CN113484821A - Novel virtual array structure and DOA estimation method thereof - Google Patents

Novel virtual array structure and DOA estimation method thereof Download PDF

Info

Publication number
CN113484821A
CN113484821A CN202110759477.8A CN202110759477A CN113484821A CN 113484821 A CN113484821 A CN 113484821A CN 202110759477 A CN202110759477 A CN 202110759477A CN 113484821 A CN113484821 A CN 113484821A
Authority
CN
China
Prior art keywords
array
sub
virtual
arrays
doa estimation
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
Application number
CN202110759477.8A
Other languages
Chinese (zh)
Other versions
CN113484821B (en
Inventor
张治�
褚建红
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing University of Posts and Telecommunications
Original Assignee
Beijing University of Posts and Telecommunications
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Beijing University of Posts and Telecommunications filed Critical Beijing University of Posts and Telecommunications
Priority to CN202110759477.8A priority Critical patent/CN113484821B/en
Publication of CN113484821A publication Critical patent/CN113484821A/en
Application granted granted Critical
Publication of CN113484821B publication Critical patent/CN113484821B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

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
    • 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

Abstract

The invention discloses a novel virtual array structure and a DOA estimation method thereof.A linear array of the interline makes uniform linear motion along a direction which forms a certain angle with a straight line of the interline, two sub-arrays of the interline are controlled at different fixed time delay positions to carry out signal sampling, then the two sub-arrays are respectively subjected to comprehensive signal processing to obtain two sub-arrays of the virtual parallelogram, the two sub-arrays are combined together to form a generalized virtual parallelogram array of the interline, and the array aperture of the linear array of the interline is expanded to two dimensions to realize two-dimensional DOA estimation. The method fully utilizes the received signals at each time delay position to create virtual array elements, realizes the two-dimensional DOA estimation of the one-dimensional mutual element linear array in the motion scene, and improves the degree of freedom, the estimation precision and the practicability of the method. Meanwhile, the invention provides a decoupling complexity-reducing MUSIC (DRC MUSIC) algorithm which is adaptive to a virtual parallelogram array, and the computational complexity of the algorithm is greatly reduced while the precision is ensured.

Description

Novel virtual array structure and DOA estimation method thereof
Technical Field
The invention relates to the technical field of signal processing, in particular to a novel virtual array structure and a DOA estimation method thereof.
Background
In the prior art, a linear array of reciprocals is considered, which moves linearly at a constant speed along the linear direction in which the linear array itself is located, performs signal sampling once after half a wavelength of movement (or after a fixed time delay), and performs phase correction processing on a received signal, wherein the movement time of the array can be controlled by controlling the size of a Time Continuous Period (TCP), and finally, the degree of freedom (DOF) can be further improved by comprehensively processing all received signals obtained within the movement time.
In the MUSIC (SS-MUSIC) algorithm based on the spatial smoothing technology of the cross element linear array, after a covariance matrix of a received signal is vectorized, a plurality of virtual array elements can be created by utilizing the thought of an array element coordinate difference set, but only the part of continuous coordinates in the difference set can be utilized, so that the utilization rate of the virtual array elements is not high, and the breakpoint part in the difference set is further filled through the time continuity of the signal by utilizing the thought of array motion, so that the difference set has no breakpoints, and the virtual array elements are fully utilized to improve the degree of freedom.
For a mutually prime area array, the received signal model X of a uniform sub-area array is obtained without coupling between antennas and without received signals being coherenti＝AiS + N, i ═ 1, 2; then, the covariance matrix of the received signal model is solved
Figure RE-GDA0003180035980000011
To RiPerforming feature decomposition to obtain noise subspace Eni(ii) a Constructing a spectral function
Figure RE-GDA0003180035980000012
Further constructing a new function by utilizing the characteristic that the noise subspace of the denominator position is orthogonal to the array flow pattern, and then obtaining a relational expression between two parameters to be estimated by solving the partial derivative and making the partial derivative equal to 0, thereby obtaining the spectral function fiAnd (u, v) replacing the function with a function only containing one parameter, so that the two-dimensional to one-dimensional RD MUSIC algorithm can be realized. Meanwhile, in the mutual prime area array, because a certain linear relation exists between the real angle and the fuzzy angle, the algorithm only needs to search in a small range to obtain a group of estimation values, and all possible DOA estimation values including the real angle and the fuzzy angle can be obtained through the linear relation. And finally, comparing DOA estimation results of the two sub-arrays, and finding the closest K (signal source number) group value to obtain a final DOA estimation value.
Although the degree of freedom can be greatly improved by the existing method, the array aperture is still limited on one dimension, and two-dimensional DOA estimation cannot be realized. While the RD MUSIC algorithm greatly reduces complexity while ensuring estimation accuracy, it cannot be directly applied to the novel virtual array configuration proposed in the present invention.
Disclosure of Invention
The invention provides a novel virtual array structure aiming at the technical problems, breaks through the limitation that a single linear array can only carry out one-dimensional DOA estimation, and can still realize the two-dimensional DOA estimation under the general motion direction (namely, the motion direction and the straight line of the array form an included angle).
In order to achieve the above purpose, the invention provides the following technical scheme:
the invention firstly provides a novel virtual array structure, which is characterized in that an inter-element linear array does uniform linear motion along a direction forming a certain angle with a straight line where the inter-element linear array is located, two sub-arrays of the inter-element linear array are controlled to carry out signal sampling at different fixed time delay positions, then comprehensive signal processing is respectively carried out on the two sub-arrays, two virtual parallelogram sub-area arrays can be obtained, and the two sub-area arrays are combined together to form a generalized virtual inter-element parallelogram array, namely the novel virtual array structure.
Further, the two sub-arrays need to keep the moving distances in the vertical direction respectively
Figure RE-GDA0003180035980000021
And
Figure RE-GDA0003180035980000022
wherein M is1And M2The array elements are a group of mutualin integers which are the array elements of two sub-arrays contained in one mutualin linear array respectively.
Further, the two sub-arrays need to keep the moving distances in the horizontal direction respectively
Figure RE-GDA0003180035980000023
And
Figure RE-GDA0003180035980000024
wherein M is1And M2The array elements are a group of mutualin integers which are the array elements of two sub-arrays contained in one mutualin linear array respectively.
Further, the moving distances of the two sub-arrays required to keep the moving directions thereof are respectively
Figure RE-GDA0003180035980000025
And
Figure RE-GDA0003180035980000026
wherein M is1And M2The array elements are a group of mutualin integers which are the array elements of two sub-arrays contained in one mutualin linear array respectively.
The invention also provides a DOA estimation method of the novel virtual array structure, which expands the array aperture of the mutual element linear array to two dimensions and realizes two-dimensional DOA estimation.
Further, the DOA estimation method of the novel virtual array structure is specifically a DRC MUSIC algorithm based on a virtual parallelogram array.
Compared with the prior art, the invention has the beneficial effects that:
the novel virtual array structure provided by the invention fully utilizes the received signals at each time delay position, creates virtual array elements, realizes two-dimensional DOA estimation of one-dimensional mutual element linear array in a motion scene, and improves the degree of freedom, estimation precision and practicability of the method. On the other hand, in the DOA estimation method based on the novel virtual array structure, considering that the higher complexity is brought by directly applying the MUSIC algorithm to the virtual parallelogram array of the invention, and meanwhile, the existing RD MUSIC algorithm cannot be directly applied to the virtual parallelogram array of the invention, the invention further provides a decoupling complexity-reducing MUSIC (drc MUSIC) algorithm adapted to the virtual parallelogram array of the invention, so that the computational complexity of the algorithm is greatly reduced while the precision is ensured.
Drawings
In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
Fig. 1 is a schematic structural diagram of a generalized virtual inter-element parallelogram array according to embodiment 1 of the present invention.
Fig. 2 is a schematic structural diagram of a virtual parallelogram array formed by the linear array of the interexchange moving according to a motion mode.
Fig. 3 is a schematic structural diagram of a virtual parallelogram array formed by the linear array of the interexchange moving according to the second motion mode in embodiment 1 of the present invention.
Fig. 4 is a schematic structural diagram of a virtual parallelogram array formed by the linear array of the interexchange according to three motions in the motion mode, provided in embodiment 1 of the present invention.
Detailed Description
The invention firstly provides a novel virtual array structure, which is characterized in that an inter-element linear array does uniform linear motion along a direction forming a certain angle with a straight line where the inter-element linear array is located, two sub-arrays of the inter-element linear array are controlled to carry out signal sampling at different fixed time delay positions, then comprehensive signal processing is respectively carried out on the two sub-arrays, two virtual parallelogram sub-area arrays can be obtained, and the two sub-area arrays are combined together to form a generalized virtual inter-element parallelogram array, namely the novel virtual array structure.
The invention also provides a DOA estimation method of the novel virtual array structure, which expands the array aperture of the mutual element linear array to two dimensions and realizes two-dimensional DOA estimation.
For a better understanding of the present solution, the method of the present invention is described in detail below with reference to the accompanying drawings.
Example 1 construction of a novel virtual array Structure
As shown in fig. 1, consider an inter-element linear array, which includes two sub-arrays. Since the first array element is overlapped, the total number of array elements is M ═ M1+M2-1, wherein M1And M2Is a group of mutual prime integers which are array element numbers of the sub-array 1 and the sub-array 2 respectively. The array element spacing of the two sub-arrays is respectively M2d and M1d, wherein d ═ λ/2 is a half wavelength. Without loss of generality, the linear array on the x axis is assumed to move linearly at a constant speed v along the direction with an included angle alpha with the positive direction of the x axis.
Assuming that K uncorrelated far-field narrow-band signals with the same wavelength λ in space are incident on the array, the K-th received signal is sk(t) of (d). Definition of
Figure RE-GDA0003180035980000041
And
Figure RE-GDA0003180035980000042
wherein theta iskAnd
Figure RE-GDA0003180035980000043
respectively the azimuth angle and the pitch angle of the k-th signal. Thus, the received signal of the array at time t is:
Figure RE-GDA0003180035980000044
wherein
Figure RE-GDA0003180035980000045
For the frequency of the signal after being influenced by the Doppler shift, the carrier frequency
Figure RE-GDA0003180035980000046
c is the propagation velocity of the electromagnetic wave, pk＝μkcos(α)+γksin (α), n (t) is an additive white Gaussian noise vector, ax(μk；ωk) Is an array flow pattern, and the expression is as follows:
Figure RE-GDA0003180035980000047
wherein d isxl＝md∈{{0，M1，…，(M2-1)M1}∪{M2，…，(M1-1)M2D, l is 1, …, and M is the abscissa of the l-th array element. For array flow pattern ax(μk；ωk) Item i of (1), will bekIs replaced by
Figure RE-GDA0003180035980000048
The following can be obtained:
Figure RE-GDA0003180035980000051
Figure RE-GDA0003180035980000052
so when v < c, equation ax(μk；ωk)＝ax(μk；ω0) This is true. Then the received signal for the initial array is:
Figure RE-GDA0003180035980000053
therefore, the received signal at time t is:
x(t)＝As(t)+n(t)，
wherein A ═ ax(μ1；ω0)，ax(μ2；ω0)，…，ax(μK；ω0)]Is a matrix of directions, and the direction matrix,
Figure RE-GDA0003180035980000054
is a signal matrix.
FIG. 1 is a schematic diagram of a generalized virtual inter-element parallelogram array. As shown in fig. 1, two sub-arrays of the inter-element linear array are sampled at different fixed time delays during the moving process, that is, the sampling time of the sub-array 1 is t + n1M2τqOf subarrays 2The sampling time is t + n2M1τqWherein n is1,n2Is a positive integer, time τqAnd q is 1,2 and 3, which represent sampling time delays in the motion modes of fig. 2,3 and 4, respectively, and satisfy v τq＝dqIn the three motion modes are
Figure RE-GDA0003180035980000055
vτ3D. FIG. 2 is a schematic diagram of a virtual parallelogram array formed by the linear array of the reciprocal element moving according to a first motion mode, in which the first motion mode refers to that the sub-array 1 and the sub-array 2 need to keep the vertical movement distances thereof respectively
Figure RE-GDA0003180035980000056
And
Figure RE-GDA0003180035980000057
i.e. the passage of time for subarrays 1 and 2, respectively
Figure RE-GDA0003180035980000058
And
Figure RE-GDA0003180035980000059
and then sampling is carried out. FIG. 3 is a schematic diagram of a virtual parallelogram array formed by the linear array of the reciprocal element moving according to the second motion mode, wherein the two sub-arrays 1 and 2 after the two-finger motion in the motion mode need to keep the horizontal moving distances thereof respectively
Figure RE-GDA0003180035980000061
And
Figure RE-GDA0003180035980000062
i.e. the passage of time for subarrays 1 and 2, respectively
Figure RE-GDA0003180035980000063
And
Figure RE-GDA0003180035980000064
and then sampling is carried out. FIG. 4 is a still another embodiment of the present inventionThe structure schematic diagram of a virtual parallelogram array formed by linear arrays moving according to three motion modes, wherein the motion distances of the subarrays 1 and 2 which need to keep the motion directions after the three fingers move in the motion modes are respectively
Figure RE-GDA0003180035980000065
And
Figure RE-GDA0003180035980000066
i.e. the passage of time for subarrays 1 and 2, respectively
Figure RE-GDA0003180035980000067
And
Figure RE-GDA0003180035980000068
and then sampling is carried out. The above three motion patterns can summarize all possible virtual inter-element parallelogram arrays that can be formed.
Setting the time continuous period TCP as TCP ═ max (M)1(M2-1),M2(M1-1))) tau, TCP determines the total time of the movement of the linear array of reciprocals along the y-axis. Thus, n1,n2Are respectively as
Figure RE-GDA0003180035980000069
And
Figure RE-GDA00031800359800000610
and finally, comprehensively processing all received signals of the two sub-arrays to obtain a virtual mutualin parallelogram array. Taking fig. 1 as an example, the sampling time of the sub-array 1 is t + n14τqThe sampling time of the subarray 2 is t + n25τq. Meanwhile, it is assumed that the environment is stable during the movement, and the position of the signal source, the signal waveform, and the like remain unchanged.
First, the received signals obtained for sub-array 1 are:
x1(t)＝A1s(t)+n1(t)，
wherein n is1(t) is a zero-mean additive white Gaussian noise vector, A1＝[a1x(μ1；ω0)，a1x(μ2；ω0)，…，a1x(μK；ω0)]Is a direction matrix, a in the direction matrix1x(μk；ω0) Is composed of
Figure RE-GDA00031800359800000611
Then at time t + M2The array output of τ is:
Figure RE-GDA00031800359800000612
wherein s isk(t+M2τq)＝sk(t)exp(jω0M2τq) At the same time define
Figure RE-GDA0003180035980000071
Multiplying the phase correction factor exp (-j omega)0M2τq) Obtaining:
Figure RE-GDA0003180035980000072
wherein
Figure RE-GDA0003180035980000073
Therefore, it is not only easy to use
Figure RE-GDA0003180035980000074
Wherein
Figure RE-GDA0003180035980000075
Similarly, at time t + n1M2τqThe synchronous received signal of (a) is:
Figure RE-GDA0003180035980000076
wherein the direction matrix
Figure RE-GDA0003180035980000077
Figure RE-GDA0003180035980000078
Finally, introduce η1＝M1-1＝max(n1) The final synchronous received signal is:
Figure RE-GDA0003180035980000079
wherein the noise vector is
Figure RE-GDA00031800359800000710
The direction matrix is:
Figure RE-GDA00031800359800000711
Figure RE-GDA00031800359800000712
Figure RE-GDA0003180035980000081
by comparing the array flow patterns of the area array, it can be known that: thus, a virtual parallelogram array can be formed.
For subarray 2, the sampling delay is M1τqI.e. each time the subarray 2 needs to pass M1τqA sample is taken. Similar to the processing procedure of the sub-array 1, the final integrated received signal of the sub-array 2 is:
Figure RE-GDA0003180035980000082
wherein n iss y2n(t) isNoise vector, direction matrix
Figure RE-GDA0003180035980000083
Figure RE-GDA0003180035980000084
Figure RE-GDA0003180035980000085
Figure RE-GDA0003180035980000086
Thus, a virtual parallelogram array can be constructed by the integrated array aperture processing of the sub-array 2.
In conclusion, because M1And M2Is a group of mutualin integers, so that the two virtual parallelogram arrays can be combined to form a generalized virtual mutualin parallelogram array.
Embodiment 2 DOA estimation method of novel virtual array structure
For the ith (i ═ 1, 2) virtual parallelogram array, the function is defined:
Figure RE-GDA0003180035980000087
wherein is
Figure RE-GDA0003180035980000088
Noise subspace, accessible by means of a covariance matrix
Figure RE-GDA0003180035980000089
And decomposing the characteristic value to obtain the characteristic value.
However, array flow pattern aiy(p；ω0) The parameter μ and the parameter γ in (1) are coupled together, so the conventional RD MUSIC algorithm is not suitable for the virtual array of the present invention. To solve this problem, we first need to address the array flow pattern a1y(p；ω0) Performing a decoupling operation, namely:
Figure RE-GDA0003180035980000091
wherein the content of the first and second substances,
Figure RE-GDA0003180035980000092
the function can be further written as:
Figure RE-GDA0003180035980000093
wherein
Figure RE-GDA0003180035980000094
Because of the function Yi(μ, γ, α) is a convex function, so an equation can be used
Figure RE-GDA0003180035980000095
To eliminate zero-valued solutions
Figure RE-GDA0003180035980000096
Wherein
Figure RE-GDA0003180035980000097
The problem we need to solve can be converted into:
Figure RE-GDA0003180035980000098
the cost function is constructed as:
Figure RE-GDA0003180035980000099
wherein epsiloniIs a constant.
For function Li(mu, gamma) can be obtained by partial derivationObtaining:
Figure RE-GDA00031800359800000910
therefore, we can further obtain the relationship between the parameter μ and the parameter γ as:
Figure RE-GDA0003180035980000101
function of generationiThe estimated value of the parameter mu can be obtained in (mu, gamma, alpha)
Figure RE-GDA00031800359800001010
Comprises the following steps:
Figure RE-GDA0003180035980000102
to this end, an estimate of the parameter μ
Figure RE-GDA0003180035980000103
Can be obtained by one-dimensional spectral peak search.
In addition, the above spectral peak search may be performed within a small range of the parameter μ. Specifically, we divide the value range of the parameter μ into:
Figure RE-GDA0003180035980000104
where j is 1,2, i ≠ j, kμiIs an integer and 1. ltoreq. kμi≤Mj. According to the linear relation between the fuzzy angle and the real angle
Figure RE-GDA0003180035980000105
The estimates of all the remaining possible parameters can be solved, where kiIs a natural number and — (k)μi-1)≤ki≤Mj-(kμi-1)。
By applying the above steps to two virtual parallelogram arrays, respectively, we can obtain estimates of two sets of parameters. Finally, the nearest K groups of values in the two groups of values are found, and the formula is expressed
Figure RE-GDA0003180035980000106
The final estimate of the parameter is obtained.
Then, the estimated value of the parameter is brought back to the global spectrum function, and the estimated value of the parameter gamma can be obtained through one-dimensional spectrum peak search:
Figure RE-GDA0003180035980000107
wherein
Figure RE-GDA0003180035980000108
Is a noise subspace, which can be determined by fitting the covariance matrix R ═ E [ x (t) xH(t)]The characteristic value is decomposed to obtain the characteristic value,
Figure RE-GDA0003180035980000109
the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: it is to be understood that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for some of the technical features thereof, but such modifications or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. The utility model provides a novel virtual array structure, its characterized in that, is the uniform velocity linear motion with the direction that is certain angle with self place straight line with the line, and its two subarrays are carried out signal sampling by the fixed time delay department of control in the difference, then synthesize signal processing to two subarrays respectively, can obtain two virtual parallelogram sub-area arrays, and two sub-area arrays unite together and form a generalized virtual interlude parallelogram array, novel virtual array structure promptly.
2. The virtual array architecture as claimed in claim 1, wherein the two sub-arrays are required to maintain their vertical movement distance respectively
Figure FDA0003148994530000011
And
Figure FDA0003148994530000012
wherein M is1And M2The array elements are a group of mutualin integers which are the array elements of two sub-arrays contained in one mutualin linear array respectively.
3. The virtual array architecture as claimed in claim 1, wherein the two sub-arrays are required to maintain their horizontal movement distance respectively
Figure FDA0003148994530000013
And
Figure FDA0003148994530000014
wherein M is1And M2The array elements are a group of mutualin integers which are the array elements of two sub-arrays contained in one mutualin linear array respectively.
4. The virtual array architecture as claimed in claim 1, wherein the two sub-arrays are required to maintain the moving distance of the moving direction thereof respectively
Figure FDA0003148994530000015
And
Figure FDA0003148994530000016
wherein M is1And M2The array elements are a group of mutualin integers which are the array elements of two sub-arrays contained in one mutualin linear array respectively.
5. A DOA estimation method of a novel virtual array structure according to claim 1, characterized in that the array aperture of the mutual prime linear array is extended to two dimensions to realize two-dimensional DOA estimation.
6. The DOA estimation method of the novel virtual array structure according to claim 5, characterized in that it is a DRC MUSIC algorithm based on virtual parallelogram array.
CN202110759477.8A 2021-07-06 2021-07-06 Novel virtual array structure and DOA estimation method thereof Active CN113484821B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110759477.8A CN113484821B (en) 2021-07-06 2021-07-06 Novel virtual array structure and DOA estimation method thereof

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110759477.8A CN113484821B (en) 2021-07-06 2021-07-06 Novel virtual array structure and DOA estimation method thereof

Publications (2)

Publication Number Publication Date
CN113484821A true CN113484821A (en) 2021-10-08
CN113484821B CN113484821B (en) 2024-04-12

Family

ID=77940967

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110759477.8A Active CN113484821B (en) 2021-07-06 2021-07-06 Novel virtual array structure and DOA estimation method thereof

Country Status (1)

Country Link
CN (1) CN113484821B (en)

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106785486A (en) * 2017-01-09 2017-05-31 南京航空航天大学 A kind of relatively prime planar array structure of broad sense and angle estimating method
CN107092004A (en) * 2017-05-05 2017-08-25 浙江大学 Relatively prime array Wave arrival direction estimating method based on signal subspace rotational invariance
CN107907855A (en) * 2017-10-25 2018-04-13 天津大学 A kind of coprime array switching DOA estimation method and device for even linear array
CN108872929A (en) * 2018-04-12 2018-11-23 浙江大学 Relatively prime array Wave arrival direction estimating method based on interpolation virtual array covariance matrix Subspace Rotation invariance
US20200200861A1 (en) * 2018-12-21 2020-06-25 King Fahd University Of Petroleum And Minerals Signal emitter location determination using sparse doa estimation based on a multi-level prime array with compressed subarray
WO2020264466A1 (en) * 2019-06-27 2020-12-30 Ning Xiang Sound source enumeration and direction of arrival estimation using a bayesian framework
WO2021068496A1 (en) * 2020-05-03 2021-04-15 浙江大学 Co-prime array two-dimensional direction of arrival estimation method based on structured virtual domain tensor signal processing
CN113156362A (en) * 2021-03-15 2021-07-23 北京邮电大学 Method and device for determining direction of arrival and method and device for acquiring signal

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106785486A (en) * 2017-01-09 2017-05-31 南京航空航天大学 A kind of relatively prime planar array structure of broad sense and angle estimating method
CN107092004A (en) * 2017-05-05 2017-08-25 浙江大学 Relatively prime array Wave arrival direction estimating method based on signal subspace rotational invariance
CN107907855A (en) * 2017-10-25 2018-04-13 天津大学 A kind of coprime array switching DOA estimation method and device for even linear array
CN108872929A (en) * 2018-04-12 2018-11-23 浙江大学 Relatively prime array Wave arrival direction estimating method based on interpolation virtual array covariance matrix Subspace Rotation invariance
US20200200861A1 (en) * 2018-12-21 2020-06-25 King Fahd University Of Petroleum And Minerals Signal emitter location determination using sparse doa estimation based on a multi-level prime array with compressed subarray
WO2020264466A1 (en) * 2019-06-27 2020-12-30 Ning Xiang Sound source enumeration and direction of arrival estimation using a bayesian framework
WO2021068496A1 (en) * 2020-05-03 2021-04-15 浙江大学 Co-prime array two-dimensional direction of arrival estimation method based on structured virtual domain tensor signal processing
CN113156362A (en) * 2021-03-15 2021-07-23 北京邮电大学 Method and device for determining direction of arrival and method and device for acquiring signal

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
ZHI ZHENG 等: "Direction-of-Arrival Estimation of Coherent Signals via Coprime Array Interpolation", IEEE SIGNAL PROCESSING LETTERS, vol. 27, 31 December 2020 (2020-12-31), pages 585 - 589 *
冯明月 等: "基于双平行互质阵列的二维高精度DOA估计", 系统工程与电子技术, vol. 39, no. 05, 31 May 2017 (2017-05-31), pages 977 - 983 *
刘声 等: "一种减小互耦的互素嵌套阵列及测向算法", 重庆大学学报, vol. 44, no. 1, 31 January 2021 (2021-01-31), pages 20 - 28 *

Also Published As

Publication number Publication date
CN113484821B (en) 2024-04-12

Similar Documents

Publication Publication Date Title
CN109633525B (en) Quick uniform circular array space spectrum direction finding realization method
CN113820711B (en) Array rapid imaging method and application thereof
CN109143190B (en) Broadband steady self-adaptive beam forming method for null broadening
CN109581388B (en) Near-field wide-view-angle beam forming method of real-time three-dimensional imaging sonar
CN107092007A (en) A kind of Wave arrival direction estimating method of virtual second order array extension
CN112307429A (en) Multidirectional point array response control method
CN110531312B (en) DOA estimation method and system based on sparse symmetric array
CN113567913B (en) Two-dimensional plane DOA estimation method based on iterative re-weighting dimension-reducible
CN114355290B (en) Sound source three-dimensional imaging method and system based on stereo array
CN109375227A (en) A kind of deconvolution Wave beam forming three-dimensional acoustic imaging method
CN109270483B (en) Three-dimensional array virtual extended coherent source two-dimensional direction of arrival estimation method
CN113625220A (en) New method for quickly estimating direction of arrival and diffusion angle of multipath signal
CN113484821A (en) Novel virtual array structure and DOA estimation method thereof
CN109507634B (en) Blind far-field signal direction-of-arrival estimation method based on propagation operator under any sensor array
CN111812580A (en) Motion linear sparse array optimization method based on underdetermined information source Cramer-Rao bound
CN110535519A (en) A kind of robust adaptive beamforming method based on space smoothing
CN103777179A (en) Subarray dimension reducing method for radar three-dimensional conformal array
CN107247250A (en) A kind of coherent distributed sources direction of arrival tracking based on particle filter
Wang et al. Uncoupled FDA beampattern synthesis by discrete element position and frequency offsets pairing
CN115480245A (en) Airborne radar forward-looking three-dimensional imaging technology based on two-dimensional super-resolution algorithm
CN111830458B (en) Parallel linear array single-snapshot two-dimensional direction finding method
CN110632606B (en) Two-dimensional fast Fourier transform three-dimensional imaging method based on spatial resampling
CN113820654A (en) S-band radar target low elevation DOA estimation method based on beam domain dimension reduction
Wang et al. Design of a low-complexity miniature underwater three-dimensional acoustical imaging system
CN113093111A (en) Method and system for demodulating two-dimensional coherent signals by uniform circular array based on compressed sensing and genetic algorithm

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