CN111157968A - High-precision angle measurement method based on sparse MIMO array - Google Patents

High-precision angle measurement method based on sparse MIMO array Download PDF

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CN111157968A
CN111157968A CN202010000765.0A CN202010000765A CN111157968A CN 111157968 A CN111157968 A CN 111157968A CN 202010000765 A CN202010000765 A CN 202010000765A CN 111157968 A CN111157968 A CN 111157968A
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angle estimation
factor
angle
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CN111157968B (en
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李琳娜
何宴辉
房磊
于锦荣
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Shanghai aerospace computer technology research institute
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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
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/42—Simultaneous measurement of distance and other co-ordinates
    • 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
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/295—Means for transforming co-ordinates or for evaluating data, e.g. using computers
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236—Special technical features
    • G01S2013/0245—Radar with phased array antenna
    • G01S2013/0254—Active array antenna
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a high-precision angle measurement method based on a sparse MIMO array, which comprises the following steps: (1) arranging a M-transmission N-reception sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal; (2) performing matched filtering on the received signal to obtain extended array data; (3) constructing a covariance matrix of the extended array data, and estimating a signal subspace; (4) obtaining a group of fuzzy angle estimation values by using the emission translation invariance factor in the signal subspace; (5) obtaining another group of fuzzy angle estimation values by utilizing the receiving translation invariance factor in the signal subspace; (6) constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value; (7) and (3) carrying out two-step deblurring processing on the fuzzy angle estimation values obtained in the steps (5) and (6) by using the low-precision non-fuzzy angle estimation value to obtain the high-precision non-fuzzy angle estimation.

Description

High-precision angle measurement method based on sparse MIMO array
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a high-precision angle measurement method based on a sparse MIMO array.
Background
The angle is a basic parameter for representing a target signal, angle estimation is an active topic in the field of signal processing, and the method is widely applied to the fields of radar, sonar, communication and the like.
The MIMO array can obtain waveform diversity by transmitting orthogonal signals and performing matching processing at a receiving end to improve the precision of parameter estimation. According to the spatial form of the Nyquist sampling theorem, the conventional MIMO array at least needs to ensure that the spacing of the transmitting or receiving array does not exceed a half wavelength, thereby ensuring a non-ambiguous parameter estimation value.
In array processing, the accuracy of parameter estimation can be improved by expanding the array aperture. However, the blurring of parameter estimation is caused by aperture expansion by increasing the array pitch, and the hardware burden and the extra amount of calculation are increased by increasing the number of array elements to realize aperture expansion.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a high-precision angle measurement method based on a sparse MIMO array. The technical scheme of the invention is as follows:
a high-precision angle measurement method based on a sparse MIMO array is used for solving the problem of low angle estimation precision of the existing MIMO array and comprises the following steps:
(1) arranging a M-transmission N-reception sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal; wherein M and N are both positive integers;
(2) performing matched filtering on the received signal to obtain extended array data;
(3) constructing a covariance matrix of the extended array data, and estimating a signal subspace;
(4) obtaining a group of fuzzy angle estimation values by using the emission translation invariance factor in the signal subspace;
(5) obtaining another group of fuzzy angle estimation values by utilizing the receiving translation invariance factor in the signal subspace;
(6) constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value;
(7) and (3) carrying out two-step deblurring processing on the fuzzy angle estimation values obtained in the steps (5) and (6) by using the low-precision non-fuzzy angle estimation value to obtain the high-precision non-fuzzy angle estimation.
Optionally, K ≧ 1 total targets are respectively located at the angle θ1，…，θK(ii) a Wherein the target refers to the detected object, the theta1，…，θKThe angles of the K targets are respectively, and K represents the number of the targets.
Optionally, the distance between the transmitting antenna units in step (1) is dtThe spacing of the receiving antenna units is dr＝Mdt+0.5 λ, λ being the carrier wavelength, and dt＞＞0.5λ。
Alternatively, the match filtered expanded array data vector in step (2) may be represented as:
Figure BDA0002353600510000021
wherein x (t) represents a received signal vector;
Figure BDA0002353600510000022
Figure BDA0002353600510000023
Figure BDA0002353600510000024
n(t)＝[n1(t)，…，nMN(t)]T
the parameters on the left side of the four equation equal signs respectively represent a receiving response vector, a transmitting response vector, a signal vector and a noise vector; in the above-mentioned four formulas, the expression,
Figure BDA0002353600510000025
representing the Kronecker product, the function based on e representing an exponential function based on a natural constant e, bk(t) is KA signal fkFor its doppler frequency, t represents a time variable.
Alternatively, the angle θ1，…，θKAre different from each other, and f1≠f2≠…≠fK。
Optionally, the covariance matrix in step (3) is estimated as follows
Figure BDA0002353600510000026
Wherein T is the number of pulses, TnRepresents the nth pulse, and the superscript H represents the conjugate transpose;
the signal subspace is estimated as follows: calculating the eigenvalue decomposition of R to obtain
R＝UVUH
V is an eigenvalue matrix of the covariance matrix R, and U is an eigenvector matrix corresponding to the eigenvalue; arranging the eigenvalues from large to small, wherein a matrix formed by the eigenvectors corresponding to the first K large eigenvalues is a signal subspace matrix Es(ii) a The first K large eigenvalues refer to the first K eigenvalues; here, "large eigenvalue" indicates that the eigenvalue belongs to a signal subspace eigenvalue.
Optionally, the set of blurred angle estimates obtained from the transmit translation invariance factor in step (4) is calculated as follows:
construction matrix
Figure BDA0002353600510000031
Figure BDA0002353600510000032
wherein ,Jt1＝[IM-1，0(M-1)，1]，Jt2＝[0(M-1)，1，IM-1]；INDenotes an identity matrix, 0M，NA zero matrix representing the dimension mxn; j. the design is a squaret1 and Jt2Representing a selection matrix.
Figure BDA0002353600510000033
The eigenvalue decomposition of (c) can be expressed as:
Figure BDA0002353600510000034
wherein the matrix T is a K-dimensional nonsingular matrix and is labeled
Figure BDA0002353600510000035
Representing a matrix pseudo-inverse;
Figure BDA0002353600510000036
is a diagonal matrix of dimension K, phit，kPhase information of the k-th diagonal element is represented. Due to dt＞＞λ/2，φt，kThe set of blur estimate values of (a) may be expressed as:
Figure BDA0002353600510000037
the numerical values are a group of fuzzy angle estimation values obtained by the emission translation invariance factor in the step (4);
wherein ,ntIs a set of integers,
Figure BDA0002353600510000038
is composed of
Figure BDA0002353600510000039
The main value of the argument of (a),
Figure BDA00023536005100000310
is composed of
Figure BDA00023536005100000311
And calculating the k characteristic value.
Optionally, the fuzzy set of angle estimates obtained from the received translation invariance factor in step (5) is calculated as follows: construction matrix
Figure BDA00023536005100000312
Figure BDA00023536005100000313
wherein ,Jr1＝[IN-1，0(N-1)，1]，Jr2＝[0(N-1)，1，IN-1]To select a matrix;
Figure BDA00023536005100000314
can be expressed as
Figure BDA00023536005100000315
wherein ,
Figure BDA00023536005100000316
due to dr＞＞λ/2，φr，kCan be expressed as
Figure BDA00023536005100000317
The numerical values are a group of fuzzy angle estimation values obtained by receiving the translation invariant factors in the step (5);
wherein ,nrIs a set of integers,
Figure BDA0002353600510000041
is composed of
Figure BDA0002353600510000042
The main value of the argument of (a),
Figure BDA0002353600510000043
is composed of
Figure BDA0002353600510000044
And calculating the k characteristic value.
Optionally, the ambiguity-free angle estimation value obtained by the half-wavelength translation invariance factor in step (6) is calculated as follows: construction matrix Ev1 and Ev2, wherein Ev1Corresponding to the last transmit antenna and the 1 st to N-1 st receive antennas, Ev2Corresponding to the 1 st transmit antenna and the 2 nd to nth receive antennas.
Figure BDA0002353600510000045
Can be expressed as
Figure BDA0002353600510000046
wherein ,
Figure BDA0002353600510000047
due to dvPhi is 0.5 lambda, phi can be obtainedv，k＝sinθk。
Optionally, the high-precision unambiguous angle estimation value in step (7) is calculated by: phit，kMiddle and phiv，kThe closest value is phit，kIs expressed as
Figure BDA0002353600510000048
Φr，kNeutralization of
Figure BDA0002353600510000049
The closest value is phir，kIs expressed as
Figure BDA00023536005100000410
According to
Figure BDA00023536005100000411
Directly calculating to obtain thetakIs estimated value of
Figure BDA00023536005100000412
Compared with the prior art, the invention has the following beneficial effects:
the method effectively solves the problem of low angle estimation precision of the existing MIMO array.
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Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a flow chart of a high-precision angle measurement method based on a sparse MIMO array according to an embodiment of the present invention;
FIG. 2 is a diagram of a MIMO array configuration according to an embodiment of the present invention;
FIG. 3 is a simulation result of an implementation of the extended aperture of the present invention;
fig. 4 is a simulation result comparing the embodiment of the present invention with a conventional MIMO array.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
As shown in fig. 1 and fig. 2, the present embodiment discloses a high-precision angle measurement method based on a sparse MIMO array, which is used for solving the problem of low angle estimation precision of the existing MIMO array, and includes the following steps:
step (1), arranging an M-transmitting N-receiving sparse MIMO array, wherein the transmitting signals of M transmitting antennas are mutually orthogonal. Wherein M and N are both positive integers.
In this embodiment, K is equal to or greater than 1 and the targets are located at the angle θ1，…，θK(ii) a Wherein the target refers to the detected object, the theta1，…，θKRespectively, the angle of each of K targets, K representing a targetAnd (4) the number.
The transmitting antenna unit interval is dtThe spacing of the receiving antenna units is dr＝Mdt+0.5 λ, λ being the carrier wavelength, and dt> 0.5 λ. In FIG. 2, R: T1-TM is transmit and R1-RM is receive. MF denotes matched filtering.
Step (2), performing matched filtering on the received signals to obtain extended array data:
Figure BDA0002353600510000051
wherein x (t) represents a received signal vector;
Figure BDA0002353600510000052
Figure BDA0002353600510000053
Figure BDA0002353600510000054
n(t)＝[n1(t)，…，nMN(t)]T
the parameters on the left side of the four equation equal signs respectively represent a receiving response vector, a transmitting response vector, a signal vector and a noise vector; in the above-mentioned four formulas, the expression,
Figure BDA0002353600510000055
representing the Kronecker product, the function based on e representing an exponential function based on a natural constant e, bk(t) is the Kth signal, fkFor its doppler frequency, t represents a time variable. Wherein K represents 1, …, K is the kth of all K, K is actually a variable, and the value is one of 1, … and K. Wherein the angle theta1，…，θKAre different from each other, and f1≠f2≠…≠fK。
Step (3), constructing a covariance matrix of the extended array data,
Figure BDA0002353600510000056
and decomposing the characteristic value to obtain a signal subspace EsIs estimated.
Wherein T is the number of pulses, TnRepresents the nth pulse, and the superscript H represents the conjugate transpose;
the signal subspace is estimated as follows: and calculating the characteristic value decomposition of R to obtain:
R＝UVUH；
v is an eigenvalue matrix of the covariance matrix R, and U is an eigenvector matrix corresponding to the eigenvalue; arranging the eigenvalues from large to small, wherein a matrix formed by the eigenvectors corresponding to the first K large eigenvalues (signal subspace eigenvalues) is a signal subspace matrix E; the first K large eigenvalues refer to the first K eigenvalues; here, "large eigenvalue" indicates that the eigenvalue belongs to a signal subspace eigenvalue.
Step (4), obtaining a group of fuzzy angle estimation values by using the emission translation invariance factor in the signal subspace; the method specifically comprises the following steps:
construction matrix
Figure BDA0002353600510000061
Figure BDA0002353600510000062
wherein ,Jt1＝[IM-1，0(M-1)，1]，Jt2＝[0(M-1)，1，IM-1]；INDenotes an identity matrix, 0M，NA zero matrix representing the dimension mxn; j. the design is a squaret1 and Jt2Representing a selection matrix.
Figure BDA0002353600510000063
The eigenvalue decomposition of (c) can be expressed as:
Figure BDA0002353600510000064
wherein the matrix T is a K-dimensional nonsingular matrix and is labeled
Figure BDA00023536005100000613
Representing a matrix pseudo-inverse;
Figure BDA0002353600510000065
is a diagonal matrix of dimension K, phit，kPhase information of the k-th diagonal element is represented. Due to dt＞＞λ/2，φt，kThe set of blur estimate values of (a) may be expressed as:
Figure BDA0002353600510000066
the numerical values are a group of fuzzy angle estimation values obtained by the emission translation invariance factor in the step (4); wherein n istIs a set of integers,
Figure BDA0002353600510000067
is composed of
Figure BDA0002353600510000068
The main value of the argument of (a),
Figure BDA0002353600510000069
is composed of
Figure BDA00023536005100000610
And calculating the k characteristic value. Through phit，kAnd obtaining a set of high-precision fuzzy angle estimated values.
Step 5, obtaining another group of fuzzy angle estimation values by using the receiving translation invariance factor in the signal subspace; the method specifically comprises the following steps: construction matrix
Figure BDA00023536005100000611
Figure BDA00023536005100000612
wherein ,Jr1＝[IN-1，0(N-1)，1]，Jr2＝[0(N-1)，1，IN-1]To select a matrix;
Figure BDA0002353600510000071
can be expressed as
Figure BDA0002353600510000072
wherein ,
Figure BDA0002353600510000073
due to dr＞＞λ/2，φr，kCan be expressed as
Figure BDA0002353600510000074
The numerical values are a group of fuzzy angle estimation values obtained by receiving the translation invariant factors in the step (5);
wherein ,nrIs a set of integers,
Figure BDA0002353600510000075
is composed of
Figure BDA0002353600510000076
The main value of the argument of (a),
Figure BDA0002353600510000077
is composed of
Figure BDA0002353600510000078
And calculating the k characteristic value. Through phir，kAnd obtaining another set of high-precision fuzzy angle estimation values.
Step (6), constructing a half-wavelength translation invariance factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value; the method specifically comprises the following steps:
construction matrix Ev1 and Ev2, wherein Ev1Corresponding to the last transmit antenna and the 1 st to N-1 st receive antennas, Ev2Corresponding to the 1 st transmit antenna and the 2 nd to nth receive antennas.
Figure BDA0002353600510000079
Can be expressed as
Figure BDA00023536005100000710
wherein ,
Figure BDA00023536005100000711
due to dvPhi is 0.5 lambda, phi can be obtainedv，k＝sinθk. Through phiv，kAnd refining to obtain a low-precision unambiguous angle estimation value.
And (7) performing two-step deblurring processing on the fuzzy angle estimation values obtained in the steps (5) and (6) by using the low-precision unambiguous angle estimation value to obtain high-precision unambiguous angle estimation. The method specifically comprises the following steps:
calculating phit，kMiddle and phiv，kThe closest value is phit，kIs expressed as
Figure BDA00023536005100000712
Φr，kNeutralization of
Figure BDA00023536005100000713
The closest value is phir，kIs expressed as
Figure BDA00023536005100000714
According to
Figure BDA00023536005100000715
Directly calculating to obtain thetakIs estimated value of
Figure BDA00023536005100000716
To further evaluate the performance of the present invention, we performed the following computer simulation experiments. Simulation conditions are as follows: the MIMO array composed of 2 transmitting and 6 receiving antennas is adopted, and the distance between the antenna units satisfies dr＝2dt+0.5 λ, the two incoherent signals being each at an angle θ1＝10°，θ2The sampling number is taken as T200 at 20 °.
Figure 3 shows the root mean square error (vertical axis) of the comparison angle 1 estimate as a function of the transmit antenna element spacing (horizontal axis). The angle estimation values corresponding to the four curves from top to bottom in the figure are respectively estimated by a virtual invariant factor, a transmitting invariant factor, a receiving invariant factor and a receiving invariant factor through one-time deblurring processing and two-time deblurring processing. It can be seen from the figure that since the cell pitch corresponding to the virtual invariant factor is always half wavelength, the corresponding angle estimation error is almost invariant. Since the receiving unit spacing is larger than the transmitting unit spacing, the angle estimation error resulting from the receive invariant factor is smaller than the angle estimation error resulting from the transmit invariant factor when the ambiguity is successfully resolved, and the estimation error decreases linearly as the unit spacing increases. Further observation, successful ambiguity resolution can be achieved when the transmission unit spacing is less than 100 λ. When the distance between the transmitting units is larger than 100 lambda, the solution ambiguity is invalid, and the estimation error is equivalent to the angle estimation error obtained by the virtual invariant factor. Thus, the method of the present invention can achieve dtAperture expansion of 100 λ.
Fig. 4 shows a plot of the estimated error (vertical axis) versus the signal-to-noise ratio (horizontal axis) comparing the method of the present invention to a conventional MIMO array whose virtual array is a uniform linear array. The upper one of the two curves in the figure corresponds to a conventional MIMO array and the lower one corresponds to a MIMO array of the present invention. It can be found that the angle estimation error of the method of the present invention is smaller than that of the conventional MIMO array. That is, the performance of the method of the present invention on angle estimation is greatly improved.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (10)

1. A high-precision angle measurement method based on a sparse MIMO array is used for solving the problem of low angle estimation precision of the existing MIMO array, and is characterized by comprising the following steps:
(1) arranging a M-transmission N-reception sparse MIMO array, wherein the transmission signals of M transmission antennas are mutually orthogonal; wherein M and N are both positive integers;
(2) performing matched filtering on the received signal to obtain extended array data;
(3) constructing a covariance matrix of the extended array data, and estimating a signal subspace;
(4) obtaining a group of fuzzy angle estimation values by using the emission translation invariance factor in the signal subspace;
(5) obtaining another group of fuzzy angle estimation values by utilizing the receiving translation invariance factor in the signal subspace;
(6) constructing a half-wavelength translation invariant factor in a signal subspace to obtain a low-precision non-fuzzy angle estimation value;
(7) and (3) carrying out two-step deblurring processing on the fuzzy angle estimation values obtained in the steps (5) and (6) by using the low-precision non-fuzzy angle estimation value to obtain the high-precision non-fuzzy angle estimation.
2. The method of claim 1, wherein K ≧ 1 targets are respectively located at the angle θ1，…，θK(ii) a Wherein the target refers to the detected object, the theta1，…，θKRespectively the angle of each of K targets, K represents the targetThe number of targets.
3. The method of claim 1, wherein in step (1) the transmit antenna elements are spaced apart by a distance dtThe spacing of the receiving antenna units is dr＝Mdt+0.5 λ, λ being the carrier wavelength, and dt＞＞0.5λ。
4. The method of claim 2, wherein the matched filtered expanded array data vector of step (2) is represented as:
Figure FDA0002353600500000011
wherein x (t) represents a received signal vector;
Figure FDA0002353600500000012
Figure FDA0002353600500000013
Figure FDA0002353600500000014
n(t)＝[n1(t)，…，nMN(t)]T
the parameters on the left side of the four equation equal signs respectively represent a receiving response vector, a transmitting response vector, a signal vector and a noise vector; in the above-mentioned four formulas, the expression,
Figure FDA0002353600500000021
representing the Kronecker product, the function based on e representing an exponential function based on a natural constant e, bk(t) is the Kth signal, fkFor its doppler frequency, t represents a time variable.
5. The method of claim 4Characterised by the angle theta1，…，θKAre different from each other, and f1≠f2≠…≠fK。
6. The method of claim 4, wherein the covariance matrix in step (3) is estimated as follows:
Figure FDA0002353600500000022
wherein T is the number of pulses, TnRepresents the nth pulse, and the superscript H represents the conjugate transpose;
the signal subspace is estimated as follows: calculating the eigenvalue decomposition of R to obtain
R＝UVUH
V is an eigenvalue matrix of the covariance matrix R, and U is an eigenvector matrix corresponding to the eigenvalue; arranging the eigenvalues from large to small, wherein a matrix formed by the eigenvectors corresponding to the first K large eigenvalues is a signal subspace matrix Es(ii) a The first K large eigenvalues refer to the first K eigenvalues; here, "large eigenvalue" indicates that the eigenvalue belongs to a signal subspace eigenvalue.
7. The method of claim 6, wherein the set of ambiguous angle estimates derived from the transmit translation invariance factor in step (4) is computed as follows: constructing a matrix:
Figure FDA0002353600500000023
Figure FDA0002353600500000024
wherein ,Jt1＝[IM-1，0(M-1)，1]，Jt2＝[0(M-1)，1，IM-1]；INDenotes an identity matrix, 0M，NA zero matrix representing the dimension mxn; j. the design is a squaret1 and Jt2Representing a selection matrix.
Figure FDA0002353600500000025
The eigenvalue decomposition of (c) can be expressed as:
Figure FDA0002353600500000026
wherein the matrix T is a K-dimensional nonsingular matrix and is labeled
Figure FDA0002353600500000027
Representing a matrix pseudo-inverse;
Figure FDA0002353600500000028
is a diagonal matrix of dimension K, phit，kPhase information of the k-th diagonal element is represented. Due to dt＞＞λ/2，φt，kThe set of blur estimate values of (a) may be expressed as:
Figure FDA0002353600500000031
the numerical values are a group of fuzzy angle estimation values obtained by the emission translation invariance factor in the step (4);
wherein ,ntIs a set of integers,
Figure FDA0002353600500000032
is composed of
Figure FDA0002353600500000033
The main value of the argument of (a),
Figure FDA0002353600500000034
is composed of
Figure FDA0002353600500000035
The k-th one obtained by calculationAnd (4) characteristic value.
8. The method of claim 7, wherein the set of blurred angle estimates obtained in step (5) from the received translation invariance factor is calculated as follows: construction matrix
Figure FDA0002353600500000036
Figure FDA0002353600500000037
wherein ,Jr1＝[IN-1，0(N-1)，1]，Jr2＝[0(N-1)，1，IN-1]To select a matrix;
Figure FDA0002353600500000038
can be expressed as
Figure FDA0002353600500000039
wherein ,
Figure FDA00023536005000000310
due to dr＞＞λ/2，φr，kCan be expressed as
Figure FDA00023536005000000311
The numerical values are a group of fuzzy angle estimation values obtained by receiving the translation invariant factors in the step (5);
wherein ,nrIs a set of integers,
Figure FDA00023536005000000312
is composed of
Figure FDA00023536005000000313
The main value of the argument of (a),
Figure FDA00023536005000000314
is composed of
Figure FDA00023536005000000315
And calculating the k characteristic value.
9. The method of claim 8, wherein the unambiguous angle estimate derived from the half-wavelength shift invariant factor in step (6) is calculated as follows: construction matrix Ev1 and Ev2, wherein Ev1Corresponding to the last transmit antenna and the 1 st to N-1 st receive antennas, Ev2Corresponding to the 1 st transmit antenna and the 2 nd to nth receive antennas.
Figure FDA00023536005000000316
Can be expressed as
Figure FDA00023536005000000317
wherein ,
Figure FDA00023536005000000318
due to dvPhi is 0.5 lambda, phi can be obtainedv，k＝sinθk。
10. The method according to claim 9, wherein the high-precision unambiguous angle estimate in step (7) is calculated by: phit，kMiddle and phiv，kThe closest value is phit，kIs expressed as
Figure FDA0002353600500000041
Φr，kNeutralization of
Figure FDA0002353600500000042
The closest value is phir，kIs expressed as
Figure FDA0002353600500000043
According to
Figure FDA0002353600500000044
Directly calculating to obtain thetakIs estimated value of
Figure FDA0002353600500000045
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