CN111257845A - Approximate message transfer-based non-grid target angle estimation method - Google Patents

Approximate message transfer-based non-grid target angle estimation method Download PDF

Info

Publication number
CN111257845A
CN111257845A CN202010086824.0A CN202010086824A CN111257845A CN 111257845 A CN111257845 A CN 111257845A CN 202010086824 A CN202010086824 A CN 202010086824A CN 111257845 A CN111257845 A CN 111257845A
Authority
CN
China
Prior art keywords
algorithm
value
angle
representing
target
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
CN202010086824.0A
Other languages
Chinese (zh)
Other versions
CN111257845B (en
Inventor
张新禹
张俊
霍凯
张双辉
刘永祥
姜卫东
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.)
National University of Defense Technology
Original Assignee
National University of Defense Technology
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 National University of Defense Technology filed Critical National University of Defense Technology
Priority to CN202010086824.0A priority Critical patent/CN111257845B/en
Publication of CN111257845A publication Critical patent/CN111257845A/en
Application granted granted Critical
Publication of CN111257845B publication Critical patent/CN111257845B/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
    • 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
    • G01S7/418—Theoretical aspects

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention belongs to the field of array signal processing, and particularly relates to an out-of-grid target angle estimation method based on approximate message transfer, which comprises the following steps of: s1 parameter gamma to be estimatedj，j＝1，2，…，N、σ0And initializing a dictionary matrix A; s2, rapidly obtaining a signal posterior probability density function at each moment by using an AMP algorithm; s3 updating the parameter gamma to be estimated by using EM algorithmjJ is 1,2 … N, and the target number optimal solution K is obtained*Updating the noise power σ0(ii) a S4 updating dictionary matrix A by gradient descent method
Figure DDA0002382349660000011
S5 determines when the algorithm iteration converges and determines the incoming wave direction and number. The invention has the following beneficial effects: the invention can automatically adjust the grid division for the target outside the angle grid node with the cost of less increased computational complexity, so that the target is positioned on the grid node and can be more accurately estimatedThe target angle has high calculation efficiency, can be applied to a real-time multi-target high-precision angle estimation system, and has important engineering application value.

Description

Approximate message transfer-based non-grid target angle estimation method
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to an off-grid (off-grid) target angle estimation method based on approximate message transfer.
Background
In the fields of radar, sonar, seismic remote sensing, and the like, target angle estimation (DOA) is a fundamental problem. In recent years, the mainstream idea is to introduce a sparse recovery algorithm, construct a sparse representation model of an array received signal according to the sparsity characteristic of the received signal, and complete real-time reconstruction of the signal. Compared with the traditional algorithm, the method has the remarkable advantage of improving the robustness of the signals with limited noise and sampling number and related signals.
Although solving such sparse recovery problems is difficult, accurate recovery is also possible for a strong sparse signal and well-designed dictionary matrices. Sparse Bayesian Learning (SBL) is one of the classic methods. There are two types of estimation in this approach. The first is a maximum a posteriori estimation based on sparse induced prior distribution. The second type of estimation operates in the hidden variable space with a variational representation of the hidden variable distribution that results in a sparse estimate of the a posteriori information beyond the mode. A series of algorithms based on the method are provided for different application scenes. These algorithms work on estimates of the hyper-parameters in the bayesian hierarchical model either by expectation-maximization iterations or by maximization iterations of the evidence functions. However, each iteration of the SBL algorithm involves large-scale matrix inversion, and particularly in multi-objective solution, the calculation complexity of the SBL algorithm is very high, so that the SBL algorithm is limited to be applied to practical engineering. In order to effectively reduce the algorithm complexity, an Approximate information transfer Algorithm (AMP) is adopted in an E-Step of the SBL (see Chinese patent for details, namely 'a rapid target angle estimation method based on sparse Bayesian learning', and the patent number is ZL 2019100130299). The AMP algorithm is used for performing loop confidence coefficient propagation by using an approximate value of a central limit theorem on a bottom-layer factor graph, and effectively compensates sparse undersampling by introducing a message transfer term into an iterative threshold scheme, so that the posterior probability distribution of signals is obtained by low-complexity operation.
Consider an array of m antennas receiving signals from different directions theta1θ2… θK]TOf K targets, here [ … ]]TRepresenting the transpose of the matrix. The signal model of the SBL algorithm may be written as
y(t)＝Ax(t)+n(t) (1)
Where y (t) represents the array received signal at time t,
Figure BDA0002382349640000011
a matrix of a dictionary is represented,
Figure BDA0002382349640000012
the steering vector of the array represents a received signal vector formed by the incidence of plane waves to the array under the far-field condition, the vector is a complex vector, the dimension is equal to the number of array elements of the array, and for a uniform linear array consisting of m antennas, the steering vector can be expressed as:
Figure BDA0002382349640000013
wherein d represents the distance between array elements, lambda represents the wavelength of the electromagnetic waves emitted by the array, pi is a circumferential rate constant, and theta represents any incident angle. In dictionary matrix A
Figure RE-GDA0002433713180000014
A grid division related to a space incident angle is formed, the finer the grid division is, the higher the resolution of target angle estimation is, generally, a possible space domain interval is divided at equal intervals, and the value of N is far larger than the number m of array elements. (1) X (t) in (1) represents the received target signal vector, its elementsThe element is in one-to-one correspondence with each column in the dictionary matrix, and when the corresponding incident angle has a target, the element of x (t) is equal to the complex value of the signal; when the corresponding angle does not have a target, the element value of x (t) is 0. n (t) represents the additive noise of the system. Here we assume that the target signals at different times are statistically independent, an assumption that is quite common in radar signal processing. In practical engineering applications, n (t) is generally assumed to be zero-mean white Gaussian noise, i.e., white Gaussian noise
Figure RE-GDA0002433713180000021
And the noise between different time instants is statistically independent, here
Figure RE-GDA0002433713180000022
A complex Gaussian distribution representing the zero mean of the complex number with a variance of σ0I，σ0Representing the power of the noise, I represents the identity matrix; as used hereinafter
Figure RE-GDA0002433713180000023
Representing a complex gaussian distribution function with a mean of α and a variance of β.
According to the signal model, the echo signals of the array can meet the distribution
Figure BDA0002382349640000024
For Bayesian derivation, the prior probability distribution of the signal vector x (t) is generally assumed to be
Figure BDA0002382349640000025
And the signals at different time instants are statistically independent, wherein
Figure BDA0002382349640000026
Is a diagonal matrix with the element gamma on the diagonaljJ is 1, and 2 … N is the variance of its corresponding element in x (t). When gamma isjWhen the angle is approximately equal to 0, the corresponding incident angle is shown
Figure BDA0002382349640000027
No target present; otherwise, the target exists. It should be noted here that although the signals at different time instants are statistically independent, the prior probability distributions of the signals at different time instants are the same for the signals at a certain incident angle due to the signals from the same emission signal source. In summary, the parameters to be estimated by the sparse bayesian algorithm include Γ, and noise power σ0And a target number K.
According to the signal model, the resolution and the angle estimation accuracy of the sparse Bayesian algorithm are determined by the dictionary matrix A reflecting the grid division density, but no matter how fine the grid is, targets outside the grid always exist, and echo signals of the targets can cause the mismatching of the dictionary matrix A, so that the target estimation performance of the system is reduced. Therefore, a new sparse bayesian algorithm is needed to process targets outside the grid, and the angle estimation accuracy of the algorithm is improved.
Disclosure of Invention
The invention mainly solves the technical problem that under the condition that a target is not positioned at a space angle grid node, the traditional target angle estimation algorithm based on Bayesian learning can only identify one grid node adjacent to the target, and the real angle of the target is difficult to accurately estimate.
The invention provides a grid-absent target angle estimation method based on approximate message transfer, aiming at the problem that the existing Bayes learning algorithm based on approximate message transfer (AMP) (Chinese patent: a rapid target angle estimation method based on sparse Bayes learning, and patent number ZL2019100131299) cannot more accurately estimate off-grid target angles.
The technical scheme adopted by the invention is as follows: an approximate message transfer based off-grid target angle estimation method comprises the following steps:
s1 parameter gamma to be estimatedj，j＝1，2，…，N、σ0And initialization of dictionary matrix A
S1.1, constructing a dictionary matrix A, A according to the required target angle estimation resolution requirement, wherein the angle corresponding to each column of the A forms the gridding division of the AMP algorithm to the space angle, and the denser the gridding division is, the higher the resolution of the angle estimation is. For the method of the invention, the A is initialized by adopting the equal interval division of the full angle space, and the initial angle corresponding to the grid is recorded as
Figure BDA0002382349640000031
S1.2 in this step, the parameters needed subsequently will be initialized. The parameter to be initialized is γ ═ γ [ γ ]1γ2… γN]TAnd noise power σ0. A good initialization parameter value can greatly accelerate the convergence speed of the following algorithm and quickly obtain a correct result. Since there is no a priori information about the target angle in general applications, initializing Γ is initialized to γ0I.e. the signal a priori variances in the respective directions are equal. The received data from T different time points Y ═ Y (1) Y (2) … Y (T) obtained by sampling]，γ0And σ0This can be obtained from the following equation:
Figure BDA0002382349640000032
in the above formula, m is the number of array elements formed by antennas, | | … | | non-conducting phosphor2Representing the two-norm of the matrix, SNR representing the pre-estimated system signal-to-noise ratio, tr (…) representing the trace of the matrix, (…)HRepresents a conjugate transpose of the matrix;
s2 uses AMP algorithm to quickly obtain signal posterior probability density function of each time
S2.1, according to the initialization result in S1, calculates the following steps for the received data y (T), T ═ 1, and 2 … T at different times, respectively (i.e., for each T, T ═ 1, and 2 … T, steps S2.1.1 to S2.1.6 are repeated until the AMP algorithm converges for the data at time T. such repeated steps are required to be performed T times in total, and for convenience of description, the time reference T is omitted in the following description of the steps, and for example, the target signal vector x (T) received at time T is abbreviated as x, and the array received signal y (T) at time T is abbreviated as y);
description of the drawings: variables occurring in steps S2.1.1-S2.1.6
Figure BDA0002382349640000033
And
Figure BDA0002382349640000034
are all intermediate variables and have no actual physical meaning; while
Figure BDA0002382349640000035
An estimated quantity representing x estimated by the following steps; the iteration of the algorithm referred to below is the iteration of steps S2.1.1-S2.1.6;
S2.1.1AMP parameter initialization: for each element of x, the initial estimated parameter values are set as follows
Figure BDA0002382349640000036
Here, the first and second liquid crystal display panels are,
Figure BDA0002382349640000037
to represent
Figure BDA0002382349640000038
The (j) th element of (a),
Figure BDA0002382349640000039
to represent
Figure BDA00023823496400000310
Initial value of the jth element of (1), xjThe jth element representing the x true,
Figure BDA00023823496400000311
presentation pair
Figure BDA00023823496400000312
The initial value obtained by the estimation is obtained,
Figure BDA00023823496400000313
representing the probability density function p (x)j|γj) By expectation, where p (x)j|γj) Is shown at known gammajValue of xjIs determined by the probability density function of (a),
Figure BDA00023823496400000314
presentation pair
Figure BDA00023823496400000315
And estimating an initial value, wherein k represents the kth iteration of the algorithm, and k is 0 to represent an initialization step.
Since we generally assume the probability density function p (x)j|γj) Is a zero mean Gaussian distribution, so we can get from (5)
Figure BDA0002382349640000041
S2.1.2 linear output step: for each i-1, 2 … m, calculate
Figure BDA0002382349640000042
In the above formula
Figure BDA0002382349640000043
Representing the process of the kth iteration of the algorithm
Figure BDA0002382349640000044
Value of aijAn element representing the ith row and jth column of the dictionary matrix A, (…)iRepresents the ith element of the vector, | … | represents the modulus of the complex number,
Figure BDA0002382349640000045
representing the process of the kth iteration of the algorithm
Figure BDA0002382349640000046
The value of the one or more of,
Figure BDA0002382349640000047
representing the process of the kth iteration of the algorithm
Figure BDA0002382349640000048
The value of the one or more of,
Figure BDA0002382349640000049
representing the process of the kth iteration of the algorithm
Figure BDA00023823496400000410
The value of the one or more of,
Figure BDA00023823496400000411
representing the k-th iteration of the algorithm
Figure BDA00023823496400000412
The value of the one or more of,
Figure BDA00023823496400000413
representing the process of the kth iteration of the algorithm
Figure BDA00023823496400000414
The value is obtained.
S2.1.3 nonlinear output step: for each i-1, 2 … m, calculate
Figure BDA00023823496400000415
yiThe i-th element representing the received data y,
Figure BDA00023823496400000416
representing the process of the kth iteration of the algorithm
Figure BDA00023823496400000417
The value of the one or more of,
Figure BDA00023823496400000418
indicating updating during the kth iteration of the algorithm
Figure BDA00023823496400000419
Value of (1), function of
Figure BDA00023823496400000420
S2.1.4 Linear input step: for each j ═ 1,2 … N, calculations were made
Figure BDA00023823496400000421
Figure BDA00023823496400000422
Representing the process of the kth iteration of the algorithm
Figure BDA00023823496400000423
The value of the one or more of,
Figure BDA00023823496400000424
representing the process of the kth iteration of the algorithm
Figure BDA00023823496400000425
Value, here (…)-1Representation matrix inversion (…)*Representing the conjugate of a complex number.
S2.1.5 nonlinear input step: for each j ═ 1,2 … N, calculations were made
Figure BDA00023823496400000426
Here, the
Figure BDA00023823496400000427
Representing the (k + 1) th iteration
Figure BDA00023823496400000428
The value of the one or more of,
Figure BDA00023823496400000429
representing the (k + 1) th iteration
Figure BDA00023823496400000430
Value, function of above
Figure BDA0002382349640000051
S2.1.6 determining whether the AMP algorithm converges: computing
Figure BDA0002382349640000052
Wherein … does not calculation1A 1-norm of the matrix is represented,
Figure BDA0002382349640000053
representing the (k + 1) th iteration
Figure BDA0002382349640000054
The values, in the same way,
Figure BDA0002382349640000055
representing the kth iteration
Figure BDA0002382349640000056
The value is obtained. If the value is greater than a set threshold epsilon1Then go back to S2.1.2 for reiteration; otherwise, the loop is skipped to S2.2 to obtain p (x)jY) of the results. Threshold epsilon1Depending on factors such as the signal-to-noise ratio of the system, it needs to be adjusted according to actual conditions. Normally, the threshold ε1Is between 0.1 and 0.001.
S2.2 through the steps, the posterior probability density function p (x) of the signal at the time t can be obtainedjResults of | y) are as follows
Figure BDA0002382349640000057
p(xj) Denotes xjA probability density function of; in the above formula
Figure BDA0002382349640000058
Is obtained by calculation according to the sample value y (t) at the time t in the step S2.1, and is obtained in the last iteration process after the AMP algorithm is judged to be converged
Figure BDA0002382349640000059
A value of (d); here gamma isjIs obtained from either S1 or S3, and in the first EM algorithm iteration, γ is obtainedjIs determined by the initial value in S1, and in other cases, γjIs calculated by the gamma calculated at S3 in the last EM algorithm cyclejAnd (4) determining.
S3 updating the parameter gamma to be estimated by using EM algorithmjJ is 1,2 … N, and the target number optimal solution K is obtained*Updating the noise power σ0
The posterior probability density function p (x) of the signal has been obtained in S2jY), according to the EM algorithm, this step updates the value of the parameter to be estimated one by one using the following expression
Figure BDA00023823496400000511
In the above formula, q ═ γ1… γNσ0]T，X＝[x(1) x(2) … x(T)]，N＝[n(1) n(2) … n(T)]， ＜…|Y；qiDenotes that the known reception data Y ═ Y (1) Y (2) … Y (t)]And given parameter value qiIn the above expression, q isiRepresents the value of q during the ith iteration of the algorithm, and qi+1Representing the q value during the (i + 1) th iteration of the algorithm. The method comprises the following steps:
s3.1 updating Gammaj,j＝1,2…N：
Due to the statistical independence between the signals at different times,and the parameter values to be estimated are the same. Due to gammajIs updated only with
Figure BDA00023823496400000510
In this regard, the probability density function when expected can therefore become p (x)j(t)|y(t)；qi) I.e. known received data y (t) and given parameter value qiX under the condition of (1)j(t) probability density function. The pair gamma can be obtained by formula derivationjThe updated expression of j ═ 1,2 … N is
Figure BDA0002382349640000061
In the above expression
Figure BDA0002382349640000062
Represents gamma in the ith iteration of the algorithmj，
Figure BDA0002382349640000063
Represents gamma in the (i + 1) th iteration of the algorithmj。
Further on gammajThe partial derivative can be obtained
Figure BDA0002382349640000064
As can be seen from the above formula, γjThe update of j 1,2 … N does not need to go through matrix operation, but is simple scalar operation, so that a large amount of operation time can be saved.
S3.2 estimating target quantity optimal solution K*: different from the Chinese invention patent 'a rapid target angle estimation method based on sparse Bayesian learning', patent number ZL2019100131299, the invention needs to determine the number of targets before estimating the noise power, so as to conveniently update the noise power sigma at S3.30The intermediate result calculated in the step can be utilized to reduce the consumption of calculation resources.
This step is described in references 1, z. -m.liu, z. -t.huang, y. -y.zhou, An effective massive method for direction-of-arrival estimation of video streaming, IEEE trans. wireless Communications 11(10) (2012) 3607-3617; 2. stoica, Y.Selen, Model-order selection a review of information criteria rules, IEEESignal Process. Mag.21(4) (2004) 36-47; 3. austin, R, L, Moses, J, N, Ash, E, Ertin, On the relationship between spark alignment and parameter estimation with model order selection, IEEE J.Sel.topics Signal Process.4(3) (2010) 560-.
As can be seen from the above references, using subspace analysis, the optimal solution for the target number is
Figure BDA0002382349640000065
Wherein I is a matrix of units and I is a matrix of units,
Figure BDA0002382349640000066
Figure BDA0002382349640000067
where K is an estimate of the target number, K*Is the optimal solution of the K, and the K is the optimal solution,
Figure BDA0002382349640000068
corresponding assumed target angle in A
Figure BDA0002382349640000069
Is given a target angle
Figure BDA00023823496400000610
Refers to gammajJ is the angle corresponding to the largest K value of 1,2 … N.
S3.3 updating the noise Power σ0：
This step is described in references p.gerstoft, c.f. mecklenbranker, a.xenaki, s.nannuru, multisenshot spot basic learning for doa, IEEE Signal process. letters 23(10) (2016) 1469-.
From the above references, one can obtain
Figure BDA00023823496400000611
Wherein
Figure BDA0002382349640000071
Here, the
Figure BDA0002382349640000072
Is that
Figure BDA0002382349640000073
The covariance matrix of each column in (1), which can be obtained from the above equation
Figure BDA0002382349640000074
According to the mapping matrix P defined by S3.2, and P ═ PH＝P2Is obtained by
PRPH-σ0PPH＝ΣY-σ0I (21)
Combining tr (R-sigma)Y) 0 can deduce σ0The update formula of (2) is:
Figure BDA0002382349640000075
comparing equation (17), it can be seen that solving for K*And σ0Can be carried out simultaneously, and saves computing resources.
S4 updating dictionary matrix A by gradient descent method
Figure BDA0002382349640000076
Through the above steps, the number of targets and the grid nodes where the targets are located (i.e., exceeding the threshold ε) have been roughly estimated5Gamma of (2)jThe corresponding grid node, i.e., the angle estimate of the target), but since the true position of the target may be between two grid nodes,therefore, the grid nodes are adjusted by adopting a gradient descent algorithm in the step, so that the grid nodes are closer to the real position of the target, and the estimation precision of the target angle is improved. Optimal solution K for target quantity calculated in S3.2*The target corresponding angle can be considered as γjJ is the first K in 1,2 … N*Maximum gammajCorresponding angle grid node
Figure BDA0002382349640000077
The angle grid nodes roughly corresponding to the targets are adjusted by using a gradient descent method, and it is noted that only the angle grid nodes currently corresponding to the targets need to be updated here
Figure BDA0002382349640000078
Without having to update the entire angle grid, to avoid high computational complexity (i.e., the angles corresponding to each target determined in S3.2)
Figure BDA0002382349640000079
And performing iterative calculation in the step until the algorithm is converged. The S4 steps collectively need to be performed K*Second). The update rule can be derived from
Figure BDA00023823496400000710
Wherein
Figure BDA00023823496400000711
A is a dictionary matrix with angle variables. From the above formula, the correlation
Figure BDA00023823496400000712
Gradient of
Figure BDA00023823496400000713
Here, the
Figure BDA00023823496400000714
Representation matrixX is the estimated amount of X found by the step S2,
Figure BDA00023823496400000715
is in A corresponds to a division
Figure BDA00023823496400000716
Outside angle
Figure BDA00023823496400000717
A matrix of a plurality of columns of (a),
Figure BDA00023823496400000718
corresponding to division in representation X
Figure BDA00023823496400000719
Outside angle
Figure BDA00023823496400000720
A matrix of rows of (a) is formed,
Figure BDA00023823496400000721
corresponding to angle in representation X
Figure BDA00023823496400000722
The matrix of rows of (a) is,
Figure BDA00023823496400000723
is the column vector in A, d (-) is the derivative of a (-).
Pass through (24) type pair
Figure BDA00023823496400000724
Is optimized by
Figure BDA00023823496400000725
Wherein α is the step size of the angle update, and the step size depends on the accuracy requirement of the angle estimation in practical applicationlThe value of the i-th iteration within this step is indicated. If the input to the function sign (. cndot.) is positiveThen equals 1 and vice versa equals-1.
After completing the angle update once, it needs to judge whether to converge. Considering that the initial dictionary grid may already meet the accuracy requirement, the number of iterations in this step is not too large, and when the condition is met
Figure BDA0002382349640000081
Or l is ≧ epsilon4When it is, consider to
Figure BDA0002382349640000082
Has satisfied the requirement, exits the loop, ε3、ε4Is the decision threshold. Wherein epsilon3The method can be determined according to the accuracy requirement of the system on angle estimation, and the value is generally 0.1 degree; epsilon4The real-time performance of the algorithm is lower when the value is larger, which is determined according to the real-time performance requirement of the system, and the value can be 1000 under the common condition.
S5 judges when the iterative process of the algorithm converges, and determines the direction and quantity of the incoming wave
Finish γ ═ γ1γ2... γN]TAnd σ0After updating, convergence is judged by the following expression:
Figure BDA0002382349640000083
ε2the threshold can be set according to the system practice for determining the threshold, and is usually between 0.1 and 0.001. If the above expression is not satisfied, returning to S2 to continue the iterative operation; if the above formula is true, the loop can be exited, and the number of incoming waves is the last calculated K*In the direction of [ gamma ] - [ gamma ]1γ2… γN]TMiddle front K*Maximum gammajCorresponding direction
Figure BDA0002382349640000084
Due to the pair in S4
Figure BDA0002382349640000085
And more accurate calculation is performed, so that the angle estimation precision of the algorithm on the off-grid target is greatly improved.
The invention has the following beneficial effects: the method can automatically adjust the grid division for the targets positioned outside the angle grid nodes at the cost of less increased calculation complexity, so that the targets are positioned on the grid nodes, the angle of the targets can be more accurately estimated, the calculation efficiency is higher, the method can be applied to a real-time multi-target high-precision angle estimation system, and the method has important engineering application value.
Drawings
FIG. 1 is a process flow diagram;
FIG. 2 is a spatial power spectrum of the method of the present invention and the conventional method when the number of array elements is 16;
FIG. 3 is a comparison of the performance of the method of the present invention with that of the conventional method with 16 array elements as a function of the signal-to-noise ratio;
FIG. 4 is a comparison of the performance of the method of the present invention with that of the conventional method with the number of samples collected when the number of array elements is 16;
FIG. 5 is a graph comparing the operation time of the method of the present invention with that of the conventional method with the number of samples when the number of array elements is 16;
FIG. 6 is a graph showing the comparison of the operation time of the method of the present invention and the conventional method with the change of the number of samples when the number of array elements is 10;
FIG. 7 is a graph showing the comparison of the operation time of the method of the present invention and the conventional method with the number of samples when the number of array elements is 16 and the angle interval is 0.5 °.
Detailed Description
The invention is further illustrated with reference to the accompanying drawings:
FIG. 1 is a general process flow of the present invention.
The invention discloses a Bayesian learning rapid target angle estimation algorithm based on generalized approximate message transmission, which comprises the following steps of:
s1 parameter gamma to be estimatedj，j＝1，2，…，N、σ0And initializing a dictionary matrix A;
s2, rapidly obtaining a signal posterior probability density function at each moment by using an AMP algorithm;
s3 updating the parameter gamma to be estimated by using EM algorithmjJ is 1,2 … N, and the target number optimal solution K is obtained*Updating the noise power σ0；
S4 updating dictionary matrix A by gradient descent method
Figure BDA0002382349640000091
S5 determines when the algorithm iteration converges and determines the incoming wave direction and number.
FIG. 2 is a spatial power spectrum of the method of the present invention and classical LASSO, RVM and Atomic Norm algorithms. The simulation is based on a uniform linear array with array elements of 16 and half-wavelength intervals. Consider two incoherent targets emitting signals incident on the array at-5 ° and 15.5 ° positions, respectively, with the signal-to-noise ratios of the target signals both being-10 dB, for a total of 50 collected samples received by the array. The four algorithms all adopt the same space grid division and dictionary matrix, namely, the division of 1-degree interval is carried out on the angle space ranging from-45 degrees to 45 degrees. As can be seen from the figure, the space universality of the four algorithms has a peak value at a target position, the LASSO algorithm has the narrowest peak value, the Atomic Norm algorithm is next to the LASSO algorithm, the RVM algorithm has the widest peak value, and the algorithm has the peak width in the middle of the Atomic Norm and the RVM algorithm. Therefore, an accurate angle estimation result can be obtained by the pole detection method.
FIG. 3 shows the variation of estimation accuracy with SNR for the Atomic Norm algorithm, the present algorithm, and the present algorithm without the S4 step. The estimation accuracy is represented by the root mean square error of the angle estimation value of 50 times of simulation, and the expression is
Figure BDA0002382349640000092
Here, the
Figure BDA0002382349640000093
The angle estimate from the i-th simulation is shown. As can be seen, the algorithm of the present invention performed better than the Atomic Norm algorithm and the algorithm without the S4 step in the tests of the two sets of targets (angles of-5 °, 15.5 ° and 5 °, 30.2 °, respectively), especially in the signal-to-noise comparisonThe performance is better at low.
Fig. 4 shows the variation of the estimation accuracy with the number of samples collected in the four methods, where the snr is-10 dB, (a) the target angle is 5 ° and 30 °, and (b) the target angle is-5 ° and 15 °. As can be seen, the RMSE exhibited a decreasing trend for all four methods as the number of samples increased. The RVM algorithm has the best estimation precision under the condition of small samples, but as the RMSE decreases slowly with the increase of the number of samples, the method disclosed by the invention has the performance similar to that of the LASSO algorithm.
FIG. 5 is a graph showing comparison of the operation time with the number of samples. The calculation complexity of each algorithm is measured by the operation time, the number of the array elements is 16, the SNR is-5 dB, the grid interval is 1 degree, and the two target incidence angles are respectively 5 degrees and 30.2 degrees. As can be seen, the computation time increases as the number of samples increases, but the computation time of the method of the present invention is orders of magnitude longer than that of LASSO, RVM and Atomic Norm algorithms. Comparing fig. 3, it can be seen that the addition of the gradient descent algorithm only slightly increases the operation time, but the DOA estimation accuracy is significantly increased.
Fig. 6 is a comparison graph of the number of array elements 10 in addition to fig. 5, showing the change in the operation time with the number of samples. Comparing with fig. 5, it can be seen that the calculation time of each algorithm is obviously reduced as the number of array elements is reduced, and the algorithm of the present invention is superior to other algorithms at all.
Fig. 7 is a comparison graph of the operation time obtained by changing the angle division interval to 0.5 ° on the basis of fig. 5 as a function of the number of samples. As can be seen from comparison of FIG. 5, the grid precision has a significant influence on the operation time, the operation time of each algorithm is greatly increased, but the operation time of the algorithm of the invention is still significantly lower than that of other algorithms.
The simulation-based experimental result shows that the algorithm has strong robustness on noise, is still effective on small sample data, has obviously higher operation efficiency and angle estimation precision than the traditional method, and meets the requirement of real-time target angle estimation. The method can realize the accurate estimation of the incident angle of multiple targets under the condition that the quality of radar echo data is limited, and particularly provides technical support for missile defense and space target identification in space target monitoring under the condition of strong confrontation, and has high engineering application value.

Claims (6)

1. An estimation method of an out-of-grid target angle based on approximate message passing, the method comprising the steps of:
s1 parameter gamma to be estimatedj，j＝1，2，…，N、σ0And initialization of dictionary matrix A
S1.1, constructing a dictionary matrix A, A according to the required target angle estimation resolution requirement, wherein the angle corresponding to each column of the A, A forms the gridding division of the AMP algorithm to the space angle, the denser the gridding division is, the higher the resolution of the angle estimation is, and the initial angle corresponding to the grid is recorded as
Figure FDA0002382349630000011
S1.2 vs. γ ═ γ1γ2…γN]TAnd noise power σ0Carrying out initialization; initialisation to gamma on initialisation of gamma0I.e. the signal prior variances in the respective directions are equal, and the sampled received data Y from T different times is [ Y (1) Y (2) … Y (T)]，γ0And σ0This can be obtained from the following equation:
Figure FDA0002382349630000012
in the above formula, m is the number of array elements formed by antennas, | | … | | non-conducting phosphor2Representing the two-norm of the matrix, SNR representing the pre-estimated system signal-to-noise ratio, tr (…) representing the trace of the matrix, (…)HRepresents a conjugate transpose of the matrix;
s2 uses AMP algorithm to quickly obtain signal posterior probability density function of each time
S2.1, in accordance with the initialization result in S1, performs calculation for the received data y (T), T1, 2 … T at different times, by repeating steps S2.1.1 to S2.1.6 for each T, T1, 2 … T until the AMP algorithm converges for the data at time T. Such repetition steps need to be performed T times in total;
S2.1.1AMP parameter initialization: for each element of x, the initial estimated parameter values are set as follows
Figure FDA0002382349630000013
Here, the first and second liquid crystal display panels are,
Figure FDA0002382349630000014
to represent
Figure FDA0002382349630000015
The (j) th element of (a),
Figure FDA0002382349630000016
to represent
Figure FDA0002382349630000017
Initial value of the jth element of (1), xjThe jth element representing the x true,
Figure FDA0002382349630000018
presentation pair
Figure FDA0002382349630000019
The initial value obtained by the estimation is obtained,
Figure FDA00023823496300000110
representing the probability density function p (x)j|γj) To expect, p (x)j|γj) Is shown at known gammajValue of xjIs determined by the probability density function of (a),
Figure FDA00023823496300000111
presentation pair
Figure FDA00023823496300000112
An initial value obtained by estimation, k represents the kth iteration of the algorithm, and k is 0 and represents an initialization stepA step of;
suppose a probability density function p (x)j|γj) Is a zero mean Gaussian distribution, so we can get from (2)
Figure FDA00023823496300000113
S2.1.2 linear output step: for each i-1, 2 … m, calculate
Figure FDA00023823496300000114
In the above formula
Figure FDA0002382349630000021
Representing the process of the kth iteration of the algorithm
Figure FDA0002382349630000022
Value of aijThe element representing the ith row and jth column of the dictionary matrix A, (…)iRepresents the ith element of the vector, | … | represents the modulus of the complex number,
Figure FDA0002382349630000023
representing the process of the kth iteration of the algorithm
Figure FDA0002382349630000024
The value of the one or more of,
Figure FDA0002382349630000025
representing the process of the kth iteration of the algorithm
Figure FDA0002382349630000026
The value of the one or more of,
Figure FDA0002382349630000027
representing the process of the kth iteration of the algorithm
Figure FDA0002382349630000028
The value of the one or more of,
Figure FDA0002382349630000029
representing the process of the kth iteration of the algorithm
Figure FDA00023823496300000210
The value of the one or more of,
Figure FDA00023823496300000211
representing the process of the kth iteration of the algorithm
Figure FDA00023823496300000212
A value;
s2.1.3 nonlinear output step: for each i-1, 2 … m, calculate
Figure FDA00023823496300000213
yiThe i-th element representing the received data y,
Figure FDA00023823496300000214
representing the process of the kth iteration of the algorithm
Figure FDA00023823496300000215
The value of the one or more of,
Figure FDA00023823496300000216
indicating updating during the kth iteration of the algorithm
Figure FDA00023823496300000217
Value of (1), function of
Figure FDA00023823496300000218
S2.1.4 Linear input step: for each j ═ 1,2 … N, calculations were made
Figure FDA00023823496300000219
Figure FDA00023823496300000220
Representing the process of the kth iteration of the algorithm
Figure FDA00023823496300000221
The value of the one or more of,
Figure FDA00023823496300000222
representing the process of the kth iteration of the algorithm
Figure FDA00023823496300000223
Value, here (…)-1Representation matrix inversion (…)*Represents the conjugate of a complex number;
s2.1.5 nonlinear input step: for each j ═ 1,2 … N, calculations were made
Figure FDA00023823496300000224
Here, the
Figure FDA00023823496300000225
Representing the (k + 1) th iteration
Figure FDA00023823496300000226
The value of the one or more of,
Figure FDA00023823496300000227
representing the (k + 1) th iteration
Figure FDA00023823496300000228
Value, function of above
Figure FDA00023823496300000229
S2.1.6 determining whether the AMP algorithm converges: computing
Figure FDA00023823496300000230
Wherein … does not calculation1A 1-norm of the matrix is represented,
Figure FDA00023823496300000231
representing the (k + 1) th iteration
Figure FDA00023823496300000232
The values, in the same way,
Figure FDA00023823496300000233
representing the kth iteration
Figure FDA00023823496300000234
A value; if the value is greater than a set threshold epsilon1Then go back to S2.1.2 for reiteration; otherwise, the loop is skipped to S2.2 to obtain p (x)jResults of | y); threshold epsilon1The signal-to-noise ratio and other factors of the system are required to be adjusted according to actual conditions;
s2.2 through the steps, the posterior probability density function p (x) of the signal at the time t can be obtainedjResults of | y) are as follows
Figure FDA0002382349630000031
p(xj) Denotes xjA probability density function of; in the above formula
Figure FDA0002382349630000032
Is obtained by calculation according to the sample value y (t) at the time t in the step S2.1, and is obtained in the last iteration process after the AMP algorithm is judged to be converged
Figure FDA0002382349630000033
A value of (d); here gamma isjIs obtained from either S1 or S3, and in the first EM algorithm iteration, γ is obtainedjIs determined by the initial value in S1, and in other cases, γjIs calculated by the gamma calculated at S3 in the last EM algorithm cyclejDetermining;
s3 updating the parameter gamma to be estimated by using EM algorithmjJ is 1,2 … N, and the target number optimal solution K is obtained*Updating the noise power σ0
The posterior probability density function p (x) of the signal has been obtained in S2jY), according to the EM algorithm, this step updates the value of the parameter to be estimated one by one using the following expression
Figure FDA0002382349630000034
In the above formula, q ═ γ1…γNσ0]T，X＝[x(1) x(2)…x(T)]，N＝[n(1) n(2)…n(T)]，＜…|Y；qiDenotes that the known reception data Y ═ Y (1) Y (2) … Y (t)]And given parameter value qiIs averaged under the condition of (1), q in the above expressioniRepresents the value of q during the ith iteration of the algorithm, and qi+1Representing the q value in the (i + 1) th iteration of the algorithm; the method comprises the following steps:
s3.1 updating Gammaj,j＝1,2…N：
The pair gamma can be obtained by formula derivationjThe updated expression of j 1,2 … N is
Figure FDA0002382349630000035
In the above expression
Figure FDA0002382349630000036
Represents gamma in the ith iteration of the algorithmj，
Figure FDA0002382349630000037
Represents gamma in the (i + 1) th iteration of the algorithmj；
Further on gammajThe partial derivative can be obtained
Figure FDA0002382349630000038
S3.2 estimating target quantity optimal solution K*：
By using subspace analysis, the optimal solution of the target number is
Figure FDA0002382349630000039
Wherein I is a matrix of units and I is a matrix of units,
Figure FDA0002382349630000041
Figure FDA0002382349630000042
k is an estimate of the target quantity, K*Is the optimal solution of the K, and the K is the optimal solution,
Figure FDA0002382349630000043
corresponding assumed target angle in A
Figure FDA0002382349630000044
Is given a target angle
Figure FDA0002382349630000045
Refers to gammajJ is the angle corresponding to the largest K value in 1,2 … N;
s3.3 updating the noise Power σ0：
According to the formula:
Figure FDA0002382349630000046
wherein
Figure FDA0002382349630000047
Here, the
Figure FDA0002382349630000048
Is that
Figure FDA0002382349630000049
The covariance matrix of each column in (1), which can be obtained from the above equation
Figure FDA00023823496300000410
According to the mapping matrix P defined by S3.2, and P ═ PH＝P2Is obtained by
PRPH-σ0PPH＝ΣY-σ0I (18)
Combining tr (R-sigma)Y) 0 can deduce σ0The update formula of (2) is:
Figure FDA00023823496300000411
s4 updating dictionary matrix A by gradient descent method
Figure FDA00023823496300000412
Optimal solution K for target quantity calculated in S3.2*The target corresponding angle can be considered as γjJ is the first K in 1,2 … N*Maximum gammajCorresponding angle grid node
Figure FDA00023823496300000413
The angle grid nodes roughly corresponding to the targets are adjusted by using a gradient descent method, and it is noted that only the angle grid nodes currently corresponding to the targets need to be updated here
Figure FDA00023823496300000414
Without having to update the entire angle grid, to avoid high computational complexity, i.e. the angles corresponding to each target determined in S3.2
Figure FDA00023823496300000415
The iterative calculation of the step is carried out until the algorithm is converged, and the step S4 needs to execute K*Secondly; the update rule can be derived from
Figure FDA00023823496300000416
Wherein
Figure FDA00023823496300000417
A is a dictionary matrix with angle variables; from the above formula, the correlation
Figure FDA00023823496300000418
Gradient of (2)
Figure FDA00023823496300000419
Here, the
Figure FDA00023823496300000420
Representing the real part of the matrix, X is the estimate for X found by step S2,
Figure FDA00023823496300000421
is in A corresponds to a division
Figure FDA00023823496300000422
Outside angle
Figure FDA00023823496300000423
A matrix of a plurality of columns of (a),
Figure FDA00023823496300000424
corresponding to division in representation X
Figure FDA00023823496300000425
Outside angle
Figure FDA00023823496300000426
A matrix of rows of (a) is formed,
Figure FDA00023823496300000427
corresponding to angle in representation X
Figure FDA00023823496300000428
The matrix of rows of (a) is,
Figure FDA00023823496300000429
is the column vector in A, d (-) is the derivative of a (-);
pass through (21) type pair
Figure FDA00023823496300000430
Is optimized by
Figure FDA0002382349630000051
α, the step size of the angle update depends on the accuracy requirement of the angle estimation in practical application, (. degree)lThe value representing the ith iteration of this step, which is equal to 1 if the input of the function sign (·) is positive, and-1 otherwise;
after one-time angle updating is completed, whether convergence exists needs to be judged; considering that the initial dictionary grid may already meet the accuracy requirement, the number of iterations in this step is not too large, and when the condition is met
Figure FDA0002382349630000052
Or l is ≧ epsilon4When it is, consider to
Figure FDA0002382349630000053
Has satisfied the requirement, exits the loop, ε3、ε4Is a decision threshold; wherein epsilon3The method can be determined according to the precision requirement of the system on angle estimation; epsilon4The real-time performance of the algorithm is determined according to the real-time performance requirement of the system, and the larger the value is, the lower the real-time performance of the algorithm is;
s5 judges when the iterative process of the algorithm converges, and determines the direction and quantity of the incoming wave
Finish γ ═ γ1γ2...γN]TAnd σ0After updating, convergence is judged by the following expression:
Figure FDA0002382349630000054
ε2the threshold can be set according to the system practice for judging the threshold; if the above expression is not satisfied, returning to S2 to continue the iterative operation; if the above formula is true, the loop can be exited, and the number of incoming waves is the last calculated K*In the direction of [ gamma ] - [ gamma ]1γ2…γN]TMiddle front K*Maximum gammajCorresponding direction
Figure FDA0002382349630000055
2. The fast target angle estimation method based on sparse Bayesian learning as recited in claim 1, wherein: in S1.1, the space angle is divided into grids by adopting equal-interval division of a full-angle space.
3. The approximate messaging based off-grid target angle estimation method according to claim 1 or 2, wherein: s2.1.6, threshold ε1Is between 0.1 and 0.001.
4. A device according to claim 1 or 2, based onThe approximate message passing non-grid target angle estimation method is characterized by comprising the following steps of: at S4, a decision threshold ε3The value is 0.1 deg.
5. The approximate messaging based off-grid target angle estimation method according to claim 1 or 2, wherein: at S4, a decision threshold ε4The value is 1000.
6. The approximate messaging based off-grid target angle estimation method according to claim 1 or 2, wherein: in S5, a decision threshold ε2The value is between 0.1 and 0.001.
CN202010086824.0A 2020-02-11 2020-02-11 Approximate message transfer-based non-grid target angle estimation method Active CN111257845B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010086824.0A CN111257845B (en) 2020-02-11 2020-02-11 Approximate message transfer-based non-grid target angle estimation method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010086824.0A CN111257845B (en) 2020-02-11 2020-02-11 Approximate message transfer-based non-grid target angle estimation method

Publications (2)

Publication Number Publication Date
CN111257845A true CN111257845A (en) 2020-06-09
CN111257845B CN111257845B (en) 2020-09-22

Family

ID=70945657

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010086824.0A Active CN111257845B (en) 2020-02-11 2020-02-11 Approximate message transfer-based non-grid target angle estimation method

Country Status (1)

Country Link
CN (1) CN111257845B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112346123A (en) * 2020-11-06 2021-02-09 中国地震灾害防御中心 VIA (visual analysis of seismic data) double-parameter analysis method
CN113281702A (en) * 2021-04-30 2021-08-20 中国人民解放军战略支援部队信息工程大学 Over-the-horizon target direct positioning method based on cooperative short wave multi-station angle and satellite time frequency
CN116879862A (en) * 2023-09-08 2023-10-13 西安电子科技大学 Single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration
CN117388791A (en) * 2023-09-13 2024-01-12 桂林电子科技大学 DOA estimation algorithm for broadband signal of 6GISCA system

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104375133A (en) * 2014-11-11 2015-02-25 西北大学 Estimation method for space two-dimensional DOA
KR101783777B1 (en) * 2016-05-17 2017-10-10 국방과학연구소 Method for estimating direction of arrival using covariance fitting
CN109116293A (en) * 2018-08-22 2019-01-01 上海师范大学 A kind of Wave arrival direction estimating method based on sparse Bayesian out of place
CN109490819A (en) * 2018-11-16 2019-03-19 南京邮电大学 A kind of Wave arrival direction estimating method out of place based on management loading
CN109658467A (en) * 2018-12-12 2019-04-19 浙江工业大学 A kind of endoscopic images sensing reconstructing method based on multiword allusion quotation modified compressed sensing framework
CN109752710A (en) * 2019-01-07 2019-05-14 中国人民解放军国防科技大学 Rapid target angle estimation method based on sparse Bayesian learning
CN110208735A (en) * 2019-06-12 2019-09-06 西北工业大学 A kind of DOA Estimation in Coherent Signal method based on management loading

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104375133A (en) * 2014-11-11 2015-02-25 西北大学 Estimation method for space two-dimensional DOA
KR101783777B1 (en) * 2016-05-17 2017-10-10 국방과학연구소 Method for estimating direction of arrival using covariance fitting
CN109116293A (en) * 2018-08-22 2019-01-01 上海师范大学 A kind of Wave arrival direction estimating method based on sparse Bayesian out of place
CN109490819A (en) * 2018-11-16 2019-03-19 南京邮电大学 A kind of Wave arrival direction estimating method out of place based on management loading
CN109658467A (en) * 2018-12-12 2019-04-19 浙江工业大学 A kind of endoscopic images sensing reconstructing method based on multiword allusion quotation modified compressed sensing framework
CN109752710A (en) * 2019-01-07 2019-05-14 中国人民解放军国防科技大学 Rapid target angle estimation method based on sparse Bayesian learning
CN110208735A (en) * 2019-06-12 2019-09-06 西北工业大学 A kind of DOA Estimation in Coherent Signal method based on management loading

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Z.M.LIU等: "An effeicient maximum likelihood method for direction of arrival estimation via sparse bayesian learning", 《IEEE TRANS. WIRELESS COMMUNICATIONS》 *
刘本源: "快速块稀疏贝叶斯学习算法的理论与应用", 《中国博士学位论文全文数据库 信息科技辑》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112346123A (en) * 2020-11-06 2021-02-09 中国地震灾害防御中心 VIA (visual analysis of seismic data) double-parameter analysis method
CN113281702A (en) * 2021-04-30 2021-08-20 中国人民解放军战略支援部队信息工程大学 Over-the-horizon target direct positioning method based on cooperative short wave multi-station angle and satellite time frequency
CN113281702B (en) * 2021-04-30 2024-02-09 中国人民解放军战略支援部队信息工程大学 Method for directly positioning beyond-view-range target by cooperating short-wave multi-station angle with satellite time frequency
CN116879862A (en) * 2023-09-08 2023-10-13 西安电子科技大学 Single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration
CN116879862B (en) * 2023-09-08 2023-12-01 西安电子科技大学 Single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration
CN117388791A (en) * 2023-09-13 2024-01-12 桂林电子科技大学 DOA estimation algorithm for broadband signal of 6GISCA system

Also Published As

Publication number Publication date
CN111257845B (en) 2020-09-22

Similar Documents

Publication Publication Date Title
CN111257845B (en) Approximate message transfer-based non-grid target angle estimation method
WO2018094565A1 (en) Method and device for beamforming under pulse noise
CN109490819B (en) Sparse Bayesian learning-based method for estimating direction of arrival of wave in a lattice
CN106646344B (en) A kind of Wave arrival direction estimating method using relatively prime battle array
CN108802683B (en) Source positioning method based on sparse Bayesian learning
CN107450045B (en) DOA estimation method based on FOCUSS secondary weighting algorithm
CN108872926B (en) Amplitude-phase error correction and DOA estimation method based on convex optimization
CN109239649B (en) Novel co-prime array DOA estimation method under array error condition
CN110244272B (en) Direction-of-arrival estimation method based on rank-denoising model
CN111337873A (en) DOA estimation method based on sparse array
CN114720938A (en) Large-scale antenna array single-bit sampling DOA estimation method based on depth expansion
CN117092585B (en) Single-bit quantized DoA estimation method, system and intelligent terminal
CN109783960B (en) Direction-of-arrival estimation method based on grid part refinement
CN115236584A (en) Meter-wave radar low elevation angle estimation method based on deep learning
CN116224219A (en) Array error self-correction atomic norm minimization DOA estimation method
CN112731273B (en) Low-complexity signal direction-of-arrival estimation method based on sparse Bayesian
CN113759303B (en) Gridless angle of arrival estimation method based on particle swarm optimization
CN111880143B (en) High-precision positioning method, storage medium and equipment for improving sparse Bayesian learning
Yang et al. A correlation-aware sparse Bayesian perspective for DOA estimation with off-grid sources
CN116299193A (en) MIMO radar intelligent DOA estimation method
CN115015832A (en) Large-scale array amplitude-phase error and target direction joint estimation method under non-uniform noise
CN114415106A (en) Mutual coupling array DOA estimation method based on improved LAMP network
Tan et al. An iterative adaptive dictionary learning approach for multiple snapshot DOA estimation
CN110471026B (en) Phase-enhanced meter-wave radar target low elevation DOA estimation method
CN109298384B (en) Non-uniform linear array direction of arrival angle estimation method based on variational Bayes inference

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