CN113075645B - Distorted matrix line spectrum enhancement method based on principal component analysis-density clustering - Google Patents
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Abstract
The invention discloses a distorted matrix line spectrum enhancement 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 the target bearing based on ideal beamforming; (4) Detecting and selecting L line spectrum positions with maximum power of a target signal; (5) Extracting features from the array relative time delay difference vectors of the L strong line spectrums by using a principal component analysis method to obtain feature vectors of L curves; (6) Classifying the L curves by using a DBSCAN density clustering algorithm; (7) Selecting more types of spectrums in the classification result, and calculating the relative delay difference vector of the average array; (8) A fidelity-enhanced target tracking beam is acquired based on the estimated delay. A distorted array line spectrum enhancement method based on principal component analysis-density clustering corrects the influence of distortion of a towed line array on beam formation through time delay estimation, and obtains a target radiation noise tracking beam with enhanced fidelity.
Description
Technical Field
The invention belongs to the field of sonar signal processing, and particularly relates to a distorted matrix line spectrum enhancement method based on principal component analysis-density clustering.
Background
The sonar systems applied at present generally comprise hydrophone shore array sonar, hydrophone towed array sonar and the like. Towed-array sonar is typically used to detect long-range underwater objects, with the length requirement being increased as the radiation noise of the underwater object is reduced. However, the longer the towing line array, the greater the influence of factors such as ocean currents, mother ship maneuvers, etc. on the array shape. This distortion severely reduces the spatial processing gain of the array sonar, and also increases the error of the sonar to the target orientation.
Two methods are proposed to obtain hydrophone array matrix estimates: firstly, actually measuring array shape, and secondly, estimating array shape. The method is realized by directly carrying out omnibearing discrete measurement, interpolation and storage on the array shape, but the method has the defects of large realization difficulty and large storage capacity and is not suitable for sea test application. In addition, array form interpolation introduces errors, and the overall effect is not obvious. The latter models the array element position, converts the array shape estimation into a parameter estimation problem, and has high solving precision. The method only needs a few auxiliary information sources in different directions, and has the advantages of simple test, small storage capacity and remarkable advantages.
The matrix estimation method can be subdivided into a matrix estimation algorithm (a narrow-sense matrix estimation) that estimates a general matrix and a subsequent matrix correction algorithm for improving accuracy.
The narrow-definition array shape estimation method mainly comprises a method based on direct measurement of a sensor, a method for matching field processing and a method based on time delay estimation. The estimation accuracy based on the sensor direct measurement method is limited by the accuracy and the number of the sensors, and can complicate the whole hydrophone array, and is only suitable as an auxiliary means. Before and after the 90 th century, people gradually convert array shape estimation into a parameter estimation problem by modeling an array error, and the two latter parameter methods are obtained. The matched field based method requires measurement and assumption of auxiliary sources with known orientations and a large number of marine acoustic parameters, and the array matrix shape is estimated by comparing the copy field (calculated field obtained by marine parameters) with the matched field (acoustic pressure field measured by hydrophone array). The method based on time delay estimation is a geometrically intuitive method, which converts the problem of array shape estimation into the problem of time delay estimation of signals received by each array element. Delay estimation is a fundamental problem in signal processing, and algorithms with different performances are developed, so that the matrix estimation method has strong adaptability and high precision.
Since the 90 s of the 20 th century, various matrix 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 through auxiliary information sources with accurately known space setting azimuth, and the operation amount is small because the signal source azimuth is not required to be estimated. However, algorithms also have high requirements on the accuracy of the azimuth information of the auxiliary signal source, so that when the azimuth information of the auxiliary signal source is deviated, the algorithms bring about errors in matrix estimation.
The self-correction algorithm generally performs joint estimation on the azimuth of the spatial information source and the disturbance parameters of the array according to a certain optimization function, and the establishment of the optimization function is generally based on the sensitivity of a characteristic subspace orientation algorithm to the array error, and further is based on the orthogonal relation between the signal subspace and the noise subspace. The self-correction algorithm can complete the estimation of the actual position of the auxiliary information source on line, so that the influence of the algorithm on the accuracy of the position of the information source is eliminated, and the correction accuracy is higher than that of the active algorithm. However, for some array structures, such as equidistant linear arrays, the unique identification of parameter estimates is often not guaranteed. More importantly, the problem of high-dimensional, multi-mode and nonlinear optimization corresponding to the parameter joint estimation in the self-correction algorithm brings huge operand, and the global convergence of the parameter estimation is often not guaranteed.
Disclosure of Invention
The invention aims to: aiming at the problems in the prior art, the invention discloses a distorted linewidth 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 matrix line spectrum enhancement method based on principal component analysis-density clustering comprises the following steps:
step 1, simulating underwater sound target radiation noise s (t) and interference line spectrum signals I (t);
step 2, simulating and observing the array signal x i (t), i=1, 2,..m, M is the number of array elements in the observation array;
step 3, roughly estimating the target azimuth based on ideal beam forming Is the lead angle when the energy of the target signal beam is maximum;
step 4, detecting L maximum power of the target signalLine spectrum position
Step 5, the array relative time delay difference vector of the L strong line spectrums extracted in the step 4Extracting features by using a principal component analysis method to obtain feature vectors z of L line spectrums l ，l＝1，...，L；
Step 6, classifying the L line spectrums by using a DBSCAN density clustering algorithm, wherein a classification cluster set is C= { C 1 ，c 2 ，....c k And (c), where c i Representing a line spectrum array time delay characteristic vector contained in the i-th class;
step 7, selecting the class with the largest line spectrum in the classification result, and estimating the array relative time delay difference vector tau with interference removed;
step 8, obtaining a target tracking beam with fidelity enhancement based on the time delay difference vector
Further, the hydroacoustic target radiation noise s (t) in step 1 includes a stationary continuous spectral component s c (t) and line spectral component s l (t) also requires the simulation of the interference line spectrum signal I (t);
the stationary continuous spectrum component s c The acquisition step of (t) is as follows:
step 1.a1, adopting a three-parameter model method to simulate a power spectrum Gxf (omega) of a stable continuous spectrum t )：
Wherein omega m ，ω c And lambda is three parameters of a three-parameter model, which determines the shape of the continuous spectrum; omega t Is frequency omega m Determining the sharpness and height of the spectral front, ω, as a sharpness factor c Determining the position of the spectral front lambdaTo determine the coefficient of the relative proportion of the amplitude of the high and low frequency ends of the power spectrum, sigma represents the energy of the stationary continuous spectrum signal;
step 1.a2, a p-order AR filter is established, wherein a Yule-Walker equation is as follows:
wherein a [ l ]]L.epsilon. {1,2, …, p } and b 0 For the p-order AR filter coefficients, delta [ k ]]Is an impact function; r is (r) x [k]Gxf (omega) t ) Is the autocorrelation function r of (2) c (τ) sample value;
step 1.a3, solving an equation (2) by adopting a Levison-Durbin algorithm to obtain a p-order AR filter coefficient; the signal obtained after Gaussian white noise passes through the AR filter is the stable continuous spectrum component s in underwater sound target radiation noise c (t)；
The line spectral component s l The acquisition step of (t) is as follows:
step 1.B1, using K sinusoidal signalsTo simulate line spectral components of a target signal, wherein A k Is the amplitude of the sine signal, f k For the frequency of a sinusoidal signal, k=1, 2..k, t e [0, t]Is the observation time;
step 1.b2, at the spectral position f k Computing stationary continuous spectral components s c Energy P of (t) Ik ；
Step 1.B3, according to the known signal-to-interference ratioCalculate the amplitude A of each sinusoidal signal k Obtaining the line spectrum component s in the underwater sound target radiation noise l (t)；
The acquisition steps of the interference line spectrum signal I (t) are as follows:
step 1.C1, using G sinusoidal signalsTo simulate the line spectrum component of the target signal, G < K, wherein A g Is the amplitude of the sine signal, f g Is the frequency of the sine signal, t is 0, T]Is the observation time;
step 1.c2, at the spectral position f g Computing stationary continuous spectral components s c Energy P of (t) lg ，g＝1，2，...，G；
Step 1.C3, according to the known signal-to-interference ratioCalculate the amplitude A of each sinusoidal signal g Obtaining the interference line spectrum signal I (t).
Further, step 2 includes the steps of:
step 2.1, the observation array adopts a towing array, a first array element in the towing array is set as a reference array element, and the array element data are as follows:
s 1 (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:
s i (t)＝s[t-TartimeDelay(i)]+I[t-IftimeDelay(i)]，i＝2，…，M；
wherein TartimeDelay (i) is the delay of the ith element relative to the reference element:
tarDis (i) is the distance between the sound source and the ith element, and v is the propagation velocity of sound in water.
Wherein IftimeDelay (i) is the delay of the ith element relative to the reference element:
IfDis (i) is the distance between the interference source and the ith element, and v is the propagation velocity of sound in water.
Step 2.3, according to the known signal-to-noise ratioCalculating the energy Pn and generating the energy P n M-way gaussian white noise n i (t), wherein i=1, …, M, s l (t) is the acoustic target radiation noise line spectral component;
step 2.4, observing the array signal x i (t) is: x is x i (t)＝s i (t)+ni(t)。
Further, step 3 includes the steps of:
step 3.1, calculating the lead angle theta of the ideal uniform linear array m Delay tau of next adjacent array element m ：
Wherein m=1, …, m+1 is the total guide angle number, and d is the distance between adjacent array elements;
step 3.2, carrying out delay addition on the array element data in the towing array to obtain a target signal beam energy diagram:
step 3.3, rough estimation of the guiding angle as the target azimuth when the beam energy maximum position is found by energy detection
Further, step 4 includes the steps of:
step 4.1, according to the roughly estimated target azimuthCalculating delay estimate of each array element>
Step 4.2, estimating each array element data according to time delayAligning with the reference array element, and coherently adding aligned array element data to obtain a target tracking beam g (t):
step 4.3, performing Fourier transform on G (t) to obtain a target signal spectrum G (omega), and simultaneously estimating a target signal continuous spectrum G by utilizing a sliding window smoothing technology c (omega) deleting the continuum G in the target signal spectrum G (omega) c (omega) influence, obtaining the line spectrum G of the target signal l (omega) estimating L maximum power line spectra using energy detectionWherein L is the number of estimated line spectrums;
step 4.4, calculating the frequency point of each array element in the towed arrayWhere i=1, …, M, l=1, …, L; the phase of the ith array element and the ith line spectrum is +.>Wherein Phase []To calculate the signal phase.
Further, step 5 includes the steps of:
step 5.1, for L strong line spectrums, the i-th array element at the position of the first line spectrum has a relative time delay difference Wherein (1)>And->The phases of the ith and the ith-1 array elements at the ith line spectrum position are respectively used for obtaining array relative time delay difference vectors of L strong line spectrums>
Step 5.2 for the entire delay matrixExtracting features by using a Principal Component Analysis (PCA) algorithm to obtain a feature matrix Z= [ Z ] with lower dimension 1 ，...，z L ]Wherein the time delay characteristic vector of the first strong line spectrum is z l ，l＝1，...，L。
Further, step 6 includes the steps of:
setting a group of neighborhood parameters (epsilon, minPts), and classifying the array delay feature vectors of the L strong line spectrums by using a DBSCAN density clustering algorithm to obtain a classification cluster C= { C 1 ，c 2 ，....c k }。
Further, step 7 includes the steps of:
step 7.1, since the beam pair has been roughly estimated to the target bearing in step 3, a class c is selected which contains the most line spectrum max Removing line spectrums of other categories;
step 7.2, taking c max The array delay vector average value containing the line spectrum is used for obtaining the array delay difference vector estimation tau= [ tau ] without interference 1 ，...τ i ，...，τ M ]Wherein τ i And the delay difference estimated value of the ith array element and the reference array element is represented.
Further, step 8 includes the steps of:
estimating tau by using array delay difference vector with interference removed to obtain target tracking wave beam with enhanced fidelity
The beneficial effects are that: the invention discloses a distorted matrix line spectrum enhancement 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 matrix; then, a tracking beam of a target signal is obtained by utilizing the incoming wave direction, then, fourier transformation is carried out on the tracking beam to obtain target spectrum characteristics, and meanwhile, target strong line spectrum detection is carried out in a frequency domain; based on the detected line spectrum information, calculating a corresponding line spectrum for each array element data by utilizing Fourier transform; the line spectrum phase of each array element is extracted, the time delay of the array element relative to the reference array element is estimated by calculating the phase difference of the array element relative to the reference array element, the array element time delay vectors of different line spectrums are used as a sample matrix for main component analysis (PCA) to extract characteristic vectors for characteristic the array element time delay vectors of each line spectrum, and the array element time delay characteristic vectors of the line spectrums are clustered by using a DBSCAN algorithm density. And selecting the class with the largest line spectrum from the classified clusters, and solving an average array delay vector. And (3) carrying out delay alignment on each array element signal by using the estimated delay, thereby realizing the beam forming with fidelity enhancement in a 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, removes the influence of interference signals, realizes the self-adaptive distortion drag array-based fidelity enhancement beam forming technology, and has the advantages of simple and direct application, low economic cost, obvious effect, small operation amount and higher correction precision.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a spectrum of the sum of the target radiated noise signal and the interference line spectral noise in embodiment 1;
FIG. 3 is a diagram showing the comparison between the positions of the array elements of the distortion towed array in example 1 and the positions of the array elements in the ideal case;
fig. 4 is a beam energy diagram based on an ideal array shape in embodiment 1;
FIG. 5 is a graph showing the strong line spectrum time delay and classification in example 1;
FIG. 6 is a graph showing the comparison of the target real time delay, the disturbance real time delay and the corrected time delay in example 1;
fig. 7 is a graph showing a comparison of the tracking beam spectrum based on the ideal position and the corrected tracking beam spectrum in embodiment 1;
fig. 8 is a graph showing the variation of the spectral amplitude error of the tracking beam according to the signal-to-noise ratio in embodiment 2.
Detailed Description
The invention is further elucidated below in connection with the drawings and the detailed description.
A distorted matrix line spectrum enhancement method based on principal component analysis-density clustering, as shown in figure 1, comprises the following steps:
step 1, simulating underwater sound target radiation noise s (t) and interference line spectrum signals I (t).
The hydroacoustic target radiation noise s (t) includes a stationary continuous spectral component sc (t) and a line spectral component s l (t), namely:
s(t)＝s c (t)+s l (t)
the stationary continuous spectrum component s c The acquisition step of (t) is as follows:
step 1.a1, a classical three-parameter model method is adopted to simulate the power spectrum Gxf (omega) of a stable continuous spectrum t )：
Wherein omega m ，ω c And lambda is three parameters of a three-parameter model, which determines the shape of the continuous spectrum; omega t Is frequency omega m Determining the sharpness and height of the spectral front, ω, as a sharpness factor c Determining the position of a spectrum front, wherein lambda determines the relative proportion of the amplitude of a high-frequency end and a low-frequency end of a power spectrum, and sigma represents the energy of a stable continuous spectrum signal;
step 1.a2, according to the Wiener-Khinchin theorem, the inverse Fourier transform of formula (1) is the autocorrelation function r of a stationary continuous spectrum signal c The autocorrelation function is the correlation degree of the same signal at different times, and can be written as:
r c (τ)＝σexp(-ω m |τ|)[cosω c τ+λsin(ω c |τ|)]
wherein τ is the time difference between two different time data of the same signal;
let F be s The autocorrelation function may be written in discrete form for sampling the time signal at equal intervals at the sampling rate,
r c (kT s )＝σ exp(-ω m |kT s |)[cosω c kT s +λsin(ω c |kT s |)]
wherein,a p-order AR filter is established according to the formula (1), wherein the Yule-Walker equation is:
wherein a [ l ]]L.epsilon. {1,2, …, p } and b 0 For the p-order AR filter coefficients, delta [ k ]]Is an impact function; r is (r) x [k]Gxf (omega) t ) Is the autocorrelation function r of (2) c (τ) sample value;
step 1.a3, solving an equation (2) by adopting a Levison-Durbin algorithm to obtain a p-order AR filter coefficient; white Gaussian noise is obtained after passing through the AR filterThe signal obtained is the stable continuous spectrum component s in the underwater sound target radiation noise c (t)；
The line spectral component s l The acquisition step of (t) is as follows:
step 1.B1, using K sinusoidal signalsTo simulate line spectral components of a target signal, wherein A k Is the amplitude of the sine signal, f k Is the frequency of the sine signal, t is 0, T]Is the observation time;
step 1.b2, at the spectral position f k Computing stationary continuous spectral components s c Energy P of (t) Ik ，k＝1，2，...，K；
Step 1.B3, according to the known signal-to-interference ratioCalculate the amplitude A of each sinusoidal signal k Obtaining the line spectrum component s in the underwater sound target radiation noise l (t)。
The acquisition steps of the interference line spectrum signal I (t) are as follows:
step 1.C1, using G (G < K) sinusoidal signalsTo simulate line spectral components of a target signal, wherein A g Is the amplitude of the sine signal, f g Is the frequency of the sine signal, t is 0, T]Is the observation time;
step 1.c2, at the spectral position f g Computing stationary continuous spectral components s c Energy P of (t) Ig ，g＝1，2，...，G；
Step 1.C3, according to the known signal-to-interference ratioCalculate the amplitude A of each sinusoidal signal g Obtaining the interference line spectrum signal I (t).
Step 2, simulating and observing the array signal x i (t)；Assume that the towed array is a distorted array with M array elements, i.e., i=1, 2, m. observed array signal obtained by steps 2.1 to 2.4:
step 2.1, the observation array adopts a towing array, a first array element in the towing array is set as a reference array element, and the array element data are as follows:
s 1 (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:
s i (t)＝s[t-TartimeDelay(i)]+I[t-IftimeDelay(i)]，i＝2，…，M；
wherein TartimeDelay (i) is the delay of the ith element relative to the reference element:
tarDis (i) is the distance between the sound source and the ith element, and v is the propagation velocity of sound in water.
Wherein IftimeDelay (i) is the delay of the ith element relative to the reference element:
IfDis (i) is the distance between the interference source and the ith element, and v is the propagation velocity of sound in water.
Step 2.3 according to the known signal to noise ratioCalculating energy P n And generate energy P n M-way gaussian white noise n i (t), wherein i=1, …, M, s l (t) is the acoustic target radiation noise line spectral component;
step 2.4, observing the array signal x i (t) is: x is x i (t)＝s i (t)+n i (t)；
Step 3, roughly estimating the target azimuth based on ideal beam forming The method is used for guiding the target signal beam to have the maximum energy, and specifically comprises the following steps:
step 3.1, because the distortion condition of the array shape cannot be known in advance, firstly, carrying out beam forming based on an ideal array shape, namely a uniform linear array; the time difference between the ith array element and the reference array element is tau i = (i-1) τ, where τ is the adjacent element delay difference. Considering the flexible structure of the towed hydrophone, the distance d between adjacent array elements is assumed to be unchanged; at a guiding angle theta m Delay tau of next adjacent array element m ：
Wherein m=1, …, m+1 is the total guide angle number, and d is the distance between adjacent array elements;
step 3.2, carrying out delay addition on the array element data to obtain a target signal beam energy diagram:
step 3.3, rough estimation of the guiding angle as the target azimuth when the beam energy maximum position is found by energy detection
Step 4, detecting L line spectrum positions with maximum power of the target signalThe method specifically comprises the following steps:
step 4.1, according to the roughly estimated target azimuthCalculating delay estimate of each array element>
Step 4.2, estimating each array element data according to time delayAligning with the reference array element, and coherently adding aligned array element data to obtain a target tracking beam g (t):
step 4.3, performing Fourier transform on G (t) to obtain a target signal spectrum G (omega), and simultaneously estimating a target signal continuous spectrum G by utilizing a sliding window smoothing technology c (omega) deleting the continuum G in the target signal spectrum G (omega) c (omega) influence, obtaining the line spectrum G of the target signal l (omega) estimating L maximum power line spectra using energy detectionWherein L is the number of estimated line spectra;
step 4.4, calculating the frequency point of each array element in the towed arrayWhere i=1, …, M, l=1, …, L; the phase of the ith array element, the 1 st line spectrum is +.>Wherein Phase []To calculate the signal phase.
Step 5, array relative time delay difference vectors of L strong line spectrumsExtracting features by using a principal component analysis method to obtain feature vectors z of L curves l L=1,.. the method comprises the following specific steps:
step 5.1, for the L strong line spectrums extracted in step 4, the i-th array element relative time delay difference at the position of the i-th line spectrumWherein->And->The phases of the ith and the ith-1 array elements at the ith line spectrum position are respectively used for obtaining array relative time delay difference vectors of L strong line spectrums>
Step 5.2 for the entire delay matrixExtracting features by using a Principal Component Analysis (PCA) algorithm to obtain a feature matrix Z= [ Z ] with lower dimension 1 ，...，z L ]Wherein the time delay characteristic vector of the first strong line spectrum is z l ，l＝1，...，L。
Step 6, classifying the L curves by using a DBSCAN density clustering algorithm, wherein the method specifically comprises the following steps:
setting a group of neighborhood parameters (epsilon, minPts), and classifying the array delay feature vectors of the L strong line spectrums by using a DBSCAN density clustering algorithm to obtain a classification cluster C= { C 1 ，c 2 ，....c k }, wherein c i Representing the line spectrum array time delay characteristic vector contained in the i type.
Step 7, selecting the class with the largest line spectrum in the classification result, and obtaining the array relative time delay difference vector estimation tau for removing the interference, which concretely comprises the following steps:
step 7.1, since the beam pair has been roughly estimated to the target bearing in step 3, a class c is selected which contains the most line spectrum max Removing line spectrums of other categories;
step 7.2, taking c max The array delay vector average value containing the line spectrum is used for obtaining the array delay difference vector estimation tau= [ tau ] without interference 1 ，...τ i ，...，τ M ]Wherein τ i And the delay difference estimated value of the ith array element and the reference array element is represented.
Step 8, obtaining a target tracking beam with fidelity enhancement based on estimated time delayThe method specifically comprises the following steps:
estimating tau by using array delay difference vector with interference removed to obtain target tracking wave beam with enhanced fidelity
Example 1:
in this embodiment, the sampling frequency fs=4khz and the propagation velocity v of sound in water was taken as 1500m/s. The power spectrum Gxf of the stable continuous spectrum of the underwater sound target radiation noise is simulated by using a three-parameter model method, and three parameters are set as follows in the simulation process: omega m ＝2π×500rad/s，ω c =2pi×1000rad/s, λ=0, and stationary continuous spectrum signal energy σ=1.
9 line spectral components of the simulated target radiation noise:3 interference line spectrum signals: />By the energy PI of the stationary continuous spectrum at the line spectrum position and the known signal-to-interference ratio sir=30, by +.>Obtaining amplitude A of each sinusoidal signal i . Frequency f of target sinusoidal signal i 109Hz,127Hz,145Hz,163Hz,198Hz,232Hz,280Hz,335Hz,385Hz, respectively. Can also be made of->Obtaining amplitude A of each interference sinusoidal signal j . Frequency f of interfering sinusoidal signals j 100Hz,180Hz,260Hz, respectively. The observation time was t=20s. The stationary continuous spectral components and the line spectral components are added up to obtain the target radiated noise signal I (t), the spectrum of the sum of the target radiated noise signal and the interference signal is shown in fig. 2.
In this embodiment, the number of towed arrays m=60, the array element spacing d=1.5, and the specific positions and ideal array element positions of each array element of the distorted array are shown in fig. 3. The included angle between the target and the normal direction of the array element is assumed to be 30 degrees, and the distance between the target and the reference array element is assumed to be 1000m. Assuming that the distance difference between the sound source and the ith array element is tarDis (i), the time delay (i) of the ith array element relative to the reference array element can be written as:
taking the signal shown in fig. 2 as the array element data of the reference array element, and for the ith array element, carrying out time delay on the reference array element signal according to a time delay formula, thereby obtaining the array data of 60 array elements. For each array element data s i (t) adding Gaussian white noise with a signal-to-noise ratio of-15 dB to obtain observed data x i (t)。
In this embodiment, the beamforming based on the ideal lineup is shown in fig. 4. Finding the beam energy maximum position by energy detection to obtain a rough estimate of the target bearing
Fig. 5 shows delay vectors and classification conditions of all strong line spectrum arrays, wherein a straight line with a star represents a category 1 and a circle represents a category 2, and as can be seen from the figure, the method disclosed by the invention can separate a target signal from an interference signal more accurately.
Fig. 6 shows the true time delay of the target azimuth and the true time delay of the interference azimuth among the distorted towed array elements and the estimated time delay of the array elements by using the method. From the figure, the method disclosed by the invention can effectively estimate the time delay of the distorted trailing line array element and reduce the influence of interference line spectrum and low signal-to-noise ratio line spectrum signals.
Fig. 7 shows a comparison diagram 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 diagram that, compared with a traditional beam forming method, the beam forming method of the present invention has higher beam spectrum gain, and the beam forming effect is enhanced in fidelity.
Example 2:
the present embodiment mainly analyzes and verifies the influence of signal-to-noise ratio on the fidelity enhancement beam forming disclosed in the present invention. The observation time was t=20s. The data signal-to-noise ratio is from-20 dB to 0dB, for each signal-to-noise ratio, the estimated beamforming amplitude relative error is set to E,A i representing the amplitude of the original data spectrum at the ith line spectrum position, PA i Representing the amplitude of the estimated beamformed spectrum at the ith line spectral position, L s Representing the number of line spectrums selected. The relative error of the tracking beam line spectrum amplitude is used as a performance evaluation index. A schematic diagram of the line spectrum reconstruction error as a function of signal to noise ratio is given in fig. 8. As can be seen from the figure, as the signal-to-noise ratio increases, the reconstruction error of the distortion correction beamforming becomes smaller gradually; while the ideal array-based beam forming method has no effective array correction capability, and follows the signal to noiseThe reconstruction error varies little with the signal to noise ratio.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (9)
1. The distorted matrix line spectrum enhancement method based on principal component analysis-density clustering is characterized by comprising the following steps of:
step 1, simulating underwater sound target radiation noise s (t) and interference line spectrum signals I (t);
step 2, simulating and observing the array signal x i (t), i=1, 2,..m, M is the number of array elements in the observation array;
step 3, roughly estimating the target azimuth based on ideal beam forming Is the lead 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
Step 5, the array relative time delay difference vector of the L strong line spectrums extracted in the step 4Extracting features by using a principal component analysis method to obtain feature vectors z of L line spectrums l ,l＝1,...,L；
Step 6, classifying the L line spectrums by using a DBSCAN density clustering algorithm, wherein a classification cluster set is C= { C 1 ,c 2 ,....c k And (c), where c i Representing the inclusion of class iA line spectrum array delay feature vector of (a);
step 7, selecting the class with the largest line spectrum in the classification result, and estimating the array relative time delay difference vector tau with interference removed;
step 8, obtaining a target tracking beam with fidelity enhancement based on the time delay difference vector
2. The method for enhancing a distorted matrix line spectrum based on principal component analysis-density clustering according to claim 1, wherein the hydroacoustic target radiation noise s (t) in step 1 includes a stationary continuous spectrum component s c (t) and line spectral component s l (t) also requires the simulation of the interference line spectrum signal I (t);
the stationary continuous spectrum component s c The acquisition step of (t) is as follows:
step 1.a1, adopting a three-parameter model method to simulate a power spectrum Gxf (omega) of a stable continuous spectrum t )：
Wherein omega m ，ω c And lambda is three parameters of a three-parameter model, which determines the shape of the continuous spectrum; omega t Is frequency omega m Determining the sharpness and height of the spectral front, ω, as a sharpness factor c Determining the position of a spectrum front, wherein lambda is a coefficient for determining the relative proportion of the amplitude of a high-frequency end and a low-frequency end of a power spectrum, and sigma represents the energy of a stable continuous spectrum signal;
step 1.a2, a p-order AR filter is established, wherein a Yule-Walker equation is as follows:
wherein a [ l ]]L.epsilon. {1,2, …, p } and b 0 For the p-order AR filter coefficients, delta [ k ]]Is an impact function; r is (r) x [k]Gxf (omega) t ) Is the autocorrelation function r of (2) c (τ) sample value;
step 1.a3, solving an equation (2) by adopting a Levison-Durbin algorithm to obtain a p-order AR filter coefficient; the signal obtained after Gaussian white noise passes through the AR filter is the stable continuous spectrum component s in underwater sound target radiation noise c (t)；
The line spectral component s l The acquisition step of (t) is as follows:
step 1.B1, using K sinusoidal signalsTo simulate line spectral components of a target signal, wherein A k Is the amplitude of the sine signal, f k For the frequency of a sinusoidal signal, k=1, 2..k, t e [0, t]Is the observation time;
step 1.b2, at the spectral position f k Computing stationary continuous spectral components s c Energy P of (t) Ik ；
Step 1.B3, according to the known signal-to-interference ratioCalculate the amplitude A of each sinusoidal signal k Obtaining the line spectrum component s in the underwater sound target radiation noise l (t)；
The acquisition steps of the interference line spectrum signal I (t) are as follows:
step 1.C1, using G sinusoidal signalsTo simulate line spectral components of a target signal, G<K, wherein A g Is the amplitude of the sine signal, f g Is the frequency of the sine signal, t is 0, T]Is the observation time;
step 1.c2, at the spectral position f g Computing stationary continuous spectral components s c Energy P of (t) Ig ，g＝1,2,...,G；
Step 1.C3, according to the known signal-to-interference ratioCalculate the amplitude A of each sinusoidal signal g Obtaining the interference line spectrum signal I (t).
3. The method for enhancing a distorted matrix line spectrum based on principal component analysis-density clustering according to claim 1, wherein the step 2 comprises the steps of:
step 2.1, the observation array adopts a towing array, a first array element in the towing array is set as a reference array element, and the array element data are as follows:
s 1 (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:
s i (t)＝s[t-TartimeDelay(i)]+I[t-IftimeDelay(i)]，i＝2,…,M；
wherein TartimeDelay (i) is the delay of the ith element relative to the reference element:
tarDis (i) is the distance between a sound source and an ith array element, and v is the propagation speed of sound in water;
wherein IftimeDelay (i) is the delay of the ith element relative to the reference element:
IfDis (i) is the distance between the interference source and the ith array element, and v is the propagation speed of sound in water;
step 2.3, according to the known signal-to-noise ratioCalculating energy P n And generate energy P n M-way gaussian white noise n i (t), wherein i=1,…,M，s l (t) is the acoustic target radiation noise line spectral component;
step 2.4, observing the array signal x i (t) is: x is x i (t)＝s i (t)+n i (t)。
4. The method for enhancing a distorted matrix line spectrum based on principal component analysis-density clustering according to claim 1, wherein the step 3 comprises the steps of:
step 3.1, calculating the lead angle theta of the ideal uniform linear array m Delay tau of next adjacent array element m ：
Wherein m=1, …, m+1 is the total guide angle number, and d is the distance between adjacent array elements;
step 3.2, carrying out delay addition on the array element data in the towing array to obtain a target signal beam energy diagram:
step 3.3, rough estimation of the guiding angle as the target azimuth when the beam energy maximum position is found by energy detection
5. The method for enhancing a distorted matrix line spectrum based on principal component analysis-density clustering according to claim 1, wherein the step 4 comprises the steps of:
step 4.1, according to the roughly estimated target azimuthCalculating delay estimate of each array element>
Step 4.2, estimating each array element data according to time delayAligning with the reference array element, and coherently adding aligned array element data to obtain a target tracking beam g (t):
step 4.3, performing Fourier transform on G (t) to obtain a target signal spectrum G (omega), and simultaneously estimating a target signal continuous spectrum G by utilizing a sliding window smoothing technology c (omega) deleting the continuum G in the target signal spectrum G (omega) c (omega) influence, obtaining the line spectrum G of the target signal l (omega) estimating L maximum power line spectra using energy detectionWherein L is the number of estimated line spectrums;
step 4.4, calculating the frequency point of each array element in the towed arrayWhere i=1, …, M, l=1, …, L; the phase of the ith array element and the ith line spectrum is +.>Wherein Phase []To calculate the signal phase.
6. The method for enhancing a distorted lineup spectrum based on principal component analysis-density clustering as claimed in claim 1, wherein the step 5 comprises the steps of:
step 5.1, for L strong line spectrums, the i-th array element at the position of the first line spectrum has a relative time delay difference Wherein (1)>And->The phases of the ith and the ith-1 array elements at the ith line spectrum position are respectively used for obtaining array relative time delay difference vectors of L strong line spectrums>
Step 5.2 for the entire delay matrixExtracting features by using a Principal Component Analysis (PCA) algorithm to obtain a feature matrix Z= [ Z ] with lower dimension 1 ,...,z L ]Wherein the time delay characteristic vector of the first strong line spectrum is z l ,l＝1,...,L。
7. The method for enhancing a distorted lineup spectrum based on principal component analysis-density clustering as claimed in claim 1, wherein the step 6 comprises the steps of:
setting a group of neighborhood parameters (epsilon, minPts), and classifying the array delay feature vectors of the L strong line spectrums by using a DBSCAN density clustering algorithm to obtain a classification cluster C= { C 1 ,c 2 ,....c k }。
8. The method for enhancing a distorted lineup spectrum based on principal component analysis-density clustering as claimed in claim 1, wherein the step 7 comprises the steps of:
step 7.1, since the beam pair has been roughly estimated to the target bearing in step 3, a class c is selected which contains the most line spectrum max Removing line spectrums of other categories;
step 7.2, taking c max The array delay vector average value containing the line spectrum is used for obtaining the array delay difference vector estimation tau= [ tau ] without interference 1 ,...τ i ,...,τ M ]Wherein τ i And the delay difference estimated value of the ith array element and the reference array element is represented.
9. The method for enhancing a distorted lineup spectrum based on principal component analysis-density clustering as claimed in claim 1, wherein the step 8 comprises the steps of:
estimating tau by using array delay difference vector with interference removed to obtain target tracking wave beam with enhanced fidelity
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