CN104965188B - A kind of Wave arrival direction estimating method under array error - Google Patents
A kind of Wave arrival direction estimating method under array error Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/78—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 electromagnetic waves other than radio waves
- G01S3/782—Systems for determining direction or deviation from predetermined direction
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
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Abstract
The Wave arrival direction estimating method under a kind of array error is claimed in the present invention; it is first with the openness of matrix; the Mutual coupling under array error is represented by solving an optimization problem, this optimization problem then is converted into an iterative algorithm realizes.Compared with DOA estimation algorithm under existing array error, method of estimation proposed by the present invention has been obviously improved estimation performance in the case where complexity is suitable, has good application prospect in orientation estimation field.
Description
Technical Field
The invention relates to a direction of arrival estimation method under array errors, in particular to a method for carrying out joint estimation on array error disturbance parameters and information source direction angles by array output signals.
Background
Array signal processing is an important branch of modern signal processing, and its main purpose is to extract the received signal and its characteristic signals, enhance the desired useful signal, and suppress unwanted interference and noise. Compared with the traditional signal processing mode based on a single sensor, the array signal processing technology applying the sensor array has the advantages of flexible beam control, high signal gain, high spatial resolution, strong anti-interference capability and the like. Spatial spectrum estimation is one of the main research directions in the field of array signal processing, and focuses on estimating spatial signals of the spatial signals, mainly aiming at estimating various parameters of the spatial signals, and the direction of arrival is just one of the most important parameters. The main research of direction-of-arrival estimation aims at estimating the direction angle of a space signal reaching an array reference array element, and the technology is widely applied to military and civil fields such as radar, communication, sonar, seismology, biomedicine and the like at the beginning of development. With the increasing expansion of the application field, the estimation of the direction of arrival has wider and wider application prospect.
In the twenty-first century, along with the proposal and improvement of the compressed sensing theory, the application of the compressed sensing theory in array signal processing is well developed. The compressive sensing theory has been proposed so far, and its superiority in the signal processing field attracts a great number of researchers, and the theory has been rapidly developed and widely applied to various fields such as wireless communication, medical imaging, optical imaging and radar. The sparse signal reconstruction algorithm can obtain more accurate spatial spectrum estimation under the conditions of small samples, low signal-to-noise ratio and high information source correlation, so that the sparse signal reconstruction algorithm becomes a research hotspot in the field of direction-of-arrival estimation in recent years.
However, almost all existing spatial spectrum direction of arrival estimation algorithms have super-resolution lateral performance based on the premise that the array popularity is accurately known. In practical engineering applications, however, the real array popularity tends to deviate to some extent with the climate, environment, and device itself. For example, due to the influence of various reasons such as production process, construction technology, construction environment, etc., the electromagnetic characteristics of each array element of the antenna may be inconsistent, coupling exists between the array elements, and the actual position and the nominal position of the array element have deviation. At this point, the performance of these super-resolution direction-finding algorithms can be significantly degraded or even completely fail. Therefore, the existence of array errors becomes a bottleneck in the practical application of the direction of arrival technology, and how to obtain accurate and robust estimation performance under the condition of array errors becomes a problem to be solved urgently.
Disclosure of Invention
Aiming at the defects of the prior art, an algorithm is provided, and the technical scheme of the invention is as follows: a method of direction of arrival estimation under array error, comprising the steps of:
101. receiving a signal to be estimated, which is incident to the uniform linear array, and obtaining an output signal model when the array error is an amplitude-phase error or a mutual coupling error, wherein the output signal model is as follows:
y (t) = GA (θ) s (t) + n (t), where a (θ) represents an array flow pattern matrix, s (t) represents a source signal vector, and n (t) represents an additive noise vector; g represents the amplitude-phase error matrix G gain Or cross-coupling error matrix G mutual ，As a matrix of amplitude and phase errors, p i Indicating the amplitude error of the ith array element,representing the phase error of the ith array element, i =1 \8230M;for the cross-coupling error matrix, toeplitz means that a Topritz matrix is generated,representing a row vector of length (M-p-1) with element values of zero, p representing the number of narrowband signals, c1, c 2 Representing the array cross-coupling coefficient, the estimated arrival direction of the array is:
minimize||y-ψ(θ)x|| 2 +τ||x|| 1 τ denotes a regularization constant, | | y- ψ (θ) x | | luminance 2 Representing the 2-norm of a vector (y- ψ (θ) x) | | x | luminance 1 Representing the 1-norm of a vector x, psi (theta) representing a dictionary consisting of angles equally divided by a normalized angle domain [0,180 DEG ] according to a whole-point grid, and x representing a variable to be solved;
102. sparse estimation is performed on the direction of arrival of the array obtained in step 101 under the condition of the amplitude-phase error or the mutual coupling error by using the sparsity of the signals to obtain an expression, and the convex optimization problem of the direction of arrival estimation under the condition of the amplitude-phase error or the mutual coupling error can be represented as follows:
minimize||x|| 1 +τ||G|| 1
subject to||y-Gψ(θ)x|| 2 <ε
and solving by adopting an iterative algorithm, wherein the iterative algorithm comprises the following steps:
a) Initializing the perturbation parameter matrix
b) Perturbing the parameter matrix with an initialized or estimated arrayq represents the iterative times of the algorithm, solves the convex optimization problem and generates the estimated value of the direction angle
c) Using the estimated value of the generated direction angleSolving the same convex optimization problem to generate an estimated value of the array disturbance parameter matrix
d) Iterating steps b) and c) until an iteration termination condition is satisfiedδ represents an iteration termination parameter;
103. receiving a signal to be estimated which is incident to the uniform linear array, and obtaining an array output signal model when the array error is an array element position error:
c＝G location vec (A (theta)) represents a column vector containing an array position error matrix, vec (A (theta)) represents a column vector arranged by rows from matrix A (theta), G location Representing an array position error matrix;
with the sparsity of the signal, the direction of arrival estimate can be expressed as:
minimize||y-ψ(θ)x|| 2 +τ||x|| 1
when there is an array position error, due to G location The method is a block diagonal matrix, only diagonal elements are not zero, and the other elements are all zero, namely the block diagonal matrix is sparse, and the estimation of the direction of arrival under the position error of the array elements by utilizing the sparsity can be expressed as follows:
wherein G is′＝G location ((k-1) M +1, (k-1) M + 1; solving by adopting an optimized iterative algorithm; the method for estimating the direction of arrival under the position error of the array element by utilizing the matrix sparsity specifically comprises the following steps:
a) Initializing the array perturbation parameter matrix
b) Perturbing the parameter matrix with an initialized or estimated arraySolving the estimation expression of the direction of arrival, and q represents the iteration times of the algorithm;
minimize||y-ψ(θ)x|| 2 +τ||x|| 1 generating an estimate of the azimuth angle
c) Using estimated values of the generated azimuthSolving the expression of estimating the direction of arrival under the position error of the array element by utilizing sparsity in the step 103:
generating estimates of a matrix of array perturbation parametersAnd fromTo obtainRepresenting an M matrix B k Is determined by the estimated value of (c),is thatThe diagonal matrix of (a) is,representing a matrix G of array perturbation parameters location Q represents the number of iterations of the algorithm; deviation of array element positionIs thatCan be obtained by the following formula:
λ represents a wavelength;
d) Iterating steps b) and c) until an iteration termination condition is metδ represents an iteration termination parameter.
The invention has the following advantages and beneficial effects:
1. the algorithm provided by the invention converts an original error matrix model into a matrix with sparsity.
2. The algorithm provided by the invention converts the optimization problem into an iterative algorithm by utilizing the sparsity of signals and the sparsity of an error matrix.
3. The algorithm provided by the invention is simple and easy to understand, and has higher accuracy and robust robustness.
Drawings
FIG. 1 illustrates a comparison of the true value and the estimated value of an error matrix of a direction of arrival estimation algorithm under an applied amplitude-phase error.
FIG. 2 is a comparison between the true value and the estimated value of the error matrix of the DOA estimation algorithm under the cross coupling error.
FIG. 3 is a comparison between the true value and the estimated value of the error matrix of the DOA estimation algorithm under the array element position error.
FIG. 4 is a comparison of the performance of the direction of arrival estimation algorithm with other algorithms under amplitude-phase errors.
FIG. 5 is a comparison of the performance of the direction of arrival estimation algorithm under cross-coupling error proposed by the present invention with other algorithms.
FIG. 6 is a comparison of the performance of the estimation algorithm of direction of arrival under the position error of the array element proposed by the present invention with other algorithms.
FIG. 7 is a flow chart of an algorithm for estimating a direction of arrival under an amplitude-phase error and a mutual coupling error.
FIG. 8 is a flow chart of a direction of arrival estimation algorithm under array element position error.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
fig. 1 to fig. 3 illustrate the comparison between the true value and the estimated value of the error matrix of the direction of arrival estimation algorithm under the array error provided by the present invention, and it can be seen that the estimated value and the true value of the error matrix are very close to each other, which illustrates the accuracy of the algorithm provided by the present invention. Fig. 4-6 illustrate the performance of the direction of arrival estimation algorithm against other algorithms under array error proposed by the present invention. It can be seen from the figure that the estimation error of each algorithm increases with the increase of the signal-to-noise ratio (SNR), but the estimation error of the algorithm proposed by the present invention is significantly smaller than that of the other two algorithms, thereby demonstrating that the algorithm proposed by the present invention has better performance. The direction of arrival estimation algorithms under array error employed in fig. 4-6 are:
origin: only the direction of arrival is estimated based on the sparsity of the signal.
S-TLS, sparse least square method, and estimating the error disturbance matrix and the direction of arrival.
The following describes an embodiment of the direction of arrival estimation algorithm under the array error.
(1) And the method for estimating the direction of arrival under the amplitude-phase error and the mutual coupling error.
Considering spatial p narrowband signals from unknown direction θ 1 ,…,θ p Incident on a uniform linear array of M array elements, assuming that the array element spacing d is half the signal wavelength, when there is no array error, the matrix representation of the array output can be written as:
y(t)＝A(θ)s(t)+n(t)
to exploit the sparsity of the signal, we J-divide the entire normalized angular domain [0, 180) in an integer grid. Then, we can construct the following dictionary:
wherein, theta j ＝180j/J,j＝0,1,…,J。
Thus, the output signal model can be written as:
y(t)＝ψ(θ)x(t)+n(t)
wherein, x (t) contains many zero elements, only few non-zero elements, and the non-zero elements correspond to the incident direction of the signal to be estimated.
Therefore, with the sparsity of the signal, the direction of arrival estimate can be expressed as:
minimize||y-ψ(θ)x|| 2 +τ||x|| 1
when the array error is amplitude phase error or mutual coupling error, the array flow pattern of the direction of arrival estimation is modifiedWhereinIs a matrix of the amplitude and phase errors,is a cross-coupling error matrix. Thus, in the presence of an amplitude-phase error or a mutual coupling error, the array output signal can be rewritten as:
y(t)＝G gain/mutual A(θ)s(t)+n(t)
due to G gain/mutual Many zero elements are contained in the medium, and only a few elements are zero, that is to say, the medium is sparse, and by using the sparsity of the signal and the sparsity of the error matrix, the direction of arrival estimation under the condition of amplitude-phase error or cross-coupling error can be expressed as follows:
minimize||x|| 1 +τ||G gain/mutual || 1
subject to||y-G gain/mutual ψ(θ)x|| 2 <ε
we note that the optimization problem in the direction of arrival estimation under amplitude-phase error or mutual coupling error described above is in the variables x and G gain/mutual While non-convex when present, in order to effectively solve the above optimization problem, the following iterative algorithm is proposed:
a) Initializing the array perturbation parameter matrix
b) Perturbing the parameter matrix with an initialized or estimated arrayq represents the number of iterations of the algorithm. Solving the convex optimization problem, an estimate of the azimuth angle is generated
c) Using the estimated value of the generated direction angleSolving the same convex optimization problem to generate an estimated value of the array disturbance parameter matrix
d) Iterating steps b) and c) until an iteration termination condition is satisfied
(2) And a specific implementation mode of the method for estimating the direction of arrival under the position error of the array element.
The steering vector of the array depends on the position of the array element, and the deviation or change of the position of the array element will cause the error of the steering vector model, so when the position of the array element has deviation, the output signal model of the array can be written as:
let Δ be 0 ＝0,Δ i I =1, \ 8230;, where M-1 represents a random position error for each array, then the array steering vector can be written as:
wherein an as is the Schur product represents a multiplication of corresponding components of the matrix, B k Is an M × M diagonal matrix, represented as follows:
thus, the array output signal can be written as:
we define a block matrix G location Describing all unknown position deviations of array elements and order
c＝G location vec(A(θ)),G location And c are in the form of:
as defined above, the array output signal model may be modified to:
from the above we know that in the absence of array errors, using the sparsity of the signal, the direction of arrival estimate can be expressed as:
minimize||y-ψ(θ)x|| 2 +τ||x|| 1
therefore, when there is an array position error, because of G location Is a block diagonal matrix, only the diagonal elements are non-zero, and the remaining elements are all zero, i.e. it is sparse. Thus exploiting the sparsity of the signals and the matrix G location The estimation of the direction of arrival under the position error of the array element can be expressed as:
minimize||x|| 1 +τ||G location || 1
wherein, G' = G location ((k-1)M+1:kM,(k-1)M+1:kM)。
We note that the optimization problem in the estimation of direction of arrival under array element position error described above is in the variable x k And G location While non-convex when present, in order to effectively solve the above optimization problem, the following iterative algorithm is proposed:
a) Initializing the array perturbation parameter matrix
b) Perturbing the parameter matrix with an initialized or estimated arraySolving the optimization problem, an estimate of the azimuth angle is generated
c) Using the estimated value of the generated direction angleSolving the same convex optimization problem to generate an estimated value of the array disturbance parameter matrixAnd fromTo obtainDeviation of array element positionIs thatCan be obtained by the following formula:
d) Iterating steps b) and c) until an iteration termination condition is satisfied
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (1)
1. A method for estimating a direction of arrival under an array error is characterized by comprising the following steps:
101. receiving a signal to be estimated which is incident to the uniform linear array, and obtaining an output signal model when the array error is an amplitude-phase error or a mutual coupling error as follows:
y (t) = GA (θ) s (t) + n (t), where a (θ) represents an array flow pattern matrix, s (t) represents a source signal vector, and n (t) represents an additive noise vector; g represents the amplitude-phase error matrix G gain Or cross-coupling error matrix G mutual ，As a matrix of amplitude and phase errors, p i Indicating the amplitude error of the ith array element,representing the phase error of the ith array element, i =1 \8230M;for the cross-coupling error matrix, toeplitz means that a Topritz matrix is generated,representing a row vector of length (M-p-1) with element values of zero, p representing the number of narrowband signals, c 1 、c 2 Representing the array cross-coupling coefficient, the estimated arrival direction of the array is:
minimize||y-ψ(θ)x|| 2 +τ||x|| 1 τ denotes a regularization constant, | | y- ψ (θ) x | | luminance 2 Representing the 2-norm of a vector (y- ψ (θ) x) | | x | luminance 1 A 1-norm representing a vector x, ψ (θ) represents a dictionary composed of angles equally divided by a normalized angle domain [0,180 °) by a whole-point grid, and x represents a variable to be solved;
102. sparse estimation is performed on the direction of arrival of the array obtained in step 101 under the condition of the amplitude-phase error or the mutual coupling error by using the sparsity of the signals to obtain an expression, and the convex optimization problem of the direction of arrival estimation under the condition of the amplitude-phase error or the mutual coupling error can be represented as follows:
minimize||x|| 1 +τ||G|| 1
subject to||y-Gψ(θ)x|| 2 <ε
and solving by adopting an iterative algorithm, wherein the iterative algorithm comprises the following steps:
a) Initializing the perturbation parameter matrix
b) Perturbing the parameter matrix with an initialized or estimated arrayq represents the iterative times of the algorithm, solves the convex optimization problem and generates the estimated value of the direction angle
c) Using estimated values of the generated azimuthSolving the same convex optimization problem to generate an estimated value of the array disturbance parameter matrix
d) Iterating steps b) and c) until an iteration termination condition is satisfiedδ represents an iteration termination parameter;
103. receiving a signal to be estimated which is incident to the uniform linear array, and obtaining an array output signal model when the array error is an array element position error:
c＝G location vec (A (theta)) represents a column vector containing an array position error matrix, vec (A (theta)) represents a column vector arranged by rows from matrix A (theta), G location Representing an array position error matrix;
with the sparsity of the signal, the direction of arrival estimate can be expressed as:
minimize||y-ψ(θ)x|| 2 +τ||x|| 1
when there is an array position error, due to G location The method is a block diagonal matrix, only diagonal elements are not zero, and the other elements are all zero, namely the block diagonal matrix is sparse, and the estimation of the direction of arrival under the position error of the array elements by utilizing the sparsity can be expressed as follows:
wherein, G' = G location ((k-1) M +1, (k-1) M + 1; solving by adopting an optimized iterative algorithm; the method for estimating the direction of arrival under the position error of the array element by utilizing the matrix sparsity specifically comprises the following steps:
a) Initializing an array perturbation parameter matrix
b) Perturbing the parameter matrix with an initialized or estimated arraySolving the estimation expression of the direction of arrival, and q represents the iteration times of the algorithm;
minimize||y-ψ(θ)x|| 2 +τ||x|| 1 generating an estimate of the azimuth angle
c) Using estimated values of the generated azimuthSolving the expression of estimating the direction of arrival under the array element position error by using sparsity in step 103:
generating estimates of a matrix of array perturbation parametersAnd fromTo obtain Representing an M matrix B k Is determined by the estimated value of (c),is thatThe diagonal matrix of (a) is,representing a matrix G of array perturbation parameters location Q represents the number of iterations of the algorithm; deviation of array element positionIs thatCan be obtained by the following formula:
λ represents a wavelength;
d) Iterating steps b) and c) until an iteration termination condition is satisfiedδ denotes an iteration termination parameter.
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| CN106569172B (en) * | 2016-10-13 | 2019-02-15 | 北京邮电大学 | Arrival direction estimation method |
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| CN107843881B (en) * | 2017-10-24 | 2020-04-03 | 中国人民解放军空军工程大学 | Radar angle estimation and error correction method |
| CN108387865B (en) * | 2018-03-07 | 2021-08-10 | 河南理工大学 | Direction-of-arrival estimation method based on vector error model |
| CN108519576B (en) * | 2018-03-21 | 2021-07-20 | 华南理工大学 | Underwater direction of arrival estimation method and device based on included angle adjustable non-uniform linear array |
| CN108717189B (en) * | 2018-06-01 | 2022-07-15 | 西安电子科技大学 | Bistatic MIMO radar imaging method based on compressed sensing theory |
| CN110426670B (en) * | 2018-12-26 | 2022-09-23 | 西安电子科技大学 | Super-resolution DOA estimation method for external radiation source radar based on TLS-CS |
| CN111079357B (en) * | 2019-10-22 | 2023-07-21 | 重庆邮电大学 | Electromagnetic interference time domain analysis method for microstrip line on PCB under electromagnetic wave action |
| CN112068070B (en) * | 2020-07-22 | 2022-08-09 | 中国人民解放军国防科技大学 | Robustness design method based on deep learning direction finding |
| CN112904270B (en) * | 2021-01-15 | 2022-06-21 | 电子科技大学 | Direction-of-arrival estimation method based on fitting model under array model error |
| CN112881972B (en) * | 2021-01-15 | 2022-06-21 | 电子科技大学 | Direction-of-arrival estimation method based on neural network under array model error |
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