CN109655801A - The angle-measuring method of radar seeker efficient spatial spectrum based on bicyclic round battle array - Google Patents
The angle-measuring method of radar seeker efficient spatial spectrum based on bicyclic round battle array 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
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- 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
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Abstract
The present invention relates to a kind of angle-measuring methods of radar seeker efficient spatial spectrum based on bicyclic round battle array, include: S1, obtaining covariance matrix according to the reception data of radar seeker；S2, Eigenvalues Decomposition is carried out to covariance matrix using improved ESPRIT algorithm, specifically: generalized eigenvalue transformation S21, is carried out to covariance matrix, makes Lanczos algorithmic statement in minimal eigenvalue；S22, using Lanczos algorithm, covariance matrix is converted by successive ignition, obtains triple diagonal matrix；S23, minimal eigenvalue is obtained to triple diagonal matrix progress Eigenvalues Decomposition using the QR algorithm with origin displacement；S3, information source number is determined according to the tuple of minimal eigenvalue；S4, space spectral function is calculated；S5, angle corresponding to the spectral peak of space spectral function, as signal incident angle are found.The present invention realizes the resolution of multiple targets in main beam in the limited situation of antenna aperature, effectively reduces calculation amount, improves processing speed.
Description
Technical Field
The invention relates to an angle measurement method of a radar seeker, in particular to an angle measurement method of a high-efficiency space spectrum of a radar seeker based on a double-ring circular array, and belongs to the technical field of angle measurement technologies of phased array radar seekers.
Background
Currently, terminal-guided radars have evolved from mechanical scanning to phased array regimes. The seeker of the phased array radar is a research hotspot and development trend of precise guidance, becomes one of main directions of seeker development in the future, and is a mark of a new generation seeker (an active phased array system is adopted).
The digital array radar seeker is a subsequent development direction of the existing analog phased array radar seeker. The digital array radar seeker cancels parts such as an analog phase shifter unit, a power division network sum-difference device and the like of the analog phased array radar seeker, and converts microwave signals into digital signals in a full digital receiving mode. Different from the problem that the traditional monopulse angle measurement technology cannot realize multi-target resolution in a main lobe of a wave beam, the digital array radar seeker can realize multi-target resolution in the same wave beam through an angle super-resolution estimation technology in array signal processing, break through the constraint condition of Rayleigh limit, improve the resolution capability of the seeker to formation invasion targets, dragging interference targets and dense targets, avoid the defect that the angle measurement system of a traditional mechanical scanning and analog phased array seeker cannot measure the angle of more than one single target in the wave beam, and remarkably improve the operational performance and the anti-interference capability of the radar seeker.
The multiple signal classification (MUSIC) algorithm and the rotation invariant (ESPRIT) algorithm are typical spatial spectrum estimation methods, and the development of the spatial spectrum estimation algorithm is greatly promoted by the two algorithms. However, the two algorithms have the problems of large calculation amount, unsuitability for real-time processing and low estimation precision under the condition of single snapshot in the application of the actual phased array radar seeker. In order to solve the problems, a parallelization efficient spatial spectrum estimation algorithm becomes one of research hotspots in the technical field of array signal direction finding.
The characteristic decomposition algorithm represented by the MUSIC algorithm and the ESPRIT algorithm has higher angle resolution and resolution precision. However, because such algorithms all need to perform feature decomposition, the calculation amount is large in the implementation process, thereby limiting the application of the algorithms in the occasions with high real-time requirements. The MUSIC algorithm needs to perform feature decomposition for calculating a spatial spectrum and scan a direction vector. The ESPRIT algorithm can obtain the incident direction of the signal without scanning the direction vector, and the calculation amount is smaller than that of the MUSIC algorithm. However, because one characteristic decomposition and one generalized characteristic decomposition are required, the calculation amount of the ESPRIT algorithm is still large, and the processing speed of the existing system is difficult to meet the requirement of practical application. Therefore, the rapid implementation of the ESPRIT algorithm is of great importance to facilitate the wide application of the algorithm.
Patent application CN201310300941.2 discloses an airborne radar short-range clutter suppression method based on an ESPRIT algorithm, and mainly solves the problem that the clutter suppression performance of STAP processing is reduced due to short-range clutter of an airborne radar non-front side view array. The method can effectively suppress short-range clutter, improves the performance of space-time adaptive processing, and can be used for suppressing the short-range clutter of the non-front side view array of the airborne radar.
Patent application CN201610905419.0 discloses a general spatial spectrum estimation method based on extended ESPRIT technology, which can calculate a newly defined general ESPRIT spatial spectrum by using the output angle estimation value and the corresponding characteristic value, and if and only if the general ESPRIT spatial spectrum has a spectral peak at the true signal incidence angle, the spectral peak of the general ESPRIT spatial spectrum is searched in the parameter space to obtain the estimation of the arrival direction of the spatial signal.
In an improved algorithm based on ESPRIT, high-resolution estimation of a target direction of arrival can be realized without carrying out generalized eigenvalue decomposition on a covariance matrix of an incoming wave signal, and effectiveness and feasibility of the improved algorithm are proved by theoretical analysis and simulation results.
In the thesis "an improved ESPRIT direction-finding algorithm based on generalized eigenvectors", the rotation invariant characteristic of a signal subspace is fully utilized, and the arrival direction estimation is performed by utilizing the relation between the signal subspace and an array manifold, so that experiments prove that the algorithm can achieve the performance similar to the MUSIC algorithm under the advantage of small calculation amount.
In an improved two-dimensional ESPRIT algorithm, an improved two-dimensional ESPRIT algorithm is provided for solving the problem of array redundancy of a covariance matrix when a signal is solved by a two-dimensional rotation invariant subspace algorithm. The algorithm constructs 2 cross-correlation matrixes by using an array structure principle, then carries out singular value decomposition by using the combined special large matrix to estimate a signal subspace, and finally realizes two-dimensional direction finding by using a 2D-ESPRIT method. The algorithm has high estimation precision and small calculation amount, and can estimate coherent signals and non-coherent signals simultaneously after spatial smoothing.
Based on the above, the present invention provides an angle measurement method for a radar seeker efficient spatial spectrum based on a double circular array, so as to solve the disadvantages and limitations existing in the prior art, and the method has not been disclosed by related patents or papers.
Disclosure of Invention
The invention aims to provide an angle measurement method of a high-efficiency space spectrum of a radar seeker based on a double-ring circular array, which is used for realizing the resolution of a plurality of targets in a main beam under the condition of limited antenna aperture, effectively reducing the calculated amount and improving the processing speed.
In order to achieve the purpose, the invention provides an angle measurement method of a radar seeker efficient space spectrum based on a double-ring circular array, which comprises the following steps of:
s1, obtaining a covariance matrix according to the received data of the radar seeker;
s2, performing eigenvalue decomposition on the covariance matrix by using an improved ESPRIT algorithm; the method specifically comprises the following steps:
s21, carrying out generalized eigenvalue transformation on the covariance matrix to make the Lanczos algorithm converge to the minimum eigenvalue;
s22, transforming the covariance matrix through multiple iterations by adopting a Lanczos algorithm to obtain a tri-diagonal matrix;
s23, decomposing the eigenvalues of the three-diagonal matrix by using a QR algorithm with origin displacement to obtain a minimum eigenvalue;
s3, determining the number of information sources according to the repeated number of the minimum characteristic value;
s4, calculating a spatial spectrum function;
and S5, finding the angle corresponding to the spectrum peak of the spatial spectrum function, namely the signal incidence angle.
In both S1 and S2, multiple processors are used for parallel processing.
The step S21 specifically includes the following steps:
the covariance matrix is asymmetric matrixes A and B of M multiplied by M order, and the decomposition of the generalized eigenvalue can be expressed as:
Ax＝λBx (1)
by transforming the matrix a we obtain:
A-1Bx＝(1/λ)x (2)
wherein, the transformed eigenvalue in the formula (2) and the original eigenvalue in the formula (1) are reciprocal.
The step S22 specifically includes the following steps:
two double normalized unit vectors w are selected1And v1So that w1 HBv1＝1；
Setting αj、βjAnd deltajAre coefficients constituting a tri-diagonal matrix T, respectively, and δ when j is 11w0＝0，β1v0＝0；
When j is 1,2, …, n and n is less than or equal to M, the following iterative calculation is performed by using Lanczos algorithm:
after n times of iterative computation are finished, n Lanczos vector pairs A are obtained-1B, performing biorthogonal transformation to obtain an n-order tri-diagonal matrix T:
T＝WHA-1BV；
WH＝[w1w2,…,wn]H；
V＝[v1v2,…,vn]；
WHV＝I；
wherein I represents an identity matrix; and calculating to obtain a three-diagonal matrix T as follows:
wherein the coefficients α of the tri-diagonal matrix Tj、βjAnd deltajCalculated by the above formula (3).
In S22, the method further includes an orthogonalization process to ensure the vector v in the iterative processj+1And wj+1Is determined.
Preferably, the orthogonalizing treatment is performed by using a schmidt orthogonalizing method, which specifically comprises the following steps:
setting a threshold as epsilon;
setting an iteration coefficient mij、nijComprises the following steps:
the iteration coefficient m in the current iteration calculationij、nijWhen the value is less than or equal to epsilon, continuing to perform iterative computation; the iteration coefficient m in the current iteration calculationij、nijWhen larger than epsilon, the vector vj+1、wj+1Performing an orthogonalization process to obtain:
in S23, the specific steps are: performing multiple plane rotation transformations on the tri-diagonal matrix T to generate a tri-diagonal matrix sequence { TkGet T out of the iterationkThe diagonal matrix Σ is approached, wherein the element on the main diagonal of the diagonal matrix Σ is the minimum eigenvalue of the tri-diagonal matrix T.
In summary, the angle measurement method for the efficient spatial spectrum of the radar seeker based on the double-loop circular array, provided by the invention, adopts parallel processing, converts the covariance matrix into the three-diagonal matrix through the Lanczos algorithm, and performs characteristic decomposition on the three-diagonal matrix by using the QR algorithm with the origin displacement, so that the number of QR iteration is greatly reduced during the characteristic decomposition, resolution of a plurality of targets in a main beam can be realized under the condition of limited antenna aperture, and the targets and the target arrival angle can be effectively resolved and measured under the condition of a certain signal-to-noise ratio.
Theoretical analysis and simulation experiments show that the invention can greatly reduce the self calculated amount of the ESPRIT algorithm, and simultaneously can improve the processing speed of the ESPRIT algorithm through parallel processing, thereby providing a good theoretical basis for the real-time application of the ESPRIT algorithm.
Drawings
FIG. 1 is a flow chart of an angle measurement method of a radar seeker efficient space spectrum based on a double-ring circular array in the invention;
FIG. 2 is a comparison of DOA estimation bias as a function of signal to noise ratio for the ESPRIT algorithm before and after modification in accordance with the present invention;
FIG. 3 is a diagram illustrating a comparison of mean square error of DOA estimation with signal-to-noise ratio for ESPRIT algorithm before and after improvement;
FIG. 4 is a comparison of the amount of computation of the ESPRIT algorithm before and after improvement as a function of the number of loop iterations in the present invention;
fig. 5 is a comparison diagram of the operation amount of the ESPRIT algorithm before and after improvement according to the array element number.
Detailed Description
The technical contents, construction features, achieved objects and effects of the present invention will be described in detail by preferred embodiments with reference to fig. 1 to 5.
As shown in fig. 1, the method for measuring an angle of a high-efficiency spatial spectrum of a radar seeker based on a double-ring circular array provided by the invention comprises the following steps:
s1, obtaining a covariance matrix according to the received data of the radar seeker;
s2, performing eigenvalue decomposition on the covariance matrix by using an improved ESPRIT algorithm; the method specifically comprises the following steps:
s21, carrying out generalized eigenvalue transformation on the covariance matrix to make the Lanczos algorithm converge to the minimum eigenvalue;
s22, transforming the covariance matrix through multiple iterations by adopting a Lanczos algorithm to obtain a tri-diagonal matrix;
s23, decomposing the eigenvalues of the three-diagonal matrix by using a QR (orthogonal trigonometry) algorithm with origin displacement to obtain a minimum eigenvalue;
s3, determining the number of information sources according to the repeated number of the minimum characteristic value;
s4, calculating a spatial spectrum function;
and S5, finding the angle corresponding to the spectrum peak of the spatial spectrum function, namely the signal incidence angle.
In both S1 and S2, multiple processors are used for parallel processing.
The step S21 specifically includes the following steps:
the covariance matrix is asymmetric matrixes A and B of M multiplied by M order, and the decomposition of the generalized eigenvalue can be expressed as:
Ax＝λBx (1)
in order to make the subsequent calculation for the eigenvalues all applicable to the complex domain, the matrix a is transformed to obtain:
A-1Bx＝(1/λ)x (2)
wherein, the transformed eigenvalue in the formula (2) and the original eigenvalue in the formula (1) are reciprocal.
Since the subsequently adopted Lanczos algorithm is the eigenvalue with the largest modulus which converges in the formula (1), after the eigenvalue transformation, the Lanczos algorithm converges in the eigenvalue with the smallest modulus in the formula (2).
The step S22 specifically includes the following steps:
two double normalized unit vectors w are selected1And v1So that w1 HBv11 is ═ 1; wherein, the superscript symbol H represents the conjugate transpose;
setting αj、βjAnd deltajAre coefficients constituting a tri-diagonal matrix T, respectively, and δ when j is 11w0＝0，β1v0＝0；
When j is 1,2, …, n (n is less than or equal to M), the following iterative calculation is carried out by adopting a Lanczos algorithm:
after n times of iterative computation are finished, n Lanczos vector pairs A are obtained-1B, performing biorthogonal transformation to obtain an n-order tri-diagonal matrix T:
T＝WHA-1BV；
WH＝[w1w2,…,wn]H；
V＝[v1v2,…,vn]；
WHV＝I；
wherein I represents an identity matrix; and calculating to obtain a three-diagonal matrix T as follows:
wherein the coefficients α of the tri-diagonal matrix Tj、βjAnd deltajJ is 1,2, …, and n (n ≦ M) can be calculated by the above formula (3).
After the covariance matrix is transformed into the tri-diagonal matrix in this step, the computation amount for performing the feature decomposition on the tri-diagonal matrix is much smaller than the computation amount for directly performing the feature decomposition on the original covariance matrix.
In S22, the vector v is rounded off during the iteration process due to rounding errorsj+1And wj+1The orthogonality of (b) is gradually lost, and thus further orthogonalization processing is required.
In a preferred embodiment of the present invention, the orthogonalization process is performed by a Gram-Schmidt (Schmidt) orthogonalization method, which specifically comprises:
a threshold epsilon is set, and the value epsilon is preferably 10 in this embodiment-3；
Setting an iteration coefficient mij、nijComprises the following steps:
the iteration coefficient m in the current iteration calculationij、nijWhen the value is less than or equal to epsilon, the iterative computation can be continued without performing orthogonalization treatment;the iteration coefficient m in the current iteration calculationij、nijWhen larger than epsilon, v needs to be correctedj+1、wj+1Carrying out orthogonalization treatment, and reassigning as follows:
the step S23 specifically includes the following steps:
according to the three-diagonal matrix T obtained by the formulas (3) and (4) in the S22, carrying out characteristic value decomposition on the three-diagonal matrix T by using a QR algorithm with origin displacement for decelerating and converging, and effectively reducing the iteration times of the QR algorithm; the QR algorithm is used for decomposing eigenvalues by decomposing a matrix into a normal orthogonal matrix Q and an upper triangular matrix R;
select the sequence of [ mu ]k}；
Array of construction numbers TkThe method comprises the following steps: let T1＝T∈RM×MTo Tk-μkCarrying out QR decomposition to obtain: t isk-μkI＝QkRkFrom this, a new matrix is constructed: t isk+1＝RkQk+μkI＝Qk HTkQk(ii) a Order to Then there is
Wherein, mu is selectedThe eigenvalues closest to α (n, k), namely:
wherein,matrix QkExcept for the (i, i), (i, i +1), (i +1, i) and (i +1) th elements, which are an identity matrix, the four elements are selected according to the following formula:
generating a tri-diagonal matrix sequence { T } from the tri-diagonal matrix T by performing a plurality of plane rotation transformations as described abovekGet T after multiple iterationskWhen the diagonal matrix Σ is approached, the element on the main diagonal of the diagonal matrix Σ is the minimum eigenvalue of the three-diagonal matrix T.
The angle measurement method of the efficient spatial spectrum of the radar seeker based on the double-ring circular array carries out simulation analysis according to the steps. As shown in fig. 2 and fig. 3, the estimation accuracy of DOA (direction of arrival) of the ESPRIT algorithm before and after the improvement by the simulation analysis is shown in comparison with the change of the signal-to-noise ratio. Fig. 2 shows the variation of the DOA estimation deviation of the signal with an incident angle of 10 ° with the signal-to-noise ratio when the number of array elements is 9, the number of fast beats is 256, and the number of loop iterations is 30. Fig. 3 shows the change of mean square error of DOA estimation of a signal with an incident angle of 10 ° with the signal-to-noise ratio when the number of array elements is 9, the number of fast beats is 256, and the number of loop iterations is 30. As can be seen from fig. 2 and 3, the DOA estimation accuracy of the improved ESPRIT algorithm is slightly lower than that of the original ESPRIT algorithm, and is more obvious in the case of low signal-to-noise ratio, but the DOA estimation accuracy can still basically meet the practical application requirements.
As shown in fig. 4 and 5, the simulation analysis is a comparative example of the calculated amount of the ESPRIT algorithm before and after improvement. Fig. 4 shows the relationship between the operation amount of the ESPRIT algorithm before and after the improvement and the loop iteration number when the array element number is 16 and the fast beat number is 20. Fig. 5 shows the relationship between the operation amount of the ESPRIT algorithm before and after the improvement and the number of array elements when the number of iterations is 30 and the number of fast beats is 20. As can be seen from fig. 4 and 5, as the loop iteration number and the array element number increase, the calculation amount tends to increase rapidly, but the calculation amount of the improved ESPRIT algorithm is significantly smaller than that of the original ESPRIT algorithm, and the calculation amount can be reduced by about one order of magnitude.
In summary, the angle measurement method for the efficient spatial spectrum of the radar seeker based on the double-loop circular array, provided by the invention, adopts parallel processing, converts the covariance matrix into the three-diagonal matrix through the Lanczos algorithm, and performs characteristic decomposition on the three-diagonal matrix by using the QR algorithm with the origin displacement, so that the number of QR iteration is greatly reduced during the characteristic decomposition, resolution of a plurality of targets in a main beam can be realized under the condition of limited antenna aperture, and the targets and the target arrival angle can be effectively resolved and measured under the condition of a certain signal-to-noise ratio.
Theoretical analysis and simulation experiments show that the invention can greatly reduce the self calculated amount of the ESPRIT algorithm, and simultaneously can improve the processing speed of the ESPRIT algorithm through parallel processing, thereby providing a good theoretical basis for the real-time application of the ESPRIT algorithm.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (7)
1. A method for measuring an angle of a radar seeker efficient space spectrum based on a double-ring circular array is characterized by comprising the following steps:
s1, obtaining a covariance matrix according to the received data of the radar seeker;
s2, performing eigenvalue decomposition on the covariance matrix by using an improved ESPRIT algorithm; the method specifically comprises the following steps:
s21, carrying out generalized eigenvalue transformation on the covariance matrix to make the Lanczos algorithm converge to the minimum eigenvalue;
s22, transforming the covariance matrix through multiple iterations by adopting a Lanczos algorithm to obtain a tri-diagonal matrix;
s23, decomposing the eigenvalues of the three-diagonal matrix by using a QR algorithm with origin displacement to obtain a minimum eigenvalue;
s3, determining the number of information sources according to the repeated number of the minimum characteristic value;
s4, calculating a spatial spectrum function;
and S5, finding the angle corresponding to the spectrum peak of the spatial spectrum function, namely the signal incidence angle.
2. The method for angle measurement of high-efficiency spatial spectrum of radar seeker based on double-ring circular array as claimed in claim 1, wherein in each of S1 and S2, multiple processors are adopted for parallel processing.
3. The method according to claim 2, wherein the step S21 comprises the following steps:
the covariance matrix is asymmetric matrixes A and B of M multiplied by M order, and the decomposition of the generalized eigenvalue can be expressed as:
Ax＝λBx (1)
by transforming the matrix a we obtain:
A-1Bx＝(1/λ)x (2)
wherein, the transformed eigenvalue in the formula (2) and the original eigenvalue in the formula (1) are reciprocal.
4. The method according to claim 3, wherein the step of S22 comprises the following steps:
two double normalized unit vectors w are selected1And v1So that w1 HBv1＝1；
Setting αj、βjAnd deltajAre coefficients constituting a tri-diagonal matrix T, respectively, and δ when j is 11w0＝0，β1v0＝0；
When j is 1,2, …, n and n is less than or equal to M, the following iterative calculation is performed by using Lanczos algorithm:
after n times of iterative computation are finished, n Lanczos vector pairs A are obtained-1B, performing biorthogonal transformation to obtain an n-order tri-diagonal matrix T:
T＝WHA-1BV；
WH＝[w1w2,…,wn]H；
V＝[v1v2,…,vn]；
WHV＝I；
wherein I represents an identity matrix; and calculating to obtain a three-diagonal matrix T as follows:
wherein the coefficients α of the tri-diagonal matrix Tj、βjAnd deltajCalculated by the above formula (3).
5. The method as claimed in claim 4, wherein the step S22 further comprises an orthogonalization process for ensuring the vector v in the iterative processj+1And wj+1Is determined.
6. The method for measuring the angle of the efficient spatial spectrum of the radar seeker based on the double-ring circular array according to claim 5, wherein in the step S22, the orthogonalization is performed by using a Schmidt orthogonalization method, specifically:
setting a threshold as epsilon;
setting an iteration coefficient mij、nijComprises the following steps:
the iteration coefficient m in the current iteration calculationij、nijWhen the value is less than or equal to epsilon, continuing to perform iterative computation; the iteration coefficient m in the current iteration calculationij、nijWhen larger than epsilon, the vector vj+1、wj+1Performing an orthogonalization process to obtain:
7. the method for angle measurement of efficient spatial spectrum of radar seeker based on double-ring circular array according to claim 4, wherein in S23, the method specifically comprises: performing multiple plane rotation transformations on the tri-diagonal matrix T to generate a tri-diagonal matrix sequence { TkGet T out of the iterationkThe diagonal matrix Σ is approached, wherein the element on the main diagonal of the diagonal matrix Σ is the minimum eigenvalue of the tri-diagonal matrix T.
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