CN113075645A - Distorted formation line spectrum enhancement method based on principal component analysis-density clustering - Google Patents

Distorted formation line spectrum enhancement method based on principal component analysis-density clustering Download PDF

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CN113075645A
CN113075645A CN202110538487.9A CN202110538487A CN113075645A CN 113075645 A CN113075645 A CN 113075645A CN 202110538487 A CN202110538487 A CN 202110538487A CN 113075645 A CN113075645 A CN 113075645A
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time delay
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CN113075645B (en
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武其松
张昊
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Southeast University
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Abstract

The invention discloses a distorted lineshape spectrum enhancing method based on principal component analysis-density clustering, which comprises the following steps: (1) simulating underwater sound target radiation noise and interference line spectrum signals; (2) simulating an observation array signal; (3) roughly estimating a target position based on ideal beamforming; (4) detecting and selecting L line spectrum positions with the maximum power of a target signal; (5) extracting characteristics of the array relative time delay difference vectors of the L strong line spectrums by using a principal component analysis method to obtain characteristic vectors of L curves; (6) classifying the L curves by using a DBSCAN density clustering algorithm; (7) selecting more types of line spectrums in the classification result, and calculating relative time delay difference vectors of the average array; (8) and acquiring a target tracking beam with enhanced fidelity based on the estimated time delay. A distorted array line spectrum enhancement method based on principal component analysis-density clustering corrects the influence of the distortion of a towed linear array on beam forming through time delay estimation to obtain a fidelity-enhanced target radiation noise tracking beam.

Description

Distorted formation line spectrum enhancement method based on principal component analysis-density clustering
Technical Field
The invention belongs to the field of sonar signal processing, and particularly relates to a distorted linespectrum enhancement method based on principal component analysis-density clustering.
Background
Currently applied sonar systems generally include hydrophone shore-based array sonars, hydrophone towed array sonars and the like. Towed array sonars are generally used for detecting long-distance underwater targets, and the length requirement of the towed array sonars is lengthened along with the reduction of radiation noise of the underwater targets. However, the longer the towed linear array, the more influenced the formation of the towed linear array by ocean currents, mother ship maneuvering, and the like. The distortion seriously reduces the liquid increase of the space processing of the array sonar and also increases the error of the sonar on the target azimuth.
The method for estimating the array shape of the hydrophone array is to obtain two methods, namely, actually measuring the array shape and estimating the array shape. The former is realized by directly carrying out omnibearing discrete measurement, interpolation and storage on an array shape, but the method has high realization difficulty and large storage capacity and is not suitable for sea trial application. In addition, array formation interpolation may introduce errors, and the overall effect is not obvious. The position of the array element is modeled by the model, the array shape estimation is converted into a parameter estimation problem, and the solving precision is high. The method only needs a plurality of auxiliary information sources in different directions, and has the advantages of simple test, small storage amount and remarkable advantages.
The pattern estimation method can be subdivided into a pattern estimation algorithm (narrowly defined pattern estimation) for estimating the rough pattern and a subsequent pattern correction algorithm for improving the accuracy.
The narrow form estimation method mainly includes a method based on direct measurement of a sensor, a method based on matching field processing and a method based on time delay estimation. The accuracy of the estimation based on the sensor direct measurement method is limited by the accuracy and number of sensors and complicates the whole hydrophone array, only suitable as an aid. Before and after the 90 s of the 20 th century, people gradually transformed array shape estimation into a parameter estimation problem by modeling array errors, and obtained the latter two parameter methods. The matching field based approach requires an auxiliary source of known bearing and measurement and assumptions of a large number of ocean acoustic parameters, and the array lineup is estimated by comparing the replica field (the calculated field obtained from the ocean parameters) with the matching field (the sound pressure field measured by the hydrophone array). The method based on time delay estimation is a geometrically intuitive method, and converts the problem of array shape estimation into the problem of time delay estimation of signals received by each array element. The time delay estimation is a basic problem in signal processing, and algorithms with different performances are developed, so that the array shape estimation method has strong adaptability and high accuracy.
Since the 90 s of the 20 th century, various formation correction algorithms have been proposed, and can be generally classified into an active correction class and a self-correction class. The active correction algorithm carries out off-line estimation on the array parameters by arranging auxiliary signal sources with accurately known directions in space, and the calculation amount is small because the signal source directions do not need to be estimated. However, the algorithm also has a high requirement on the accuracy of the azimuth information of the auxiliary signal source, so when the azimuth information of the auxiliary signal source has a deviation, the algorithm brings about an error of the formation estimation.
The self-correcting algorithm generally performs joint estimation on the orientation of a spatial information source and disturbance parameters of an array according to a certain optimization function, and the establishment of the optimization function is usually based on the sensitivity of a feature subspace orientation algorithm to array errors, and further based on the orthogonal relationship between a signal subspace and a noise subspace. The self-correcting algorithm can complete the estimation of the actual direction of the auxiliary information source on line, and eliminates the influence of the algorithm on the accuracy dependence of the direction of the information source, so the correction accuracy is higher than that of the active algorithm. However, for some array structures, such as an equidistant linear array, the unique identification of parameter estimation cannot be guaranteed. More importantly, huge calculation amount is brought by the high-dimensional, multi-mode and nonlinear optimization problem corresponding to parameter joint estimation in the self-correcting algorithm, and the global convergence of parameter estimation cannot be guaranteed.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention discloses a distorted array shape linear spectrum enhancement method based on principal component analysis-density clustering.
The technical scheme is as follows: the invention adopts the following technical scheme:
a distorted lineshape spectrum enhancing method based on principal component analysis-density clustering comprises the following steps:
step 1, simulating underwater sound target radiation noise s (t) and an interference line spectrum signal I (t);
step 2, simulating and observing array signal xi(t)，i＝1,2,...,M，M is the number of array elements in the observation array;
step 3, roughly estimating the target position based on ideal beam forming
Figure BDA0003070795830000021
Figure BDA0003070795830000022
The guiding angle when the energy of the target signal beam is maximum;
step 4, detecting L line spectrum positions with maximum power of the target signal
Figure BDA0003070795830000023
Step 5, the array relative time delay difference vectors of the L strong line spectrums extracted in the step 4 are processed
Figure BDA0003070795830000024
Extracting features by using principal component analysis method to obtain feature vectors z of L line spectrumsl,l＝1,...,L；
Step 6, classifying the L line spectrums by using a DBSCAN density clustering algorithm, wherein the classified cluster set is C ═ C1,c2,....ckIn which c isiRepresenting a line spectrum array time delay characteristic vector contained in the ith class;
step 7, selecting the class with the most line spectra in the classification result, and estimating the array relative time delay difference vector tau without interference;
step 8, obtaining fidelity-enhanced target tracking wave beam based on time delay difference vector
Figure BDA0003070795830000031
Further, the underwater acoustic target radiation noise s (t) in step 1 includes stationary continuum component sc(t) and line spectral components sl(t), simulating an interference line spectrum signal I (t);
the stationary continuum component sc(t) the acquisition step is as follows:
step 1.a1, adopting a three-parameter model method to simulate a stable continuumPower spectrum Gxf (ω)t)：
Figure BDA0003070795830000032
Wherein, ω ism，ωcAnd λ is the three parameters of the three-parameter model, determining the shape of the continuum; omegatIs the frequency, omegamThe sharpness and height of the spectral front, ω, are determined as a sharpness factorcDetermining the position of a spectrum front, wherein lambda is a coefficient for determining the relative proportion of the amplitudes of the high and low frequency ends of the power spectrum, and sigma represents the energy of a stable continuous spectrum signal;
step 1, a2, establishing a p-order AR filter, wherein a Yule-Walker equation is as follows:
Figure BDA0003070795830000033
wherein, a [ l ]]L ∈ {1,2, …, p } and b0For the P order AR filter coefficients, δ k]Is a shock function; r isx[k]Is Gxf (omega)t) Is the autocorrelation function rc(τ) sample values;
step 1, a3, solving the equation of formula (2) by adopting a Levison-Durbin algorithm to obtain a p-order AR filter coefficient; the signal obtained after the Gaussian white noise passes through the AR filter is the steady continuous spectrum component s in the underwater sound target radiation noisec(t)；
The line spectral component sl(t) the acquisition step is as follows:
step 1, b1, adopting K sinusoidal signals
Figure BDA0003070795830000034
To simulate the line spectral components of the target signal, wherein AkIs the amplitude of the sinusoidal signal, fkIs the frequency of the sinusoidal signal, K ═ 1,2]Is the observation time;
step 1.b2, at line spectrum position fkTo calculate the stationary continuum component scEnergy P of (t)Ik；
And (1).b3 according to known signal to interference ratio
Figure BDA0003070795830000035
Calculate the amplitude A of each sinusoidal signalkObtaining the line spectrum component s in the underwater sound target radiation noisel(t)；
The interference line spectrum signal I (t) is obtained by the following steps:
step 1, c1, adopting G sinusoidal signals
Figure BDA0003070795830000036
To simulate the line spectral components, G, of the target signal<K, wherein AgIs the amplitude of the sinusoidal signal, fgFor the frequency of the sinusoidal signal, T ∈ [0, T]Is the observation time;
step 1.c2, at line spectrum position fgTo calculate the stationary continuum component scEnergy P of (t)Ig，g＝1,2,...,G；
Step 1.c3, according to the known signal interference ratio
Figure BDA0003070795830000041
Calculate the amplitude A of each sinusoidal signalgAnd obtaining the line spectrum component I (t) in the underwater sound target radiation noise.
Further, step 2 comprises the following steps:
step 2.1, adopting a towed array as an observation array, setting a first array element in the towed array as a reference array element, wherein the array element data is as follows:
s1(t)＝s(t)+I(t)；
step 2.2, array element data of the rest M-1 array elements in the towed array are as follows:
si(t)＝s[t-TartimeDelay(i)]+I[t-IftimeDelay(i)]，i＝2,…,M；
wherein, tartimedelay (i) is the time delay of the ith array element relative to the reference array element:
Figure BDA0003070795830000042
tardis (i) is the distance between the sound source and the ith array element, and v is the speed of sound propagation in water.
Wherein, iftimedelay (i) is the time delay of the ith array element relative to the reference array element:
Figure BDA0003070795830000043
ifdis (i) is the distance between the interference source and the i-th array element, and v is the propagation speed of sound in water.
Step 2.3, according to the known signal-to-noise ratio
Figure BDA0003070795830000044
Calculating the energy PnAnd generates energy as PnOf white Gaussian noise ni(t) wherein i is 1, …, M, sl(t) is the line spectral component of the underwater acoustic target radiation noise;
step 2.4, observe array signal xi(t) is: x is the number ofi(t)＝si(t)+ni(t)。
Further, step 3 comprises the steps of:
step 3.1, calculating the guiding angle theta of the ideal uniform linear arraymTime delay tau of lower adjacent array elementm：
Figure BDA0003070795830000045
Wherein M is 1, …, M +1 is the total number of the guide angles, d is the distance between adjacent array elements;
step 3.2, carrying out time-delay addition on the array element data in the drag array to obtain a target signal beam energy diagram:
Figure BDA0003070795830000051
step 3.3, finding the position of the maximum value of the beam energy through energy detection, wherein the guide angle is coarse of the target azimuthEstimating
Figure BDA0003070795830000052
Further, step 4 comprises the following steps:
step 4.1, based on the roughly estimated target orientation
Figure BDA0003070795830000053
Calculating a delay estimate for each array element
Figure BDA0003070795830000054
Figure BDA0003070795830000055
Step 4.2, estimating each array element data according to time delay
Figure BDA0003070795830000056
Aligning with a reference array element, and carrying out coherent addition on the aligned array element data to obtain a target tracking beam g (t):
Figure BDA0003070795830000057
step 4.3, Fourier transform is carried out on G (t) to obtain a target signal frequency spectrum G (omega), and meanwhile, a sliding window smoothing technology is utilized to estimate a target signal continuous spectrum Gc(ω) deleting the continuum G in the target signal spectrum G (ω)c(omega) to obtain a line spectrum G of the target signall(omega), estimating L line spectrums with maximum power by using energy detection
Figure BDA0003070795830000058
Wherein L is the number of estimated line spectra;
step 4.4, calculating the frequency point of each array element in the towed array
Figure BDA0003070795830000059
Wherein i is 1, …, M, l is 1, …L; the phase of the ith array element and the ith line spectrum is
Figure BDA00030707958300000510
Wherein Phase 2]To calculate the phase of the signal.
Further, step 5 comprises the steps of:
step 5.1, for L strong line spectrums, the relative delay difference of the ith array element at the position of the ith line spectrum
Figure BDA00030707958300000511
Figure BDA00030707958300000512
Wherein the content of the first and second substances,
Figure BDA00030707958300000513
and
Figure BDA00030707958300000514
respectively the phase positions of the ith and (i-1) th array elements at the ith line spectrum position to obtain L array relative time delay difference vectors of strong line spectrums
Figure BDA00030707958300000515
Figure BDA00030707958300000516
Step 5.2, for the whole time delay matrix
Figure BDA00030707958300000517
Extracting features by using a Principal Component Analysis (PCA) algorithm to obtain a feature matrix Z ═ Z with lower dimensionality1,...,zL]Wherein the time delay characteristic vector of the first strong line spectrum is zl,l＝1,...,L。
Further, step 6 comprises the steps of:
setting a group of neighborhood parameters (epsilon, MinPts), and classifying the array time delay characteristic vectors of L strong line spectrums by using a DBSCAN density clustering algorithm to obtain a classification cluster C ═ { C }1,c2,....ck}。
Further, step 7 comprises the steps of:
step 7.1, since the beam pairs have already been aligned to roughly estimate the target position in step 3, here the class c containing the most line spectra is selectedmaxRemoving line spectrums of other categories;
step 7.2, get cmaxThe average value of the array time delay vector containing the line spectrum is obtained to obtain the array time delay difference vector estimation tau [ tau ] for removing the interference1,...τi,...,τM]Wherein, τiAnd the estimated time delay difference value of the ith array element and the reference array element is shown.
Further, step 8 comprises the steps of:
estimating tau by the array time delay difference vector with interference removed to obtain the target tracking wave beam with enhanced fidelity
Figure BDA0003070795830000061
Figure BDA0003070795830000062
Has the advantages that: the invention discloses a distorted array shape line spectrum enhancing method based on principal component analysis-density clustering, which comprises the steps of firstly, roughly estimating the incoming wave direction of a target signal by using a beam forming method based on an ideal array shape; then, obtaining a tracking wave beam of a target signal by utilizing an incoming wave direction, then carrying out Fourier transform on the tracking wave beam to obtain target frequency spectrum characteristics, and simultaneously carrying out target strong line spectrum detection in a frequency domain; calculating a corresponding line spectrum for each array element data by utilizing Fourier transform based on the detected line spectrum information; extracting the line spectrum phase of each array element, estimating the time delay of the array element relative to the reference array element by calculating the phase difference of the array element relative to the reference array element, performing Principal Component Analysis (PCA) on the time delay vectors of the array elements of different line spectrums as a sample matrix to extract the characteristic vector of the time delay vector of each line spectrum array element, and performing density clustering on the time delay characteristic vector of the array element of the line spectrums by using a DBSCAN algorithm. And selecting the class with the most line spectrums from the classification clusters to obtain an average array delay vector. And carrying out delay alignment on each array element signal by utilizing the estimated delay, thereby realizing the fidelity-enhanced beam forming under the distorted array environment. Compared with the prior art, the method disclosed by the invention has the following advantages: the beam forming method disclosed by the invention directly estimates the line spectrum from the received array element data, estimates the time delay between adjacent array elements based on the estimated line spectrum phase and removes the influence of interference signals, realizes the self-adaptive fidelity-enhanced beam forming technology based on the distorted towed array, and has the advantages of simple and direct application, low economic cost, obvious effect, small calculation amount and higher correction precision.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a frequency spectrum of the sum of a target radiation noise signal and interference line spectral noise in embodiment 1;
FIG. 3 is a graph comparing the position of the array elements of the distorted towed array with the position of the array elements of the ideal case in example 1;
FIG. 4 is a diagram of beam energy based on an ideal formation in example 1;
FIG. 5 is a diagram of strong line spectrum delay and classification in embodiment 1;
FIG. 6 is a comparison graph of the target real time delay, the interference real time delay and the corrected time delay in example 1;
FIG. 7 is a graph comparing the tracking beam spectrum based on the ideal position and the corrected tracking beam spectrum in example 1;
fig. 8 is a graph showing the amplitude error of the tracking beam line spectrum as a function of the signal-to-noise ratio in example 2.
Detailed Description
The invention is further elucidated with reference to the drawings and the detailed description.
A distorted lineshape spectrum enhancement method based on principal component analysis-density clustering is disclosed, as shown in figure 1, and comprises the following steps:
step 1, simulating underwater sound target radiation noise s (t) and an interference line spectrum signal I (t).
The underwater acoustic target radiation noise s (t) includes stationary continuum components sc(t) and line spectral components sl(t), namely:
s(t)＝sc(t)+sl(t)
the stationary continuum component sc(t) the acquisition step is as follows:
step 1.a1, simulating power spectrum Gxf (omega) of stable continuous spectrum by adopting a classical three-parameter model methodt)：
Figure BDA0003070795830000071
Wherein, ω ism，ωcAnd λ is the three parameters of the three-parameter model, determining the shape of the continuum; omegatIs the frequency, omegamThe sharpness and height of the spectral front, ω, are determined as a sharpness factorcDetermining the position of a spectrum front, determining the relative proportion of the amplitudes of high and low frequency ends of a power spectrum by lambda, and expressing the energy of a stable continuous spectrum signal by sigma;
step 1, a2, according to Wiener-Khinchi theorem, the inverse Fourier transform of the formula (1) is the autocorrelation function r of the stationary continuous spectrum signalc(τ), the autocorrelation function is the degree of correlation of the same signal at different times, which can be written as:
rc(τ)＝σexp(-ωm|τ|)[cosωcτ+λsin(ωc|τ|)]
wherein tau is the time difference of two sections of different time data of the same signal;
suppose with FsFor a sampling rate, which is equal-spaced sampling of the time domain signal, the above-mentioned autocorrelation function can be written in a discrete form as,
rc(kTs)＝σexp(-ωm|kTs|)[cosωckTs+λsin(ωc|kTs|)]
wherein the content of the first and second substances,
Figure BDA0003070795830000072
establishing a p-order AR filter according to the formula (1), wherein a Yule-Walker equation is as follows:
Figure BDA0003070795830000073
wherein, a [ l ]]L ∈ {1,2, …, p } and b0For the P order AR filter coefficients, δ k]Is a shock function; r isx[k]Is Gxf (omega)t) Is the autocorrelation function rc(τ) sample values;
step 1, a3, solving the equation of formula (2) by adopting a Levison-Durbin algorithm to obtain a p-order AR filter coefficient; the signal obtained after the Gaussian white noise passes through the AR filter is the steady continuous spectrum component s in the underwater sound target radiation noisec(t)；
The line spectral component sl(t) the acquisition step is as follows:
step 1, b1, adopting K sinusoidal signals
Figure BDA0003070795830000081
To simulate the line spectral components of the target signal, wherein AkIs the amplitude of the sinusoidal signal, fkFor the frequency of the sinusoidal signal, T ∈ [0, T]Is the observation time;
step 1.b2, at line spectrum position fkTo calculate the stationary continuum component scEnergy P of (t)Ik，k＝1,2,...,K；
Step 1.b3, according to the known signal interference ratio
Figure BDA0003070795830000082
Calculate the amplitude A of each sinusoidal signalkObtaining the line spectrum component s in the underwater sound target radiation noisel(t)。
The interference line spectrum signal I (t) is obtained by the following steps:
step 1.c1, using G (G)<K) A sine signal
Figure BDA0003070795830000083
To simulate the line spectral components of the target signal, where AgIs the amplitude of the sinusoidal signal, fgFor the frequency of the sinusoidal signal, T ∈ [0, T]Is the observation time;
step 1.c2, at line spectrum position fgMean of squareStationary continuum component scEnergy P of (t)Ig，g＝1,2,...,G；
Step 1.c3, according to the known signal interference ratio
Figure BDA0003070795830000084
Calculate the amplitude A of each sinusoidal signalgAnd obtaining the line spectrum component I (t) in the underwater sound target radiation noise.
Step 2, simulating and observing array signal xi(t); assuming that the towed array is a distorted array with M array elements, i.e., i ═ 1, 2.. times.m, the observed array signals are obtained through steps 2.1 to 2.4:
step 2.1, adopting a towed array as an observation array, setting a first array element in the towed array as a reference array element, wherein the array element data is as follows:
s1(t)＝s(t)+I(t)；
step 2.2, array element data of the rest M-1 array elements in the towed array are as follows:
si(t)＝s[t-TartimeDelay(i)]+I[t-IftimeDelay(i)]，i＝2,…,M；
wherein, tartimedelay (i) is the time delay of the ith array element relative to the reference array element:
Figure BDA0003070795830000091
tardis (i) is the distance between the sound source and the ith array element, and v is the speed of sound propagation in water.
Wherein, iftimedelay (i) is the time delay of the ith array element relative to the reference array element:
Figure BDA0003070795830000092
ifdis (i) is the distance between the interference source and the i-th array element, and v is the propagation speed of sound in water.
Step 2.3 based on the known signal-to-noise ratio
Figure BDA0003070795830000093
Calculating the energy PnAnd generates energy as PnOf white Gaussian noise ni(t) wherein i is 1, …, M, sl(t) is the line spectral component of the underwater acoustic target radiation noise;
step 2.4, observe array signal xi(t) is: x is the number ofi(t)＝si(t)+ni(t)；
Step 3, roughly estimating the target position based on ideal beam forming
Figure BDA0003070795830000094
Figure BDA0003070795830000095
The method specifically comprises the following steps of:
3.1, firstly, forming a beam based on an ideal array, namely a uniform linear array, because the distortion condition of the array cannot be known in advance; the time difference between the ith array element and the reference array element is tauiAnd (i-1) tau, wherein tau is the time delay difference of adjacent array elements. Considering the flexible structure of the towed hydrophone, assuming that the distance d between adjacent array elements is kept unchanged; at a lead angle thetamTime delay tau of lower adjacent array elementm：
Figure BDA0003070795830000096
Wherein M is 1, …, M +1 is the total number of the guide angles, d is the distance between adjacent array elements;
and 3.2, carrying out time delay addition on the array element data to obtain a target signal beam energy diagram:
Figure BDA0003070795830000097
step 3.3, the guiding angle when the position of the maximum value of the beam energy is found through energy detection is rough estimation of the target azimuth
Figure BDA0003070795830000098
Step 4, detecting L line spectrum positions with maximum power of the target signal
Figure BDA0003070795830000099
The method specifically comprises the following steps:
step 4.1, based on the roughly estimated target orientation
Figure BDA00030707958300000910
Calculating a delay estimate for each array element
Figure BDA00030707958300000911
Figure BDA00030707958300000912
Step 4.2, estimating each array element data according to time delay
Figure BDA0003070795830000101
Aligning with a reference array element, and carrying out coherent addition on the aligned array element data to obtain a target tracking beam g (t):
Figure BDA0003070795830000102
step 4.3, Fourier transform is carried out on G (t) to obtain a target signal frequency spectrum G (omega), and meanwhile, a sliding window smoothing technology is utilized to estimate a target signal continuous spectrum Gc(ω) deleting the continuum G in the target signal spectrum G (ω)c(omega) to obtain a line spectrum G of the target signall(omega), estimating L line spectrums with maximum power by using energy detection
Figure BDA0003070795830000103
Wherein L is the number of estimated line spectra;
step 4.4, calculating the frequency point of each array element in the towed array
Figure BDA0003070795830000104
Wherein i is 1, …, M, L is 1, …, L; the phase of the ith array element and the ith line spectrum is
Figure BDA0003070795830000105
Wherein Phase 2]To calculate the phase of the signal.
Step 5, array relative time delay difference vectors of L strong line spectrums
Figure BDA0003070795830000106
Extracting features by using a principal component analysis method to obtain feature vectors z of L curveslL1., L, the specific steps are as follows:
step 5.1, for the L strong line spectrums extracted in step 4, the relative time delay difference of the ith array element at the position of the ith line spectrum
Figure BDA0003070795830000107
Wherein
Figure BDA0003070795830000108
And
Figure BDA0003070795830000109
respectively the phase positions of the ith and (i-1) th array elements at the ith line spectrum position to obtain L array relative time delay difference vectors of strong line spectrums
Figure BDA00030707958300001010
Figure BDA00030707958300001011
Step 5.2, for the whole time delay matrix
Figure BDA00030707958300001012
Extracting features by using a Principal Component Analysis (PCA) algorithm to obtain a feature matrix Z ═ Z with lower dimensionality1,...,zL]Wherein the time delay characteristic vector of the first strong line spectrum is zl,l＝1,...,L。
Step 6, classifying the L curves by using a DBSCAN density clustering algorithm, and specifically comprising the following steps:
setting a group of neighborhood parameters (epsilon, MinPts), and classifying the array time delay characteristic vectors of L strong line spectrums by using a DBSCAN density clustering algorithm to obtain a classification cluster C ═ { C }1,c2,....ckIn which c isiDenotes the ith
The class contains a line spectrum array delay feature vector.
And 7, selecting the class with the most line spectra in the classification result, and obtaining the array relative time delay difference vector estimation tau without interference, wherein the method specifically comprises the following steps:
step 7.1, since the beam pairs have already been aligned to roughly estimate the target position in step 3, here the class c containing the most line spectra is selectedmaxRemoving line spectrums of other categories;
step 7.2, get cmaxThe average value of the array time delay vector containing the line spectrum is obtained to obtain the array time delay difference vector estimation tau [ tau ] for removing the interference1,...τi,...,τM]In which τ isiAnd the estimated time delay difference value of the ith array element and the reference array element is shown.
Step 8, obtaining the fidelity-enhanced target tracking wave beam based on the estimated time delay
Figure BDA0003070795830000111
The method specifically comprises the following steps:
estimating tau by the array time delay difference vector with interference removed to obtain the target tracking wave beam with enhanced fidelity
Figure BDA0003070795830000112
Figure BDA0003070795830000113
Example 1:
in this embodiment, the sampling frequency FsThe sound propagation velocity v in water was taken to be 1500m/s at 4 kHz. Simulating Gxf power spectrum of steady continuous spectrum of underwater sound target radiation noise by using three-parameter model methodThe three parameters in the real process are set as follows: omegam＝2π×500rad/s，ω c2 pi × 1000rad/s, λ 0, and stationary continuum signal energy σ 1.
The 9 line spectral components of the target radiation noise are simulated:
Figure BDA0003070795830000114
and 3 interfering line spectrum signals:
Figure BDA0003070795830000115
passing the energy P of the stationary continuum at the spectral positionIAnd a known signal-to-interference ratio, SIR, of 30, consisting of
Figure BDA0003070795830000116
Obtaining the amplitude A of each sinusoidal signali. Frequency f of the target sinusoidal signali109Hz,127Hz,145Hz,163Hz,198Hz,232Hz,280Hz,335Hz,385Hz, respectively. Or can be made of
Figure BDA0003070795830000117
Obtaining the amplitude A of each interference sinusoidal signalj. Frequency f of interfering sinusoidal signalsjRespectively 100Hz,180Hz and 260 Hz. The observation time T was 20 s. The stationary continuous spectral components and the line spectral components are added to obtain a target radiation noise signal i (t), and the frequency spectrum of the sum of the target radiation noise signal and the interference signal is shown in fig. 2.
In this embodiment, the number M of the towed arrays is 60, the array element spacing d is 1.5, and the specific position of each array element of the distorted array and the ideal array element position are shown in fig. 3. The target is assumed to be at an angle of 30 ° to the normal direction of the array element, and at a distance of 1000m from the reference array element. Assuming that the distance difference between the sound source and the ith array element is tardis (i), the delay time delay (i) of the ith array element relative to the reference array element can be written as:
Figure BDA0003070795830000118
using the signal shown in FIG. 2 as array element data of the reference array element, for the ithAnd the array element delays the reference array element signal according to a delay formula, so that array data of 60 array elements is obtained. For each array metadata si(t) adding white Gaussian noise with a signal-to-noise ratio of-15 dB to obtain observed data xi(t)。
In this embodiment, beamforming based on an ideal lineup is shown in fig. 4. Finding the position of the maximum value of the beam energy through energy detection to obtain a rough estimation of the target azimuth
Figure BDA0003070795830000121
Fig. 5 shows all strong line spectrum array delay vectors and classification conditions, where a straight line with a star represents a class 1 and a circle represents a class 2, and it can be seen from the figure that the method disclosed by the present invention can more accurately separate a target signal from an interference signal.
Fig. 6 shows the true time delay of the target azimuth and the true time delay of the interference azimuth among the distorted and towed array elements and the time delay of the array elements estimated by using the method. As can be seen from the figure, the method disclosed by the invention can effectively estimate the time delay of the distorted towed linear array elements and reduce the influence of the interference linear spectrum and the low signal-to-noise ratio linear spectrum signals.
Fig. 7 shows a comparison graph of an original data spectrum, a tracking beam spectrum based on an ideal position, and a corrected tracking target spectrum, and it can be seen from the graph that, compared with the conventional beam forming method, the beam spectrum formed by the fidelity-enhanced beam forming method disclosed by the invention has higher gain, and the beam forming effect is enhanced in fidelity.
Example 2:
the present embodiment mainly analyzes and verifies the influence of the signal-to-noise ratio on the fidelity enhanced beamforming disclosed in the present invention. The observation time T was 20 s. The data signal-to-noise ratio is from-20 dB to 0dB, and for each signal-to-noise ratio, let the amplitude relative error of the estimated beamforming be E,
Figure BDA0003070795830000122
Airepresenting the amplitude, PA, of the original data spectrum at the ith line spectral positioniRepresentation estimationAmplitude, L, of the beamformed spectrum at the ith line spectral positionSRepresenting the number of selected line spectra. And taking the relative error of the linear spectrum amplitude of the tracking beam as a performance evaluation index. Fig. 8 shows a schematic diagram of the line spectrum reconstruction error as a function of the signal-to-noise ratio. As can be seen from the figure, as the signal-to-noise ratio increases, the reconstruction error of the distortion correction beam forming becomes smaller; the beam forming method based on the ideal array has no effective array correction capability, and the reconstruction error of the method is slightly changed along with the signal-to-noise ratio along with the improvement of the signal-to-noise ratio.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (9)

1.A distorted lineshape spectrum enhancement method based on principal component analysis-density clustering is characterized by comprising the following steps:
step 1, simulating underwater sound target radiation noise s (t) and an interference line spectrum signal I (t);
step 2, simulating and observing array signal xi(t), i ═ 1, 2.., M is the number of array elements in the observation array;
step 3, roughly estimating the target position based on ideal beam forming
Figure FDA0003070795820000011
Figure FDA0003070795820000012
The guiding angle when the energy of the target signal beam is maximum;
step 4, detecting L line spectrum positions with maximum power of the target signal
Figure FDA0003070795820000013
Step 5, the array relative time delay difference vectors of the L strong line spectrums extracted in the step 4 are processed
Figure FDA0003070795820000014
Extracting features by using principal component analysis method to obtain feature vectors z of L line spectrumsl,l＝1,...,L；
Step 6, classifying the L line spectrums by using a DBSCAN density clustering algorithm, wherein the classified cluster set is C ═ C1,c2,....ckIn which c isiRepresenting a line spectrum array time delay characteristic vector contained in the ith class;
step 7, selecting the class with the most line spectra in the classification result, and estimating the array relative time delay difference vector tau without interference;
step 8, obtaining fidelity-enhanced target tracking wave beam based on time delay difference vector
Figure FDA0003070795820000015
2. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the underwater acoustic target radiation noise s (t) in step 1 comprises stationary continuous spectrum components sc(t) and line spectral components sl(t), simulating an interference line spectrum signal I (t);
the stationary continuum component sc(t) the acquisition step is as follows:
step 1.a1, simulating power spectrum Gxf (omega) of stable continuous spectrum by adopting a three-parameter model methodt)：
Figure FDA0003070795820000016
Wherein, ω ism，ωcAnd λ is the three parameters of the three-parameter model, determining the shape of the continuum; omegatIs the frequency, omegamThe sharpness and height of the spectral front, ω, are determined as a sharpness factorcDetermining the position of a spectrum front, wherein lambda is a coefficient for determining the relative proportion of the amplitudes of the high and low frequency ends of the power spectrum, and sigma represents the energy of a stable continuous spectrum signal;
step 1, a2, establishing a p-order AR filter, wherein a Yule-Walker equation is as follows:
Figure FDA0003070795820000017
wherein, a [ l ]]L ∈ {1,2, …, p } and b0For the P order AR filter coefficients, δ k]Is a shock function; r isx[k]Is Gxf (omega)t) Is the autocorrelation function rc(τ) sample values;
step 1, a3, solving the equation of formula (2) by adopting a Levison-Durbin algorithm to obtain a p-order AR filter coefficient; the signal obtained after the Gaussian white noise passes through the AR filter is the steady continuous spectrum component s in the underwater sound target radiation noisec(t)；
The line spectral component sl(t) the acquisition step is as follows:
step 1, b1, adopting K sinusoidal signals
Figure FDA0003070795820000021
To simulate the line spectral components of the target signal, wherein AkIs the amplitude of the sinusoidal signal, fkIs the frequency of the sinusoidal signal, K ═ 1,2]Is the observation time;
step 1.b2, at line spectrum position fkTo calculate the stationary continuum component scEnergy P of (t)Ik；
Step 1.b3, according to the known signal interference ratio
Figure FDA0003070795820000022
Calculate the amplitude A of each sinusoidal signalkObtaining the line spectrum component s in the underwater sound target radiation noisel(t)；
The interference line spectrum signal I (t) is obtained by the following steps:
step 1, c1, adopting G sinusoidal signals
Figure FDA0003070795820000023
To simulateLine spectral components of the target signal, G<K, wherein AgIs the amplitude of the sinusoidal signal, fgFor the frequency of the sinusoidal signal, T ∈ [0, T]Is the observation time;
step 1.c2, at line spectrum position fgTo calculate the stationary continuum component scEnergy P of (t)Ig，g＝1,2,...,G；
Step 1.c3, according to the known signal interference ratio
Figure FDA0003070795820000024
Calculate the amplitude A of each sinusoidal signalgAnd obtaining the line spectrum component I (t) in the underwater sound target radiation noise.
3. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 2 comprises the following steps:
step 2.1, adopting a towed array as an observation array, setting a first array element in the towed array as a reference array element, wherein the array element data is as follows:
s1(t)＝s(t)+I(t)；
step 2.2, array element data of the rest M-1 array elements in the towed array are as follows:
si(t)＝s[t-TartimeDelay(i)]+I[t-IftimeDelay(i)]，i＝2,…,M；
wherein, tartimedelay (i) is the time delay of the ith array element relative to the reference array element:
Figure FDA0003070795820000025
tardis (i) is the distance between the sound source and the ith array element, and v is the speed of sound propagation in water.
Wherein, iftimedelay (i) is the time delay of the ith array element relative to the reference array element:
Figure FDA0003070795820000031
ifdis (i) is the distance between the interference source and the i-th array element, and v is the propagation speed of sound in water.
Step 2.3, according to the known signal-to-noise ratio
Figure FDA0003070795820000032
Calculating the energy PnAnd generates energy as PnOf white Gaussian noise ni(t) wherein i is 1, …, M, sl(t) is the line spectral component of the underwater acoustic target radiation noise;
step 2.4, observe array signal xi(t) is: x is the number ofi(t)＝si(t)+ni(t)。
4. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 3 comprises the following steps:
step 3.1, calculating the guiding angle theta of the ideal uniform linear arraymTime delay tau of lower adjacent array elementm：
Figure FDA0003070795820000033
Wherein M is 1, …, M +1 is the total number of the guide angles, d is the distance between adjacent array elements;
step 3.2, carrying out time-delay addition on the array element data in the drag array to obtain a target signal beam energy diagram:
Figure FDA0003070795820000034
step 3.3, the guiding angle when the position of the maximum value of the beam energy is found through energy detection is rough estimation of the target azimuth
Figure FDA0003070795820000035
5. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 4 comprises the following steps:
step 4.1, based on the roughly estimated target orientation
Figure FDA0003070795820000036
Calculating a delay estimate for each array element
Figure FDA0003070795820000037
Figure FDA0003070795820000038
Step 4.2, estimating each array element data according to time delay
Figure FDA0003070795820000039
Aligning with a reference array element, and carrying out coherent addition on the aligned array element data to obtain a target tracking beam g (t):
Figure FDA00030707958200000310
step 4.3, Fourier transform is carried out on G (t) to obtain a target signal frequency spectrum G (omega), and meanwhile, a sliding window smoothing technology is utilized to estimate a target signal continuous spectrum Gc(ω) deleting the continuum G in the target signal spectrum G (ω)c(omega) to obtain a line spectrum G of the target signall(omega), estimating L line spectrums with maximum power by using energy detection
Figure FDA00030707958200000311
Wherein L is the number of estimated line spectra;
step 4.4, calculating the frequency point of each array element in the towed array
Figure FDA0003070795820000041
Wherein i is 1, …, M, L is 1, …, L; the phase of the ith array element and the ith line spectrum is
Figure FDA0003070795820000042
Wherein Phase 2]To calculate the phase of the signal.
6. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 5 comprises the following steps:
step 5.1, for L strong line spectrums, the relative delay difference of the ith array element at the position of the ith line spectrum
Figure FDA0003070795820000043
Figure FDA0003070795820000044
Wherein the content of the first and second substances,
Figure FDA0003070795820000045
and
Figure FDA0003070795820000046
respectively the phase positions of the ith and (i-1) th array elements at the ith line spectrum position to obtain L array relative time delay difference vectors of strong line spectrums
Figure FDA0003070795820000047
Figure FDA0003070795820000048
Step 5.2, for the whole time delay matrix
Figure FDA0003070795820000049
Extracting features by using a Principal Component Analysis (PCA) algorithm to obtain a feature matrix Z ═ Z with lower dimensionality1,...,zL]Wherein the time delay characteristic vector of the first strong line spectrum is zl,l＝1,...,L。
7. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 6 comprises the following steps:
setting a group of neighborhood parameters (epsilon, MinPts), and classifying the array time delay characteristic vectors of L strong line spectrums by using a DBSCAN density clustering algorithm to obtain a classification cluster C ═ { C }1,c2,....ck}。
8. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 7 comprises the following steps:
step 7.1, since the beam pairs have already been aligned to roughly estimate the target position in step 3, here the class c containing the most line spectra is selectedmaxRemoving line spectrums of other categories;
step 7.2, get cmaxThe average value of the array time delay vector containing the line spectrum is obtained to obtain the array time delay difference vector estimation tau [ tau ] for removing the interference1,...τi,...,τM]Wherein, τiAnd the estimated time delay difference value of the ith array element and the reference array element is shown.
9. The distorted lineshape spectrum enhancement method based on principal component analysis-density clustering as claimed in claim 1, wherein the step 8 comprises the following steps:
estimating tau by the array time delay difference vector with interference removed to obtain the target tracking wave beam with enhanced fidelity
Figure FDA00030707958200000410
Figure FDA00030707958200000411
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