CN112816936B - Two-dimensional sparse linear array direction-of-arrival estimation method based on matrix matching - Google Patents
Two-dimensional sparse linear array direction-of-arrival estimation method based on matrix matching 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
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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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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- Radar, Positioning & Navigation (AREA)
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Abstract
The invention relates to a method for estimating the direction of arrival, in particular to a two-dimensional sparse linear array direction of arrival estimation method based on matrix matching, which comprises the following steps: establishing a basic model of two-dimensional sparse linear array two-dimensional direction-of-arrival estimation, and defining the incident angle of the first signal as (theta) l ,) Assuming that L far-field narrowband signals are totally incident into an array, obtaining received data of two subarrays in the array at k time, obtaining a received data covariance matrix of the two subarrays according to the received data, obtaining virtual received data of continuous ULA parts in the virtual array formed by the two subarrays on an x axis and a y axis, constructing a Toeplitz matrix by utilizing the virtual received data, and then respectively obtaining estimated values of two-dimensional angles by constructing a spatial spectrum functionAndhypothesis and estimateIn (a)The corresponding another dimension angle estimate isSequentially carrying out a least square algorithm and matrix characteristic decomposition to obtain an angle estimated value as follows
Description
Technical Field
The invention relates to a method for estimating a direction of arrival, in particular to a two-dimensional sparse linear array direction of arrival estimation method based on matrix matching.
Background
The direction of arrival (DOA, direction of Arrival) estimation is an important component of radar signal processing, and the linear array structure can only realize one-dimensional angle estimation, and cannot estimate two-dimensional angle information of signals at the same time, so that for the case of needing to estimate pitch and azimuth information of signals at the same time, a two-dimensional array structure is generally needed. The two-dimensional DOA estimation in the two-dimensional linear array is widely studied due to the simple structure, and the two-dimensional DOA estimation suitable for the two-dimensional sparse linear array is proposed for further expanding the degree of freedom of the two-dimensional DOA estimation. Compared with the traditional two-dimensional DOA estimation algorithm applied to a two-dimensional sparse linear array, the two-dimensional matching DOA (2Dimensional Paired DOA,2-D PDOA) estimation algorithm in the prior art utilizes the sparse characteristic of each dimension array of the L-shaped sparse array, improves the degree of freedom of two-dimensional DOA estimation, utilizes one-dimensional arrays to estimate one-dimensional angles, and utilizes the cross-correlation matrix of data received by the two-dimensional arrays and the characteristics of mutual matching of the two-dimensional angles to estimate other one-dimensional angles, thereby realizing simultaneous estimation and matching of the two-dimensional DOA.
However, the two-dimensional angle estimation by the 2-D PDOA estimation algorithm is separately estimated, wherein one dimension directly utilizes a sparse array to perform angle estimation, and the angle estimation of the other dimension is obtained on the basis of the angle estimation of the other dimension, so that the angle estimation error of the other dimension is larger.
Disclosure of Invention
The invention aims to provide a two-dimensional sparse linear array direction-of-arrival estimation method based on matrix matching, which solves the problem that the two-dimensional angle estimation process in the current direction-of-arrival two-dimensional angle estimation is related, so that the angle estimation error of the other dimension is larger.
In order to solve the technical problems, the invention adopts the following technical scheme:
a two-dimensional sparse linear array direction of arrival estimation method based on matrix matching comprises the following steps:
s1, establishing a basic model of two-dimensional direction-of-arrival estimation of a two-dimensional sparse linear array, wherein the array model comprises M 1 =2d and M 2 Two subarrays of =3d, where d is half wavelength, two subarrays on x, y axes are referred to asAnd->
S2, defining the incident angle of the first signal asWherein θ is l 、/>The included angles between the signal incidence direction and the xoz and yoz surfaces are respectively, and the receiving data of two subarrays in the array at the k moment are obtained on the assumption that L far-field narrowband signals are totally incident into the array;
s3, obtaining received data covariance matrixes of the two subarrays according to the received data;
s4, forming virtual received data of continuous ULA parts in the virtual array on an x axis and a y axis according to the received data covariance matrixes of the two subarrays;
s5, constructing a Toeplitz matrix by utilizing virtual received data, and then respectively obtaining estimated values of two-dimensional angles by constructing a spatial spectrum functionAnd->
S6, assumption and estimation valueMiddle->The corresponding other dimension angle estimate is +.>Wherein->Is toIs->Wherein T is {0,1 }) L×L Is a column transformation matrix;
s7, sequentially carrying out a least square algorithm and matrix characteristic decomposition to obtainThen the angle estimation value is obtained as +.>
The further technical scheme is that the received data of the two subarrays at the k moment are respectively:
and
the further technical scheme is that the covariance matrixes of the received data of the two subarrays are respectively:
and->
In a further technical scheme, the virtual received data of continuous ULA parts in the virtual array formed by the two subarrays on the x axis and the y axis are respectively:
and->
The further technical scheme is that Toeplitz matrixes constructed by utilizing virtual received data are respectively as follows:
and->
The further technical proposal is that the constructed spatial spectrum function is as follows:
wherein the method comprises the steps ofRepresenting U x,n Go up->Direction vector of direction,/>Representing U y,n And a steering vector in the upward theta direction.
Compared with the prior art, the invention has the beneficial effects that: compared with the existing 2-D PDOA estimation algorithm, the estimation method carries out the two-dimensional angle estimation respectively, avoids the influence of one-dimensional angle estimation errors on the other-dimensional angle estimation, realizes the matching of two-dimensional direction-of-arrival estimation values, and improves the accuracy of angle estimation.
Drawings
Fig. 1 is a basic model of an array receiving signal in two-dimensional direction of arrival estimation of a two-dimensional sparse linear array in the present invention.
Fig. 2 is a graph of RMSE versus SNR for a DOA estimate in accordance with the present invention, where k=200.
FIG. 3 is a graph showing the performance analysis of the matrix transformation-based two-dimensional sparse linear array DOA estimation algorithm in the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1:
the two-dimensional sparse linear array direction of arrival estimation method based on matrix matching in the embodiment specifically comprises the following steps:
s1, establishing a basic model of two-dimensional direction-of-arrival estimation of a two-dimensional sparse linear array, wherein the array model comprises M 1 =2d and M 2 Two subarrays of =3d, where d is half wavelength;
s2, defining the incident angle of the first signal asWherein θ is l 、/>The included angles between the signal incidence direction and the xoz and yoz surfaces are respectively, and the receiving data of two subarrays in the array at the k moment are obtained on the assumption that L far-field narrowband signals are totally incident into the array;
s3, obtaining received data covariance matrixes of the two subarrays according to the received data;
s4, forming virtual received data of continuous ULA parts in the virtual array on an x axis and a y axis according to the received data covariance matrixes of the two subarrays;
s5, constructing a Toeplitz matrix by utilizing virtual received data, and then respectively obtaining estimated values of two-dimensional angles by constructing a spatial spectrum functionAnd->
S6, assumption and estimation valueMiddle->The corresponding other dimension angle estimate is +.>Wherein->Is toIs->Wherein T is {0,1 }) L×L Is a column transformation matrix;
s7, sequentially carrying out a least square algorithm and matrix characteristic decomposition to obtainThen the angle estimation value is obtained as +.>
Wherein, the received data of the two subarrays at the k moment are respectively:
and
the covariance matrixes of the received data of the two subarrays are respectively as follows:
and->
Wherein, the virtual receiving data of the continuous ULA part in the virtual array formed by the two subarrays on the x axis and the y axis are respectively:
and->
The Toeplitz matrix constructed by virtual received data is respectively as follows:
and->
Wherein the constructed spatial spectrum function is as follows:
and->
Wherein the method comprises the steps ofRepresenting U x,n Go up->Direction vector of direction,/>Representing U y,n And a steering vector in the upward theta direction.
Example 2:
as shown in FIG. 1, the basic model for two-dimensional DOA estimation of a two-dimensional sparse linear array is established by taking an L-shaped Coprime array as an example, and is an L-shaped Coprime array formed by two Coprime arrays with the same array structure, wherein the two array models comprise M 1 =2d and M 2 An array of 3d, where d is half wavelength, then define the angle of incidence of the first signal asWherein θ is l 、/>The included angles between the signal incidence direction and the xoz and yoz planes are respectively called as +.>Andwherein (1)>Is the set of the position distribution of the Coprime array elements on the x-axis, M x The total number of array elements of the Coprime array on the x axis; />M is the set of the position distribution of Coprime array elements on the y axis y Is the total number of array elements of the Coprime array on the y-axis. Assuming that L far-field narrowband signals are totally incident into the array, the received data of two subarrays in the array at the moment k are respectively:
and
Wherein,representation->Go up->A steering vector of the direction;
representation->Is a manifold matrix of arrays;
representation->Upward θ l A steering vector of the direction;
representation->Is a manifold matrix of arrays;
representing an incident signal waveform;
and->Respectively indicate->And->And the noise signal received.
The received data covariance matrices of the two Coprime matrices are respectively:
and
Wherein,an autocorrelation matrix representing an incident signal; />And->And the unit matrixes are respectively corresponding to the dimensions.
Definition of the definitionAnd->The successive ULA parts forming the virtual array are respectively +.>And->It can be seen that->Andthe virtual received data on the data can be expressed as:
and->
Wherein,representation->An element located at element u. (e.g. when the array element position is distributed +.>Receive data is +.>There is->)
Wherein,and->Respectively defined as:
and
Wherein,to be positioned at position m 1 And m 2 The cross-correlation value between the real array element received data is defined as:
constructing a Toeplitz matrix by using virtual received data to obtain:
and
Wherein,
by constructing the following spatial spectrum functions, it can be estimated separatelyAnd->
And->
Wherein the method comprises the steps ofRepresenting U x,n Go up->Direction vector of direction,/>Representing U y,n And a steering vector in the upward theta direction.
The two-dimensional angle estimated values can be obtained by carrying out spectrum peak search on the first two formulasAnd->But is not aware of->And->And therefore it is also necessary to match the two angles.
The matching mode is as follows:
assuming that the estimated angles are respectivelyAnd->And is in charge of>Middle->The arrangement order of the angles of the other dimension of the one-to-one correspondence is +.>Obviously can be regarded as +.>Is to->Reordered, i.e. write:
wherein T is {0,1} L×L For a column transform matrix, i.e. only one element per column per row is 1, the remainder are 0.
Suppose that the flow is composed ofThe calculated array manifold matrix is +.>From the foregoing, it can be seen that: />
Thus, it can be considered a matrixSum matrix->Is matched, i.e. there is: />
Will beCarry to->In (1)/(2)>
The matching problem of the angle is converted into a solving problem of a transformation matrix, and the matrix T can be solved by a minimized optimization model as follows:
in particular, when L.ltoreq.M is satisfied T,x When the former formula is least square problem, matrixHas an explicit expression:
pair matrixThe characteristic decomposition can be carried out to obtain: />
Wherein,respectively represent matrix->A signal subspace and a noise subspace of (2); />Then is by the corresponding U x,s 、U x,n A diagonal matrix of eigenvalues of (a).
Due toAlso Zhang Chengzi space is possible, thus matrix R s It can be estimated that: />
Will beCarry in->The method can obtain:
for the estimated matrixThere is no guarantee that there are only 1 element per column and 1 per row, so for an estimated matrix/>Further processing is required, the processing mode is as follows:
setting the maximum element of each row and each column to 1, and setting the rest elements to 0 to satisfyAnd finally to: />
The final angle estimated value is
As shown in fig. 2 and fig. 3, compared with the existing estimation algorithm, the one-dimensional estimation algorithm results are completely coincident, the two-dimensional estimation algorithm results are consistent with the existing algorithm, and the deviation of the other bit is smaller than that of the existing algorithm, namely, the two-dimensional angle is estimated respectively by the algorithm and the 2-D PDOA estimation algorithm, so that the influence of one-dimensional angle estimation errors on the angle estimation of the other dimension is avoided, and the accuracy of angle estimation is improved while the matching of two-dimensional DOa estimation values is realized.
The process of estimating first and then matching is realized by utilizing the characteristic construction optimization problem of the two-dimensional angle matching of the incoming wave direction to calculate the transformation matrix, and the error of estimating one-dimensional angle is prevented from increasing the estimation error of the other-dimensional angle.
Although the invention has been described herein with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the scope and spirit of the principles of this disclosure. More specifically, various variations and modifications may be made to the component parts and/or arrangements of the subject combination arrangement within the scope of the disclosure, drawings and claims of this application. In addition to variations and modifications in the component parts and/or arrangements, other uses will be apparent to those skilled in the art.
Claims (6)
1. A two-dimensional sparse linear array direction of arrival estimation method based on matrix matching is characterized by comprising the following steps:
s1, establishing a basic model of two-dimensional direction-of-arrival estimation of a two-dimensional sparse linear array, wherein the basic model of two-dimensional direction-of-arrival estimation of the two-dimensional sparse linear array comprises M 1 =2d and M 2 Two subarrays of =3d, where d is half wavelength, two subarrays on x, y axes are referred to asAnd->
S2, defining the incident angle of the first signal asWherein θ is l 、/>The included angles between the signal incidence direction and the xoz and yoz surfaces are respectively, and the receiving data of two subarrays in the array at the k moment are obtained on the assumption that L far-field narrowband signals are totally incident into the array;
s3, obtaining received data covariance matrixes of the two subarrays according to the received data;
s4, forming virtual received data of continuous ULA parts in the virtual array on an x axis and a y axis according to the received data covariance matrixes of the two subarrays;
s5, constructing a Toeplitz matrix by utilizing virtual received data, and then respectively obtaining estimated values of two-dimensional angles by constructing a spatial spectrum functionAnd->
S6, assumption and estimation valueMiddle->The corresponding other dimension angle estimate is +.>Wherein->Is toIs->Wherein T is {0,1 }) L×L Is a column transformation matrix;
s7, suppose that byThe calculated array manifold matrix is +.>From the foregoing, it can be seen that: />Thus, the matrix can be considered +.>Sum matrix->Is matched, i.e. there is: />Will be
Carry to->In (1)/(2)>The matching problem of the angle is converted into a solving problem of a transformation matrix, and the matrix T can be solved by a minimized optimization model as follows:
in particular, when L.ltoreq.M is satisfied T,x When the former formula is least square problem, matrixHas an explicit expression:
alignment arrayIs a received data covariance matrix->The characteristic decomposition can be carried out to obtain: />Wherein (1)>Respectively represent matrix->A signal subspace and a noise subspace of (2);then is by the corresponding U x,s 、U x,n A diagonal matrix of eigenvalues of (a); due to subarrays->Array manifold matrix->Can also be Zhang Chengzi space, thus the autocorrelation matrix R of the incident signal s It can be estimated that:will->Carry in->The method can obtain:
for the estimated matrixThere is no guarantee that only 1 element per column and 1 per row is present, so for the estimated matrix +.>Further processing is required, the processing mode is as follows:
setting the maximum element of each row and each column to 1, and setting the rest elements to 0 to satisfyAnd finally to: />The angle estimation value finally obtained is +.>
2. The matrix matching-based two-dimensional sparse linear array direction of arrival estimation method of claim 1, wherein the method is characterized by: the received data of the two subarrays at the k moment are respectively:
and
3. the matrix matching-based two-dimensional sparse linear array direction of arrival estimation method of claim 2, wherein the method is characterized by: the covariance matrices of the received data of the two subarrays are respectively:and
wherein,an autocorrelation matrix representing an incident signal; />And->And the unit matrixes are respectively corresponding to the dimensions.
4. The matrix matching-based two-dimensional sparse linear array direction-of-arrival estimation method of claim 3, wherein: the two subarrays form virtual received data of successive ULA parts in the virtual array on the x-axis and the y-axis, respectively, as follows:
wherein,to be positioned at position m 1 And m 2 The cross-correlation value between the real array element received data is defined as:
5. the matrix matching-based two-dimensional sparse linear array direction of arrival estimation method of claim 4, wherein the method comprises the following steps of: toeplitz matrices constructed using virtual received data are:
wherein,
6. the matrix matching-based two-dimensional sparse linear array direction of arrival estimation method of claim 5, wherein the method comprises the following steps of:
the constructed spatial spectrum function is as follows:
wherein the method comprises the steps ofRepresenting U x,n Go up->Direction vector of direction,/>Representing U y,n And a steering vector in the upward theta direction.
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