CN111123192B - Two-dimensional DOA positioning method based on circular array and virtual extension - Google Patents

Two-dimensional DOA positioning method based on circular array and virtual extension Download PDF

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CN111123192B
CN111123192B CN201911197751.6A CN201911197751A CN111123192B CN 111123192 B CN111123192 B CN 111123192B CN 201911197751 A CN201911197751 A CN 201911197751A CN 111123192 B CN111123192 B CN 111123192B
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CN111123192A (en
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巩朋成
张祺
张正文
饶鼎
郑毅豪
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Hubei University of 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
    • G01S3/80—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 ultrasonic, sonic or infrasonic waves
    • G01S3/802—Systems for determining direction or deviation from predetermined direction
    • 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

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Abstract

The invention discloses a two-dimensional DOA positioning method based on a circular array and virtual expansion, which comprises the following steps: step 1, according to actual needs and characteristics of a circular array system, establishing a circular array receiving model based on a coherent signal source according to coherent signal incident frequency, array radius and array element number; step 2, virtualizing UCA in an array element space into ULA in a mode space by using a mode space algorithm according to the received data of the incident signal to obtain the received data of a virtual linear array and a new array flow pattern matrix; step 3, obtaining a plurality of sub-arrays and receiving data of the sub-arrays; and 4, constructing a spatial spectrum cost function and searching through a spectrum peak to obtain an azimuth angle and a pitch angle of the sound source signal. Therefore, the invention has the following advantages: (1) DOA estimation of multiple coherent sound source signals is achieved. (2) Interference factors during sound source DOA estimation are reduced, and the positioning performance of the algorithm is improved.

Description

Two-dimensional DOA positioning method based on circular array and virtual extension
Technical Field
The invention belongs to the field of array signal processing, and relates to a two-dimensional positioning method based on a circular array, matrix virtual expansion and subarray processing.
Background
Microphone arrays have been widely used in the fields of speech recognition and speech enhancement, and are also a new research hotspot in the field of speech signal processing as sound source localization which is one of the key technologies of microphone array signal processing. The aim of research based on a microphone array sound source positioning algorithm is to provide an accurate and rapid sound source positioning method to determine the azimuth of an effective signal, so as to analyze and utilize the effective signal and suppress an interference signal.
Currently, research on microphone array sound source localization technology is roughly divided into the following three directions:
positioning algorithms based on delay estimation are the most practical methods. However, before this method is applied to processing a highly reverberant speech signal, the speech signal needs to be preprocessed first.
The algorithm can be realized by two steps:
(1) TDOA estimation
The estimated time delay is used to estimate the time difference between sounds from the sound source to the different microphones. Common methods are the Generalized cross-correlation (GCC) and the Least mean square error (LMS) adaptive filtering.
(2) Positioning with TDOA
The second step in TDOA-based sound source localization is to identify the sound source location based on the TDOA estimates. Theoretically, to determine the specific coordinates of a three-dimensional spatial target, three independent TDOA values are required, i.e., at least four microphones are required for the location from which the acoustic source is to be acquired. Common methods for location using TDOA values include maximum likelihood estimation and least squares estimation. By means of the correlation method, the spatial coordinates of the sound source can be determined.
However, in practical applications, many disadvantages are still reflected, and firstly, the method needs to estimate the time delay before the positioning can be realized, which causes errors in secondary estimation. Secondly, the time delay estimation precision is very easily influenced by a plurality of factors such as array element positions, indoor reverberation, space noise, space interference signals and the like, and the positioning effect is relatively poor.
Controllable beam forming technology based on maximum output power: the beamforming method is classified into conventional beamforming and adaptive beamformer. Conventional beamforming is the simplest beamforming method, which computes a beam by weighting each microphone signal and directs the beam to find the direction of the sound source. Wherein the weighting value for each microphone signal depends on the phase delay of the sound arriving at the microphone. And the latter is related to the sound source position. When the maximum signal power is obtained, the direction corresponding to the beam can be regarded as the direction from which the sound comes. The adaptive beamforming algorithm is based on a conventional beamforming algorithm and performs adaptive filtering of the space domain on the noise signal. In the adaptive beam forming algorithm, the amplitude weighted value of each microphone signal depends on the received signal and is adaptively adjusted according to a certain optimal criterion. Common criteria are LMS, LS, maximum SNR, etc.
The positioning method based on high-resolution spectrum estimation comprises the following steps: the irrelevance of a signal space and a noise space is utilized, and a series of algorithms of signal processing and matrix theory are adopted to extract the spatial information of the signal. The method is an algorithm related to extreme class solving and has strong resolution, so the method is favored by numerous scholars at home and abroad. High resolution based spatial spectrum estimation algorithms include ESPRIT, subspace fitting, MUSIC, etc. The algorithm performs eigen decomposition on the covariance matrix of the sound signals received by the microphone array to construct a spatial spectrum (i.e., a spectrum with respect to the direction of the sound source). The Direction corresponding to the maximum of the spatial spectrum is the Direction of Arrival (DOA). This type of method can be used in the case of multiple sound sources and its localization accuracy is not limited by the beam width and aperture of the microphone array. Thus, high direction finding accuracy and resolution can be achieved (the spectral peak can be very sharp when the input SNR is high enough). Meanwhile, the algorithm can be applied to broadband signals, but array errors have large influence on the positioning accuracy of the method, including position errors of microphones, performance differences of microphones of all paths and the like. Generally, such a method can achieve high positioning accuracy in a far-field environment (i.e., the distance between a sound source and a microphone array is far greater than the distance between microphones), but the positioning accuracy is rapidly reduced in a near-field environment, and the amount of computation is large because the peak of a spatial spectrum is searched.
Compared with a time delay estimation method, the high-resolution spectrum estimation positioning method has higher flexibility and positioning accuracy, more fully utilizes the resources of a microphone array to extract information, and combines three sound source information of a time domain, a frequency domain and a space domain. Compared with the adaptive beam forming algorithm, the method is less influenced by external interference and less sensitive to the characteristics of voice signals. The high-resolution spectrum estimation-based algorithm theory research has great significance, although the large deficiency of the current algorithm is large calculation amount, the algorithm still has good positioning effect under the complex and changeable environment, and meanwhile, the geometric structure of the array is of great importance to the design of the positioning algorithm and the quality of the positioning performance.
Disclosure of Invention
The invention aims to provide a two-dimensional sound source DOA estimation system based on matrix virtual expansion aiming at the defects of the existing method, and aims to obtain more long positions of sound source positioning information by utilizing the matrix virtual expansion, and simultaneously obtain the pitch angle and azimuth angle information of a signal source and higher resolution precision, and the technical idea of the invention is as follows: a circular microphone array receiving model is designed firstly, a circular array virtualization linear array is applied to a space smoothing technology, effective array element information is extracted, redundant data are removed, a reconstruction matrix is obtained, and finally a spectrum peak is searched to obtain an azimuth angle and a pitch angle of an expected sound source signal.
A two-dimensional DOA positioning method based on a circular array and virtual extension is characterized by comprising the following steps of establishing a circular array receiving model and virtual extension:
step 1, establishing a receiving model of a circular microphone array, based on the following formula:
Figure BDA0002295086390000031
step 2, performing virtualization processing on the received data according to the data of the incident signal received in the step 1: the m-th array element output of the UCA is obtained as:
Figure BDA0002295086390000032
the formula (2) is subjected to a Discrete Fourier Transform (DFT) of M points in space, and includes:
Figure BDA0002295086390000033
let uq＝v-qFormula (3) is rewritten as a matrix form:
Figure BDA0002295086390000034
equivalents thereof
Figure BDA0002295086390000041
Thus, for spatial DFT, equation (3) can be rewritten to a matrix form, i.e.
Figure BDA0002295086390000042
The combined vertical type (4), (5) and (6) can be obtained
Figure BDA0002295086390000043
From equation (7), the matrix
Figure BDA0002295086390000044
Has a van der mond form, thus realizing the equivalence of M-ary UCAs to 2K + 1-ary virtual ULA;
the steering vector b (φ, θ) after array expansion is:
Figure BDA0002295086390000045
step 3, splitting the virtual linear microphone array to obtain a plurality of sub-arrays and received data of the sub-arrays
According to the derivation, the method of mode space transformation is adopted to carry out array preprocessing on the formula (10), and the following results are obtained:
Figure BDA0002295086390000046
therefore, the uniform circular microphone array is converted into a 2K + 1-element virtual uniform linear microphone, in order to estimate coherent signals, a spatial smoothing technique is added, the virtual linear array is divided into L sub-arrays, and similarly, the data vector y (t) is also divided into L sub-vectors, so equation (9) can be rewritten as:
Figure BDA0002295086390000047
step 4, utilizing each obtained subarray receiving data to reconstruct a matrix, constructing a spatial spectrum cost function, and searching a spectrum peak to obtain an azimuth angle and a pitch angle of a sound source signal:
after the sub-arrays are divided, the data are received by utilizing the signals of each sub-array, and the data y of the first sub-array after the division is aimed atl(t) reconstructing the matrix to achieve an estimation of the coherent signal DOA;
by using
Figure BDA0002295086390000048
Constructing a sub-array fourth-order accumulation matrix, and marking the sub-array fourth-order accumulation matrix as Cl′：
Figure BDA0002295086390000049
All C are addedl' addition yields an improved fourth order cumulant matrix:
Figure BDA0002295086390000051
fourth-order cumulant matrix to be constructed
Figure BDA0002295086390000052
Decomposing the characteristic values, and descending the obtained P characteristic values1＞λ2＞…＞λPArrangement, signal subspace is ES＝(e1,e2,…,eN) Noise subspace of EN＝(eN+1，eN+2，…，eP)；
Thereby establishing a spatial spectrum cost function as
Figure BDA0002295086390000053
Wherein the content of the first and second substances,
Figure BDA0002295086390000054
and then
Figure BDA0002295086390000055
The guide vector of the first sub-array is obtained by splitting the virtual linear array obtained after the mode space transformation, so that the formula (35) is used for carrying out spectrum peak estimation in a two-dimensional space (phi, theta), and a space spectrum cost function P is usedI-FOC-MUSICFinding the angle corresponding to the N maximum points in (phi, theta) to determine the position of the sound source signal, i.e. determining the position of the sound source signal
Figure BDA0002295086390000056
Therefore, the invention has the following advantages: (1) aiming at the problems of limitation of the MUSIC algorithm on the number of sound sources and inaccurate estimation of coherent signals, the invention utilizes the mode space algorithm to carry out virtual linear array processing on a circular microphone array in advance, introduces the space smoothing technology to carry out decorrelation on the coherent signals, and finally adds a fourth-order cumulant matrix to reconstruct received data, thereby realizing DOA estimation on a plurality of coherent sound source signals. (2) When a fourth-order cumulant matrix is constructed, redundant data are removed by extracting effective matrix element information so as to reduce the calculated amount; compared with the traditional accumulation matrix construction, the method does not use the kronecker product to construct the accumulation matrix, so that the signal subspace is not expanded, interference factors during the DOA estimation of the sound source are reduced, and the positioning performance of the algorithm is improved.
Drawings
FIG. 1.1 shows the UCA-RB-MUSIC three-dimensional positioning.
FIG. 1.2 shows the three-dimensional positioning of UCA-I-FOC-MUSIC.
FIG. 2.1 shows the UCA-RB-MUSIC one-dimensional projection positioning.
FIG. 2.2 shows the UCA-I-FOC-MUSIC one-dimensional projection positioning.
FIG. 3.1 is the projection of UCA-RB-MUSIC in azimuth.
FIG. 3.2 is the projection of UCA-I-FOC-MUSIC in azimuth.
FIG. 4.1 shows the first case of the UCA-I-FOC-MUSIC algorithm for estimating 5 coherent sound source signals.
FIG. 4.2 shows the second case of the UCA-I-FOC-MUSIC algorithm for estimating 5 coherent sound source signals.
FIG. 4.3 shows the case three of the UCA-I-FOC-MUSIC algorithm for 5 coherent sound source signal estimation.
Fig. 5.1 is a performance curve (success rate/%) for different algorithms as a function of signal to noise ratio.
Figure 5.2 is a plot of performance (estimated root mean square error) for different algorithms as the signal to noise ratio varies.
FIG. 6 is a schematic flow chart of the method of the present invention.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example (b):
1. the principle of the method.
The invention mainly comprises the following steps
Step 1, establishing a circular microphone array receiving model:
consider a two-dimensional DOA estimation with a circular microphone array. Assume that a uniform circular microphone array model is used, with M arrays evenly distributed over a circle of radius R and independent of each other. Supposing N far-field narrow-band sound source signals Si(t) incident on UCA, with the origin of coordinates O as a reference point and the radius of the first microphone as a reference line (dotted line in the figure), any sound source signal Si(t) projection on the xoy planeIs OL, the included angle between the projected line OL and the reference line is an azimuth angle phii，SiThe included angle between (t) and the z axis is the pitch angle thetaiWherein the azimuth angle phii∈[0°,360°]Angle of pitch thetai∈[0°,90°]Taking the counter-clockwise direction as the positive direction, the array signal model can be expressed as
Figure BDA0002295086390000061
Writing equation (1) in matrix form:
X(t)＝AS(t)+N(t) (2)
wherein, X (t) is an array M multiplied by 1 dimension output data matrix; s (t) is an Nx 1 dimensional data output matrix of the far-field voice signal; n (t) is a M × 1 dimensional noise data matrix, the noise is additive white gaussian noise, the noise on each array element is uncorrelated, and a ═ a1(w0)a2(w0)...aN(w0)]Is an array M multiplied by N dimensional array flow pattern matrix.
The circular microphone array reception model steering vector is given below
ai(w0) N is a steering vector, which may be expressed as
Figure BDA0002295086390000071
Wherein w0Is an angular frequency of a received signal, and
Figure BDA0002295086390000072
τMirepresenting the time delay of the reception of the ith signal relative to the mth element of the reference element, c being the speed of sound.
As can be seen from fig. 1, for the circular microphone array, the j-th microphone (j ═ 1,2, … M) azimuth angle is:
φji＝φi-2π(j-1)/M (4)
at this time, the propagation delay of the signal reaching the jth microphone relative to the reference origin is:
Figure BDA0002295086390000073
then, the steering vector in equation (3) is converted into:
Figure BDA0002295086390000074
according to equation (6), the array flow pattern matrix can be defined as:
Figure BDA0002295086390000075
using equations (1) - (7), the mathematical model of the incidence of the N independent sound source signals to the M uniform circular microphone reception data can be converted into:
Figure BDA0002295086390000081
in particular, when the mathematical expression between the sound source signal sources satisfies a certain rule, such as the signal sources are coherent signals, there are:
Si(t)＝αiS1(t),i＝1,2,...,N (9)
therefore, the N coherent signals received by the uniform circular microphone array can be regarded as S coherent signals1(t) is generated, and S1(t) also known as the signal source, bringing equation (9) into equation (2) yields a mathematical model of a uniform circular microphone array coherent signal source:
Figure BDA0002295086390000082
step 2, performing virtualization processing on the received data according to the data of the incident signal received in the step 1:
according to the formula (2) and the formula (3), the m-th array element output of UCA is obtained as follows:
Figure BDA0002295086390000083
a Discrete Fourier Transform (DFT) of M points in space is performed on equation (11), and there are:
Figure BDA0002295086390000091
let uq＝v-qEquation (12) is rewritten in matrix form as:
Figure BDA0002295086390000092
equivalents thereof
Figure BDA0002295086390000093
Thus, for spatial DFT, equation (12) can be rewritten to a matrix form, i.e.
Figure BDA0002295086390000094
Combined type (13), (14) and (15), can obtain
Figure BDA0002295086390000095
From the formula (16), the matrix
Figure BDA0002295086390000096
Has the form of van der mond, thus realizing the equivalence of M-ary UCAs to 2K + 1-ary virtual ULA.
The steering vector b (φ, θ) after array expansion is:
Figure BDA0002295086390000097
step 3, splitting the virtual linear microphone array to obtain a plurality of sub-arrays and received data of the sub-arrays
According to the derivation, the method of mode space transformation is adopted to carry out array preprocessing on the formula (10), and the following results are obtained:
Figure BDA0002295086390000098
therefore, the uniform circular microphone array is converted into a 2K + 1-element virtual uniform linear microphone, in order to estimate the coherent signal, a spatial smoothing technique is added, the virtual linear array is divided into L sub-arrays, and similarly, the data vector y (t) is also divided into L sub-vectors, so that the formula (18) can be rewritten as follows:
Figure BDA0002295086390000101
step 4, utilizing each obtained subarray receiving data to reconstruct a matrix, constructing a spatial spectrum cost function, and searching a spectrum peak to obtain an azimuth angle and a pitch angle of a sound source signal:
after the sub-arrays are divided, the data are received by utilizing the signals of each sub-array, and the data y of the first sub-array after the division is aimed atl(t), the reconstruction matrix enables estimation of the coherent signal DOA.
By using
Figure BDA0002295086390000102
Constructing a sub-array fourth-order accumulation matrix, and marking the sub-array fourth-order accumulation matrix as Cl′：
Figure BDA0002295086390000103
All C are addedl' addition yields an improved fourth order cumulant matrix:
Figure BDA0002295086390000104
fourth-order cumulant matrix to be constructed
Figure BDA0002295086390000105
Decomposing the characteristic values, and descending the obtained P characteristic values1＞λ2＞...＞λPArrangement, signal subspace is ES＝(e1,e2,...,eN) Noise subspace of EN＝(eN+1，eN+2，...，eP)。
Thereby establishing a spatial spectral cost function of
Figure BDA0002295086390000106
Wherein the content of the first and second substances,
Figure BDA0002295086390000107
while
Figure BDA0002295086390000108
The guide vector of the first sub-array is obtained by splitting the virtual linear array obtained after the mode space transformation, so that the formula (35) is used for carrying out spectrum peak estimation in a two-dimensional space (phi, theta), and a space spectrum cost function P is usedI-FOC-MUSICFinding the corresponding angles of the N maximum value points in (phi, theta) to determine the position of the sound source signal, namely:
Figure BDA0002295086390000109
2. and (5) simulation analysis.
2.1 Sound Source Signal Angle estimation
Simulation experiment 1: the algorithm proposed herein was compared to the UCA-RB-MUSIC algorithm in a simulation experiment. In simulation, a two-dimensional uniform circular microphone array is selected, 16 microphones are uniformly distributed on a circumference with the radius of 22cm on an XOY plane, noise is Gaussian white noise, azimuth angles (60 degrees, 50 degrees) and azimuth angles (200 degrees and 30 degrees) of two far-field coherent sound source signals are incident to the circular array, the fast beat number is 300, the number of sub-arrays is set to be 3, the signal-to-noise ratio is sequentially selected from three typical conditions of-5 dB, 10dB and 20dB, the search step lengths of phi and theta angles are taken to be 1 degree, the search range of the phi angle is taken to be [ 0-360 degrees ], and the search range of the theta angle is taken to be [ 0-90 degrees ]. The simulation results are shown in FIGS. 1 to 5. FIG. 1 shows the three-dimensional positioning of two algorithms, compared to the present algorithm, the UCA-RB-MUSIC algorithm is misaligned in low SNR; FIG. 2 shows the projection of two algorithms in the direction of a one-dimensional plane; fig. 3 shows the projection of the two algorithms in azimuth.
As can be seen from fig. 1, the algorithm provided herein can accurately obtain the azimuth estimated values of two coherent sound source signals, and compared with the classical UCA-RB-MUSIC algorithm, the algorithm provided herein also has higher positioning accuracy under the condition of low signal-to-noise ratio, and the angle estimation accuracy is improved by 4 °. Meanwhile, as can be seen from fig. 2, the projection aperture size of the UCA-RB-MUSIC algorithm is not significantly changed and is concentrated on one point under different signal-to-noise ratios, while the projection aperture obtained by the UCA-RB-MUSIC algorithm under low signal-to-noise ratio is larger and significantly changes along with the change of the signal-to-noise ratio. Finally, as can be seen from fig. 3, the spectral peaks of the spatial spectrum on the azimuthal projection obtained by the algorithm are sharper under different signal-to-noise ratios. Therefore, the algorithm is proved to be superior to the traditional UCA-RB-MUSIC three-dimensional sound source positioning algorithm in overall estimation performance.
Simulation experiment 2: validation utilizes the algorithm presented herein under a number of target conditions. Considering the condition that the signal-to-noise ratio is 20dB, and selecting 5 far-field coherent sound source signals with azimuth angles of (60 °,30 °), (120 °,50 °), (160 °,70 °), (200 °,50 °) and (240 °,30 °), the other experimental conditions are the same, and the simulation result is shown in fig. 4.
As can be seen from fig. 4, the algorithm herein can realize the estimation of multiple coherent sound source signals under the condition of high signal-to-noise ratio, and the positioning accuracy is higher under the condition of high signal-to-noise ratio.
Therefore, simulation experiments 1 and 2 show that the algorithm provided by the method has higher accuracy in sound source positioning compared with the traditional UCA-RB-MUSIC algorithm, can realize the estimation of a plurality of coherent signals, has no obvious change in the accuracy of the algorithm under the condition of signal-to-noise ratio change, and still has higher positioning accuracy under the condition of low signal-to-noise ratio.
2.2 Sound Source localization accuracy analysis
In order to further examine the positioning performance of the algorithm, a performance curve graph between the DOA estimation performance of the UCA-FOC-MUSIC algorithm, the UCA-ESPRIT algorithm, the UCA-RB-MUSIC algorithm and the UCA-I-FOC-MUSIC algorithm and the signal-to-noise ratio of the sound source signal is simulated, the time required by positioning of each algorithm and the success rate of each algorithm are calculated, the DOA estimation performance is generally compared by the root mean square error, and the two-dimensional angle measurement is related in the text, so the root mean square error is composed of an azimuth angle error and a pitch angle error and is represented by the following formula:
Figure BDA0002295086390000121
wherein M represents the number of Monte Carlo simulation experiments,
Figure BDA0002295086390000122
and
Figure BDA0002295086390000123
indicating estimated values of azimuth angle and pitch angle of the mth sound source signal obtained by the jth simulation experimentmjAnd thetamjI.e. the values of the true azimuth and pitch angles.
Simulation experiment 3: under the condition that the signal-to-noise ratio is 20dB, the search step length of phi and theta angles is 1 degrees, the azimuth angles and the pitch angles of two sound sources are respectively (60 degrees ) and (200 degrees and 30 degrees), 300 Monte Carlo simulation experiments are carried out, the sound source direction estimation time of each algorithm is calculated, analysis running time is carried out by using a MATLAB 2014a version during measurement, and the sound source direction estimation time runs on a standard PC (provided with an Intel 2.6GHz core i5 CPU and a 4GB RAM).
TABLE 1 four Algorithm calculation times
Figure BDA0002295086390000124
As seen from the above table, the time for the UCA-ESPRIT algorithm to complete sound source localization is the shortest and the time consuming is the UCA-FOC-MUSIC algorithm, but the UCA-ESPRIT algorithm and the UCA-RB-MUSIC algorithm have difficulties in low signal-to-noise ratio and multi-sound source localization, and the estimation time required by the algorithm is shorter than that required by the conventional fourth-order cumulative MUSIC algorithm under the same condition.
Simulation experiment 4: setting the number of fast beats to be 300, setting the success probability that the deviation between the estimated value and the true value is less than 1 degree, and carrying out 300 Monte Carlo simulation experiments under the same other conditions as the simulation experiment 3.
As can be seen from FIG. 5.1, the success rate of the algorithm is superior to that of the other three algorithms, the success rate is close to 80% when the signal-to-noise ratio is-5 dB, and the success rates of the other algorithms are not over 70% until the signal-to-noise ratio is greater than 10dB, the success rates of the four algorithms are close to 100%, and meanwhile, the root mean square error results of FIG. 5.2 show that the UCA-ESPRIT algorithm and the UCA-RB-MUSIC algorithm have large errors under the condition of low signal-to-noise ratio, but the four algorithms have good estimation performance under the condition of high signal-to-noise ratio. Therefore, compared with the other three algorithms, the algorithm can realize high-precision estimation of the coherent signal DOA.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (1)

1. A two-dimensional DOA positioning method based on a circular array and virtual extension is characterized by comprising the following steps of establishing a circular array receiving model and virtual extension:
step 1, establishing a circular microphone array receiving model based on the following formula:
Figure FDA0003384206990000011
step 2, performing virtualization processing on the received data according to the data of the incident signal received in the step 1: the m-th array element output of the UCA is obtained as:
Figure FDA0003384206990000012
the formula (2) is subjected to a Discrete Fourier Transform (DFT) of M points in space, and includes:
Figure FDA0003384206990000013
Figure FDA0003384206990000014
let uq＝v-qFormula (3) is rewritten as a matrix form:
Figure FDA0003384206990000015
equivalents thereof
Figure FDA0003384206990000016
Thus, for spatial DFT, equation (3) can be rewritten to a matrix form, i.e.
Figure FDA0003384206990000017
The combined vertical type (4), (5) and (6) can be obtained
Figure FDA0003384206990000021
From equation (7), the matrix
Figure FDA0003384206990000022
Has a van der mond form, thus realizing the equivalence of M-member UCA to 2K + 1-member virtual ULA;
the steering vector b (φ, θ) after array expansion is:
Figure FDA0003384206990000023
step 3, splitting the virtual linear microphone array to obtain a plurality of sub-arrays and received data of the sub-arrays, and performing array preprocessing on the formula (7) by adopting a mode space transformation method according to the derivation to obtain:
Figure FDA0003384206990000024
therefore, the uniform circular microphone array is converted into a 2K + 1-element virtual uniform linear microphone, in order to estimate the coherent signal, a spatial smoothing technique is added, the virtual linear array is divided into L sub-arrays, and similarly, the data vector y (t) is also divided into L sub-vectors, so that the formula (9) can be rewritten as follows:
Figure FDA0003384206990000025
step 4, utilizing each obtained subarray receiving data to reconstruct a matrix, constructing a spatial spectrum cost function, and searching a spectrum peak to obtain an azimuth angle and a pitch angle of a sound source signal: after the sub-arrays are divided, the signals of each sub-array are utilized to receive data, and the data y of the first sub-array after the sub-arrays are split is aimed atl(t) reconstruction of the matrix to achieve coherenceEstimating a signal DOA;
by using
Figure FDA0003384206990000026
Constructing a sub-array fourth-order accumulation matrix, and marking the four-order accumulation matrix as C'l：
Figure FDA0003384206990000027
All of C'lThe addition yields an improved fourth order cumulant matrix:
Figure FDA0003384206990000028
fourth-order cumulant matrix to be constructed
Figure FDA0003384206990000029
Decomposing the characteristic values, and descending the obtained P characteristic values1＞λ2＞…＞λPArrangement, signal subspace is ES＝(e1,e2,...,eN) Noise subspace of EN＝(eN+1，eN+2，...，eP)；
Thereby establishing a spatial spectral cost function of
Figure FDA0003384206990000031
Wherein the content of the first and second substances,
Figure FDA0003384206990000032
while
Figure FDA0003384206990000033
Is the guide vector of the first sub-array obtained by splitting the virtual linear array obtained after the mode space conversion, thereby utilizingEquation (13) performs spectral peak estimation in two dimensions (phi, theta) using a spatial spectral cost function PI-FOC-MUSICFinding the angles corresponding to the N maximum value points in (phi, theta) to determine the position of the sound source signal, namely:
Figure FDA0003384206990000034
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