscillation frequency ω i Extremes greater than zero are selected.

[0058] The target pole must satisfy the condition 2πf min <ω i <2πf max Those that do not meet the conditions will be removed;

[0059] Calculate the energy value E i =|R i | / σ i |(R i Let E be the residue corresponding to the pole. i =E i / max(E i ), will satisfy E i The pole of >p is retained, and the value of p is 0.001;

[0060] The number of modes is dynamically set, and a sliding window is used to traverse the response sequence.

[0061] In the preferred scheme, step S3 involves dynamically setting the number of modes and using a sliding window for traversal:

[0062] Based on the start time, late responses are extracted to obtain the late response sequence y(n), n=1,2,…N;

[0063] Set the number of modes M and the range M min ~M max Minimum M min Not less than 10, maximum M max Less than N / 6;

[0064] Set the sliding window size N w For M min ~M max For each M within the range, slide the window from time n=1, starting from the obtained late response sequence, to time n=NN. w At time +1, W is generated. num =NN w +1 sliding windows are used, and the matrix bundle method is applied to each window to remove some spurious poles, finally obtaining the set of possible poles.

[0065] In the preferred embodiment, step S4 further includes the following step: using a density peak clustering algorithm:

[0066] Given a dataset of size N×M, where N is the number of samples and M is the sample dimension, the local density of a sample point can be calculated in two ways: for discrete values, a truncation kernel is used, and for continuous values, a Gaussian kernel is used.

[0067] Truncating the nucleus:

[0068]

[0069] Gaussian kernel:

[0070] In the formula, d ij Let d be the Euclidean distance between data point i and data point j. c The neighborhood cutoff distance of the data point;

[0071] Local density ρ calculated using a truncated kernel i The number of sample points is equal to the number of sample points distributed within the neighborhood cutoff distance of sample point i; the local density ρ is calculated using Gaussian methods. i It equals the sum of the Gaussian distances from all sample points to sample point i;

[0072] relative distance δ i The relative distance refers to the minimum distance between sample point i and other points with higher density. Before calculating sample point i, the local density of each data point needs to be sorted. For the sample with the highest density, the relative distance is defined as:

[0073]

[0074] For the remaining data points, the relative distance is defined as:

[0075]

[0076] Find the local density ρ simultaneously through the decision value γ. i Higher and relative distance δ i Density peak under larger conditions:

[0077] γ i =ρ i ×δ i .

[0078] In the preferred embodiment, the selection of the cutoff distance includes the following steps:

[0079] Given the local densities ρ1, ρ2, ..., ρ of n sample points n When the density values ​​of each sample point are equal, the greater the uncertainty of the data distribution, the greater the Shannon entropy. Conversely, the smallest uncertainty corresponds to the smallest Shannon entropy. The density estimation entropy is introduced to measure the reasonableness of the local density estimation of sample points, i.e.:

[0080]

[0081] Where Z is a normalization coefficient;

[0082] The optimal value of the cutoff distance is obtained when the density estimation entropy reaches its minimum value.

[0083] In the preferred embodiment, step S4 further includes determining the cluster centers, which requires using a γ decision graph:

[0084] γ i The larger the value, the more likely it is to be a cluster center; therefore, for Sort the data in descending order, label the sorted points (i represents the label), and obtain the sorted graph of γ; use the slope k to describe the degree of change of γ. i This represents the slope of the line segment between the i-th point and the (i+1)-th point. When i is the point with the largest index among the points with slopes greater than the average, i is a critical point.

[0085] Points in the sorting graph whose index is before the critical point are considered as potential cluster centers.

[0086] In the preferred embodiment, step S4 further includes: deduplication of suspected cluster centers, including the following steps:

[0087] Determine whether the distance between two suspected cluster centers is less than the cutoff distance. If the distance between two suspected cluster centers is less than the cutoff distance, then take the point with the greater local density between them as the actual cluster center. If the local densities of the two are the same, then take the average of the two as the cluster center, and finally obtain the set of actual cluster centers.

[0088] To determine if the distance between two suspected cluster centers is less than the cutoff distance, if the distance between two suspected cluster centers is less than the cutoff distance, the point with the greater local density between them is taken as the actual cluster center; if the local densities are the same, the average of the two is taken as the cluster center, and finally the set of actual cluster centers is obtained.

[0089] In the preferred embodiment, step SS4 further includes: classifying the remaining points into clusters, specifically including the following steps:

[0090] After determining the actual set of cluster centers, the remaining points need to be assigned to their corresponding clusters. This involves sequentially determining the distance between each remaining point and every point in the actual set of cluster centers, and finding the actual cluster center closest to that point.

[0091] When the distance is less than the cutoff distance d c If so, it is classified into the cluster of this cluster center;

[0092] When the distance between this point and every point in the actual cluster center set is greater than the cutoff distance d c If the condition is met, then that point is considered a noise point.

[0093] In the preferred embodiment, step S4 further includes the following steps:

[0094] Calculate the number of points in the cluster to which each cluster center belongs. If the number is greater than the set density threshold, the cluster is considered a true pole cluster; otherwise, it is considered a false pole cluster and is removed.

[0095] The cluster centers of the true pole clusters are the desired poles.

[0096] The beneficial effects of this invention are as follows: This invention utilizes the clustering and orientation invariance of true poles, proposing an improved matrix bundle method using a density peak clustering algorithm. Dynamically traversing the pattern order avoids errors caused by the unknown order of complex target patterns. Simultaneously, a sliding window is introduced, sliding backward from the earliest theoretical start time, reducing the impact of aliasing on true poles. Clustering the obtained possible poles further determines the true pole cluster. Results show that the algorithm is robust, accurate, and effectively solves the parameter dependency problem of the matrix bundle method. Attached Figure Description

[0097] Figure 1 This is a schematic diagram of the early and late response;

[0098] Figure 2 This is a flowchart of the algorithm of the present invention;

[0099] Figure 3 This is a diagram showing the extraction effect of the conductor sphere using the basic matrix bundle method;

[0100] Figure 4 This is a diagram showing the results of the DPC-SWMPM algorithm for extracting conductor spheres.

[0101] Figure 5 It is a drawing of an airplane model;

[0102] Figure 6 This is a diagram showing the results of extracting targets from ten directions using the fundamental matrix bundle method.

[0103] Figure 7 This is a diagram showing the results of extracting the aircraft target from ten directions using the DPC-SWMPM method. Detailed Implementation

[0104] 1. Obtain the target time domain response from the scattered radio frequency echo data: Obtain the target frequency domain scattered echo data, perform conjugate symmetry on the frequency domain scattered data, and obtain the target time domain response by inverse Fourier transform.

[0105] The target frequency band [f] is obtained using the method of moments. min ,f max The internal frequency interval is δ f Scattered echo data:

[0106]

[0107] H(ω) is the frequency domain impulse response of the target.

[0108] If the time-domain incident signal is a Singer signal:

[0109] e i (t)=Sa(ω c t),

[0110] ω c If the maximum calculation frequency is given, then the frequency domain expression of the scattered echo signal is:

[0111]

[0112] This equation shows that if the incident signal is a Singer signal, then truncating the frequency domain response will yield the frequency domain scattered signal data. Since actual time-domain impulse signals are real signals, H(ω) should have a conjugate symmetric form:

[0113]

[0114] The time-domain scattered echo signal is:

[0115]

[0116] in:

[0117]

[0118] Therefore, the time-domain signal obtained by performing conjugate symmetry on the frequency-domain scattered echo data calculated by the method of moments and then performing inverse Fourier transform is equivalent to the time-domain transient response signal obtained by applying the Singer signal to the target.

[0119] Ideally, frequency domain data should be infinitely long. Frequency truncation leads to sidelobe energy leakage in the time-domain transient response signal. When an incident signal is incident on a target, the signal's sidelobes also convolve with the target's system response. This process is cumulative, and the energy of the sidelobes cannot be ignored. To avoid sidelobe energy leakage, a Hamming window function is applied to the frequency domain data, concentrating the signal energy in the main lobe before performing an inverse Fourier transform, thus making the obtained time-domain response data more accurate.

[0120] 2. Obtain the theoretical late response start time based on the target size and signal duration to obtain the target's late response:

[0121] If the signal transmission and reception positions are the same, the early response start time is T1, and the pulse signal width is T. p The time it takes for the signal to travel through the target is T. r The start time of a late response is typically defined as:

[0122] t1 = T1 + 2T r +T p

[0123] However, due to the signal propagation delay, there is a time difference between the responses generated by the target parts that first and last come into contact with the signal. This time delay leads to aliasing between early and late responses. Although the late response start time defined above can ensure that there are no early responses in the late response, it will result in the loss of some information and energy from the late response. The loss of late response information can cause inaccurate pole extraction, easily leading to the loss of relevant poles. Therefore, the late response start time needs to be defined in advance as follows:

[0124] t2 = T1 + T r +T p

[0125] This definition allows for a more complete understanding of the information and energy of the late response. Extracting this theoretical time point as the starting point of the late response minimizes interference from the early response while ensuring no loss of high-energy time-domain signals. Early and late responses are as follows: Figure 1 As shown.

[0126] The zero-time of the transient response obtained by the inverse Fourier transform of the frequency-domain scattered electric field data corresponds to the moment when the center of the incident signal reaches the origin of the coordinate system. Therefore, there will be a time difference of 1 / 2T in the incident time. ep The delay. To find the true starting moment of the interaction between the incident signal and the target, it is necessary to calculate the distance from the origin to the spatial point where the wavefront of the incident wave just contacts the target, and the equivalent signal width T of the incident signal. ep If we define the projected distance from the line connecting the earliest point of contact between the target and the incident signal to the origin to the incident signal's incident direction as L1, then the corresponding echo delay T1 = 2L1 / c, where c is the speed of light. The incident signal used is in the equivalent form of a Singer signal, with an equivalent signal width T. ep The width of the main lobe can be calculated based on its first zero point:

[0127]

[0128] f m It is the highest frequency corresponding to the incident signal.

[0129] 3. Dynamically set the number of modes and use a sliding window to traverse the late response sequence to obtain a set of possible poles:

[0130] Matrix beam extraction principle:

[0131] The late transient response of the target can be expressed in the form of a sum of decaying exponents on the complex plane:

[0132]

[0133] Where R i =α i+jβ i s i =σ i +jω i ;R i It is a residue, s i It is the pole; σ i and ω i These are the attenuation factor and the attenuation angular frequency, respectively.

[0134] Let the sampled discrete form of the late-time transient response y(t) in the time domain be y(n), expressed as:

[0135]

[0136] Where N is the number of sampling points, and M is the number of modes (number of poles). Define the Hankel matrix:

[0137]

[0138] Where L is the bundle parameter, in order to overcome noise interference, singular value decomposition is performed on the above equation to remove smaller non-zero singular values:

[0139]

[0140] where Σ=diag{σ1,σ2,...,σ M},σ1,σ2,...,σ M Let Σ' be the M largest singular values ​​of Y, and let Σ' be a diagonal matrix containing eigenvalues ​​with relatively small noise information. Take a low-rank approximation Y' of Y:

[0141] Y'=UΣV H =[Y1' y0]=[y L Y2']

[0142] The matrix Y1' is obtained by removing the last column from Y', and Y2' is obtained by removing the first column from Y'.

[0143] By solving Y1' + The eigenvalues ​​of Y2' are used to obtain the target pole z. i Y1' + It is the generalized inverse of Y1'.

[0144] The residues corresponding to the poles can be obtained using the least squares method:

[0145] x=(A T A) -1 A T b

[0146] in:

[0147]

[0148] x=[R1,R2,...,R M ] T ,

[0149] b = [y(0), y(1), ..., y(N-1)] T ,

[0150] After extracting the poles using the matrix bundle method, some spurious poles are removed.

[0151] Criteria for spurious pole removal:

[0152] (1) The poles are conjugate symmetric. Generally, only the poles in the second quadrant are considered, and the attenuation factor σ is used. i Less than zero, oscillation frequency ω i Extremes greater than zero are selected.

[0153] (2) The target pole must satisfy the condition 2πf min <ω i <2πf max Those that do not meet the conditions will be removed;

[0154] (3) Calculate the energy value E i =|R i | / σ i |(R i Let E be the residue corresponding to the pole. i =E i / max(E i ), will satisfy E i The poles of >p (where p is usually 0.001) are retained.

[0155] For high-Q and simple objects, the above method can obtain relatively accurate poles. However, for complex and low-Q objects, the extraction results are not accurate enough, and spurious poles are difficult to remove. In addition, the number of poles for complex objects is unknown. Previous methods for estimating the order include the minimum description length (MDL) method and calculating the error between the reconstructed signal and the original signal for different M values. However, the MDL method generally yields more poles than the actual number for both simulated and measured signals. Methods for calculating reconstruction error have problems such as being unable to eliminate reconstruction errors caused by residue errors and being unable to remove spurious poles introduced by the signal itself. Therefore, it is necessary to dynamically set the number of modes and use a sliding window to traverse the response sequence.

[0156] Dynamically set the number of modes, using a sliding window for traversal:

[0157] Based on the theoretical start time mentioned above, late responses are extracted to obtain the late response sequence y(n), n=1,2,…N.

[0158] Set the number of modes M and the range Mmin ~M max Minimum M min Generally not less than 10, maximum M max Generally less than N / 6.

[0159] Set the sliding window size N w For M min ~M max For each M within the range, slide the window from time n=1, starting from the obtained late response sequence, to time n=NN. w At time +1, W is generated. num =NN w +1 sliding windows are used, and the matrix bundle method is applied to each window to remove some spurious poles, finally obtaining the set of possible poles.

[0160] 4. Perform density peak clustering on the set of possible poles to obtain the final poles.

[0161] Density Peaks Clustering (DPC) is a density-based clustering algorithm that has advantages such as not requiring the specification of the number of clusters and being able to discover non-spherical clusters.

[0162] Two important concepts in the DPC algorithm:

[0163] (1) Local density

[0164] Given a dataset of size N×M, where N is the number of samples and M is the sample dimension.

[0165] For the local density of sample point i, there are two ways to calculate the local density: discrete values ​​are calculated using a truncated kernel, while continuous values ​​are calculated using a Gaussian kernel.

[0166] Truncating the nucleus:

[0167]

[0168] Gaussian kernel:

[0169]

[0170] In the formula, d ij Let d be the Euclidean distance between data point i and data point j. c This is the neighborhood cutoff distance for the data point.

[0171] Local density ρ calculated using a truncated kernel i It equals the number of sample points distributed within the neighborhood cutoff distance of sample point i; while the local density ρ calculated using Gaussians... i It equals the sum of the Gaussian distances from all sample points to sample point i.

[0172] (2) Relative distance

[0173] relative distance δ i This refers to the minimum distance between sample point i and other points with higher density. Before calculating sample point i, the local density of each data point needs to be sorted.

[0174] For the samples with the highest density, the relative distance is defined as:

[0175]

[0176] For the remaining data points, the relative distance is defined as:

[0177]

[0178] Since there are no points with higher density than the highest-density sample, DPC considers this point to be the density peak (cluster center), and artificially sets its relative distance to the maximum value. The remaining density peaks must simultaneously satisfy two conditions: local density ρ i Higher, relative distance δ i Larger. This type of density peak is found through the decision value γ:

[0179] γ i =ρ i ×δ i

[0180] Cutoff distance selection:

[0181] In information theory, Shannon entropy serves as a measure of system uncertainty. Given the local density ρ1, ρ2, ..., ρ of n sample points... n If the density value of each sample point is equal, the greater the uncertainty of the data distribution, the greater the Shannon entropy; conversely, the minimum uncertainty results in the minimum Shannon entropy. The density estimation entropy is introduced to measure the reasonableness of the local density estimation of sample points, i.e.:

[0182]

[0183] Where Z is a normalization coefficient.

[0184] The optimal value of the cutoff distance can be obtained when the density estimation entropy reaches its minimum value.

[0185] Selection of cluster centers:

[0186] Density Peak Clustering (DPC) algorithm assumes that cluster centers simultaneously possess a large local density ρ i and relative distance δ iCluster centers are determined manually using a gamma decision map. However, for certain special or complex datasets, the generated decision map often fails to visually identify the cluster centers. Since DPC's clustering process is not iterative, incorrect cluster center selection directly impacts the accuracy of the final clustering results.

[0187] γ i The larger the value, the more likely it is to be a cluster center. Therefore, for Sort the data in descending order, and label the sorted points, where i represents the label, to obtain the sorted graph of γ. The slope k is used to describe the degree of change in γ. i This represents the slope of the line segment between point i and point i+1. When i is the point with the largest index among points whose slopes are greater than the average, i is a critical point. Points in the sorted graph whose index precedes the critical point are considered potential cluster centers.

[0188] Deduplication of suspected cluster centers:

[0189] Determine if the distance between two suspected cluster centers is less than the cutoff distance. If the distance between two suspected cluster centers is less than the cutoff distance, then the point with the higher local density between them is taken as the actual cluster center; if the local densities are the same, then the average of the two densities is taken as the cluster center. This ultimately yields the set of actual cluster centers.

[0190] The remaining points are classified into clusters:

[0191] After determining the actual set of cluster centers, the remaining points need to be assigned to their corresponding clusters. This is done by sequentially checking the distance between each remaining point and every point in the actual set of cluster centers, finding the nearest actual cluster center to that point, and if the distance is less than the cutoff distance d... c If the distance between a point and every point in the actual cluster center set is greater than the cutoff distance d, then the point is classified into the cluster of this cluster center; c If so, then that point is considered a noise point.

[0192] The true pole cluster is obtained:

[0193] Calculate the number of points in the cluster to which each cluster center belongs. If the number is greater than a set density threshold, the cluster is considered a true pole cluster; otherwise, it is considered a false pole cluster and is removed. The cluster centers of the true pole clusters are the desired poles.

[0194] The specific process of the algorithm (DPC-SWMPM) is as follows: Figure 2 As shown.

[0195] 5. Result Comparison

[0196] (1) Simple low-Q target comparison: conductor sphere.

[0197] For a conducting sphere with radius *a* of 0.075 m, scattered electric field data at 200 frequency points from 10 MHz to 5.5 GHz were calculated. The results were compared using the fundamental matrix beam method and our algorithm (DPC-SWMPM). The number of modes in the fundamental matrix beam method was set to 50, while the number of modes in our algorithm ranged from 40 to 60. The results were normalized to *c / a*, where *a* is the sphere radius and *c* is the speed of light. Figure 3 The comparison of the basic matrix bundle method for extracting conductor spheres is shown. Figure 4 The DPC-SWMPM algorithm's conductor sphere extraction results are shown. It can be seen that the basic matrix bundle method has problems such as the inability to remove false poles and the extraction values ​​differing significantly from the theoretical values. DPC-SWMPM clusters the poles extracted by different number of modes, further removing false poles, and the poles are closer to the theoretical values. The results are significantly better than the basic matrix bundle method.

[0198] (2) Comparison of complex target extraction: aircraft model.

[0199] right Figure 5 Aircraft model simulations were conducted in the frequency range of 50kHz-80MHz to obtain monostatic scattered echo data from ten azimuth angles. The data were extracted using both the fundamental matrix beam method and our proposed algorithm (DPC-SWMPM). Due to the azimuth invariance of poles, the group of poles with the highest number of poles was selected as the base poles. A window was then applied around the base poles, and the average value of the poles within the window was obtained. The number of modes in the fundamental matrix beam method was set to 60, while the number of modes in our proposed algorithm ranged from 40 to 80. The results were normalized to πc / L, where L is the aircraft length (18.6m) and c is the speed of light.

[0200] contrast Figure 7 DPC-SWMPM algorithm extraction effect and Figure 6 The basic matrix bundle method extraction results show that the DPC-SWMPM algorithm extracts more concentrated poles in each direction, and under the same windowing integration conditions, DPC-SWMPM obtains more poles than the matrix bundle method. Poles with high attenuation and small residues are difficult to extract accurately; this example also clearly shows that the DPC-SWMPM extracts more accurate pole attenuation factors.

[0201] By comparing the extraction results for simple and complex targets, it is demonstrated that the proposed algorithm achieves good results in the pole extraction problem. The pole features extracted by this algorithm are consistent across all orientations, and the pole attenuation factor is more accurate than that of the basic matrix bundle method.

[0202] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for extracting features of complex target poles using density peak clustering, characterized by: Includes the following steps: S1. Obtain the target time domain response based on the scattered radio frequency domain echo data; S2. Obtain the theoretical late response start time based on the target size and signal duration to obtain the target's late response; S3. Dynamically set the number of modes and use a sliding window to traverse the late response sequence to obtain a set of possible poles; S4. Perform density peak clustering on the possible pole set to obtain the final pole; Using density peak clustering algorithm: Given a data size of The dataset, For the number of samples, Let be the dimension of the sample, for each sample point. The local density can be calculated in two ways: discrete values ​​are calculated using a truncated kernel, while continuous values ​​are calculated using a Gaussian kernel. Truncating the nucleus: ; ； Gaussian kernel: ; In the formula, For data points With data points Euclidean distance, The neighborhood cutoff distance of the data point; Local density calculated using truncated kernels Equal to the distribution of sample points The number of sample points within the neighborhood cutoff distance; Local density calculated using Gaussians Equal to all sample points to sample points The sum of Gaussian distances; relative distance Sample points The minimum distance between sample points and other points with higher density is calculated in the sample point calculation. First, the local density of each data point needs to be sorted. For the sample with the highest density, the relative distance is defined as: ； For the remaining data points, the relative distance is defined as: ； Through decision value Finding local density Higher and relative distance Density peak under larger conditions: ； Selecting the cutoff distance includes the following steps: Given Local density of each sample point When the density values ​​of each sample point are equal, the greater the uncertainty of the data distribution, the greater the Shannon entropy. Conversely, the smallest uncertainty corresponds to the smallest Shannon entropy. The density estimation entropy is introduced to measure the reasonableness of the local density estimation of sample points, i.e.: ； in It is a normalization coefficient; The optimal value of the cutoff distance is obtained when the density estimation entropy reaches its minimum value; Determining cluster centers requires based on Decision diagram implementation: The larger the value, the more likely it is to be a cluster center; therefore, for Sort the data in descending order and then label the sorted points. Indicate the label, and obtain Sort chart; select slope To describe The degree of change, Indicates the first The point and the first The slope of the line segment between points, when When it is the point with the largest index among the points with a slope greater than the average, It is the critical point; Points in the sorting graph whose index is before the critical point are considered as potential cluster centers; Deduplication of suspected cluster centers includes the following steps: Determine whether the distance between two suspected cluster centers is less than the cutoff distance. If the distance between two suspected cluster centers is less than the cutoff distance, then take the point with the greater local density between them as the actual cluster center. If the local densities of the two are the same, then take the average of the two as the cluster center, and finally obtain the set of actual cluster centers. Determine whether the distance between two suspected cluster centers is less than the cutoff distance. If the distance between two suspected cluster centers is less than the cutoff distance, then take the point with the greater local density between them as the actual cluster center; if the local densities are the same, then take the mean of the two as the cluster center, and finally obtain the set of actual cluster centers. The remaining points are then categorized into clusters, which involves the following steps: After determining the actual set of cluster centers, the remaining points need to be assigned to their corresponding clusters. This involves sequentially determining the distance between each remaining point and every point in the actual set of cluster centers, and finding the actual cluster center closest to that point. When the distance is less than the cutoff distance If so, it is classified into the cluster of this cluster center; When the distance between this point and every point in the actual cluster center set is greater than the cutoff distance If so, then that point is considered a noise point; Calculate the number of points in the cluster to which each cluster center belongs. If the number is greater than the set density threshold, the cluster is considered a true pole cluster; otherwise, it is considered a false pole cluster and is removed. The cluster centers of the true pole clusters are the desired poles.

2. The method for extracting features of complex target poles using density peak clustering as described in claim 1, characterized in that: Step S1 specifically includes the following steps: The target frequency band is obtained using the method of moments. , The internal frequency interval is Scattered echo data: ； It is the frequency domain impulse response of the target; When the incident signal in the time domain is a Singer signal: ； If the maximum calculation frequency is given, then the frequency domain expression of the scattered echo signal is: ； This formula shows that if the incident signal is a Singer signal, then truncating the frequency domain response will yield the frequency domain scattered signal data. Actual time-domain impulse signals are all real signals. It should have a conjugate symmetric form: ； The time-domain scattered echo signal is: ； in: ； Therefore, the time-domain signal obtained by performing conjugate symmetry on the frequency-domain scattered echo data calculated by the method of moments and then performing inverse Fourier transform is equivalent to the time-domain transient response signal obtained by the Singer signal acting on the target. A Hamming window function is applied to the frequency domain data to concentrate the signal energy in the main lobe before performing an inverse Fourier transform.

3. The method for extracting features of complex target poles using density peak clustering as described in claim 1, characterized in that: Step S2 specifically includes the following steps: When the signal transmission and reception locations are the same, the early response start time is The width of the pulse signal is The time it takes for the signal to travel through the target is The start time of the late response is defined as: ； Due to the delay in signal propagation, there is a time difference between the responses generated by the target portion that first comes into contact with the signal and the target portion that comes into contact with the signal last. The earlier start time of the late response is defined as: ； The calculation involves the spatial point where the wavefront of the incident wave just contacts the target, the distance from the origin, and the equivalent signal width of the incident signal. Let the projected distance from the line connecting the earliest point of contact between the target and the incident signal and the origin to the incident signal direction be... The corresponding echo delay , It is the speed of light, and the incident signal used is in the equivalent form of a Singer signal, with an equivalent signal width of... The main lobe width is calculated based on its first zero point: ； It is the highest frequency corresponding to the incident signal.

4. The method for extracting features of complex target poles using density peak clustering as described in claim 1, characterized in that: Step S2 also includes the following steps: The late-stage transient response of the target is expressed in the form of a sum of decaying exponents on the complex plane: ； in , ; It is a residue. It is the extreme point; and These are the attenuation factor and the attenuation angular frequency, respectively. Assume late-time transient response The sampled discrete form is , is represented as: ； in, It is the number of sampling points. Number of patterns; Define the Hankel matrix: ； Where L is the bundle parameter, in order to overcome noise interference, singular value decomposition is performed on the above equation to remove smaller non-zero singular values: ； in , yes The largest A singular value, It is a diagonal matrix containing eigenvalues ​​with relatively low noise information; Pick low-rank approximation : ； Where the matrix yes The result after removing the last column is: yes The result after removing the first column; By solving eigenvalues ​​are used to obtain the target pole. ,in yes The generalized inverse; The residues corresponding to the poles can be obtained using the least squares method: ； in: ； ； ； After extracting the poles using the matrix bundle method, some spurious poles are removed.

5. The method for extracting features of complex target poles using density peak clustering as described in claim 4, characterized in that: The criteria for spurious pole removal include: The poles are conjugate symmetric; considering only the poles in the second quadrant, the attenuation factor is... Less than zero, oscillation frequency Extremes greater than zero are selected. The target pole must meet the following conditions Those that do not meet the conditions will be removed; Calculate energy value , Let be the residue corresponding to the pole. , will satisfy The extreme point remains, The value is 0.001; The number of modes is dynamically set, and a sliding window is used to traverse the response sequence.

6. The method for extracting features of complex target poles using density peak clustering as described in claim 1, characterized in that: In step S3, the number of modes is dynamically set using a sliding window for traversal: Late responses are extracted based on their start times to obtain the late response sequence. ; Set number of modes scope minimum Not less than 10, maximum Less than ; Set the size of the sliding window ,for Each within the range The window is set to begin with the obtained late response sequence. Slide to At that moment, it was produced A sliding window is used to apply the matrix bundle method to each window and remove some spurious poles, ultimately obtaining a set of possible poles.

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