CN111736111A - Coherent source DOA estimation method based on concentric uniformly distributed double circular arrays - Google Patents

Coherent source DOA estimation method based on concentric uniformly distributed double circular arrays Download PDF

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CN111736111A
CN111736111A CN202010625989.0A CN202010625989A CN111736111A CN 111736111 A CN111736111 A CN 111736111A CN 202010625989 A CN202010625989 A CN 202010625989A CN 111736111 A CN111736111 A CN 111736111A
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coherent
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董静薇
闫宁
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Harbin University of Science and Technology
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Harbin University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae

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Abstract

A coherent source DOA estimation method based on a concentric uniformly distributed double circular array belongs to the field of positioning. The positioning precision of the traditional uniform circular array algorithm is low, and the positioning effect on the coherent source is extremely poor. A coherent source DOA estimation method based on concentric evenly distributed double circular arrays calculates the center frequency of a coherent sound source through a frequency estimation method of delay data; constructing a real-value beam former by a multi-turn phase mode method; and obtaining a cost function in the beam space through calculation, and performing two-dimensional search on the cost function to obtain an estimated value of the coherent source DOA. The method of the invention obtains accurate estimation result.

Description

Coherent source DOA estimation method based on concentric uniformly distributed double circular arrays
Technical Field
The invention relates to a coherent source DOA estimation method based on a concentric uniformly distributed double circular array.
Background
Direction of Arrival (DOA) estimation of spatial signals is widely used in the fields of radar, communication, sonar, and the like. One-dimensional DOA estimation is usually performed using Uniform Linear Array (ULA). However, in practical application, 360-degree and 180-degree scanning needs to be performed on the horizontal direction and the vertical direction of a sound source respectively, and characteristics such as gain and directivity of the linear array are changed along with different scanning angles, which limits practical application of the linear array to a certain extent. In comparison, the uniform circular array has excellent omnidirectional scanning capability in both horizontal and vertical directions, and the direction-finding range of the uniform circular array is larger than that of the uniform linear array under normal conditions. Especially for large underwater equipment, due to the limitation of space, the topological structure of the array often directly influences the positioning result. Also, because of the advantages of the uniform circular array, two-dimensional DOA estimation based on the uniform circular array is rapidly developed.
Traditional sound source direction-of-arrival algorithms are based on incoherent sources. The Multiple Signal Classification algorithm (MUSIC) proposed by Schmidt in 1979 and the Signal Parameter Estimation rotation invariant technology (ESPRIT) proposed by Roy et al in 1986 realize the span from the traditional direction finding to the modern high-resolution direction finding, and open up a new field of feature subspace Classification algorithms. In the late 80 s of the 20 th century, Weighted Subspace Fitting (WSF) was proposed to transform such a problem into a multi-dimensional parametric optimization problem. However, the frequency of the sound bait of the enemy submarine is consistent with the frequency of the enemy submarine in actual sea warfare, so that the torpedo cannot accurately strike the enemy submarine, and the coherent source cannot be accurately positioned by the algorithm. The localization effect of the above algorithm is very poor if the coherence between sound sources is particularly strong. Therefore, solving the coherence between sound sources is also an important research part of array signal processing.
The invention researches the estimation of the two-dimensional direction of arrival of a coherent source in a wide frequency band by using a concentric uniformly distributed double-circular array on the basis of the existing algorithm. Through computer simulation, on the premise that the number of required array elements accords with the size of an underwater platform, the two-dimensional DOA estimation of a broadband coherent sound source has higher estimation precision, and the two-dimensional DOA estimation is analyzed under the conditions of different signal-to-noise ratios and different frequencies, so that a better positioning effect is shown.
Disclosure of Invention
The invention aims to estimate the direction of a coherent source of a uniform circular array, which is an important component of the array signal processing direction, and the traditional uniform circular array algorithm has lower positioning precision and extremely poor positioning effect on the coherent source. In order to solve the problems, the invention provides a coherent source two-dimensional direction of arrival estimation method suitable for a wide frequency band on the basis of a uniform circular array.
A coherent source DOA estimation method based on a concentric uniformly distributed double circular array is realized by the following steps:
step one, calculating the center frequency of a coherent sound source by a frequency estimation method of delay data:
establishing a signal model; then establishing a receiving array model; deducing an array delay output signal vector by using a receiving array model;
step two, constructing a real-value beam former by a multi-circle phase mode method;
and step three, obtaining a cost function in the beam space through calculation, and performing two-dimensional search on the cost function to obtain an estimated value of the coherent source DOA.
The invention has the beneficial effects that:
the invention uses two circles of even circular array to estimate DOA of three coherent sources. The center frequency is determined by a frequency estimation method. A real-value beam former is constructed to obtain a cost function, and the cost function is searched to obtain an angle estimation value. Experiments show that the algorithm has good effect within 1000 Hz-2000 Hz. Meanwhile, when the signal-to-noise ratio is 0dB to 15dB, the peak is also generated, the searching effect is good, and the estimation result is more accurate.
Drawings
FIG. 1: the invention relates to a schematic diagram of a two-circle uniform circular array model;
FIG. 2: a sound source power spectral density map;
FIG. 3: a direction of arrival pattern at a frequency of 2000 Hz;
FIG. 4: a direction of arrival pattern at a frequency of 2000 Hz;
FIG. 5: a direction of arrival pattern at a frequency of 1700 Hz;
FIG. 6: a direction of arrival pattern at a frequency of 1700 Hz;
FIG. 7: a pattern of arrival at a frequency of 1250 Hz;
FIG. 8: a pattern of arrival at a frequency of 1250 Hz;
FIG. 9: a direction of arrival pattern at a frequency of 1000 Hz;
FIG. 10: a direction of arrival pattern at a frequency of 1000 Hz;
FIG. 11: a direction of arrival pattern at a frequency of 800 Hz;
FIG. 12: a direction of arrival pattern at a frequency of 800 Hz;
FIG. 13: a pattern of arrival at a frequency of 630 Hz;
FIG. 14: a pattern of arrival at a frequency of 630 Hz;
FIG. 15: a direction of arrival pattern at a frequency of 500 Hz;
FIG. 16: a direction of arrival pattern at a frequency of 500 Hz;
FIG. 17: a search plot with a signal-to-noise ratio of 15 dB;
FIG. 18: a search plot with a signal-to-noise ratio of 15 dB;
FIG. 19: a search pattern with a signal-to-noise ratio of 10 dB;
FIG. 20: a search pattern with a signal-to-noise ratio of 10 dB;
FIG. 21: a search plot with a signal-to-noise ratio of 5 dB;
FIG. 22: a search plot with a signal-to-noise ratio of 5 dB;
FIG. 23: a search pattern with a signal-to-noise ratio of 0 dB;
FIG. 24: a search pattern with a signal-to-noise ratio of 0 dB;
FIG. 25: a search plot with a signal-to-noise ratio of-5 dB;
FIG. 26: a search plot with a signal-to-noise ratio of-5 dB;
FIG. 27 is a schematic view showing: a search plot with a signal-to-noise ratio of-10 dB;
FIG. 28: a search plot with a signal-to-noise ratio of-10 dB;
FIG. 29: a search pattern with a signal-to-noise ratio of 20 dB;
FIG. 30: a search pattern with a signal-to-noise ratio of 20 dB;
FIG. 31: a search pattern with a signal-to-noise ratio of 20 dB;
FIG. 32: a search pattern with a signal-to-noise ratio of 20 dB;
FIG. 33: a search pattern with a signal-to-noise ratio of 20 dB;
FIG. 34: the method of the invention is a flow chart.
Detailed Description
The first embodiment is as follows:
in this embodiment, as shown in fig. 34, a method for estimating a coherent source DOA based on a concentric uniformly distributed double circular array is implemented by the following steps:
step one, calculating the center frequency of a coherent sound source by a frequency estimation method of delay data;
step two, constructing a real-value beam former by a multi-circle phase mode method;
and step three, obtaining a cost function in the beam space through calculation, and performing two-dimensional search on the cost function to obtain an estimated value of the coherent source DOA.
The second embodiment is as follows:
different from the first specific embodiment, in the first method for estimating coherent source DOA based on concentric uniformly distributed double circular arrays of this embodiment, the step of calculating the center frequency of the coherent sound source by the frequency estimation method of the delay data specifically includes:
step one, establishing a signal model;
step two, establishing a receiving array model;
and step three, deriving an array delay output signal vector by the receiving array model.
The third concrete implementation mode:
different from the second specific embodiment, in the method for estimating a coherent source DOA based on a concentric uniformly distributed double circular array according to the second embodiment, the process of establishing a signal model in the first step is specifically:
in the process of high-resolution processing, establishment of a reasonable signal model is the basis for obtaining an accurate DOA estimation value.
For a broadband sound source, assuming that the bandwidth of a signal is B, there are M mutually independent sound sources, and L array elements perform data reception, the reception data of the L-th array element is expressed as:
Figure BDA0002564748070000043
L＝1，2，3…M
in the formula, xL(t) represents a received data vector,
Figure BDA0002564748070000042
is a sound source, nL(t) is a noisy data vector; dividing the observation time into K subsegments, then dividing the signal source with the bandwidth of B into J sub-bands, and for different frequency points f1，f2，…fJJ equations (2) hold, and finally, a wideband sound source model is obtained by performing discrete fourier transform:
Xk(fj)＝A(fj)Sk(fj)+Nk(fj) (2)
k＝1，2，3...K；j＝1，2，3...J
in the formula, Xk(fj)、Sk(fj)、Nk(fj) Discrete fourier transform representing received data, discrete fourier transform of an original sound source, discrete fourier transform of a noise data vector, respectively; its array manifold matrix A (f)j)：
A(fj)＝[a1(fj)，a2(fj)，...nM(fj)](3)
Figure BDA0002564748070000041
Because only one complex constant is different between coherent sound sources; suppose there are M coherent sound sources, namely:
sk(t)＝αls0(t) (5)
l＝1，2，3…M
in the formula, s0(t) is a broadband sound source, αlIs a complex constant; substituting equation (5) into (1) yields a signal model of the coherent sound source as:
X(t)＝Aρs0(t)+N(t) (6)
where ρ is [ α ]1，α2，…αK]TIs a K × 1 dimensional vector consisting of a series of complex constants, a denotes the steering matrix of the array,N(t)＝[n1(t)，n2(t)，...nM(t)]。
the second embodiment is as follows:
different from the first specific embodiment, in the method for estimating a coherent source DOA based on a concentric uniformly distributed double circular array of the first embodiment, the second step of the process for establishing a receiving array model specifically includes:
two circles of uniform circular arrays form a receiving array, and the radius of the circular array from inside to outside is respectively taken as r1、r2The number of the inner and outer circle array elements is N1、N2(ii) a Array element spacing of
Figure BDA0002564748070000051
Wherein λ represents a wavelength corresponding to the sound source; suppose that there are M sound sources independent of each other and the center frequencies are all fcThe azimuth angle and the pitch angle of each sound source are respectively thetai、
Figure BDA0002564748070000052
As shown in fig. 1.
The array received noise is zero mean and σ variance2White gaussian noise of (1); the received signal of the uniform circular array is then expressed as:
X(t)＝AS(t)+N(t) (7)
in the formula (I), the compound is shown in the specification,
Figure BDA0002564748070000053
is a snapshot data vector; s (t) ═ s1(t)，s2(t)，…sM(t)]TIs a spatial signal vector;
Figure BDA0002564748070000054
is a noisy data vector; a represents a steering vector array of a uniform circular array and
Figure BDA0002564748070000055
in the formula, the steering vector:
Figure BDA0002564748070000056
in the formula:
Figure BDA0002564748070000057
in the formula:
Figure BDA0002564748070000058
where c represents the speed of sound propagation through water.
The fifth concrete implementation mode:
different from the first specific embodiment, in the first embodiment, a method for estimating a coherent source DOA based on a concentric uniformly distributed double circular array includes the following steps:
the signal frequency estimation is an important component of information science in the field of signal processing, and the signal frequency estimation is to estimate the signal frequency submerged in noise by calculating and transforming a signal sampling value; in order to ensure that the orthogonality between the signal subspace and the noise subspace in the MUSIC algorithm can be maintained, the frequency of the signal must be estimated in advance to obtain the center frequency, and then the sound source can be located. The invention adopts a frequency estimation method of delay data to obtain the center frequency of the sound source.
The array delay output signal vector is derived from equation (7):
Y(t)＝x(t-τ)＝AS(t-τ)+N(t-τ) (11)
in the formula (I), the compound is shown in the specification,
Figure BDA0002564748070000061
and lambdamaxThe wavelength corresponding to the highest working frequency in the whole system is represented;
let X (t) correspond to a covariance matrix of RxY (t) and X (t) are related to a cross covariance matrix PYX(ii) a Construct the following matrix
Figure BDA0002564748070000062
In the formula, R0＝Rx-σ2I; i represents and RxThe unit matrix of the same order, + represents the pseudo-inverse of the matrix; then the following relation is obtained according to an improved multiple signal classification algorithm for estimating the direction of arrival of the two-dimensional signal:
Figure BDA0002564748070000063
l＝1，2，3...M
in formula (13), λlIs R1The ith non-zero eigenvalue of (c); similarly, the value of the time delay tau in the improved multi-signal classification algorithm estimated according to the direction of arrival of a two-dimensional signal is different, namely 2 pi fc≤2πτlThe center frequency of the signal can be obtained from equation (13):
Figure BDA0002564748070000064
l＝1，2，3...M
where arg denotes the complex angle of an arbitrary complex number.
The sixth specific implementation mode:
different from the first embodiment, in the method for estimating coherent source DOA based on concentric uniformly distributed double circular arrays of this embodiment, the process of constructing the real-valued beamformer by the multi-turn phase mode in step two specifically includes:
let α be the polar angle of the array element in the polar coordinate system,
Figure BDA0002564748070000065
for a uniform circular array, the excitation function ω (α) is a periodic function with a period of 2 π, which is decomposed into Fourier function
Figure BDA0002564748070000066
For any one of the components, the response of the uniform circular array is
Figure BDA0002564748070000067
Wherein Jm(ξ) is a Bessel function of order m, and further, the response of each array corresponds to a phase pattern for
Figure BDA0002564748070000068
Called visible region, when m > ξ, Jm(ξ) neglecting in the visible region, and obtaining the maximum number of phase modes which can be excited according to the uniform circular array response
Figure BDA0002564748070000069
For the two-turn uniform circular array proposed by the present invention, the excitation function omega is pairedm(α) discrete spatial sampling is performed at the uniform circular array position to obtain an excitation sequence as follows:
Figure BDA00025647480700000610
the excitation sequence corresponds to an array response component of
Figure BDA00025647480700000611
Wherein R (theta, ξ) is remainder, and N is satisfied when the total number of array elements1+N2When the time domain signal processing is more than 2M, the residual term R (theta, ξ) is ignored, the array response can well approach a continuous uniform circular array, and if M is defined as the sampling frequency of the space, the condition is consistent with the Nyquist sampling theorem in the time domain signal processing.
However, in the algorithm of the invention, to process the broadband signal, the value of M must be transformed along with the estimation of frequency, and M always satisfies the requirement
Figure BDA0002564748070000071
It is ensured that no information is lost during the beamforming process. Thus, when designing the array, the total number of array elements must be satisfied
Figure BDA0002564748070000072
Wherein K is the number of turns of the uniform circular array, rmaxThe radius of the outer ring;
constructing a real-valued beamformer Fr on the basis of the phase pattern satisfies the following equation
Figure BDA0002564748070000073
Wherein
Figure BDA0002564748070000074
Cv＝diag{j-M，...j-1，j0，j-1，...j-M} (18)
Figure BDA0002564748070000075
Figure BDA0002564748070000076
M＝2πr2fc/c (21)。
The seventh embodiment:
different from the first specific embodiment, in the method for estimating a coherent source DOA based on a concentric uniformly-distributed double circular array according to the first embodiment, the third step is a process of obtaining a cost function in the beam space through calculation, and performing two-dimensional search on the cost function to obtain an estimated value of the coherent source DOA, and specifically includes:
by using
Figure BDA0002564748070000077
Weighting the steering matrix A of the array element space to obtain the manifold matrix of the wave beam space
Figure BDA0002564748070000078
By using
Figure BDA0002564748070000079
To two circlesWeighting the output signal of the uniform circular array, solving the covariance matrix of the output signal, and performing characteristic decomposition on the covariance matrix to obtain
Figure BDA00025647480700000710
Wherein, ΛsIs composed of the largest M characteristic values, EsIs a matrix composed of corresponding characteristic vectors; and EnIs formed by a characteristic value of sigma2Matrix of corresponding eigenvectors, σ2Representing the noise power;
thus, a cost function of the two-dimensional weighted subspace fitting algorithm is obtained:
Figure BDA00025647480700000711
wherein P isb＝b(bHb-1)bHIs a projection matrix of the beam space steering matrix,
Figure BDA00025647480700000712
is an optimal weighting matrix, rt (-) represents the inversion operator of the matrix; and (4) carrying out two-dimensional search on the formula (22) to obtain estimated values of the azimuth angle and the pitch angle.
Simulation and analysis:
in order to prove the feasibility of the algorithm, an MATLAB simulation platform is adopted for analysis.
The experimental sound source adopts 3 coherent sources, and the expression of the 3 coherent sources is the same. The azimuth angle and the pitch angle of the coherent source are (60.5 °, 20.5 °), (50.5 °, 40.5 °), (80.5 °, 60.5 °), respectively. Two circles of uniform circular arrays are adopted in the experiment, the radiuses of the inner circle and the outer circle are respectively 3m and 6m, and the number of array elements of the inner circle and the outer circle is 24 and 48. The frequency of the experimental sound source is 1000 Hz-2000 Hz. The sound source power spectral density is shown in fig. 2; FIG. 3: a direction of arrival pattern at a frequency of 2000 Hz; FIG. 4: a direction of arrival pattern at a frequency of 2000 Hz; FIG. 5: a direction of arrival pattern at a frequency of 1700 Hz; FIG. 6: a direction of arrival pattern at a frequency of 1700 Hz; FIG. 7: a pattern of arrival at a frequency of 1250 Hz; FIG. 8: a pattern of arrival at a frequency of 1250 Hz; FIG. 9: a direction of arrival pattern at a frequency of 1000 Hz; FIG. 10: frequency of 100A 0Hz direction of arrival pattern; FIG. 11: a direction of arrival pattern at a frequency of 800 Hz; FIG. 12: a direction of arrival pattern at a frequency of 800 Hz; FIG. 13: a pattern of arrival at a frequency of 630 Hz; FIG. 14: a pattern of arrival at a frequency of 630 Hz; FIG. 15: a direction of arrival pattern at a frequency of 500 Hz; FIG. 16: a direction of arrival pattern at a frequency of 500 Hz; as can be seen from fig. 3 to 16, for sound sources with different center frequencies and a signal-to-noise ratio of 10dB, there are different estimation effects on the direction of arrival estimation. Wherein, fig. 3 to fig. 10 are the direction of arrival diagram obtained by one third of frequency doubling between the frequency of 1000Hz and 2000 Hz. It can be seen from the figures that fig. 3 to 10 can obtain better spikes, while fig. 12 and 14 can also obtain the arrival direction of the sound source, but the spike effect is not as good as that of the previous figures. While FIG. 16 has not been able to accurately determine the direction of arrival of the sound source, this is in contrast to
Figure BDA0002564748070000081
The equation proposed holds true. Table 1 shows the comparison between the estimated direction of arrival angle and the actual angle at different frequencies.
TABLE 1 Direction of arrival estimation with a signal-to-noise ratio of 10dB
Table 1 Search map with signal to noise ratio of 10dB
Figure BDA0002564748070000082
Figure BDA0002564748070000091
FIG. 17: a search plot with a signal-to-noise ratio of 15 dB; FIG. 18: a search plot with a signal-to-noise ratio of 15 dB; FIG. 19: a search pattern with a signal-to-noise ratio of 10 dB; FIG. 20: a search pattern with a signal-to-noise ratio of 10 dB; FIG. 21: a search plot with a signal-to-noise ratio of 5 dB; FIG. 22: a search plot with a signal-to-noise ratio of 5 dB; FIG. 23: a search pattern with a signal-to-noise ratio of 0 dB; FIG. 24: a search pattern with a signal-to-noise ratio of 0 dB; FIG. 25: a search plot with a signal-to-noise ratio of-5 dB; FIG. 26: a search plot with a signal-to-noise ratio of-5 dB; FIG. 27 is a schematic view showing: a search plot with a signal-to-noise ratio of-10 dB; FIG. 28: the signal-to-noise ratio is-10 dB.
As can be seen from fig. 17 to 28, for a center frequency of 1000Hz, different signal-to-noise ratios have different estimation effects on the direction-of-arrival estimation. Wherein FIGS. 17-26 are the direction of arrival patterns with signal-to-noise ratios between 15dB and-5 dB. It can be seen from the graphs that fig. 17 to 26 can obtain better peaks, and the arrival direction of the sound source can be accurately estimated. When the signal-to-noise ratio is-10 dB, as shown in fig. 27 and 28, the position of the sound source is blurred and cannot be accurately located. Table 2 shows the comparison between the estimated direction of arrival angle and the actual angle at different signal-to-noise ratios.
TABLE 2 Direction of arrival estimation at a frequency of 1000Hz
Table 2 Search map with frequency of 1000Hz
Figure BDA0002564748070000092
And simulating the resolution of the two circles of uniform circular arrays. The simulation conditions were as above. The angles of the 3 coherent sources are (50.5, 55.5), (65.5, 60.5), (75.5, 70.5), respectively. The frequency was 1250 Hz. The signal-to-noise ratio is 20 dB.
As shown in FIG. 29: the search pattern with a signal-to-noise ratio of 20dB, as can be seen from fig. 29, when the pitch and azimuth intervals are 5 degrees, the circular array cannot be resolved.
And (3) modifying simulation conditions, wherein the radiuses of the inner circle and the outer circle are 6m and 12m respectively, and the number of array elements of the inner circle and the outer circle is 144 and 256.
When only the inner and outer circle radii of the array are changed from 3m, 6m to 6m, 12m and other conditions are the same, the array search map is as shown in fig. 31 to 32. FIG. 30: a search pattern with a signal-to-noise ratio of 20 dB; FIG. 31: a search pattern with a signal-to-noise ratio of 20 dB; when only the number of arrays is changed from 12, 16 to 144, 256 and other conditions are the same, the array search map is as shown in FIG. 33.
FIG. 32: a search pattern with a signal-to-noise ratio of 20 dB; FIG. 33: a search pattern with a signal-to-noise ratio of 20 dB;
as can be seen from FIGS. 30 to 33, when the simulation conditions are modified, the resolution of the array can be significantly improved, which is similar to that of the circular array
Figure BDA0002564748070000101
Illustrated hold consistent[7]. I.e. the resolution of the array becomes better as the number of array elements increases. Wherein r represents the radius of the uniform circular array and m represents the number of array elements.
In summary, the invention uses two circles of uniform circular arrays to perform DOA estimation on three coherent sources. The center frequency is determined by a frequency estimation method. A real-value beam former is constructed to obtain a cost function, and the cost function is searched to obtain an angle estimation value. Experiments show that the algorithm has good effect within 1000 Hz-2000 Hz. Meanwhile, when the signal-to-noise ratio is 0 dB-15 dB, the peak is also generated, the searching precision is high, and the effect is good.

Claims (7)

1. A coherent source DOA estimation method based on a concentric uniform distribution double-circle array is characterized in that: the method is realized by the following steps:
step one, calculating the center frequency of a coherent sound source by a frequency estimation method of delay data;
step two, constructing a real-value beam former by a multi-circle phase mode method;
and step three, obtaining a cost function in the beam space through calculation, and performing two-dimensional search on the cost function to obtain an estimated value of the coherent source DOA.
2. The method for estimating the DOA of the coherent source based on the concentric uniformly distributed double circular arrays as claimed in claim 1, wherein: step one, the process of calculating the center frequency of the coherent sound source by the frequency estimation method of the delay data specifically includes:
step one, establishing a signal model;
step two, establishing a receiving array model;
and step three, deriving an array delay output signal vector by the receiving array model.
3. The method for estimating the DOA of the coherent source based on the concentric uniformly distributed double circular arrays as claimed in claim 2, wherein: the process of establishing the signal model in the first step specifically comprises the following steps:
for a broadband sound source, assuming that the bandwidth of a signal is B, there are M mutually independent sound sources, and L array elements perform data reception, the reception data of the L-th array element is expressed as:
Figure FDA0002564748060000011
L＝1,2,3…M
in the formula, xL(t) represents a received data vector,
Figure FDA0002564748060000012
is a sound source, nL(t) is a noisy data vector; dividing the observation time into K subsegments, then dividing the signal source with the bandwidth of B into J sub-bands, and for different frequency points f1，f2，…fJJ equations (2) hold, and finally, a wideband sound source model is obtained by performing discrete fourier transform:
Xk(fj)＝A(fj)Sk(fj)+Nk(fj) (2)
k＝1，2，3…K；j＝1，2，3…J
in the formula, Xk(fj)、Sk(fj)、Nk(fj) Discrete fourier transform representing received data, discrete fourier transform of an original sound source, discrete fourier transform of a noise data vector, respectively; its array manifold matrix A (f)j)：
A(fj)＝[a1(fj)，a2(fj)，…aM(fj)](3)
Figure FDA0002564748060000013
Since coherent sound sources differ only by a complex constant; suppose there are M coherent sound sources, namely:
sk(t)＝αls0(t) (5)
l＝1,2,3…M
in the formula, s0(t) is a broadband sound source, αlIs a complex constant; substituting equation (5) into (1) yields a signal model of the coherent sound source as:
X(t)＝Aρs0(t)+N(t) (6)
where ρ is [ α ]1，α2，…αK]TIs a K × 1-dimensional vector composed of a series of complex constants, A represents the steering matrix of the array, and N (t) is [ n ]1(t)，n2(t)，…nM(t)]。
4. The method for estimating the DOA of the coherent source based on the concentric uniformly distributed double circular array as claimed in claim 2 or 3, wherein: the process of establishing the receiving array model in the second step is specifically as follows:
two circles of uniform circular arrays form a receiving array, and the radius of the circular array from inside to outside is respectively taken as r1、r2The number of the inner and outer circle array elements is N1、N2(ii) a Array element spacing of
Figure FDA0002564748060000021
Wherein λ represents a wavelength corresponding to the sound source; suppose that there are M sound sources independent of each other and the center frequencies are all fcThe azimuth angle and the pitch angle of each sound source are respectively thetai、
Figure FDA0002564748060000022
The array received noise is zero mean and σ variance2White gaussian noise of (1); the received signal of the uniform circular array is then expressed as:
X(t)＝AS(t)+N(t) (7)
in the formula (I), the compound is shown in the specification,
Figure FDA0002564748060000023
is a snapshot data vector; s (t) ═ s1(t)，s2(t)，…sM(t)]TIs a spatial signal vector;
Figure FDA0002564748060000024
is a noisy data vector; a represents a steering vector array of a uniform circular array and
Figure FDA0002564748060000025
in the formula, the steering vector:
Figure FDA0002564748060000026
in the formula:
Figure FDA0002564748060000027
in the formula:
Figure FDA0002564748060000028
where c represents the speed of sound propagation through water.
5. The method for estimating the DOA of the coherent source based on the concentric uniformly distributed double circular array as claimed in claim 2 or 4, wherein: the frequency estimation process in the first step and the third step specifically comprises the following steps:
the array delay output signal vector is derived from equation (7):
Y(t)＝X(t-τ)＝AS(t-τ)+N(t-τ) (11)
in the formula (I), the compound is shown in the specification,
Figure FDA0002564748060000031
and lambdamaxThe wavelength corresponding to the highest working frequency in the whole system is represented;
let X (t) correspond to a covariance matrix of RxY (t) and X (t) are associated with a cross-covariance matrix RYX(ii) a Construct the following matrix
Figure FDA0002564748060000032
In the formula, R0＝Rx-σ2I; i represents and RxThe unit matrix of the same order, + represents the pseudo-inverse of the matrix; then according to an improved multi-signal classification algorithm for estimating the direction of arrival of the two-dimensional signal, the following relation is obtained:
Figure FDA0002564748060000033
l＝1，2，3…M
in formula (13), λlIs R1The ith non-zero eigenvalue of (c); similarly, the value of the time delay tau in the improved multi-signal classification algorithm estimated according to the direction of arrival of a two-dimensional signal is different, namely 2 pi fc≤2πτlThe center frequency of the signal can be obtained from equation (13):
Figure FDA0002564748060000034
l＝1，2，3…M
where arg denotes the complex angle of an arbitrary complex number.
6. The method for estimating the DOA of the coherent source based on the concentric evenly distributed double circular array as claimed in claim 1, 2 or 5, wherein: the process of constructing the real-valued beamformer by the multi-turn phase mode method described in the second step specifically includes:
let α be the polar angle of the array element in the polar coordinate system,
Figure FDA0002564748060000035
for a uniform circular array, the excitation function ω (α) is a periodic function with a period of 2 π, which is decomposed into Fourier function
Figure FDA0002564748060000036
For any one of the components, the response of the uniform circular array is
Figure FDA0002564748060000037
Wherein Jm(ξ) is a Bessel function of order m, and further, the response of each array corresponds to a phase pattern for
Figure FDA0002564748060000038
Called visible region, when m > ξ, Jm(ξ) neglecting in the visible region, and obtaining the maximum number of phase modes which can be excited according to the uniform circular array response
Figure FDA0002564748060000039
For the excitation function omegam(α) obtaining an excitation sequence by discrete spatial sampling at the uniform circular array position, as follows:
Figure FDA00025647480600000310
the excitation sequence corresponds to an array response component of
Figure FDA00025647480600000311
Wherein R (theta, ξ) is remainder, and N is satisfied when the total number of array elements1+N2When the sampling frequency is larger than 2M, the remainder term R (theta, ξ) is ignored, the array response can well approach to a continuous uniform circular array, M is defined as the sampling frequency of the space, and M satisfies the requirement
Figure FDA0002564748060000041
When the array is designed, the total array element number meets the requirement
Figure FDA0002564748060000042
Wherein K is the number of turns of the uniform circular array, rmaxThe radius of the outer ring;
constructing a real-valued beamformer Fr on the basis of the phase pattern satisfies the following equation
Figure FDA0002564748060000043
Wherein
Figure FDA0002564748060000044
Cv＝diag{j-M，…，j-1，j0，j-1，…j-M} (18)
Figure FDA0002564748060000045
Figure FDA0002564748060000046
M＝2πr2fc/c (21)。
7. The method for estimating the DOA of the coherent source based on the concentric uniformly distributed double circular arrays as claimed in claim 6, wherein: step three, the process of obtaining the cost function in the beam space through calculation and performing two-dimensional search on the cost function to obtain the estimated value of the coherent source DOA specifically comprises:
by using
Figure FDA0002564748060000047
Weighting the steering matrix A of the array element space to obtain the manifold matrix of the wave beam space
Figure FDA0002564748060000048
By using
Figure FDA0002564748060000049
To carry out the two circles of uniform circular array output signalsWeighting and solving the covariance matrix, and performing characteristic decomposition on the covariance matrix to obtain
Figure FDA00025647480600000410
Wherein, ΛsIs composed of the largest M characteristic values, EsIs a matrix composed of corresponding characteristic vectors; enIs formed by a characteristic value of sigma2Matrix of corresponding eigenvectors, σ2Representing the noise power;
thus, a cost function of the two-dimensional weighted subspace fitting algorithm is obtained:
Figure FDA00025647480600000411
wherein P isb＝b(bHb-1)bHIs a projection matrix of the beam space steering matrix,
Figure FDA00025647480600000412
is an optimal weighting matrix, and tr (-) represents an inversion operator of the matrix; and (4) carrying out two-dimensional search on the formula (22) to obtain estimated values of the azimuth angle and the pitch angle.
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