CN112904321B - Method for calibrating even linear array cross coupling and array element gain-phase error - Google Patents
Method for calibrating even linear array cross coupling and array element gain-phase error Download PDFInfo
- Publication number
- CN112904321B CN112904321B CN201911256593.7A CN201911256593A CN112904321B CN 112904321 B CN112904321 B CN 112904321B CN 201911256593 A CN201911256593 A CN 201911256593A CN 112904321 B CN112904321 B CN 112904321B
- Authority
- CN
- China
- Prior art keywords
- matrix
- array
- echo signal
- linear array
- uniform linear
- 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.)
- Active
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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
- G01S7/52004—Means for monitoring or calibrating
Abstract
The invention provides a method for calibrating mutual coupling and array element gain-phase errors of a uniform linear array, which is characterized in that the mutual coupling effect and the array element gain-phase errors are uniformly described by an error matrix, an ideal signal model and an echo signal model when the two errors are considered are given, the uniform linear array is arranged on a platform moving at a constant speed, the received echo signals form a signal subspace, and the signal subspace is determined by the platform moving speed and system parameters of the uniform linear array. According to an ideal signal model and a subspace projection theory, the estimation of an error matrix is described as a standard convex optimization solving problem, a convex optimization tool box is used for solving the problem to obtain the error matrix, and the error matrix obtained through estimation is used for completing array calibration. The method can calibrate the uniform linear array, simplifies the calculation process and improves the accuracy of the calibration of the uniform linear array.
Description
Technical Field
The invention belongs to the field of antenna/underwater acoustic arrays and signal processing thereof, and particularly relates to a method for calibrating uniform linear array cross coupling and array element gain-phase errors.
Background
Array signal processing is a very important research direction in the field of modern signal processing. Compared with a single antenna, the array antenna has higher degree of freedom, and has stronger and more advantageous signal processing capability. In theoretical research and practical application, array signal processing is concerned with, so that the array signal processing is developed rapidly, and the array signal processing is widely applied to military industry such as radars and sonars, scientific research projects such as radio astronomy and medical imaging, and social production and life such as voice, wireless communication, seismic detection and unmanned vehicles.
However, in application, there are inevitably various errors due to the manufacture and installation of the array, such as: the mutual coupling between array elements, the gain-phase errors of the array elements and the like seriously degrade the performance of the existing array signal processing algorithm, so that the array calibration work is very important in the field of array signal processing.
In order to solve the problem of algorithm performance degradation caused by array errors, the prior art provides some robust array signal processing algorithms. For example: a linear constraint minimum variance beam forming method aiming at gain-phase errors existing in array elements; a worst case optimal beamforming method; a steering vector estimation method; a stopband constraint robust space domain beam forming method and the like. In the other intermediate subarray decoupling method, partial array elements at two ends of the array are provided with auxiliary arrays, and mutual coupling of the arrays is superposed to be a constant at the intermediate array elements.
Although the above methods for dealing with the performance degradation of the algorithm caused by the array error by adding the disturbance term with the constraint have certain robustness to the array error, they all need to provide some empirical constraint parameters, and only consider the case that the array has a single array error, but do not consider the case that the array has the mutual coupling effect and the array element gain-phase error at the same time, and in the application, the two must exist at the same time, and at the same time, the added disturbance term also reduces the estimation accuracy, so the application is limited greatly.
Disclosure of Invention
In order to solve the problems, the invention adopts the following technical scheme:
a method for calibrating mutual coupling and array element gain-phase error of uniform linear array includes using an error matrix to uniformly describe mutual coupling effect and array element gain-phase error, giving echo signal model when two errors are considered, placing uniform linear array on a platform moving at uniform speed, forming a signal subspace by received echo signals and determining said subspace by platform moving speed and uniform linear array system parameters. According to an ideal signal model and a subspace projection theory, the method describes the estimation of an error matrix as a standard convex optimization solving problem, and utilizes the error matrix obtained by estimation to complete array calibration, and is characterized by comprising the following steps:
s1, placing a uniform linear array on a platform moving at a constant speed, placing a plurality of objects with sectional areas at the periphery of the platform moving at the constant speed within a coherent processing interval, wherein the objects with the sectional areas have larger reflection sectional areas, obtaining echo signals with stronger energy through reflection, establishing a corresponding ideal echo signal model according to system parameters of the uniform linear array, and an echo signal model with cross coupling and array element gain-phase errors, and obtaining an error matrix describing the cross coupling and the array element gain-phase errors;
s2, obtaining a projection matrix of an orthogonal subspace according to the system parameters of the uniform linear array and the platform moving at a uniform speed and a subspace estimation theory;
s3, describing the estimation of the error matrix into a standard convex optimization solving problem and solving the problem by using the echo signal data and the projection matrix of the orthogonal subspace to obtain an estimation value of the error matrix;
and S4, carrying out error calibration on array data received by the uniform linear array in practical application by using the estimated value of the error matrix obtained by estimation.
Further, the step S1 of the method for calibrating the mutual coupling and the gain-phase error of the array element of the uniform linear array provided by the invention specifically includes the following steps:
s1.1, placing a uniform linear array on a platform moving at a constant speed, receiving echo signals by the uniform linear array within a coherent processing interval, wherein the echo signals are mainly signals reflected by stationary objects around the platform moving at the constant speed, and placing a plurality of objects with reflection sectional areas around the platform moving at the constant speed so as to obtain echo signals with stronger energy;
s1.2, establishing a corresponding ideal echo signal model according to the uniform linear array parameters to obtain an observed value x of the ideal echo signal at the moment t c (t) is:
wherein, the first and the second end of the pipe are connected with each other,
represents the kronecker product, alpha (f) s ,f d ) Is the amplitude, s, of the echo signal s (f s ) Is a space steering vector, s d (f d ) For time-oriented vectors, s is defined separately s (f s ) And s d (f d ) Comprises the following steps:
wherein N is the number of array elements, M is the number of pulses in a coherent processing interval, f s = dsin theta/lambda is space frequency, d is antenna array element spacing, theta is incidence angle of echo signal, and lambda isWavelength of echo signal, f d = (= (2 vTsin θ)/λ is normalized doppler frequency, v represents the motion speed of the platform moving at a constant speed, and T is the pulse repetition period;
step S1.3, according to the ideal echo signal model, establishing an echo signal model with mutual coupling and array element gain-phase error, and obtaining the observed value x to e of the echo signal model at the time t c (t) is:
wherein, the matrix Q d EC describes uniformly the effect of uniform linear array cross-coupling and the effect of array element gain-phase error on the spatial steering vector, C is the cross-coupling matrix, which is a strip-symmetric toeplitz matrix:
wherein, c i Is the array element coupling coefficient.
E is an array element gain-phase error matrix, which is a diagonal matrix:
wherein, γ i Is the gain error, ξ 1 Is the phase error.
Property of the product according to Crohn's product
To obtain
Comprises the following steps:
is obtained back toWave signal model
Model x of ideal echo signal c (t) relationship between:
wherein the error matrix
Further, in the method for calibrating the uniform linear array mutual coupling and the array element gain-phase error provided by the invention, the step S2 specifically comprises the following steps:
step S2.1, for the uniform linear array, assuming that the motion speed v of the platform carrying the array is constant within a coherent processing interval time, the echo subspace formed by the echo wave signals received by the uniform linear array is constant within the time period, according to the echo signal model established in the step S1 and the known radar system parameters applying the array, the motion speed v of the platform moving at a uniform speed, the array element interval d, the pulse repetition period T and the wavelength lambda are artificially given, and the echo signal incidence angle theta is given i Generating an echo signal v (i), where θ i ＝[-90°,90°]Obtaining the covariance matrix R of the generated echo signal C ：
Wherein L is the number of generated echo signals;
step S2.2, covariance matrix R C And (3) carrying out characteristic value decomposition:
R C ＝UΛU H
wherein Λ = diag { λ 1 ,λ 2 ,…,λ NM The expression of diag { a } is that a diagonal matrix is constructed by a vector a, lambda i Is a covariance matrix R C The ith eigenvalue in descending order, U being the covariance matrix R C A matrix of eigenvectors with ith column of λ i Corresponding eigenvectors, the first few columns of the matrix U corresponding to the signal subspace, i.e. the echo subspace U, according to the subspace theory c The remaining column vectors correspond to the noise subspace, i.e. the orthogonal subspace of the echo subspace
Obtaining a projection matrix of orthogonal subspaces
Is composed of
Further, step S3 of the method for calibrating the mutual coupling and the gain-phase error of the array element of the uniform linear array provided by the present invention specifically includes the following steps:
echo signal contained in uniform linear array received data
And a noise term to array the data actually received by the uniform linear array
Expressed as:
defining a matrix G = Q -1 According to
Obtaining:
substituting the matrix G in the above formula into
Obtaining:
echo signal x in the formula c (t k ) According to the theoretical signal model description, the ideal echo signal has an orthogonal subspace according to the definite proportional relation between the space frequency and the normalized Doppler frequency of the ideal echo signal, so that
This gives:
the above equation converts the echo x by a projection matrix c (t k ) After cancellation, only the noise term is included and the matrix G is estimated by minimizing the noise energy of the above equation, i.e. the following optimization problem is solved:
G d ＞0
wherein G is d The meaning of > 0 is the matrix G d All elements in the matrix are greater than 0, the optimization problem belongs to a standard convex optimization problem, the problem is solved by using a convex optimization tool box to obtain an estimated value G ' of a matrix G, and then a transposed matrix Q ' = (G ') of an error matrix Q is obtained -1 。
Further, step S4 of the method for calibrating the mutual coupling and the gain-phase error of the array element of the uniform linear array provided by the present invention specifically includes the following steps:
actually received using uniform linear arrayData array
And the estimated value G' of the inverse matrix G of the error matrix Q, calibrating the uniform linear array cross coupling and the array element gain-phase error, and receiving the data
Converted to x' (t) satisfying the description of the ideal echo model,
and completing the calibration.
Action and Effect of the invention
According to the method for calibrating the uniform linear array cross coupling and the array element gain-phase error, provided by the invention, an echo signal model which simultaneously considers the uniform linear array cross coupling effect and the array element gain-phase error is given, an error matrix is defined to uniformly describe the errors, the estimation problem of the error matrix is described as a standard convex optimization problem according to an ideal echo signal model and a subspace projection theory, the array calibration is completed by using the estimated error matrix, when the cross coupling effect and the array element gain-phase error exist simultaneously, the target parameters can still be accurately estimated, the filtering result basically has no artifacts, the filtering effect is ideal, and the error calibration is more accurate.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention for calibrating a uniform linear array;
FIG. 2 is a power spectrum of an echo signal containing a target to be detected according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating target detection results of a conventional beamformer in an embodiment of the present invention;
FIG. 4 is a target detection result of a middle sub-array decoupling method in an embodiment of the present invention;
fig. 5 is a target detection result after calibration in the embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings.
< example >
FIG. 1 is a flow chart of the present invention for calibrating a uniform linear array.
As shown in fig. 1, the validity of the proposed algorithm is verified by using analog simulation of a uniform linear array airborne radar, and the following steps are performed:
step S1, placing a uniform linear array on a platform moving at a constant speed, placing a plurality of objects with sectional areas at the periphery of the platform moving at the constant speed in a coherent processing interval, wherein the sectional areas of the objects with the sectional areas are larger in reflection, obtaining echo signals with stronger energy through reflection, establishing a corresponding ideal echo signal model and an echo signal model with mutual coupling and array element gain-phase errors according to system parameters of the uniform linear array, and obtaining an error matrix describing the mutual coupling and the array element gain-phase errors, wherein the specific steps are as described in steps S1.1-S1.3.
Step S1.1, the uniform linear array is placed on a platform moving at a constant speed, the uniform linear array receives echo signals in a coherent processing interval, the echo signals are mainly signals reflected by stationary objects around the platform moving at the constant speed, and a plurality of objects with reflection cross-sectional areas are placed around the platform moving at the constant speed so as to obtain echo signals with stronger energy.
S1.2, establishing a corresponding ideal echo signal model according to the uniform linear array parameters to obtain an observed value x of the ideal echo signal at the moment t c (t) is:
wherein the content of the first and second substances,
represents the kronecker product, alpha (f) s ,f d ) Is the amplitude, s, of the echo signal s (f s ) Is a space steering vector, s d (f d ) For time-oriented vectors, s is defined separately s (f s ) And s d (f d ) Comprises the following steps:
wherein, the main simulation parameters are that the number of array elements N =8, the pulse number M =12 in a coherent processing interval s (= dsin θ/λ) spatial frequency, f d = 2vTsin θ)/λ is normalized doppler frequency, the antenna element spacing d =5cm, θ is the incident angle of the randomly generated echo signal, the wavelength of the echo signal λ =0.01m, the motion speed v =5m/s of the platform moving at a uniform speed, and the pulse repetition period T =0.0005s.
Step S1.3, according to the ideal echo signal model, establishing an echo signal model with mutual coupling and array element gain-phase error, and obtaining the observed value x to e of the echo signal model at the time t c (t) is:
wherein, the matrix Q d And = EC describes the effect of uniform linear array cross coupling and the influence of array element gain-phase error on space steering vector, C is a cross coupling matrix, and is a strip-shaped symmetrical Toplitz matrix:
array element coupling coefficient c 1 ＝0.75e -jπ/3 ，c 2 ＝0.55e -jπ/6 ，c 3 ＝0.35e -jπ/10 ，c 4 ＝0.15e -jπ/6 ，c 5 ＝0.05e -jπ/10 ，c 6 ＝0，c 7 ＝0。
E is an array element gain-phase error matrix, which is a diagonal matrix:
gain error gamma i Is [ -0.1,0.1 [ ]]Random variable within range, phase error xi 1 Is [ -3 °,3 ° ]]Random variables within the range.
Properties of the Crohn's product
To obtain
Comprises the following steps:
obtaining an echo signal model
And an ideal echo signal model x c (t) relationship between:
wherein the error matrix
And S2, obtaining a projection matrix of an orthogonal subspace according to the system parameters of the uniform linear array and the platform moving at the uniform speed and a subspace estimation theory, wherein the specific steps are as described in the steps S2.1-S2.2.
Step S2.1, for the uniform linear array, assuming that the motion speed v of the platform carrying the array is constant within a coherent processing interval time, the echo subspace formed by the echo wave signals received by the uniform linear array is constant within the time period, and according to the echo signal model established in the step S1 and the known radar applying the arrayReaching system parameters, the motion speed of the platform moving at a constant speed is v, the array element interval is d, the pulse repetition period is T and the wavelength is lambda, and artificially setting the incidence angle theta of the echo signal i The specific value being θ i Generating echo signals v (i) to obtain covariance matrix R of the generated echo signals C ：
Where L is the number of echo signals generated, L =180.
Step S2.2, covariance matrix R C And (3) carrying out characteristic value decomposition:
R C ＝UΛU H
wherein Λ = diag { λ 1 ,λ 2 ,…,λ NM Denotes the construction of a diagonal matrix with vector a, λ i Is a covariance matrix R C The ith eigenvalue in descending order, U being the covariance matrix R C A matrix of eigenvectors with ith column of λ i Corresponding eigenvectors, the first few columns of the matrix U corresponding to the signal subspace, i.e. the echo subspace U, according to the subspace theory c The remaining column vectors correspond to the noise subspace, i.e. the orthogonal subspace of the echo subspace
Obtaining a projection matrix of orthogonal subspaces
Is composed of
And S3, describing the estimation of the error matrix into a standard convex optimization solving problem by using the echo signal data and the projection matrix of the orthogonal subspace, and solving to obtain the estimation value of the error matrix, wherein the specific steps are as follows.
Echo signal contained in uniform linear array received data
And a noise term to array the data actually received by the uniform linear array
Expressed as:
defining a matrix G = Q -1 According to
Obtaining:
substituting the matrix G in the above formula into
Obtaining:
echo signal x in the formula c (t k ) According to the theoretical signal model description, the ideal echo signal has an orthogonal subspace according to the definite proportional relation between the space frequency and the normalized Doppler frequency of the ideal echo signal, so that
This gives:
the above equation converts the echo x by a projection matrix c (t k ) After eliminationThe matrix G is estimated by minimizing the noise energy of the above equation, containing only the noise term, i.e. solving the following optimization problem:
G d ＞0
wherein G is d The meaning of > 0 is the matrix G d All elements in the matrix are greater than 0, the optimization problem belongs to a standard convex optimization problem, the problem is solved by using a convex optimization tool box to obtain an estimated value G ' of a matrix G, and then a transposed matrix Q ' = (G ') of an error matrix Q is obtained -1 。
And S4, carrying out error calibration on the data array received by the uniform linear array in practical application by using the estimated value of the error matrix obtained by estimation, wherein the specific steps are as follows.
Data array actually received using uniform linear array
And an estimated value G' of an inverse matrix G of the error matrix Q, calibrating the uniform linear array cross coupling and the array element gain-phase error, and receiving the data
Converted to x' (t) satisfying the description of the ideal echo model,
and completing calibration.
Step S5, using a multiple signal classification algorithm, searching for a possible target in x' (t).
The effectiveness of the invention is verified through the simulation experiment, and compared with the traditional reduced rank space-time adaptive processing algorithm and the middle subarray decoupling method.
Fig. 2 is a power spectrum of an echo signal containing a target to be detected in an embodiment of the present invention.
Fig. 3 is a target detection result of a conventional beamformer in an embodiment of the present invention.
As shown in fig. 3, since the reduced rank space-time adaptive processing algorithm cannot compensate for the array error, a false target appears in the detection result, which indicates that when the array has an error, the conventional reduced rank space-time adaptive processing algorithm cannot effectively complete the target detection task at this time.
Fig. 4 is a target detection result of the intermediate sub-array decoupling method in the embodiment of the present invention.
As shown in fig. 4, compared with the result of the reduced rank space-time adaptive processing algorithm, the detection result of the middle subarray decoupling method is obviously improved, but there are always more and partially stronger artifacts in the detection result, the normalized doppler frequency of the target is estimated more accurately, but due to the presence of the gain-phase error of the array element, there is a large deviation in the estimation of the target azimuth angle.
Fig. 5 is a target detection result after calibration in the embodiment of the present invention.
As shown in fig. 5, the detection result of the method of the present invention is best, when the mutual coupling effect and the array element gain-phase error exist simultaneously, the target parameter can still be accurately estimated, and the filtering result has substantially no artifact and is relatively ideal, which verifies the effectiveness of the method of the present invention in removing the mutual coupling effect and the array element gain-phase error.
Effects and effects of the embodiments
A method for calibrating the cross coupling and the gain-phase error of an array element of a uniform linear array uniformly describes the cross coupling effect and the gain-phase error of the array element by using an error matrix, and provides an echo signal model considering the two errors, so that the model is simplified.
The uniform linear array is placed on a platform which moves at a constant speed, the received echo signals form a signal subspace, and the subspace is determined by the platform moving speed and the system parameters of the uniform linear array. According to the ideal signal model and the subspace projection theory, the estimation of the error matrix is described as a standard convex optimization solving problem, the array calibration is completed by using the error matrix obtained by the estimation, the calculation process is simplified, and meanwhile, the accuracy of the uniform linear array calibration is improved.
The above embodiments are merely used to illustrate the implementation and operation results of the method for calibrating the mutual coupling and gain-phase error of the uniform linear arrays provided by the present invention, but the present invention is not limited to the above embodiments, and the method provided by the present invention is also effective for other types of uniform linear arrays.
Claims (4)
1. A method for calibrating even linear array mutual coupling and array element gain-phase errors is used for carrying out error calibration on an even linear array, and is characterized by comprising the following steps:
s1, placing the uniform linear array on a platform moving at a constant speed, placing a plurality of objects with reflection sectional areas on the periphery of the platform moving at the constant speed in a coherent processing interval, obtaining echo signals with stronger energy through reflection, establishing a corresponding ideal echo signal model and an echo signal model with cross coupling and array element gain-phase errors according to system parameters of the uniform linear array, and obtaining an error matrix for describing the cross coupling and the array element gain-phase errors;
s2, obtaining a projection matrix of an orthogonal subspace according to the uniform linear array, system parameters of the platform moving at the uniform speed and a subspace estimation theory;
s3, describing the estimation of the error matrix into a standard convex optimization solving problem and solving the problem by using the echo signal data and the projection matrix of the orthogonal subspace to obtain an estimation value of the error matrix;
s4, performing error calibration on array data received by the uniform linear array in practical application by using the estimated value of the error matrix obtained by estimation;
wherein, the step S3 comprises the following steps:
the echo signal is included in the received data of the uniform linear array
And a noise term for arraying the data actually received by the uniform linear array
Expressed as:
defining a matrix G = Q -1 According to
Obtaining:
substituting the matrix G in the above formula
Obtaining:
wherein the echo signal x c (t k ) According to the model description of the ideal echo signal, the ideal echo signal has an orthogonal subspace according to the definite proportional relation between the space frequency and the normalized Doppler frequency of the ideal echo signal, so that
This gives:
the above equation converts the echo x by the projection matrix c (t k ) After cancellation, only the noise term is contained, and the matrix G is estimated by minimizing the noise energy of the above equation, i.e. the following optimization problem is solved:
wherein, G d The meaning of > 0 is the matrix G d All elements in the matrix are more than 0, the optimization problem belongs to a standard convex optimization problem, a convex optimization tool box is used for solving the problem to obtain an estimated value G ' of the matrix G, and then a transposed matrix Q ' = (G ') of the error matrix Q is obtained -1 。
2. The method for calibrating uniform linear array mutual coupling and array element gain-phase error as recited in claim 1, wherein said step S1 comprises the steps of:
step S1.1, placing the uniform linear array on a platform moving at a constant speed, and in a coherent processing interval, receiving the echo signals by the uniform linear array, wherein the echo signals are mainly signals reflected by stationary objects around the platform moving at the constant speed, and placing a plurality of objects with reflection sectional areas around the platform moving at the constant speed so as to obtain echo signals with stronger energy;
s1.2, establishing a corresponding ideal echo signal model according to the uniform linear array parameters to obtain an observed value x of the ideal echo signal at the moment t c (t) is:
wherein the content of the first and second substances,
represents the kronecker product, alpha (f) s ,f d ) Is the amplitude of the echo signal, s s (f s ) Is a space steering vector, s d (f d ) For time-oriented vectors, s is defined separately s (f s ) And s d (f d ) Comprises the following steps:
wherein N is the number of array elements, M is the number of pulses in the coherent processing interval, f s = d sin theta/lambda is space frequency, d is antenna array element spacing, theta is the incident angle of the echo signal, lambda is the echo signal wavelength, f d = (= (2 vTsin θ)/λ is normalized doppler frequency, v represents the motion speed of the platform moving at a constant speed, and T is pulse repetition period;
s1.3, according to the ideal echo signal model, establishing the echo signal model with mutual coupling and array element gain-phase error to obtain an observed value of the echo signal model at the moment t
Comprises the following steps:
wherein, the matrix Q d = EC describes uniformly the effect of mutual coupling of the uniform linear array and the influence of the gain-phase error of the array elements on the space steering vector, C is a mutual coupling matrix, and is a strip-shaped symmetric Toeplitz momentThe matrix E is a matrix element gain-phase error matrix, a diagonal matrix, and the property of the kronecker product
To obtain
Comprises the following steps:
obtaining the echo signal model containing errors
With the ideal echo signal model x c (t) relationship between:
wherein the error matrix
3. The method for calibrating uniform linear array mutual coupling and array element gain-phase error as claimed in claim 1, wherein said step S2 comprises the steps of:
step S2.1, for the uniform linear array, assuming that the motion speed v of the platform carrying the array is constant within one coherent processing interval time, in the time period, the echo signal subspace formed by the echo signal received by the uniform linear array is constant, according to the echo signal model established in the step S1 and the known radar system parameters applying the array, the motion speed v of the platform moving at a uniform speed is v, the array element spacing is d, the pulse repetition period is T and the wavelength is lambda, and the echo signal incident angle theta is artificially given i Generating said ideal echo signal v (i), where θ i ＝[-90°,90°]To obtain a covariance matrix R for generating the echo signal C ：
Wherein L is the number of the ideal echo signals generated;
step S2.2, for the covariance matrix R C And (3) carrying out characteristic value decomposition:
R C ＝UΛU H
wherein Λ = diag { λ 1 ,λ 2 ,…,λ NM The expression of diag { a } is that a diagonal matrix is constructed by a vector a, lambda i Is the covariance matrix R C The ith eigenvalue in descending order, U being the covariance matrix R C A matrix of eigenvectors with ith column of λ i Corresponding eigenvectors, the first few columns of the matrix U corresponding to the signal subspace, i.e. the echo signal subspace U, according to the subspace theory c The remaining column vectors correspond to a noise subspace, i.e. the orthogonal subspace of the echo signal subspace
Obtaining the projection matrix of the orthogonal subspace
Is composed of
4. The method for calibrating uniform linear array mutual coupling and array element gain-phase error as claimed in claim 1, wherein said step S4 comprises the steps of:
data array actually received using the uniform linear array
And an estimated value G' of an inverse matrix G of the error matrix Q, calibrating the uniform linear array cross coupling and the array element gain-phase error, and receiving data
Converted to x' (t) satisfying the ideal echo model description,
and completing the calibration.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911256593.7A CN112904321B (en) | 2019-12-03 | 2019-12-03 | Method for calibrating even linear array cross coupling and array element gain-phase error |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911256593.7A CN112904321B (en) | 2019-12-03 | 2019-12-03 | Method for calibrating even linear array cross coupling and array element gain-phase error |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112904321A CN112904321A (en) | 2021-06-04 |
| CN112904321B true CN112904321B (en) | 2023-01-17 |
Family
ID=76111231
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911256593.7A Active CN112904321B (en) | 2019-12-03 | 2019-12-03 | Method for calibrating even linear array cross coupling and array element gain-phase error |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112904321B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2005257298A (en) * | 2004-03-09 | 2005-09-22 | Yokohama Tlo Co Ltd | Calibration method and calibration device for array antenna |
| CN104076332A (en) * | 2014-06-25 | 2014-10-01 | 西安电子科技大学 | Estimation method for magnitudes and phases of radar uniform linear array |
| CN106707250A (en) * | 2017-01-24 | 2017-05-24 | 西安电子科技大学 | Mutual coupling correction-based radar array adaptive beamforming method |
| CN109738854A (en) * | 2018-12-14 | 2019-05-10 | 北京邮电大学 | A kind of angle-of- arrival estimation method of aerial array arrival bearing |
| CN110361697A (en) * | 2019-07-09 | 2019-10-22 | 西安电子科技大学 | A kind of robust ada- ptive beamformer method based on covariance matrix mixing reconstruct |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7199753B2 (en) * | 2005-06-16 | 2007-04-03 | Raytheon Company | Calibration method for receive only phased array radar antenna |
-
2019
- 2019-12-03 CN CN201911256593.7A patent/CN112904321B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2005257298A (en) * | 2004-03-09 | 2005-09-22 | Yokohama Tlo Co Ltd | Calibration method and calibration device for array antenna |
| CN104076332A (en) * | 2014-06-25 | 2014-10-01 | 西安电子科技大学 | Estimation method for magnitudes and phases of radar uniform linear array |
| CN106707250A (en) * | 2017-01-24 | 2017-05-24 | 西安电子科技大学 | Mutual coupling correction-based radar array adaptive beamforming method |
| CN109738854A (en) * | 2018-12-14 | 2019-05-10 | 北京邮电大学 | A kind of angle-of- arrival estimation method of aerial array arrival bearing |
| CN110361697A (en) * | 2019-07-09 | 2019-10-22 | 西安电子科技大学 | A kind of robust ada- ptive beamformer method based on covariance matrix mixing reconstruct |
Non-Patent Citations (7)
| Title |
|---|
| Joint Gain/Phase and Mutual Coupling Array Calibration Technique with Single Calibrating Source;Wei Chen et al.;《International Journal of Antennas and Propagation》;20120920;全文 * |
| Robust Joint Calibration of Mutual Coupling and Channel Gain/Phase Inconsistency for Uniform Circular Array;Song Liu et al.;《IEEE Antennas and Wireless Propagation Letters》;20151231;第15卷;全文 * |
| 基于降维的双基地MIMO雷达收发阵列互耦和幅相误差校正算法;杨守国等;《系统工程与电子技术》;20181116;第40卷(第12期);全文 * |
| 复杂环境下阵列幅相误差的校正;曾奋;《中国优秀博硕士学位论文全文数据库(硕士)信息科技辑》;20111215;第6-16页 * |
| 导向矢量和协方差矩阵联合迭代估计的稳健波束形成算法;杨志伟 等;《电子与信息学报》;20181231;第40卷(第12期);第2874-2879页 * |
| 阵列模型误差条件下稳健的DOA估计算法;郭艺夺等;《上海航天》;20100225(第01期);全文 * |
| 鲁棒成形极化敏感阵列波束的方法及极化估计;虞翔 等;《航空学报》;20170625;第38卷(第6期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112904321A (en) | 2021-06-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110109051B (en) | Frequency control array-based cross coupling array DOA estimation method | |
| CN105137409B (en) | The sane space-time adaptive processing method of echo signal mutually constrained based on width | |
| CN109765521B (en) | Beam domain imaging method based on subarray division | |
| CN109597041B (en) | Segmented linear frequency modulation waveform design method based on coherent FDA | |
| CN103837861A (en) | Submatrix level linear constraint self-adaptive beam forming method based on feature subspaces | |
| CN108469601B (en) | Transceiving joint robust optimization method for improving worst detection performance of MIMO-STAP | |
| Wang et al. | Nested array receiver with time‐delayers for joint target range and angle estimation | |
| CN111751800A (en) | Frequency control array radar angle-distance parameter decoupling method | |
| Li et al. | Broadband constant beamwidth beamforming for suppressing mainlobe and sidelobe interferences | |
| CN110196417B (en) | Bistatic MIMO radar angle estimation method based on emission energy concentration | |
| CN112180339A (en) | Radar echo signal accurate direction finding method based on sparse processing | |
| Hiemstra | Robust implementations of the multistage Wiener filter | |
| CN109491009B (en) | Optical fiber combined array and grating lobe suppression method based on optical fiber combined array | |
| Zhang et al. | Improved main-lobe cancellation method for space spread clutter suppression in HFSSWR | |
| CN112904321B (en) | Method for calibrating even linear array cross coupling and array element gain-phase error | |
| CN109597034B (en) | Space-time adaptive processing method based on Euclidean distance | |
| CN111812612A (en) | Partial correlation waveform design method of MIMO radar based on subarray orthogonal LFM signal | |
| CN110535519A (en) | A kind of robust adaptive beamforming method based on space smoothing | |
| De et al. | Angle estimation using modified subarray level monopulse ratio algorithm and s-curve in digital phased array radar | |
| Pandey et al. | Space Time Adaptive Processing for High Signal to Clutter Ratio Target's Detection Radar System | |
| CN114755628A (en) | Method for estimating direction of arrival of acoustic vector sensor array under non-uniform noise | |
| Wang et al. | Nested array with time-delayers for target range and angle estimation | |
| Xiong et al. | Space time adaptive processing for airborne MIMO radar based on space time sampling matrix | |
| CN110018466B (en) | MUSIC beam forming method based on molecular array preprocessing | |
| CN111537974A (en) | Decoupling space-time self-adaptive signal processing method |
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 | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |