CN111366891B - Pseudo covariance matrix-based uniform circular array single snapshot direction finding method - Google Patents
Pseudo covariance matrix-based uniform circular array single snapshot direction finding method Download PDFInfo
- Publication number
- CN111366891B CN111366891B CN202010208559.9A CN202010208559A CN111366891B CN 111366891 B CN111366891 B CN 111366891B CN 202010208559 A CN202010208559 A CN 202010208559A CN 111366891 B CN111366891 B CN 111366891B
- Authority
- CN
- China
- Prior art keywords
- array
- data
- circular array
- signal
- covariance matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000011159 matrix material Substances 0.000 title claims abstract description 46
- 238000000034 method Methods 0.000 title claims abstract description 14
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 7
- 230000009466 transformation Effects 0.000 claims abstract description 6
- 239000000126 substance Substances 0.000 claims description 5
- 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
- 230000000694 effects Effects 0.000 abstract description 2
- 238000001228 spectrum Methods 0.000 description 3
- 238000003491 array Methods 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000009499 grossing Methods 0.000 description 2
- 238000004891 communication Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- 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
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention belongs to the technical field of electronic countermeasure, and particularly relates to a uniform circular array single snapshot direction finding method based on a pseudo covariance matrix. 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. Finally, the MUSIC algorithm is used for the pseudo-covariance matrix, namely, the covariance matrix is subjected to characteristic decomposition, and then the orthogonality of the guide vector and the noise subspace is searched, so that the incident azimuth angle of the signal is obtained. 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 uniform circular array single snapshot direction finding method based on a pseudo covariance matrix.
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 the uniform circular array of M array elementsThe 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:
wherein the content of the first and second substances,θiis the azimuth angle, s, of the i-th signal incidenceiIs the ith signal.
The steering vector of the circular array is
Spatial DFT of array snapshot data
Wherein the Bessel function:
when the number of the array elements is uniformWhen there is JkM-q(. beta.) approximately equals 0, so 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
p,k=1,2,…K+1(p+k-1≤K+1)
In the formula nkIs a noise matrix nzThe kth element of (1).
R can be written as
R=BDBH+Nr (22)
Wherein the content of the first and second substances,
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.
Performing characteristic decomposition on the pseudo covariance matrix R obtained above:
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 (26)
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:
drawings
FIG. 1 is a schematic diagram of a circular array received signal model, discussed herein as pitch angleIn the case of 90 deg..
FIG. 2 is a flow chart of a pseudo covariance matrix-based uniform circular array single snapshot array direction finding algorithm.
FIG. 3 is a plot of the spectral estimation of direction finding using the present algorithm.
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 5, preprocessing the received signal x, wherein y is Tx;
step 6, obtaining a matrix z from the K +1 th row to the 2K +1 th row of y;
step 7, constructing a matrix R by the formula (20);
step 8, performing characteristic decomposition on the R to obtain a signal subspace USSum noise subspace UN;
And 9, according to the formula (28), 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 pseudo covariance matrix-based uniform circular array single snapshot direction finding algorithm has the effects that:
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 pseudo covariance matrix-based uniform circular array single snapshot direction finding method 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 the content of the first and second substances,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(. beta.) represents the K-th order Bessel function of the first kind, K belongs to K, -K +1, … K-1, K is the maximum phase mode number 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 the data on the k-th row of the matrix y, i.e. the k-th array 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; is provided with
In the formula nkIs a noise matrix nzThe kth element of (1);
r can be written as
R=BDBH+Nr
Wherein the content of the first and second substances,
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, performing characteristic decomposition on the pseudo covariance matrix R obtained in the step:
obtaining a signal subspace USSum noise subspace UN;
S7, 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 |
---|---|---|---|
CN202010208559.9A CN111366891B (en) | 2020-03-23 | 2020-03-23 | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010208559.9A CN111366891B (en) | 2020-03-23 | 2020-03-23 | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method |
Publications (2)
Publication Number | Publication Date |
---|---|
CN111366891A CN111366891A (en) | 2020-07-03 |
CN111366891B true CN111366891B (en) | 2022-03-29 |
Family
ID=71210633
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202010208559.9A Active CN111366891B (en) | 2020-03-23 | 2020-03-23 | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN111366891B (en) |
Families Citing this family (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111368256B (en) * | 2020-03-23 | 2023-03-03 | 电子科技大学 | Single snapshot direction finding method based on uniform circular array |
Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP2105758A2 (en) * | 2008-03-28 | 2009-09-30 | Fujitsu Ltd. | Direction-of-arrival estimation apparatus |
CN104698433A (en) * | 2015-03-16 | 2015-06-10 | 电子科技大学 | Single-snapshot data-based coherent signal DOA (direction of arrival) estimating method |
CN105425205A (en) * | 2015-11-03 | 2016-03-23 | 天津津航计算技术研究所 | High-resolution circular and non-circular signal mixed incidence DOA estimation method |
CN108614235A (en) * | 2018-05-25 | 2018-10-02 | 哈尔滨工程大学 | A kind of single snap direction-finding method of more dove group information exchanges |
CN109581275A (en) * | 2018-12-13 | 2019-04-05 | 华南理工大学 | The underwater DOA estimation method of two dimension and device based on non-circular signal and three-dimensional orthogonal battle array |
-
2020
- 2020-03-23 CN CN202010208559.9A patent/CN111366891B/en active Active
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP2105758A2 (en) * | 2008-03-28 | 2009-09-30 | Fujitsu Ltd. | Direction-of-arrival estimation apparatus |
CN104698433A (en) * | 2015-03-16 | 2015-06-10 | 电子科技大学 | Single-snapshot data-based coherent signal DOA (direction of arrival) estimating method |
CN105425205A (en) * | 2015-11-03 | 2016-03-23 | 天津津航计算技术研究所 | High-resolution circular and non-circular signal mixed incidence DOA estimation method |
CN108614235A (en) * | 2018-05-25 | 2018-10-02 | 哈尔滨工程大学 | A kind of single snap direction-finding method of more dove group information exchanges |
CN109581275A (en) * | 2018-12-13 | 2019-04-05 | 华南理工大学 | The underwater DOA estimation method of two dimension and device based on non-circular signal and three-dimensional orthogonal battle array |
Non-Patent Citations (4)
Title |
---|
"2-D angle of arrival estimation with two parallel uniform linear arrays for coherent signals";T.Q.Xia等;《2007 IEEE radar conference》;20071231;第244-247页 * |
"一种基于双平行线阵相干源二维波达方向估计的新方法";曾操等;《雷达科学与技术》;20030831;第1卷(第2期);第104-108页 * |
"二维波达方向估计方法研究";夏铁骑;《中国优秀博硕士学位论文全文数据库(博士)信息科技辑》;20090415;第I136-34页 * |
"卫星干扰源定位及干扰抑制技术研究";王爱莹;《中国优秀博硕士学位论文全文数据库(硕士)信息科技辑》;20160315;第I136-1730页 * |
Also Published As
Publication number | Publication date |
---|---|
CN111366891A (en) | 2020-07-03 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN110208735B (en) | Sparse Bayesian learning-based coherent signal DOA estimation method | |
CN109490820B (en) | Two-dimensional DOA estimation method based on parallel nested array | |
CN106980106B (en) | Sparse DOA estimation method under array element mutual coupling | |
CN109061554B (en) | Target arrival angle estimation method based on dynamic update of spatial discrete grid | |
CN110197112B (en) | Beam domain Root-MUSIC method based on covariance correction | |
CN107870315B (en) | Method for estimating direction of arrival of any array by using iterative phase compensation technology | |
CN111046591B (en) | Joint estimation method for sensor amplitude-phase error and target arrival angle | |
CN109946643B (en) | Non-circular signal direction-of-arrival angle estimation method based on MUSIC solution | |
CN113567913B (en) | Two-dimensional plane DOA estimation method based on iterative re-weighting dimension-reducible | |
CN111368256B (en) | Single snapshot direction finding method based on uniform circular array | |
CN108398659B (en) | Direction-of-arrival estimation method combining matrix beam and root finding MUSIC | |
CN111965591A (en) | Direction-finding estimation method based on fourth-order cumulant vectorization DFT | |
CN110531312B (en) | DOA estimation method and system based on sparse symmetric array | |
CN109696651B (en) | M estimation-based direction-of-arrival estimation method under low snapshot number | |
CN113835063B (en) | Unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method | |
CN111366891B (en) | Pseudo covariance matrix-based uniform circular array single snapshot direction finding method | |
CN112763972B (en) | Sparse representation-based double parallel line array two-dimensional DOA estimation method and computing equipment | |
CN111948599B (en) | High-resolution positioning method for coherent signals under influence of angle-dependent mutual coupling | |
CN109870670B (en) | Mixed signal parameter estimation method based on array reconstruction | |
CN112363108A (en) | Signal subspace weighted super-resolution direction-of-arrival detection method and system | |
CN109507634B (en) | Blind far-field signal direction-of-arrival estimation method based on propagation operator under any sensor array | |
CN113341371B (en) | DOA estimation method based on L array and two-dimensional ESPRIT algorithm | |
CN114265004A (en) | Subspace cancellation-based target angle estimation method under interference | |
CN113093143B (en) | Dimensionality reduction parameter estimation method based on conformal frequency control array MIMO radar | |
CN115421098A (en) | Two-dimensional DOA estimation method for nested area array dimension reduction root finding MUSIC |
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 | ||
TR01 | Transfer of patent right |
Effective date of registration: 20240315 Address after: No. 351 Tiyu Road, Xiaodian District, Taiyuan City, Shanxi Province 030000 Patentee after: NORTH AUTOMATIC CONTROL TECHNOLOGY INSTITUTE Country or region after: China Address before: 611731, No. 2006, West Avenue, hi tech West District, Sichuan, Chengdu Patentee before: University of Electronic Science and Technology of China Country or region before: China |
|
TR01 | Transfer of patent right |