CN112487703A - Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes - Google Patents

Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes Download PDF

Info

Publication number
CN112487703A
CN112487703A CN202011238167.3A CN202011238167A CN112487703A CN 112487703 A CN112487703 A CN 112487703A CN 202011238167 A CN202011238167 A CN 202011238167A CN 112487703 A CN112487703 A CN 112487703A
Authority
CN
China
Prior art keywords
sparse
signal
noise
array
signals
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011238167.3A
Other languages
Chinese (zh)
Inventor
郭业才
胡国乐
田佳佳
李晨
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Binjiang College of Nanjing University of Information Engineering
Original Assignee
Binjiang College of Nanjing University of Information Engineering
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Binjiang College of Nanjing University of Information Engineering filed Critical Binjiang College of Nanjing University of Information Engineering
Priority to CN202011238167.3A priority Critical patent/CN112487703A/en
Publication of CN112487703A publication Critical patent/CN112487703A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • 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
    • 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
    • G01S3/86—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 with means for eliminating undesired waves, e.g. disturbing noises
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/10—Noise analysis or noise optimisation

Abstract

The invention discloses a DOA estimation method of underdetermined broadband signals in an unknown noise field based on sparse Bayes, which comprises the steps of firstly introducing a co-prime array, reconstructing a spatial covariance matrix by adopting a minimum sparse scale in the co-prime array, and adopting a non-uniform sampling method; vectorizing the covariance matrix, and obtaining a virtual manifold matrix from the co-prime array by using a kronecker product; secondly, preprocessing the opposite quantization covariance matrix, preliminarily inhibiting unknown noise signals in the acquired signals, and weakening the interference of noise on the positioning of target signals; and finally, introducing a sparse Bayesian algorithm, applying the sparse Bayesian algorithm to a sparse signal recovery model, obtaining posterior probability through a Bayesian rule, estimating all hyper-parameters, and updating the true arrival angle estimation of the target signal. The method can solve the non-convex optimization problem, automatically determine the sparsity by utilizing fixed-point updating, and have better processing effect under the condition of collecting a small amount of samples, particularly under the condition of low signal-to-noise ratio.

Description

Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes
Technical Field
The invention belongs to the technical field of DOA estimation of microphone array signals, and particularly relates to a DOA estimation method of underdetermined broadband signals in an unknown noise field based on sparse Bayes.
Background
Estimating the Direction of Arrival (DOA) of a wide band using a sensor array is an active research topic because it has a wide range of applications, requiring the estimation of the so-called angular spectrum, e.g. in radar, sonar, wireless communication and positioning, etc. Since DOA estimation accuracy is determined by the Degree of Freedom (DOF) of the sensor array, the uniformly spaced array requires an increased number of sensors to obtain a higher DOF, thereby increasing manufacturing cost and difficulty of array calibration. Sparse arrays, i.e., nested arrays and co-prime arrays, can achieve higher DOF numbers, resolving more sources than physical sensor numbers using non-uniform sensor locations. Furthermore, for sparse arrays, an increase in DOF is achieved with an extended covariance matrix, with virtual sensor positions determined by continuous and discontinuous lag differences between physical sensors.
Sparse Bayesian Learning (SBL) is implemented as a Compressed Sensing (CS) that remedies the disadvantage that multiple Sparse solutions may correspond to one source when jointly processing multiple frequencies and multiple snapshots to locate one or more sources. As a probabilistic method, SBL calculates the posterior distribution of sparse weight vectors and gives their covariance and mean values[12]. The SBL idea is applied to a Single Measurement Vector (SMV) model for sparse signal recovery, and the posterior probability p (x | y; theta) is obtained through a Bayesian rule, wherein the theta indicates all hyper-parameters. Hyper-parameters are derived from data by marginalizing on x, then performing evidence maximization or type ii maximum likelihoodIs estimated. The appeal of SBL is that its global minimum is always the least rare one, whereas the popular is based on l1The optimization algorithm of norm is not globally convergent. Therefore, the optimization algorithm based on SBL is obviously superior to the traditional optimization algorithm based on l1-optimization algorithm of norm.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a DOA estimation method of an underdetermined broadband signal in an unknown noise field based on sparse Bayes, which mainly researches the estimation of the DOA of the underdetermined broadband of an off-grid source in the unknown noise field based on an SBL algorithm of a cross-prime array, and has better processing effect under the condition of low signal-to-noise ratio.
The technical scheme is as follows: the invention relates to a DOA estimation method of underdetermined broadband signals in an unknown noise field based on sparse Bayes, which specifically comprises the following steps:
(1) introducing a co-prime array, wherein the co-prime array adopts a minimum sparse scale to reconstruct a spatial covariance matrix and adopts a non-uniform sampling method;
(2) vectorizing the covariance matrix, and obtaining a virtual manifold matrix from the co-prime array by using a kronecker product;
(3) preprocessing the vectorized covariance matrix obtained in the step (2), preliminarily inhibiting unknown noise signals in the collected signals, and weakening the interference of noise on the positioning of the target signals;
(4) introducing a sparse Bayesian algorithm, applying the sparse Bayesian algorithm to a sparse signal recovery model, obtaining posterior probability through a Bayesian rule, estimating all hyper-parameters, and updating the true arrival angle estimation of the target signal.
Further, the step (1) is realized as follows:
(11) introducing a co-prime array comprising two uniform linear arrays of N and 2M transducers, wherein the element spacing of the first sub-array is M λ/2, the element spacing of the second sub-array is N λ/2, λ is the central wavelength of the signal; assuming K far-field broadband sources, the kth signal is denoted as sk(t) at an incident angle θkIncident on a co-prime array, where K1, 2, K, the signal observed at the w-th sensor of the co-prime arrayExpressed as:
Figure BDA0002767473770000021
wherein w is more than or equal to 0 and less than or equal to 2M + N-1, sk(t) is the kth signal, nw(t) represents the unknown noise signal at the w-th sensor, τw(θk) Representing the k-th incident signal at an angle of incidence thetakA time delay to reach the w-th sensor of the co-prime array;
(12) an L-point discrete fourier transform is applied to the observed sensor signal, and in the frequency domain, the data vector received at the w-th sensor can be represented as:
Figure BDA0002767473770000022
wherein the content of the first and second substances,
Figure BDA0002767473770000023
is the kth incident signal skL-point DFT, N of (t)w(l) Is the point L DFT of discrete time noise at the w-th sensor of the co-prime array, L1sRepresenting the sampling frequency, the output signal model in the DFT domain is:
X(l)＝A(l,θ)S(l)+N(l)
wherein a (l, θ) [ [ a (l, θ ]) ]1),...,a(l,θK)]Is a direction matrix, where θ ═ θ1,θ2,...,θK}，a(l,θK) Is corresponding to the incident angle thetaKA steering vector after undergoing an l-point DFT;
(13) the covariance matrix of the data vector can be found as:
Figure BDA0002767473770000031
wherein E {. is the desired operator, {. is {. the }HIs the hermitian transpose operator and,
Figure BDA0002767473770000032
represents the power of the k-th incident signal, and
Figure BDA0002767473770000033
representing the corresponding noise power, a (l, θ)k) Is a guide vector; estimating a sample covariance matrix using T available segments
Figure BDA0002767473770000034
As follows:
Figure BDA0002767473770000035
further, the step (2) is realized as follows:
to RlVectorization was performed and the following virtual array model was obtained using the kronecker product:
Figure BDA0002767473770000036
in the formula, Bl＝[b(l,θ1),...,b(l,θK)]For a matrix of equivalent steering vectors, equivalent steering vectors
Figure BDA0002767473770000037
Figure BDA0002767473770000038
Is a matrix sum of the powers of K incident signals
Figure BDA0002767473770000039
Wherein the symbol' denotes a complex conjugate, the symbol
Figure BDA00027674737700000310
Representing the kronecker product, vec (-) represents the vectorization operation.
Further, the step (3) is realized as follows:
representing a set of D steering vectors as
Figure BDA00027674737700000311
The off-grid virtual array model is represented as:
Figure BDA00027674737700000312
wherein v islRepresenting a vector, which is a set of noise parts, consisting of all zeros except for the kth entry;
Figure BDA00027674737700000313
is a sparse vector whose elements are all zeros (except those corresponding to true DOA), vlBy every two different zlThe calculation between eliminates:
Figure BDA00027674737700000314
wherein m is 1, 2.. multidot.h,
Figure BDA00027674737700000315
further, the step (4) is realized by the following steps:
the unknown noise is cancelled and the likelihood is expressed as:
Figure BDA0002767473770000041
in the formula, zmqRepresenting an off-grid virtual array model z at the qth indexm，
Figure BDA0002767473770000042
Represents a sparse vector at the qth index whose elements are the power of the incident signal.
Figure BDA0002767473770000043
Real-valued likelihood is, for real numbers and non-negative numbers:
Figure BDA0002767473770000044
wherein the content of the first and second substances,
Figure BDA0002767473770000045
and
Figure BDA0002767473770000046
the use of a gaussian distribution is used,
Figure BDA0002767473770000047
a priori of (a):
Figure BDA0002767473770000048
wherein, gamma ismq＝diag(γmq,1,...,γmq,D)＝diag(γmq) Is expressed as a vector y in each range depth unit thetamqDiagonal covariance of source amplitude as source power, and vector γmqEach element in (1) is a control
Figure BDA0002767473770000049
The variance of the corresponding element in the data;
let Ymq＝[ymq,...,yhq]Representing a set of T snapshots, the corresponding set of source variance vectors being
Figure BDA00027674737700000410
The multi-frequency likelihood is:
Figure BDA00027674737700000411
by mixing
Figure BDA00027674737700000412
To obtain evidence p (Y) by averaging all real partsmq)：
Figure BDA00027674737700000413
Wherein the content of the first and second substances,
Figure BDA00027674737700000414
maximize joint evidence:
Figure BDA0002767473770000051
the derivative of the objective function is equal to zero:
Figure BDA0002767473770000052
Figure BDA0002767473770000053
has the advantages that: compared with the prior art, the invention has the beneficial effects that: the SBL algorithm developed under the sparse Bayesian framework can approximately solve the non-convex optimization problem, and fixed-point updating is utilized to automatically determine sparsity; the broadband DOA estimation scheme based on the SBL has better processing effect under the condition of collecting a small amount of samples, particularly under the condition of low signal-to-noise ratio.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a physical array element structure of a co-prime array;
FIG. 3 is a anechoic chamber environmental panorama;
FIG. 4 is a DOA estimated spatial spectrum of the proposed method and three other methods;
FIG. 5 is a plot of root mean square error as a function of SNR for the present invention and other methods;
FIG. 6 is a graph of RMS error as a function of fast beat number for the present invention and other methods.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings.
As shown in FIG. 1, the invention provides a DOA estimation method of underdetermined broadband signals in an unknown noise field based on sparse Bayes, a spatial covariance matrix is reconstructed by adopting a minimum sparse scale in a co-prime array, a non-uniform sampling method is adopted, a small number of samples are advocated to be collected, and aliasing of the broadband signals is avoided. And vectorizing the covariance matrix, obtaining a virtual manifold matrix from the co-prime array by using a kronecker product, and obtaining DOA estimation of the broadband signal by using an SBL algorithm.
Step 1: introducing a co-prime array, as shown in fig. 2, the co-prime array reconstructs a spatial covariance matrix using a minimum sparse scale, and a non-uniform sampling method is used.
Consider a co-prime array comprising two uniform linear arrays of N and 2M transducers, wherein the element spacing of the first subarray is M λ/2, the element spacing of the second subarray is N λ/2, λ being the central wavelength of the signal; assuming K far-field broadband sources, the kth signal is denoted as sk(t) at an incident angle θkIncident on the co-prime array, the signal observed at the w-th sensor of the co-prime array is represented as:
Figure BDA0002767473770000061
wherein w is more than or equal to 0 and less than or equal to 2M + N-1, sk(t) is the kth signal, nw(t) represents the unknown noise signal at the w-th sensor, τw(θk) Representing the k-th incident signal at an angle of incidence thetakA time delay to reach the w-th sensor of the co-prime array;
an L-point Discrete Fourier Transform (DFT) is then applied to the observed sensor signals, and in the frequency domain, the data vector received at the w-th sensor is represented as:
Figure BDA0002767473770000062
wherein the content of the first and second substances,
Figure BDA0002767473770000063
is the kth incident signal skL-point DFT, N of (t)w(l) Is the point L DFT of discrete time noise at the w-th sensor of the co-prime array, L1sRepresenting the sampling frequency, the output signal model in the DFT domain is:
X(l)＝A(l,θ)S(l)+N(l)
wherein a (l, θ) [ [ a (l, θ ]) ]1),...,a(l,θK)]Is a direction matrix, where θ ═ θ1,θ2,...,θK}，a(l,θK) Is corresponding to the incident angle thetaKA steering vector after undergoing an l-point DFT;
the covariance matrix of the data vector is:
Figure BDA0002767473770000064
wherein E {. is the desired operator, {. is {. the }HIs the hermitian transpose operator.
Figure BDA0002767473770000065
Represents the power of the k-th incident signal, and
Figure BDA0002767473770000066
representing the corresponding noise power, a (l, θ)k) Is a steering vector.
In practical cases, the theoretical covariance matrix RlNot available, the sample covariance matrix can be estimated using the T available segments (frequency snapshots)
Figure BDA0002767473770000067
As follows:
Figure BDA0002767473770000071
step 2: and vectorizing the covariance matrix, and obtaining a virtual manifold matrix from the co-prime array by using a kronecker product.
To RlVectorization was performed and the following virtual array model was obtained using the kronecker product:
Figure BDA0002767473770000072
in the formula, Bl＝[b(l,θ1),...,b(l,θK)]For a matrix of equivalent steering vectors, equivalent steering vectors
Figure BDA0002767473770000073
Figure BDA0002767473770000074
Is a matrix sum of the powers of K incident signals
Figure BDA0002767473770000075
Wherein the symbol' denotes a complex conjugate, the symbol
Figure BDA0002767473770000076
Representing the kronecker product, and vec (·) represents the vectorization operation.
From matrix BlThe position of the sensor (treated as a manifold matrix for a larger virtual array) in self-differencing diversity:
Ls＝{ls|ls＝Nm,1≤m≤2M-1}∪{ls|ls＝Mn,0≤n≤N-1}
cross difference set:
Lc＝{(Mn-Nm),0≤n≤N-1,1≤m≤2M-1}
corresponding mirror self-differencing set
Figure BDA00027674737700000711
And phaseCorresponding mirror image difference set Lc＝{-lc|lc∈Lc}. Thus, the total lag set from the larger virtual array is
Figure BDA00027674737700000710
Using the total lag, the resulting array can provide more degrees of freedom to resolve more signal sources than the number of physical sensors.
And step 3: and (3) preprocessing the vectorization covariance matrix obtained in the step (2), preliminarily inhibiting unknown noise signals in the acquired signals, and weakening the interference of the noise on the positioning of the target signals.
Representing a set of D steering vectors as
Figure BDA0002767473770000077
The off-grid virtual array model is represented as:
Figure BDA0002767473770000078
wherein v islThe representation vector is a set of noise parts, divided by the kth entry (corresponding to n)w(t) the variance of the kth element) which consists of all zeros;
Figure BDA0002767473770000079
is a sparse vector whose elements are all zeros (except those corresponding to true DOA).
Noise part vlCan be determined by every two different zlThe calculated elimination between, as shown in the following equation:
Figure BDA0002767473770000081
wherein m is 1,2, a, h, wherein
Figure BDA0002767473770000082
And 4, step 4: introducing a sparse Bayesian algorithm, applying the sparse Bayesian algorithm to a sparse signal recovery model, obtaining posterior probability through a Bayesian rule, estimating all hyper-parameters, and updating the true arrival angle estimation of the target signal.
Suppose to exist asqQ1.. Q is an indexed Q ≦ L DFT bins that may or may not occupy contiguous bands within the signal bandwidth.
The unknown noise is cancelled and the likelihood is expressed as:
Figure BDA0002767473770000083
in the formula, zmqRepresenting an off-grid virtual array model z at the qth indexm，
Figure BDA0002767473770000084
Represents a sparse vector at the qth index whose elements are the power of the incident signal.
Due to the fact that
Figure BDA0002767473770000085
Real and non-negative, so the above equation is converted to the following real-valued likelihood form:
Figure BDA0002767473770000086
here, the
Figure BDA0002767473770000087
And
Figure BDA0002767473770000088
the use of a gaussian distribution is used,
Figure BDA0002767473770000089
can be expressed as:
Figure BDA00027674737700000810
wherein, gamma ismq＝diag(γmq,1,...,γmq,D)＝diag(γmq) Is expressed as a vector y in each range depth unit thetamqDiagonal covariance of source amplitude as source power, and vector γmqEach element in (1) is a control
Figure BDA00027674737700000811
The variance of the corresponding element in the set.
Let Ymq＝[ymq,...,yhq]Representing a set of T snapshots, and a corresponding set of source variance vectors represented as
Figure BDA00027674737700000812
The multi-frequency likelihood is expressed as:
Figure BDA00027674737700000813
by mixing
Figure BDA0002767473770000091
To obtain evidence p (Y) by averaging all real partsmq)：
Figure BDA0002767473770000092
Here, the
Figure BDA0002767473770000093
To estimate the representation
Figure BDA0002767473770000094
Gamma of (2)mqMaximize joint evidence:
Figure BDA0002767473770000095
to obtain the minimum of the objective function, the derivative of the objective function is equal to zero:
Figure BDA0002767473770000096
Figure BDA0002767473770000097
as shown in fig. 3, a linear microphone array structure is installed in the anechoic chamber to pick up spatial information of spatial voice; the sound in the sound pick-up system equipment is placed to provide a sound source for the microphone array and the anechoic chamber is 5.5m 3.3m 2.3m in size.
The coprime array consists of a pair of sparse linear arrays (ULA) of M-3 and N-4, for a total of nine physical sensors, whose positions are set to S [0,3,4,6,8,9,12,16,20] λ/2. Suppose that K-12 wideband signals are incident on a co-prime array with M-3 and N-4, the fast beat count is 100, and the input signal-to-noise ratio SNR is fixed at 0 dB. The simulation result is shown in fig. 4, wherein fig. 4(a) is the DOA estimated spatial spectrum of the proposed method of the present invention, fig. 4(b) is the DOA estimated spatial spectrum of the SOMP _ LS algorithm, fig. 4(c) is the DOA estimated spatial spectrum of the SOMP _ TLS, and fig. 4(d) is the DOA estimated spatial spectrum of the OGSBI.
As shown in fig. 5, at a fast beat number of 200, the four algorithms vary with the signal-to-noise ratio, and the simulation result of the SBL algorithm shows better estimation performance than the other three algorithms, especially at a low signal-to-noise ratio, the RMSE of the SBL algorithm is significantly smaller than the other three algorithms, and shows better performance on DOA estimation of the broadband signal.
As shown in fig. 6, when the signal-to-noise ratio is 0dB, the performance of the algorithm (SBL) of the present invention is significantly better than that of the other three algorithms along with the increase of the fast beat number, and under the same condition, the root mean square error of the algorithm of the present invention is the smallest and the accuracy is higher.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (5)

1. A DOA estimation method of an underdetermined broadband signal in an unknown noise field based on sparse Bayes is characterized by comprising the following steps:
(1) introducing a co-prime array, wherein the co-prime array adopts a minimum sparse scale to reconstruct a spatial covariance matrix and adopts a non-uniform sampling method;
(2) vectorizing the covariance matrix, and obtaining a virtual manifold matrix from the co-prime array by using a kronecker product;
(3) preprocessing the vectorized covariance matrix obtained in the step (2), preliminarily inhibiting unknown noise signals in the collected signals, and weakening the interference of noise on the positioning of the target signals;
(4) introducing a sparse Bayesian algorithm, applying the sparse Bayesian algorithm to a sparse signal recovery model, obtaining posterior probability through a Bayesian rule, estimating all hyper-parameters, and updating the true arrival angle estimation of the target signal.
2. The DOA estimation method for underdetermined broadband signals in unknown noise fields based on sparse Bayes as in claim 1, wherein said step (1) is implemented as follows:
(11) introducing a co-prime array comprising two uniform linear arrays of N and 2M transducers, wherein the element spacing of the first sub-array is M λ/2, the element spacing of the second sub-array is N λ/2, λ is the central wavelength of the signal; assuming K far-field broadband sources, the kth signal is denoted as sk(t) at an incident angle θkIncident on the co-prime array, the signal observed at the w-th sensor of the co-prime array is represented as:
Figure FDA0002767473760000011
wherein w is more than or equal to 0 and less than or equal to 2M + N-1, sk(t) is the kth signal, nw(t) at the w-th passUnknown noise signal at the sensor, tauw(θk) Representing the k-th incident signal at an angle of incidence thetakA time delay to reach the w-th sensor of the co-prime array;
(12) an L-point discrete fourier transform is applied to the observed sensor signal, and in the frequency domain, the data vector received at the w-th sensor can be represented as:
Figure FDA0002767473760000012
wherein the content of the first and second substances,
Figure FDA0002767473760000013
is the kth incident signal skL-point DFT, N of (t)w(l) Is the point L DFT of discrete time noise at the w-th sensor of the co-prime array, L1sRepresenting the sampling frequency, the output signal model in the DFT domain is:
X(l)＝A(l,θ)S(l)+N(l)
wherein a (l, θ) [ [ a (l, θ ]) ]1),...,a(l,θK)]Is a direction matrix, where θ ═ θ1,θ2,...,θK}，a(l,θK) Is corresponding to the incident angle thetaKA steering vector after undergoing an l-point DFT;
(13) the covariance matrix of the data vector can be found as:
Figure FDA0002767473760000021
wherein E {. is the desired operator, {. is {. the }HIs the hermitian transpose operator and,
Figure FDA0002767473760000022
represents the power of the k-th incident signal, and
Figure FDA0002767473760000023
to representCorresponding noise power, a (l, theta)k) Is a guide vector; estimating a sample covariance matrix using T available segments
Figure FDA0002767473760000024
As follows:
Figure FDA0002767473760000025
3. the DOA estimation method for underdetermined broadband signals in unknown noise fields based on sparse Bayes as in claim 1, wherein said step (2) is implemented as follows:
to RlVectorization was performed and the following virtual array model was obtained using the kronecker product:
Figure FDA0002767473760000026
in the formula, Bl＝[b(l,θ1),...,b(l,θK)]For a matrix of equivalent steering vectors, equivalent steering vectors
Figure FDA0002767473760000027
Is a matrix sum of the powers of K incident signals
Figure FDA0002767473760000028
Wherein the symbol' denotes a complex conjugate, the symbol
Figure FDA0002767473760000029
Representing the kronecker product, vec (-) represents the vectorization operation.
4. The DOA estimation method for underdetermined broadband signals in unknown noise fields based on sparse Bayes as in claim 1, wherein said step (3) is implemented as follows:
representing a set of D steering vectors as
Figure FDA00027674737600000210
The off-grid virtual array model is represented as:
Figure FDA00027674737600000211
wherein v islRepresenting a vector, which is a set of noise parts, consisting of all zeros except for the kth entry;
Figure FDA00027674737600000212
is a sparse vector whose elements are all zeros (except those corresponding to true DOA), vlBy every two different zlThe calculation between eliminates:
Figure FDA0002767473760000031
wherein m is 1, 2.. multidot.h,
Figure FDA0002767473760000032
5. the DOA estimation method for underdetermined broadband signals in unknown noise fields based on sparse Bayes as in claim 1, wherein said step (4) is implemented as follows:
the unknown noise is cancelled and the likelihood is expressed as:
Figure FDA0002767473760000033
in the formula, zmqRepresenting an off-grid virtual array model z at the qth indexm，
Figure FDA0002767473760000034
Representing a sparse vector at the qth index whose elements are the power of the incident signal;
Figure FDA0002767473760000035
real-valued likelihood is, for real numbers and non-negative numbers:
Figure FDA0002767473760000036
wherein the content of the first and second substances,
Figure FDA0002767473760000037
and
Figure FDA0002767473760000038
the use of a gaussian distribution is used,
Figure FDA0002767473760000039
a priori of (a):
Figure FDA00027674737600000310
wherein, gamma ismq＝diag(γmq,1,...,γmq,D)＝diag(γmq) Is expressed as a vector y in each range depth unit thetamqDiagonal covariance of source amplitude as source power, and vector γmqEach element in (1) is a control
Figure FDA00027674737600000311
The variance of the corresponding element in the data;
let Ymq＝[ymq,...,yhq]Representing a set of T snapshots, the corresponding set of source variance vectors being
Figure FDA00027674737600000312
The multi-frequency likelihood is:
Figure FDA00027674737600000313
by mixing
Figure FDA00027674737600000314
To obtain evidence p (Y) by averaging all real partsmq)：
Figure FDA0002767473760000041
Wherein the content of the first and second substances,
Figure FDA0002767473760000042
maximize joint evidence:
Figure FDA0002767473760000043
the derivative of the objective function is equal to zero:
Figure FDA0002767473760000044
Figure FDA0002767473760000045
CN202011238167.3A 2020-11-09 2020-11-09 Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes Pending CN112487703A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011238167.3A CN112487703A (en) 2020-11-09 2020-11-09 Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011238167.3A CN112487703A (en) 2020-11-09 2020-11-09 Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes

Publications (1)

Publication Number Publication Date
CN112487703A true CN112487703A (en) 2021-03-12

Family

ID=74928928

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011238167.3A Pending CN112487703A (en) 2020-11-09 2020-11-09 Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes

Country Status (1)

Country Link
CN (1) CN112487703A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113093093A (en) * 2021-04-07 2021-07-09 南京邮电大学 Vehicle positioning method based on linear array direction of arrival estimation
CN113589255A (en) * 2021-08-23 2021-11-02 武汉大学 Arrival angle estimation method based on multi-frequency joint sparse Bayesian learning

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109407045A (en) * 2018-10-10 2019-03-01 苏州大学 A kind of non-homogeneous sensor array broadband signal Wave arrival direction estimating method
CN109444810A (en) * 2018-12-24 2019-03-08 哈尔滨工程大学 A kind of relatively prime array non-grid DOA estimation method under non-negative sparse Bayesian learning frame

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109407045A (en) * 2018-10-10 2019-03-01 苏州大学 A kind of non-homogeneous sensor array broadband signal Wave arrival direction estimating method
CN109444810A (en) * 2018-12-24 2019-03-08 哈尔滨工程大学 A kind of relatively prime array non-grid DOA estimation method under non-negative sparse Bayesian learning frame

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
冯明月;何明浩;陈昌孝;韩俊;: "基于Bessel先验快速稀疏贝叶斯学习的互质阵列DOA估计", 电子与信息学报, no. 07 *
董天宝;汪海兵;曾芳玲;: "基于稀疏贝叶斯学习的DOA估计", 火力与指挥控制, no. 03, pages 42 - 45 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113093093A (en) * 2021-04-07 2021-07-09 南京邮电大学 Vehicle positioning method based on linear array direction of arrival estimation
CN113093093B (en) * 2021-04-07 2023-08-18 南京邮电大学 Vehicle positioning method based on linear array direction of arrival estimation
CN113589255A (en) * 2021-08-23 2021-11-02 武汉大学 Arrival angle estimation method based on multi-frequency joint sparse Bayesian learning
CN113589255B (en) * 2021-08-23 2023-08-01 武汉大学 Arrival angle estimation method based on multi-frequency joint sparse Bayesian learning

Similar Documents

Publication Publication Date Title
CN110031794B (en) Coherent information source DOA estimation method based on difference common matrix reconstruction
WO2021139208A1 (en) One-dimensional doa estimation method based on combined signals at specific frequencies
CN108375763B (en) Frequency division positioning method applied to multi-sound-source environment
CN109375154B (en) Coherent signal parameter estimation method based on uniform circular array in impact noise environment
CN112130111B (en) Single-snapshot two-dimensional DOA estimation method in large-scale uniform cross array
Zhang et al. Bounded non-linear covariance based ESPRIT method for noncircular signals in presence of impulsive noise
CN108802667A (en) Wave arrival direction estimating method based on generalized orthogonal match tracing
CN112487703A (en) Underdetermined broadband signal DOA estimation method in unknown noise field based on sparse Bayes
Ahmad et al. Wideband DOA estimation based on incoherent signal subspace method
CN108398659B (en) Direction-of-arrival estimation method combining matrix beam and root finding MUSIC
Shaw et al. Estimation of angles of arrivals of broadband signals
CN111693947A (en) Improved MUSIC method based on co-prime array DOA estimation
US5315308A (en) Method for eletromagnetic source localization
CN108828586B (en) Bistatic MIMO radar angle measurement optimization method based on beam domain
CN113267746A (en) Weighted broadband direction of arrival estimation method based on group sparsity
CN111551892B (en) Steady self-adaptive beam forming method and device
CN111368256B (en) Single snapshot direction finding method based on uniform circular array
CN111610488A (en) Method for estimating wave arrival angle of any array based on deep learning
CN110579737A (en) Sparse array-based MIMO radar broadband DOA calculation method in clutter environment
He et al. DOA estimation of wideband signals based on iterative spectral reconstruction
CN109061564B (en) Simplified near-field positioning method based on high-order cumulant
CN114755628A (en) Method for estimating direction of arrival of acoustic vector sensor array under non-uniform noise
CN112698263A (en) Orthogonal propagation operator-based single-basis co-prime MIMO array DOA estimation algorithm
Li et al. DOA Estimation Based on Sparse Reconstruction via Acoustic Vector Sensor Array under Non-uniform Noise
Tayem et al. Capon root-MUSIC-like direction of arrival estimation based on real data

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination