[go: nahoru, domu]

CN116224212A - Bayesian learning-based sparse array angle estimation method and device - Google Patents

Bayesian learning-based sparse array angle estimation method and device Download PDF

Info

Publication number
CN116224212A
CN116224212A CN202111461641.3A CN202111461641A CN116224212A CN 116224212 A CN116224212 A CN 116224212A CN 202111461641 A CN202111461641 A CN 202111461641A CN 116224212 A CN116224212 A CN 116224212A
Authority
CN
China
Prior art keywords
matrix
dimensional
output signal
spectrum
array
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
CN202111461641.3A
Other languages
Chinese (zh)
Inventor
吴敏
郝程鹏
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.)
Institute of Acoustics CAS
Original Assignee
Institute of Acoustics CAS
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 Institute of Acoustics CAS filed Critical Institute of Acoustics CAS
Priority to CN202111461641.3A priority Critical patent/CN116224212A/en
Publication of CN116224212A publication Critical patent/CN116224212A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Radar Systems Or Details Thereof (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention belongs to the technical field of signal processing, and particularly relates to a sparse array angle estimation method and a device thereof based on Bayesian learning, wherein the method comprises the following steps: each array element in the sparse array receives a corresponding received signal and carries out vectorization processing to obtain an output signal in a vector form, the sparse array outputs the output signal in the vector form to obtain a two-dimensional output signal model, and the two-dimensional output signal model is subjected to dimension reduction processing to obtain a one-dimensional output signal model; extracting a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic; and solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and performing constant false alarm detection on the space spectrum to obtain the azimuth estimation of the target.

Description

Bayesian learning-based sparse array angle estimation method and device
Technical Field
The invention belongs to the technical field of signal processing and beam direction estimation of radar signals, acoustic signals and electromagnetic signals, and particularly relates to a sparse array angle estimation method and device based on Bayesian learning.
Background
The beam forming is an important task of array signal processing, is widely applied to the fields of radar, sonar, communication and the like, can inhibit spatial interference, and estimates the arrival direction of signals, thereby realizing detection and positioning of targets. In modern array signal processing, in a multi-target and clustered target environment, the requirements on angular resolution are higher and higher, the array size is increased, the difference of azimuth information of signals among different array elements is increased, higher resolution capability can be brought, but high hardware manufacturing cost can be brought. Therefore, under the sparse array condition, the spatial gain and the angular resolution are improved, and the hot spot problem in the field of array signal processing is formed. When the number of array elements is limited, the sampling of the array elements to the spatial signal does not meet the nyquist sampling theorem, and the conventional beam forming algorithm is difficult to ensure the angle estimation performance.
Common beamforming methods sometimes Delay-and-sum (DAS) and minimum variance undistorted (MVDR) beamformers; the DAS obtains beam output by summing after compensating the delay difference of each channel, and has low calculation complexity and high robustness; the MVDR beamformer proposed by Capon uses a minimum variance criterion to minimize the output power and maximize the array gain. Meanwhile, some subspace high-resolution azimuth estimation algorithms have emerged in recent 30 years, wherein the most representative is a multiple signal classification (Multiple Signal Classification, MUSIC) algorithm, the MUSIC algorithm firstly constructs a covariance matrix for array received data, then carries out feature decomposition on the covariance matrix, so as to obtain a signal subspace and a noise subspace corresponding to signal components and noise components, then constructs a spatial spectrum function by utilizing orthogonality of the signal subspace and the noise subspace, searches spectrum peaks, estimates angle information of signals, overcomes Rayleigh criterion theoretically, and can obtain super-resolution estimation of target angles.
However, the conventional DAS algorithm has a low spatial resolution due to the limitation of the aperture size, and increasing the resolution by increasing the number of array elements increases the hardware cost of the system. The MVDR algorithm and the MUSIC algorithm are required to decompose covariance matrixes and search spectral peaks, and the method is greatly influenced by noise and has high calculation complexity.
Disclosure of Invention
In order to solve the above-mentioned defects existing in the prior art, the invention provides a sparse array angle estimation method based on Bayesian learning, which comprises the following steps:
each array element in the sparse array receives a corresponding received signal and carries out vectorization processing to obtain an output signal in a vector form, the sparse array outputs the output signal in the vector form to obtain a two-dimensional output signal model, and the two-dimensional output signal model is subjected to dimension reduction processing to obtain a one-dimensional output signal model;
extracting a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic;
and solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and performing constant false alarm detection on the space spectrum to obtain the azimuth estimation of the target.
As one of the improvements of the above technical solution, each array element in the sparse array receives a corresponding received signal and performs vectorization processing to obtain a vector-form output signal, the sparse array outputs the vector-form output signal to obtain a two-dimensional output signal model, and the two-dimensional output signal model is subjected to dimension reduction processing to obtain a one-dimensional output signal model; the specific implementation process is as follows:
assuming that the sparse array is a random array with M array elements, and adopting rectangular coordinates for representation; assuming that N remote incoming waves in the directions exist in the space, each array element receives the remote incoming waves in each direction as a receiving signal;
the m-th array element receives the corresponding receiving signal y m (t) and takes it as output: m=1, 2,3, …, M, …, M;
Figure BDA0003388980070000021
wherein ,τm,n The delay of the arrival of the remote incoming wave in the nth direction at the mth array element compared with the arrival of the remote incoming wave at the reference point; τ m,n ＝R m,n C; wherein c is the propagation speed of the remote incoming wave; r is R m,n Distance from the target located in the nth direction to the mth array element; s (t- τ) m,n ) Target incoming waves in the nth direction received by the mth array element; t is the receiving time of the target incoming wave;
ε m (t) is noise of the mth array element;
for the narrowband case, the delay is equivalent to the phase shift, noted as
Figure BDA0003388980070000022
wherein ,fc Carrier frequency of the narrow-band signal;
Figure BDA0003388980070000031
Then y m And (t) rewriting as:
Figure BDA0003388980070000032
vector form of the output signals of M array elements:
Figure BDA0003388980070000033
wherein y (t) is the vector array output of M array elements; wherein y (t) = [ y ] 1 (t),y 2 (t),…,y M (t)] T； wherein ,yM (t) is the vector output of the mth element;
s (t) is the incoming spatial spectrum; wherein s (t) = [ s ] 0 (t),s 1 (t),…,s n (t),…,s (N-1) (t)] T ；s n (t) is the target arrival spatial spectrum in the nth direction;
epsilon (t) is noise; wherein ε (t) = [ ε ] 1 (t),ε 2 (t),…,ε M (t)] T ；ε M (t) is noise received by the mth array element;
a(θ n ) A guide vector for the nth observation angle;
wherein
Figure BDA0003388980070000034
A is a guide matrix; wherein a= [ a (θ 0 ),a(θ 1 ),…,a(θ N-1 )]；
Dividing the observation angle range into H observation angle units, and changing the corresponding guide matrix A into an M multiplied by H matrix:
A＝[a(θ 0 ),a(θ 1 ),…,a(θ h ),…,a(θ H-1 )]；
wherein ,a(θh ) A guide vector for the h observation angle;
wherein ,
Figure BDA0003388980070000035
when the received data y (t) has K snapshots, vectorizing output signals of M array elements to obtain an output signal matrix in a vector form, and marking the output signal matrix as a two-dimensional output signal model y:
y＝As+ε (17)
wherein y= [ y (1) y (2) … y (K)]Representing a matrix of size M x K; s is a two-dimensional space spectrum matrix to be recovered, and the elements of the kth row and the kth column are s n (k) The method comprises the steps of carrying out a first treatment on the surface of the Epsilon is a noise vector matrix;
performing dimension reduction processing on the two-dimensional output signal model to obtain a one-dimensional output signal model Y;
Figure BDA0003388980070000041
wherein ,
Figure BDA0003388980070000042
is a measurement matrix of MK×HK dimension; wherein (1)>
Figure BDA0003388980070000043
Wherein y=vec (Y); s=vec (S); e=vec (epsilon).
As one of the improvements of the above technical scheme, a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered are extracted from the obtained one-dimensional output signal model; when the two-dimensional space spectrum matrix to be recovered meets the RIP characteristic, constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix; the specific process is as follows:
extracting a measurement matrix from the obtained one-dimensional output signal model Y
Figure BDA0003388980070000044
And a two-dimensional spatial spectrum matrix S to be recovered;
judging whether the two-dimensional space spectrum matrix S to be recovered meets RIP characteristics or not; wherein, the meeting condition is:
Figure BDA0003388980070000045
wherein ,
Figure BDA0003388980070000046
wherein ,
Figure BDA0003388980070000047
for matrix->
Figure BDA0003388980070000048
Is a correlation vector of (2);
Figure BDA0003388980070000049
θ p is the p-th observation angle;
Figure BDA00033889800700000410
θ q the q observation angle;
if the requirements are not met, the two-dimensional spatial spectrum matrix S to be recovered does not meet the RIP characteristics, and the process is finished;
if the above satisfaction conditions are satisfied, the two-dimensional spatial spectrum matrix S to be recovered satisfies RIP characteristics, and an optimization function is further constructed:
S＝argmin{J(S)} (19)
wherein ,
Figure BDA00033889800700000411
wherein I F Representing the F matrix norm; min (·) is a minimization operation; ρ is a sparse coefficient.
As one of the improvements of the above technical scheme, the method comprises the steps of solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and performing constant false alarm detection to obtain the azimuth estimation of the target; the specific process is as follows:
calculating conjugate gradient of the optimization function with respect to the spatial spectrum matrix S by adopting a conjugate gradient method
Figure BDA0003388980070000051
Figure BDA0003388980070000052
Wherein H (S) is a Hessian matrix;
Figure BDA0003388980070000053
is a measurement matrix; (. Cndot. H The conjugate H (S) representing the matrix is a coefficient matrix of S, which can be expressed as
H(S)＝2Y H Y+ρΛ(S) (21)
Wherein ρ is a sparse coefficient;
Figure BDA0003388980070000054
wherein S (hk) is the element value of the h row and the k column of the matrix S; diag [ ] is a diagonal matrix; τ is a very small positive value, 0.01;
as can be seen by adopting the Newton iterative algorithm, the (1+1) th iteration of S is Newton iterative:
Figure BDA0003388980070000055
wherein, beta is iteration step length, [. Cndot.] -1 Representing the inverse of the matrix;
gradient conjugate
Figure BDA0003388980070000056
The expression of (2) is substituted into the iterative expression (16), and the deduction is obtained:
Figure BDA0003388980070000057
assuming an iteration step β=1, iteration (16) can be converted into
Figure BDA0003388980070000058
The equation (18) is optimized, and the Hessian matrix needs to be updated to H (S) at each iteration l )＝2Y H Y+ρΛ(S l )；
When the iteration satisfies the following conditions, the algorithm is terminated to obtain a two-dimensional space-time spectrum s h (k) Representing the space-time spectrum of the kth snapshot of the h azimuth;
Figure BDA0003388980070000059
accumulating the obtained two-dimensional space-time spectrum in time to obtain a target angle space spectrum
Figure BDA00033889800700000510
Figure BDA00033889800700000511
For a pair of
Figure BDA00033889800700000512
And carrying out conventional constant false alarm detection to obtain the azimuth estimation of the target.
The invention also provides a sparse array angle estimation device based on Bayesian learning, which comprises:
the model acquisition module is used for vectorizing received signals received by each array element in the sparse array to obtain output signals in a vector form, outputting the output signals in the vector form by the sparse array to obtain a two-dimensional output signal model, and performing dimension reduction processing on the two-dimensional output signal model to obtain a one-dimensional output signal model;
the optimization function construction module is used for extracting a measurement matrix and a two-dimensional space spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic; and
the azimuth estimation module is used for solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and then carrying out constant false alarm detection on the space spectrum to obtain azimuth estimation of the target.
The invention also provides a computer device for target position estimation, comprising a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, the processor implementing the method when executing the computer program.
The present invention also provides a computer-readable storage medium comprising a stored computer program; wherein the computer program, when run, controls a device in which the computer readable storage medium resides to perform the method.
The invention also provides an information data processing terminal which is used for realizing the method.
Compared with the prior art, the invention has the beneficial effects that:
1. the method is a sparse array azimuth estimation method based on compressed sensing, can effectively improve the target angle resolution, and has the advantages of low side lobe and strong noise robustness; the sparse array azimuth estimation method based on compressed sensing is generally not lower than the traditional algorithm, and has sharper beam response under the conditions of low signal to noise ratio and limited array elements which are superior to MVDR and MUSIC algorithms;
2. in the method, the sparse coefficient is deduced through the Bayes compressed sensing theory, so that the noise robustness of the algorithm is ensured;
3. the method improves the algorithm efficiency by adopting the conjugate gradient algorithm, and the algorithm can realize super-resolution angle estimation by using fewer snapshots under the sparse array scene.
Drawings
FIG. 1 is a flow chart of a Bayesian learning-based sparse array angle estimation method of the present invention;
FIG. 2 is a schematic diagram of the results of angle estimation for each method for a single target of the method of the present invention and a conventional DAS, MVDR, MUSIC method;
FIG. 3 is a diagram showing the relationship between the angle estimation error and the signal to noise ratio of the method of the present invention and the conventional DAS, MVDR, MUSIC method;
FIG. 4 is a diagram showing the relationship between the angle estimation error and the number of array elements of the method of the present invention and the conventional DAS, MVDR, MUSIC method;
FIG. 5 (a) is a schematic diagram comparing the results of the method of the present invention with the results of the conventional DAS, MVDR, MUSIC method with target orientations of-5 and 5;
fig. 5 (b) is a schematic diagram showing the comparison of the results of the method of the present invention with the target azimuth of-3 ° and 3 ° of the conventional DAS, MVDR, MUSIC method.
Detailed Description
The invention will now be further described with reference to the accompanying drawings.
The invention provides a sparse array angle estimation method based on Bayesian learning, which adopts a sparse array azimuth estimation algorithm based on compressed sensing, wherein the algorithm is a novel target angle estimation method utilizing target space domain sparse priori information, and is also a super-resolution angle estimation algorithm under the condition of limited array elements. Because the scene background noise is considered when the constraint condition of the optimization problem is constructed, the optimization algorithm can effectively inhibit the noise, and the estimation quality is further improved; sparse coefficients are deduced through Bayes compressed sensing, so that the method can self-adaptively recover the target azimuth, and the algorithm is stable; the correction Newton method is designed to solve the optimization problem, and the correction Newton method is independent of solving software, so that the hardware deployment of the algorithm is facilitated.
As shown in fig. 1, the method includes:
each array element in the sparse array receives a corresponding received signal and carries out vectorization processing to obtain an output signal in a vector form, the sparse array outputs the output signal in the vector form to obtain a two-dimensional output signal model, and the two-dimensional output signal model is subjected to dimension reduction processing to obtain a one-dimensional output signal model;
specifically, the sparse array can be divided into a linear array, an area array and a volume array according to different array element placement positions.
Assuming that the sparse array is a random array with M array elements, and adopting rectangular coordinates for representation; assuming that N remote incoming waves in the directions exist in the space, each array element is a sensor with receiving and transmitting functions, and the remote incoming waves in all directions are received and used as receiving signals; all sensors are isotropic.
The m-th array element receives the corresponding receiving signal y m (t) and takes it as output: m=1, 2,3, …, M, …, M;
Figure BDA0003388980070000081
wherein ,τm,n The delay of the arrival of the remote incoming wave in the nth direction at the mth array element compared with the arrival of the remote incoming wave at the reference point; τ m,n ＝R m,n C; wherein c is the propagation speed of the remote incoming wave; r is R m,n Distance from the target located in the nth direction to the mth array element; s (t- τ) m,n ) Target incoming waves in the nth direction received by the mth array element; t is the receiving time of the target incoming wave;
ε m (t) is the noise of the mth element, where it is assumed that the noise is statistically independent of the incoming wave;
for the narrowband case, the delay is equivalent to the phase shift, noted as
Figure BDA0003388980070000082
wherein ,fc Carrier frequency of the narrow-band signal;
Figure BDA0003388980070000083
Then y m And (t) rewriting as:
Figure BDA0003388980070000084
vector form of the output signals of M array elements:
Figure BDA0003388980070000085
wherein y (t) is the vector array output of M array elements; wherein y (t) = [ y ] 1 (t),y 2 (t),…,y M (t)] T； wherein ,yM (t) is the vector output of the mth element;
s (t) is the incoming spatial spectrum; wherein s (t) = [ s ] 0 (t),s 1 (t),…,s n (t),…,s (N-1) (t)] T ；s n (t) is the target arrival spatial spectrum in the nth direction;
epsilon (t) is noise; wherein ε (t) = [ ε ] 1 (t),ε 2 (t),…,ε M (t)] T ；ε M (t) is noise received by the mth array element;
a(θ n ) The phase difference between the target direction and each array element position is represented by the guide vector of the nth observation angle; wherein the method comprises the steps of
Figure BDA0003388980070000086
A is a guide matrix; wherein a= [ a (θ 0 ),a(θ 1 ),…,a(θ N-1 )]；
Dividing the observation angle range into H observation angle units, and changing the corresponding guide matrix A into an M multiplied by H matrix:
A＝[a(θ 0 ),a(θ 1 ),…,a(θ h ),…,a(θ H-1 )]；
wherein ,a(θh ) A guide vector for the h observation angle;
wherein ,
Figure BDA0003388980070000091
when the received data has K snapshots, vectorizing output signals of M array elements to obtain an output signal matrix in a vector form, and marking the output signal matrix as a two-dimensional output signal model y:
y＝As+ε (30)
wherein y= [ y (1) y (2) … y (K)]Representing a matrix of size M x K; s is a two-dimensional space spectrum matrix to be recovered, and the elements of the kth row and the kth column are s n (k) The method comprises the steps of carrying out a first treatment on the surface of the Epsilon is a noise vector matrix;
performing dimension reduction processing on the two-dimensional output signal model to obtain a one-dimensional output signal model Y;
Figure BDA0003388980070000092
wherein ,
Figure BDA0003388980070000093
is a measurement matrix of MK×HK dimension; wherein (1)>
Figure BDA0003388980070000094
Wherein y=vec (Y); vec (y) is the operation of sequentially stacking each column of vectors of the two-dimensional output signal model y to form one vector;
s=vec (S) is an operation of sequentially stacking each column vector of the two-dimensional spatial spectrum matrix S to be recovered to form one vector;
e=vec (epsilon) is the operation of stacking each column vector of the noise vector matrix epsilon in turn to form one vector;
where vec (·) may represent the operation of stacking the column vectors of the matrix in turn to form one vector. It is assumed that in the multi-snapshot observation, the target angle does not change, i.e. the space-time is not coupled, so that the space-time spectrum is accumulated in time and can be used as the space-spectrum estimation
Figure BDA0003388980070000095
Figure BDA0003388980070000096
The non-zero value position and number of the target represent the position estimation value and the target number of the target, the target is only in a few positions in the target scene, namely N < H, the space spectrum has strong sparse characteristic, and the position spectrum estimation process can be converted into the process of solving the optimization function by utilizing the characteristic.
In practical application, the number of targets is smaller than the number of array elements,
Figure BDA0003388980070000097
is a high-dimensional to low-dimensional measurement matrix, and recovering a two-dimensional spatial spectrum from finite data is a pathological process. CS theory shows that under a priori that S is a sparse matrix, if the matrix is measured +.>
Figure BDA0003388980070000098
The RIP characteristic is satisfied, the unknown spectrum matrix S can be recovered from the received signal Y. Wherein the RIP characteristic is met, i.e. there is a constraint of the equidistant constant delta epsilon (0, 1) to +.>
Figure BDA0003388980070000099
This is true. RIP characteristics are related to the correlation of the basis vectors constituting the measurement matrix, and the smaller the correlation coefficient is, the better the orthogonality of the basis.
Figure BDA0003388980070000101
For normalized basis vector sets, the correlation coefficients between each other are
Figure BDA0003388980070000102
When the spatial spectrum matrix satisfies the following condition
Figure BDA0003388980070000103
When (Restricted Isometry Property, limited equidistant properties) RIP characteristics are met.
Under the signal sparse condition, the disease state solving problem is converted into l 1 And optimizing the norm, thereby obtaining the target angle information.
Extracting a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic;
specifically, from the obtained one-dimensional output signal model Y, a measurement matrix is extracted
Figure BDA0003388980070000104
And a two-dimensional spatial spectrum matrix S to be recovered;
judging whether the two-dimensional space spectrum matrix S to be recovered meets RIP characteristics or not; wherein, the meeting condition is:
Figure BDA0003388980070000105
wherein ,
Figure BDA0003388980070000106
wherein ,
Figure BDA0003388980070000107
for matrix->
Figure BDA0003388980070000108
Is a correlation vector of (2);
Figure BDA0003388980070000109
θ p is the p-th observation angle;
Figure BDA00033889800700001010
θ q the q observation angle;
if the requirements are not met, the two-dimensional spatial spectrum matrix S to be recovered does not meet the RIP characteristics, and the process is finished;
if the above satisfaction conditions are satisfied, the two-dimensional spatial spectrum matrix S to be recovered satisfies RIP characteristics, and an optimization function is further constructed:
S＝argmin{J(S)} (34)
wherein ,
Figure BDA0003388980070000111
wherein I F Representing the F matrix norm; min (·) is a minimization operation; ρ is a sparse coefficient.
And solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and performing constant false alarm detection on the space spectrum to obtain the azimuth estimation of the target.
Specifically, a conjugate gradient method is adopted to calculate the conjugate gradient of the optimization function relative to the spatial spectrum matrix S
Figure BDA0003388980070000112
Figure BDA0003388980070000113
Wherein H (S) is a Hessian matrix;
Figure BDA0003388980070000114
is a measurement matrix; (. Cndot. H The conjugate H (S) representing the matrix is a coefficient matrix of S, which can be expressed as
H(S)＝2Y H Y+ρΛ(S) (36)
Wherein ρ is a sparse coefficient;
Figure BDA0003388980070000115
wherein S (hk) is the element value of the h row and the k column of the matrix S; diag [ ] is a diagonal matrix; τ is a very small positive value, 0.01;
as can be seen by adopting the Newton iterative algorithm, the (1+1) th iteration of S is Newton iterative:
Figure BDA0003388980070000116
wherein, beta is iteration step length, [. Cndot.] -1 Representing the inverse of the matrix;
gradient conjugate
Figure BDA0003388980070000117
The expression of (2) is substituted into the iterative expression (16), and the deduction is obtained:
Figure BDA0003388980070000118
assuming an iteration step β=1, iteration (16) can be converted into
Figure BDA0003388980070000119
The equation (18) is optimized, and the Hessian matrix needs to be updated to H (S) at each iteration l )＝2Y H Y+ρΛ(S l )；
When the iteration satisfies the following conditions, the algorithm is terminated to obtain a two-dimensional space-time spectrum s h (k) Representing the space-time spectrum of the kth snapshot of the h azimuth;
Figure BDA00033889800700001110
accumulating the obtained two-dimensional space-time spectrum in time to obtain a target angle space spectrum
Figure BDA00033889800700001111
Figure BDA0003388980070000121
For a pair of
Figure BDA0003388980070000122
And carrying out conventional constant false alarm detection to obtain the azimuth estimation of the target. The non-zero value position and number after the constant false alarm detection represent the azimuth estimated value of the target and the number of the target.
The invention also provides a sparse array angle estimation device based on Bayesian learning, which comprises:
the model acquisition module is used for vectorizing received signals received by each array element in the sparse array to obtain output signals in a vector form, outputting the output signals in the vector form by the sparse array to obtain a two-dimensional output signal model, and performing dimension reduction processing on the two-dimensional output signal model to obtain a one-dimensional output signal model;
the optimization function construction module is used for extracting a measurement matrix and a two-dimensional space spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic; and
the azimuth estimation module is used for solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and then carrying out constant false alarm detection on the space spectrum to obtain azimuth estimation of the target.
The invention also provides a computer device for target position estimation, comprising a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, the processor implementing the method when executing the computer program.
The present invention also provides a computer-readable storage medium comprising a stored computer program; wherein the computer program, when run, controls a device in which the computer readable storage medium resides to perform the method.
The invention also provides an information data processing terminal which is used for realizing the method.
The conventional algorithm of the beam forming optimization solution is generally a convex optimization method, the existing convex optimization solution algorithm adopts internal point method solvers such as CVX, SEDUMI and the like, has the problem of overlarge operand, and utilizes a quasi-Newton algorithm to solve the optimization problem of (8). In order to ensure the noise robustness of the algorithm, sparse coefficients in the optimization problem are firstly deduced, and the noise matrix E is assumed to obey complex Gaussian distribution, the mean value is zero, and the variance is sigma 2 The probability density function of E is
Figure BDA0003388980070000123
Thus, when S is known, the probability density function of Y can be expressed as
Figure BDA0003388980070000124
Based on Bayes compressed sensing principle, on the premise that the spatial spectrum has strong sparsity, the sparse signal obeys Laplace distribution, and the probability density function of S can be expressed as
Figure BDA0003388980070000131
wherein ,
Figure BDA0003388980070000132
is the Laplace function scale factor. When the sparse array receiving matrix Y is known, the super-resolution spatial spectrum can be estimated by utilizing the maximum posterior probability criterion, and the maximum posterior probability estimation of S is that
Figure BDA0003388980070000133
Substituting (10) and (11) into (12) to obtain
Figure BDA0003388980070000134
Thus, the sparse coefficient can be passed through
Figure BDA0003388980070000135
Determining, wherein sigma 2 and
Figure BDA0003388980070000136
Can be determined statistically and by maximum likelihood, respectively, by analyzing the spatial characteristics of the target distribution.
To solve for the spatial spectrum matrix S, a conjugate gradient is calculated for the cost function of equation (8) with respect to S
Figure BDA0003388980070000137
Wherein the Hessian matrix is a coefficient matrix of S, which can be expressed as
H(S)＝2Y H Y+ρΛ(S) (48)
wherein ,
Figure BDA0003388980070000138
the traditional Newton method and the quasi-Newton method are not suitable for processing optimization problems containing non-quadratic forms, particularly, the cost function contains a modulus of S, and the complexity of solving is greatly increased. The invention solves the optimization problem with a modified newton iterative algorithm. As can be seen from Newton' S method, the 1+1st iteration of S is
Figure BDA0003388980070000139
Wherein, beta is iteration step length, [] -1 Representing the inverse of the matrix. Substituting the conjugate gradient formula (14) into the above iterative derivation
Figure BDA0003388980070000141
If the iteration step is set to be beta=1, the iteration can be converted into
Figure BDA0003388980070000142
In the optimization solution, the Hessian matrix needs to be updated H (S) at each iteration l )＝2Y H Y+ρΛ(S l ) The algorithmic calculation is therefore mainly focused on the Hessian matrix H (S w ) From the above derivation, it is known that H (S w ) Is a matrix of size HK×HK, decomposed with conventional Cholesky, and is needed for each iteration (HK) 3 /3+2(HK) 2 The multiplication operation is carried out for a plurality of times, and the operation amount of the algorithm is overlarge. The algorithm adopts a conjugate gradient method to solve, which solves the problem of large operand caused by Hessian matrix inversion. The algorithm terminates when the iteration satisfies the following condition.
Figure BDA0003388980070000143
The obtained two-dimensional space-time spectrum is accumulated in time to obtain the target angle space spectrum
Figure BDA0003388980070000144
For a pair of
Figure BDA0003388980070000145
The conventional constant false alarm detection can be carried out to obtain the azimuth estimation of the target. The non-zero value position and number obtained after the constant false alarm detection represent the azimuth estimated value of the target and the number of the target.
Performance analysis
As shown in FIG. 2, in the simulation experiment, the sound velocity is 1500m/s, the carrier frequency of the signal is 1kHz, and the half wavelength is 0.75m. Let the sparse array be a random wire-laid linear array of length 12M, the number of array elements m=10. And Gaussian white noise with the average value of 0 is added into the received data of each array element, and the signal-to-noise ratio SNR=0-10 dB.
Firstly, single-target simulation is carried out, the real azimuth angle of the underwater sound target is 0 degrees, the snapshot times are K=20, and the signal-to-noise ratio SNR=10 dB. As can be seen from fig. 2, for the sparse deployment array, the azimuth estimation algorithm based on compressed sensing can accurately estimate the target azimuth, and the sidelobes are at-70 dB, which is far lower than DAS, MVDR and MUSIC algorithms. Fig. 3 shows the mean square error of the position estimate as a function of the signal to noise ratio, the number of experiments being 50, the signal to noise ratio being between 0dB and 10dB, the separation being 2dB. Because the array is sparse, under the condition of low signal-to-noise ratio, the DAS algorithm fails, the target azimuth angle cannot be accurately estimated, the MUSIC algorithm cannot recover the target angle due to the lack of received data, the estimated mean square error of the MVDR algorithm and the CS algorithm is kept consistent, and the mean square error is lower.
Next, to verify the sparse recovery performance of the algorithms, experimental analysis was performed on each algorithm with different numbers of array elements. Fig. 4 shows the relationship between the angle estimation error and the number of array elements, and the number of array elements 6 to 16 are selected for experiments, the array elements are randomly laid, snr=10db, and the snapshot number is 20. From the results, when the number of the array elements is larger than 10, the mean square error estimated by the DAS, the MVDR and the CS algorithm is small, the MUSIC is not stable under the sparse array element condition, and the CS algorithm provided by the invention can still recover the target angle with higher precision when the number of the array elements is 6, so that the hardware cost of practical application is greatly reduced.
Finally, by the super-resolution performance of the multi-target angle estimation verification algorithm, fig. 5 (a) and 5 (b) are angle estimation results with azimuth angles of [ -5 °,5 ° ] and [ -3 °,3 ° ], respectively. From the result, the CS algorithm estimates that the main lobe is the sharpest, the angular resolution is the highest, and when two targets are further close, the traditional DAS, MVDR, MUSIC algorithm can not distinguish the two targets, but the method provided by the invention can still obtain a good super-resolution result.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.

Claims (8)

1. A sparse array angle estimation method based on Bayesian learning comprises the following steps:
each array element in the sparse array receives a corresponding received signal and carries out vectorization processing to obtain an output signal in a vector form, the sparse array outputs the output signal in the vector form to obtain a two-dimensional output signal model, and the two-dimensional output signal model is subjected to dimension reduction processing to obtain a one-dimensional output signal model;
extracting a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic;
and solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and performing constant false alarm detection on the space spectrum to obtain the azimuth estimation of the target.
2. The bayesian learning-based sparse array angle estimation method according to claim 1, wherein each array element in the sparse array receives a corresponding received signal and carries out vectorization processing to obtain a vector-form output signal, the sparse array outputs the vector-form output signal to obtain a two-dimensional output signal model, and dimension reduction processing is carried out to obtain a one-dimensional output signal model; the specific implementation process comprises the following steps:
assuming that the sparse array is a random array with M array elements, and adopting rectangular coordinates for representation; assuming that N remote incoming waves in the directions exist in the space, each array element receives the remote incoming waves in each direction as a receiving signal;
the m-th array element receives the corresponding receiving signal y m (t) and takes it as output: m=1, 2,3, …, M, …, M;
Figure FDA0003388980060000011
wherein ,τm,n The delay of the arrival of the remote incoming wave in the nth direction at the mth array element compared with the arrival of the remote incoming wave at the reference point; τ m,n ＝R m,n C; wherein c is the propagation speed of the remote incoming wave; r is R m,n Distance from the target located in the nth direction to the mth array element; s (t- τ) m,n ) Target incoming waves in the nth direction received by the mth array element; t is the receiving time of the target incoming wave;
ε m (t) is noise of the mth array element;
for the narrowband case, the delay is equivalent to the phase shift, noted as
Figure FDA0003388980060000012
wherein ,fc Carrier frequency of the narrow-band signal;
Figure FDA0003388980060000013
Then y m And (t) rewriting as:
Figure FDA0003388980060000014
vector form of the output signals of M array elements:
Figure FDA0003388980060000021
wherein y (t) is the vector array output of M array elements; wherein y (t) = [ y ] 1 (t),y 2 (t),…,y M (t)] T； wherein ,yM (t) is the vector output of the mth element;
s (t) is the incoming spatial spectrum; wherein s (t) = [ s ] 0 (t),s 1 (t),…,s n (t),…,s (N-1) (t)] T ；s n (t) is the target arrival spatial spectrum in the nth direction;
epsilon (t) is noise; wherein ε (t) = [ ε ] 1 (t),ε 2 (t),…,ε M (t)] T ；ε M (t) is noise received by the mth array element;
a(θ n ) A guide vector for the nth observation angle;
wherein
Figure FDA0003388980060000022
A is a guide matrix; wherein a= [ a (θ 0 ),a(θ 1 ),…,a(θ N-1 )]；
Dividing the observation angle range into H observation angle units, and changing the corresponding guide matrix A into an M multiplied by H matrix:
A＝[a(θ 0 ),a(θ 1 ),…,a(θ h ),…,a(θ H-1 )]；
wherein ,a(θh ) A guide vector for the h observation angle;
wherein ,
Figure FDA0003388980060000023
when the received data y (t) has K snapshots, vectorizing output signals of M array elements to obtain an output signal matrix in a vector form, and marking the output signal matrix as a two-dimensional output signal model y:
y＝As+ε (4)
wherein y= [ y (1) y (2) … y (K)]Representing a matrix of size M x K; s is a two-dimensional space spectrum matrix to be recovered, and the elements of the kth row and the kth column are s n (k) The method comprises the steps of carrying out a first treatment on the surface of the Epsilon is a noise vector matrix;
performing dimension reduction processing on the two-dimensional output signal model to obtain a one-dimensional output signal model Y;
Figure FDA0003388980060000024
wherein ,
Figure FDA0003388980060000025
is a measurement matrix of MK×HK dimension; wherein (1)>
Figure FDA0003388980060000026
Wherein y=vec (Y); s=vec (S); e=vec (epsilon).
3. The method for estimating the angles of the sparse array based on Bayesian learning according to claim 2, wherein a measurement matrix and a two-dimensional spatial spectrum matrix to be recovered are extracted from the obtained one-dimensional output signal model; when the two-dimensional space spectrum matrix to be recovered meets the RIP characteristic, constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix; the specific process comprises the following steps:
extracting a measurement matrix from the obtained one-dimensional output signal model Y
Figure FDA0003388980060000031
And a two-dimensional spatial spectrum matrix S to be recovered;
judging whether the two-dimensional space spectrum matrix S to be recovered meets RIP characteristics or not; wherein, the meeting condition is:
Figure FDA0003388980060000032
wherein ,
Figure FDA0003388980060000033
wherein ,
Figure FDA0003388980060000034
for matrix->
Figure FDA0003388980060000035
Is a correlation vector of (2);
Figure FDA0003388980060000036
θ p Is the p-th observation angle;
Figure FDA0003388980060000037
θ q The q observation angle;
if the requirements are not met, the two-dimensional spatial spectrum matrix S to be recovered does not meet the RIP characteristics, and the process is finished;
if the above satisfaction conditions are satisfied, the two-dimensional spatial spectrum matrix S to be recovered satisfies RIP characteristics, and an optimization function is further constructed:
S＝argmin{J(S)} (6)
wherein ,
Figure FDA0003388980060000038
wherein I F Representing the F matrix norm; min (·) is a minimization operation; ρ is a sparse coefficient.
4. The method for estimating the angles of the sparse array based on Bayesian learning according to claim 3, wherein the constructed optimization function is solved to obtain a two-dimensional space-time spectrum, the obtained two-dimensional space-time spectrums are accumulated in time to obtain a spatial spectrum of the target, and then the spatial spectrum is subjected to constant false alarm detection to obtain the azimuth estimation of the target; the specific process comprises the following steps:
calculating conjugate gradient of the optimization function with respect to the spatial spectrum matrix S by adopting a conjugate gradient method
Figure FDA0003388980060000041
Figure FDA0003388980060000042
Wherein H (S) is a Hessian matrix;
Figure FDA0003388980060000043
is a measurement matrix; (. Cndot. H The conjugate H (S) representing the matrix is a coefficient matrix of S, which can be expressed as
H(S)＝2Y H Y+ρΛ(S) (8)
Wherein ρ is a sparse coefficient;
Figure FDA0003388980060000044
wherein S (hk) is the element value of the h row and the k column of the matrix S; diag [ ] is a diagonal matrix; τ is a very small positive value, 0.01;
as can be seen by adopting the Newton iterative algorithm, the (1+1) th iteration of S is Newton iterative:
Figure FDA0003388980060000045
wherein, beta is iteration step length, [. Cndot.] -1 Representing the inverse of the matrix;
gradient conjugate
Figure FDA0003388980060000046
The expression of (2) is substituted into the iterative expression (16), and the deduction is obtained:
Figure FDA0003388980060000047
assuming an iteration step β=1, iteration (16) can be converted into
Figure FDA0003388980060000048
The equation (18) is optimized, and the Hessian matrix needs to be updated to H (S) at each iteration l )＝2Y H Y+ρΛ(S l )；
When the iteration satisfies the following conditions, the algorithm is terminated to obtain a two-dimensional space-time spectrum s h (k) Representing the space-time spectrum of the kth snapshot of the h azimuth;
Figure FDA0003388980060000049
accumulating the obtained two-dimensional space-time spectrum in time to obtain a target angle space spectrum
Figure FDA00033889800600000410
Figure FDA00033889800600000411
For a pair of
Figure FDA00033889800600000412
And carrying out conventional constant false alarm detection to obtain the azimuth estimation of the target. />
5. A sparse array angle estimation device based on bayesian learning, the device comprising:
the model acquisition module is used for vectorizing received signals received by each array element in the sparse array to obtain output signals in a vector form, outputting the output signals in the vector form by the sparse array to obtain a two-dimensional output signal model, and performing dimension reduction processing on the two-dimensional output signal model to obtain a one-dimensional output signal model;
the optimization function construction module is used for extracting a measurement matrix and a two-dimensional space spectrum matrix to be recovered from the obtained one-dimensional output signal model; adopting a Bayesian learning method, and constructing an optimization function according to the obtained one-dimensional output signal model and the measurement matrix when the two-dimensional spatial spectrum matrix to be recovered meets the RIP characteristic; and
the azimuth estimation module is used for solving the constructed optimization function to obtain a two-dimensional space-time spectrum, accumulating the obtained two-dimensional space-time spectrum in time to obtain a space spectrum of the target, and then carrying out constant false alarm detection on the space spectrum to obtain azimuth estimation of the target.
6. A computer device for target position estimation, comprising a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, the processor implementing the method of any of claims 1-4 when the computer program is executed.
7. A computer readable storage medium, wherein the computer readable storage medium comprises a stored computer program; wherein the computer program, when run, controls a device in which the computer readable storage medium is located to perform the method according to any one of claims 1-4.
8. An information data processing terminal, characterized in that the information data processing terminal is adapted to implement the method according to any of claims 1-4.
CN202111461641.3A 2021-12-02 2021-12-02 Bayesian learning-based sparse array angle estimation method and device Pending CN116224212A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111461641.3A CN116224212A (en) 2021-12-02 2021-12-02 Bayesian learning-based sparse array angle estimation method and device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111461641.3A CN116224212A (en) 2021-12-02 2021-12-02 Bayesian learning-based sparse array angle estimation method and device

Publications (1)

Publication Number Publication Date
CN116224212A true CN116224212A (en) 2023-06-06

Family

ID=86575511

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111461641.3A Pending CN116224212A (en) 2021-12-02 2021-12-02 Bayesian learning-based sparse array angle estimation method and device

Country Status (1)

Country Link
CN (1) CN116224212A (en)

Similar Documents

Publication Publication Date Title
CN108802683B (en) Source positioning method based on sparse Bayesian learning
CN103954950B (en) A kind of Wave arrival direction estimating method openness based on sample covariance matrix
CN110045323B (en) Matrix filling-based co-prime matrix robust adaptive beamforming algorithm
US8669901B2 (en) Method for determining azimuth and elevation angles of arrival of coherent sources
CN109375154B (en) Coherent signal parameter estimation method based on uniform circular array in impact noise environment
US20100106440A1 (en) Method and Apparatus for Spectral Cross Coherence
CN107340512B (en) Near-far field mixed source passive positioning method based on subarray division
CN107092007A (en) A kind of Wave arrival direction estimating method of virtual second order array extension
EP1423726A2 (en) Adaptive digital beamforming radar method and system for maintaining multiple source angle super-resolution capability in jamming
CN106226754A (en) The low elevation angle based on time reversal Wave arrival direction estimating method
CN109298383A (en) A kind of relatively prime battle array direction of arrival angle estimation method based on variational Bayesian
CN107290732B (en) Single-base MIMO radar direction finding method for large-quantum explosion
CN113030843B (en) Low-altitude target direction finding method based on improved IAA beam forming
CN109471063B (en) Uniform linear array high-resolution direction-of-arrival estimation method based on delayed snapshot
CN111693947A (en) Improved MUSIC method based on co-prime array DOA estimation
CN107450046B (en) Direction of arrival estimation method under low elevation angle multi-path environment
CN113466782B (en) Mutual coupling correction DOA estimation method based on Deep Learning (DL)
CN115236584A (en) Meter-wave radar low elevation angle estimation method based on deep learning
CN111650574B (en) Underwater space-time self-adaptive processing method and system based on sparse recovery
CN113625220A (en) New method for quickly estimating direction of arrival and diffusion angle of multipath signal
CN110320492B (en) Low-complexity DOA estimation method based on symmetric characteristics of steering vectors
CN110133641B (en) Scale-adaptive through-wall imaging radar target tracking method
CN116226611A (en) Chirp signal direction-of-arrival estimation method based on fractional domain deconvolution beam forming
CN116299176A (en) Target space feature extraction and fusion positioning method based on Hough transformation
CN114167346B (en) DOA estimation method and system based on covariance matrix fitting array element expansion

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