CN111368256A - Single snapshot direction finding method based on uniform circular array - Google Patents
Single snapshot direction finding method based on uniform circular array Download PDFInfo
- Publication number
- CN111368256A CN111368256A CN202010209642.8A CN202010209642A CN111368256A CN 111368256 A CN111368256 A CN 111368256A CN 202010209642 A CN202010209642 A CN 202010209642A CN 111368256 A CN111368256 A CN 111368256A
- Authority
- CN
- China
- Prior art keywords
- array
- matrix
- data
- circular array
- uniform circular
- 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.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 21
- 239000011159 matrix material Substances 0.000 claims abstract description 47
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 6
- 230000009466 transformation Effects 0.000 claims abstract description 6
- 238000005457 optimization Methods 0.000 claims description 3
- 238000007781 pre-processing Methods 0.000 claims description 3
- 230000003595 spectral effect Effects 0.000 claims description 3
- 238000009825 accumulation Methods 0.000 claims 1
- 230000000694 effects Effects 0.000 abstract description 4
- 238000001228 spectrum Methods 0.000 description 3
- 238000003491 array Methods 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 2
- 238000009499 grossing Methods 0.000 description 2
- 238000004891 communication Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
- G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Analysis (AREA)
- Databases & Information Systems (AREA)
- Algebra (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Discrete Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computing Systems (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
Abstract
The invention belongs to the technical field of electronic countermeasure, and particularly relates to a single snapshot direction finding method based on a uniform circular array. For the array receiving data of the uniform circular array, the invention firstly converts the data into the receiving data of the virtual linear array through mode space transformation, thereby leading the array flow pattern to have a Vandemonde form. And then constructing the pseudo covariance matrix to enable the pseudo covariance matrix for subsequent processing to reach a full rank, so that subsequent eigen decomposition can correctly divide the signal subspace and the noise subspace. The method firstly converts the array flow pattern of the uniform circular array into a virtual linear array, then constructs a pseudo covariance matrix, and finally carries out the MUSIC algorithm. The method has the advantages that the single snapshot direction finding can be carried out by using the uniform circular array, the method is simple, and the effect is good.
Description
Technical Field
The invention belongs to the technical field of electronic countermeasure, and relates to a single snapshot direction finding method based on a uniform circular array.
Background
Angle of arrival (DOA) estimation is one of the main problems to be studied in array signal processing, and has wide application in the fields of radio communication, electronic reconnaissance and the like. And single snapshot DOA estimation, namely, only the data of a single snapshot is processed, so that the estimation of the direction of arrival of the input signal is realized. At present, with the continuous improvement of DOA estimation on the real-time requirement, the algorithm operation amount is reduced by reducing the sampling fast beat number, the system real-time is improved, and the DOA estimation method becomes a hot spot of research in the DOA estimation field in recent years.
Among the single-snapshot direction finding algorithms, the most widely applied is the study based on the pseudo covariance matrix and spatial smoothing. The spatial smoothing method divides an array under a certain rule into a plurality of sub-arrays, each sub-array has the same rule, and an array covariance matrix corresponding to each sub-array is obtained. The new covariance matrix is constructed by processing the data to replace the whole matrix which is not divided into sub-matrices. The other method is a pseudo covariance matrix method, which converts a covariance matrix into a pseudo covariance matrix by processing received data under the condition of single snapshot, thereby increasing useful information quantity, enabling the rank of the matrix to reach the signal source number, and further applying the classical direction finding algorithm to the condition of single snapshot with the limit of fast snapshot number. However, both methods can only process matrices having the vandermode form, and when uniform circular arrays are used, single snapshot direction finding cannot be directly performed.
Disclosure of Invention
Aiming at the problems, the invention provides a uniform circular array single snapshot direction finding method based on a pseudo covariance matrix.
The technical scheme adopted by the invention is as follows:
and for the received single snapshot data, converting the array flow pattern of the circular array into a virtual linear array by using mode space conversion, wherein the processed data is equivalent to the array flow pattern of the virtual linear array multiplied by a signal. The array flow pattern now has the vandenonde form. And constructing a pseudo covariance matrix by taking the processed data. And (3) carrying out eigenvalue decomposition on the matrix, and utilizing the fact that the guide vector of the signal subspace is orthogonal to the noise subspace under the ideal condition, the product is very small under the actual condition, carrying out spectrum peak search on the azimuth angle from 0 degree to 360 degrees, wherein the angle corresponding to the maximum value point is the signal incidence direction.
Consider a uniform circular array of discrete fourier transforms that receive data. Suppose N far-field signal sources (θ)1,…,θN) Is incident on a uniform circular array of M array elements, the circular array elements are isotropic, and the received data matrix is x ═ As + n (1)
Where n is the noise matrix.
If each signal only receives a single snapshot, the snapshot data on the array element l is:
The steering vector of the circular array is
Spatial DFT of array snapshot data
In J, Jk(- β) denotes the K-th order Bessel function of the first kind, K ∈ -K, -K +1, … K-1, K, the definition of Bessel function being:
when the number of the array elements is uniformWhen there is JkM-q(- β) ≈ 0, so that the above formula can be simplified to
if u orderedq=v-qThen the above equation can be written in the form of a matrix as follows:
writing the above equation in matrix form:
namely:
the re-exploration space DFT itself has
The above formula is abbreviated as
u=FHx (12)
Namely, it is
Is provided with
FHF=MI (14)
F is an orthogonal matrix.
Obtaining a pre-processing matrix
Carrying out mode space transformation on single snapshot data x obtained by us from a uniform circular array through a matrix:
after transformation, the uniform circular array becomes a virtual linear array, and the number of array elements is M' ═ 2K +1,
taking the data from the K +1 th line to the 2K +1 th line of y, namely the data from the K +1 th array element to the 2K +1 th array element of the virtual linear array, including
Wherein y iskIs the data on the k-th row of the matrix y, i.e. the k-th array element of the virtual line array.nzLines K +1 to 2K +1 of Tn. It can be seen that the component of the kth array element of the steering vector corresponding to signal i is:
bk(θi)=exp(j(k-1)θi) (19)
constructing the pseudo covariance matrix with z as follows:
wherein z iskIs the kth data of matrix z. Is provided with
In the formula nkIs a noise matrix nzThe kth element of (1).
R can be written as
R=BDBH+Nr(22)
Wherein,
it is clear that the rank of D is the number of incident signals N, and since B is a Van der Monde matrix, B and BDBHThe rank of R is N, so that the rank of R is N, and the subsequent eigen decomposition can separate N large eigenvalues and M-N small eigenvalues, namely, the signal subspace and the noise subspace can be decomposed correctly.
In order to further improve the algorithm performance, the conjugate information of the data output by the array is fully utilized, and the following matrix is constructed on the basis of the formula (22):
R'=[R,QR*Q](25)
in the formula, Q is an inverse-diagonal matrix, i.e., elements on the inverse-diagonal are all 1, and other elements are 0.
Originally, the pseudo covariance matrix of (K +1) × (K +1) dimension is expanded to (K +1) × 2(K +1) dimension, the effect of increasing effective information is achieved, and the direction finding precision of the algorithm is further improved.
The new matrix in equation (25) that has been combined with the conjugate enhancement method is then second order accumulated:
for the above obtained pseudo covariance matrix RISSPerforming characteristic decomposition:
obtaining a signal subspace USSum noise subspace UN. Steering vector b of signal subspace after mode space conversion under ideal conditionsH(theta) and noise subspace UNOrthogonal:
bH(θ)UN=0 (28)
and in practice bH(theta) and UNAnd are not perfectly orthogonal. The azimuth angle θ can be obtained from a 1 degree to 360 degree search by a minimum optimization search:
the spectral estimation formula is:
the method has the advantages that the single snapshot direction finding can be carried out by using the uniform circular array, the method is simple, and the effect is good.
Drawings
FIG. 1 is a model of a circular array received signal, the invention is based on pitch angleIn the case of 90 deg..
FIG. 2 is a flow chart of a uniform circular array single snap array direction-finding algorithm based on the ISS-MUISC method.
FIG. 3 is a plot of spectral estimation using the method of the present invention for direction finding.
Fig. 4 shows the positioning error for different signal-to-noise ratios.
Detailed Description
The present invention will be described in detail with reference to examples below:
examples
In this embodiment, matlab is used to verify the single snapshot array direction finding algorithm scheme based on the uniform circular array, and for simplification, the following assumptions are made for the algorithm model:
1. all engineering errors are superposed into equivalent noise;
2. assuming the target is stationary;
step 6, obtaining a matrix z from the K +1 th row to the 2K +1 th row of y;
and 7, constructing a matrix R by the formula (20), and obtaining the matrix R by the formula (25) and the formula (26)ISS;
Step 8, for RISSPerforming characteristic decomposition to obtain a signal subspace USSum noise subspace UN;
And 9, according to the formula (30), performing minimum optimization search on the azimuth angle theta from 1 degree to 360 degrees to obtain an accurate positioning result of the target.
The ISS-MUSIC method-based uniform circular array single snapshot direction finding algorithm has the following effects:
as shown in fig. 3, a spectrum peak diagram of the target appearing in the observation region can be seen, and the position of the spectrum peak is the positioning result of the target. Fig. 4 shows the trend of the positioning error with the signal-to-noise ratio.
Claims (1)
1. A single snapshot direction finding method based on a uniform circular array is characterized by comprising the following steps:
s1, receiving data by using a uniform circular array, N far-field signal sources (theta)1,…,θN) The signal is incident on a uniform circular array of M array elements, the circular array elements are isotropic, and single snapshot data received by the array are
x=As+n
Where A is the array pattern of the uniform circular array, and s is the signal vector formed by the N signals, i.e. s ═ s1,s2,…sN]TAnd n is a noise data,
if each signal only receives a single snapshot, the snapshot data on the array element l is:
wherein,λ is the wavelength, r is the radius of the circular array, nlIs the i-th element, θ, of the noise data niIs the azimuth angle, s, of the i-th signal incidenceiIs the ith signal;
the steering vector of the circular array is
S2, making mode space transformation to the received data matrix, and constructing the mode space transformation matrix
Wherein
In J, Jk(- β) represents K order Bessel function of the first kind, K ∈ -K, -K +1, … K-1, K being the maximum number of phase modes that the uniform circular array can excite
r is the radius of the circular array;
s3, preprocessing single snapshot data x obtained from the uniform circular array:
whereinAfter the mode space is transformed, the array flow pattern of the virtual linear array is as follows:
after transformation, the uniform circular array becomes a virtual linear array, and the number of array elements is M' ═ 2K +1,
s4, taking the data from the K +1 th line to the 2K +1 th line of y, namely the data from the K +1 th array element to the 2K +1 th array element of the virtual linear array, including
Wherein y iskIs momentThe data on the k-th line of the array y, i.e. the k-th element of the virtual line array,b is an array flow pattern formed by the K array element to the 2K +1 array element of the virtual linear array, nzTaking lines K +1 to 2K +1 for Tn, the component of the kth array element of the steering vector corresponding to signal i is:
bk(θi)=exp(j(k-1)θi)
s5, constructing a pseudo covariance matrix by using z as follows:
wherein z iskIs the kth data of matrix z:
in the formula nkIs a noise matrix nzThe kth element of (1);
write R as
R=BDBH+Nr
Wherein,
the rank of D is the number of incident signals N, and B is a Van der Monde matrix, so B and BDBHIs N, so the rank of R is N;
s6, constructing the following matrix on the basis of the matrix R:
R'=[R,QR*Q]
in the formula, Q is an anti-diagonal matrix, namely elements on anti-diagonal lines are all 1, and other elements are 0;
and then carrying out second-order accumulation on the matrix R':
obtaining a pseudo covariance matrix RISS;
S7, obtaining the pseudo covariance matrix RISSPerforming characteristic decomposition:
obtaining a signal subspace USSum noise subspace UN;
S8, obtaining an azimuth angle theta from 1-360-degree search through minimum optimization search:
wherein B (theta) is a guide vector corresponding to the array flow pattern B, namely:
the spectral estimation formula is:
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010209642.8A CN111368256B (en) | 2020-03-23 | 2020-03-23 | Single snapshot direction finding method based on uniform circular array |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010209642.8A CN111368256B (en) | 2020-03-23 | 2020-03-23 | Single snapshot direction finding method based on uniform circular array |
Publications (2)
Publication Number | Publication Date |
---|---|
CN111368256A true CN111368256A (en) | 2020-07-03 |
CN111368256B CN111368256B (en) | 2023-03-03 |
Family
ID=71210653
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202010209642.8A Active CN111368256B (en) | 2020-03-23 | 2020-03-23 | Single snapshot direction finding method based on uniform circular array |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN111368256B (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN112858994A (en) * | 2021-01-11 | 2021-05-28 | 电子科技大学 | Amplitude comparison direction finding method based on uniform circular array |
CN113126021A (en) * | 2021-04-19 | 2021-07-16 | 电子科技大学 | Single-snapshot two-dimensional DOA estimation method based on three parallel linear arrays |
Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106019252A (en) * | 2016-05-18 | 2016-10-12 | 西安电子科技大学 | Sum-difference tracking angle measurement method based on Nested array |
US9559417B1 (en) * | 2010-10-29 | 2017-01-31 | The Boeing Company | Signal processing |
CN109188346A (en) * | 2018-08-31 | 2019-01-11 | 西安电子科技大学 | Macroscale homogenous cylindrical array list snap DOA estimation method |
CN110208741A (en) * | 2019-06-28 | 2019-09-06 | 电子科技大学 | A kind of direct localization method of over the horizon single goal for surveying phase based on more circle battle arrays |
CN111366891A (en) * | 2020-03-23 | 2020-07-03 | 电子科技大学 | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method |
-
2020
- 2020-03-23 CN CN202010209642.8A patent/CN111368256B/en active Active
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US9559417B1 (en) * | 2010-10-29 | 2017-01-31 | The Boeing Company | Signal processing |
CN106019252A (en) * | 2016-05-18 | 2016-10-12 | 西安电子科技大学 | Sum-difference tracking angle measurement method based on Nested array |
CN109188346A (en) * | 2018-08-31 | 2019-01-11 | 西安电子科技大学 | Macroscale homogenous cylindrical array list snap DOA estimation method |
CN110208741A (en) * | 2019-06-28 | 2019-09-06 | 电子科技大学 | A kind of direct localization method of over the horizon single goal for surveying phase based on more circle battle arrays |
CN111366891A (en) * | 2020-03-23 | 2020-07-03 | 电子科技大学 | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method |
Non-Patent Citations (5)
Title |
---|
QIANG LI 等: "Accurate DOA Estimation for Large-Scale Uniform Circular Arrary Using a Single Snapshot" * |
WENTAO SHI 等: "The Beamspace Conjugate MUSIC for Non-circular Source" * |
张薇;韩勇;闫锋刚;刘帅;王军;金铭;: "基于均匀圆阵Toeplitz矩阵集重构解相干算法" * |
汪鹏 等: "基于均匀圆阵伪协方差矩阵的单快拍测向方法" * |
熊钊: "基于均匀圆阵的测向与主动反侦察技术研究" * |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN112858994A (en) * | 2021-01-11 | 2021-05-28 | 电子科技大学 | Amplitude comparison direction finding method based on uniform circular array |
CN113126021A (en) * | 2021-04-19 | 2021-07-16 | 电子科技大学 | Single-snapshot two-dimensional DOA estimation method based on three parallel linear arrays |
CN113126021B (en) * | 2021-04-19 | 2022-03-29 | 电子科技大学 | Single-snapshot two-dimensional DOA estimation method based on three parallel linear arrays |
Also Published As
Publication number | Publication date |
---|---|
CN111368256B (en) | 2023-03-03 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
WO2021139208A1 (en) | One-dimensional doa estimation method based on combined signals at specific frequencies | |
CN109061554B (en) | Target arrival angle estimation method based on dynamic update of spatial discrete grid | |
CN109490820B (en) | Two-dimensional DOA estimation method based on parallel nested array | |
CN110109050B (en) | Unknown mutual coupling DOA estimation method based on sparse Bayes under nested array | |
CN108896954B (en) | Estimation method of angle of arrival based on joint real-value subspace in co-prime matrix | |
CN110197112B (en) | Beam domain Root-MUSIC method based on covariance correction | |
CN106950529B (en) | Acoustic vector near field sources ESPRIT and MUSIC method for parameter estimation | |
CN106405487B (en) | A kind of general Estimation of Spatial Spectrum method based on extension ESPRIT technologies | |
CN110531312B (en) | DOA estimation method and system based on sparse symmetric array | |
CN109946643B (en) | Non-circular signal direction-of-arrival angle estimation method based on MUSIC solution | |
CN113835063B (en) | Unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method | |
CN113567913B (en) | Two-dimensional plane DOA estimation method based on iterative re-weighting dimension-reducible | |
CN113671439B (en) | Unmanned aerial vehicle cluster direction finding system and method based on non-uniform intelligent super-surface array | |
CN112462363B (en) | Non-uniform sparse polarization array coherent target parameter estimation method | |
CN111368256B (en) | Single snapshot direction finding method based on uniform circular array | |
CN109696651B (en) | M estimation-based direction-of-arrival estimation method under low snapshot number | |
CN112763972B (en) | Sparse representation-based double parallel line array two-dimensional DOA estimation method and computing equipment | |
CN111366891B (en) | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method | |
CN114460531A (en) | Uniform linear array MUSIC spatial spectrum estimation method | |
CN116699511A (en) | Multi-frequency point signal direction of arrival estimation method, system, equipment and medium | |
CN115469286B (en) | Super-resolution angle measurement method based on millimeter wave automobile radar minimum redundancy MIMO array | |
CN109507634A (en) | A kind of blind far-field signal Wave arrival direction estimating method based on sensing operator under any sensor array | |
CN114265004A (en) | Subspace cancellation-based target angle estimation method under interference | |
CN115421098A (en) | Two-dimensional DOA estimation method for nested area array dimension reduction root finding MUSIC | |
CN112799008B (en) | Quick two-dimensional direction-of-arrival estimation method irrelevant to sound velocity |
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 |