CN110412499B - Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory - Google Patents

Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory Download PDF

Info

Publication number
CN110412499B
CN110412499B CN201910638851.1A CN201910638851A CN110412499B CN 110412499 B CN110412499 B CN 110412499B CN 201910638851 A CN201910638851 A CN 201910638851A CN 110412499 B CN110412499 B CN 110412499B
Authority
CN
China
Prior art keywords
matrix
signal
focusing
estimation
array
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910638851.1A
Other languages
Chinese (zh)
Other versions
CN110412499A (en
Inventor
窦慧晶
梁霄
张文倩
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 Technology
Original Assignee
Beijing University of 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 Beijing University of Technology filed Critical Beijing University of Technology
Priority to CN201910638851.1A priority Critical patent/CN110412499B/en
Publication of CN110412499A publication Critical patent/CN110412499A/en
Application granted granted Critical
Publication of CN110412499B publication Critical patent/CN110412499B/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
    • G01S3/04—Details
    • G01S3/10—Means for reducing or compensating for quadrantal, site, or like errors
    • 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
    • G01S3/04—Details
    • G01S3/12—Means for determining sense of direction, e.g. by combining signals from directional antenna or goniometer search coil with those from non-directional antenna
    • 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
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • 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

A broadband DOA estimation algorithm based on an RSS algorithm under a compressed sensing theory belongs to the relevant fields of array signal processing, radar detection and the like. The invention samples the signal at a rate far lower than the Nyquist sampling theorem requirement under the condition of ensuring no information loss, and can completely recover the signal at the same time. The invention realizes 'sharing' of data at each frequency point and data at the reference frequency point, thereby avoiding the azimuth pre-estimation and improving the estimation precision. The invention combines the compressed sensing theory and DOA estimation, divides the broadband signals into the narrowband signals by using the focusing idea, and solves the problem by using the narrowband idea, thereby greatly reducing the huge calculation amount of the original broadband estimation. The estimation accuracy is improved on the premise of the same sampling.

Description

Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory
Technical Field
The invention relates to a direction of arrival (DOA) estimation algorithm, which is applied to tasks such as wireless communication, medical imaging, electronic countermeasure and the like and can automatically complete the estimation of a one-dimensional direction of arrival angle. The invention belongs to the relevant fields of array signal processing, radar detection and the like.
Background
The array signal processing is also called airspace signal processing, is an important branch of modern signal processing, is commonly used in the fields of mobile satellite communication, seismic monitoring, radio astronomy, national economy and the like, and is widely researched and developed. The array signal processing is mainly to place a group of sensors at different positions in space in a fixed mode, perform corresponding data processing and theoretical analysis on signals received by the sensors, extract useful signals in electromagnetic signals and suppress noise and interference signals.
The most fundamental problem in the field of array signal processing is the estimation of the direction of arrival (DOA) of a spatial signal, and the energy distribution of a signal source in all directions in the space can be represented by its spatial spectrum, i.e. the spatial spectrum represents the direction of arrival of the signal. DOA estimation is to determine the spatial positions of a plurality of interested signals in a space by using an array signal processing method according to the signals received by an array antenna in a complex electromagnetic environment, and further to obtain the direction angles of the signals reaching the array. The DOA estimation has very important research value and application value, is widely applied to radar and communication systems, and has become a hotspot of research in the field of array signal processing.
The DOA estimation theory is researched and developed for decades, and a relatively perfect theoretical system and a classical algorithm are formed. Currently, the high-resolution DOA estimation algorithm is mainly classified into three types: the first is a linear prediction algorithm represented by a Capon adaptive beam forming method, and a space spectrum of a signal is obtained by improving utilization information of the signal to form an expected beam shape; the second is a subspace decomposition algorithm represented by multiple signal classification (MUSIC), and a high-resolution spatial spectrum peak is constructed according to subspace decomposition and spans to a new field of DOA estimation; the third is subspace fitting algorithm represented by Maximum Likelihood (ML) algorithm, which needs to search multi-dimensional spectral peaks, and has excellent statistical performance, but the operation is complex and needs appropriate initial values. The classical DOA estimation algorithms have certain limitations when applied, cannot break through the limitation of subspace algorithms, cannot accurately estimate the direction of arrival when the signal-to-noise ratio is low, the snapshot is small and the space distance between information sources is small, and has certain limitation on practicability.
In recent years, with the appearance and continuous improvement of a compressed sensing theory system, the sparse signal reconstruction of the core theory thereof draws attention of scholars at home and abroad. The appearance of sparse theory and compressed sensing leads to a new direction of the space spectrum estimation problem, namely, a DOA estimation sparse model is established by utilizing the space domain sparse characteristic of signals, received signals are recovered by utilizing a sparse reconstruction algorithm, and the defects of the traditional DOA estimation algorithm are overcome. The compressed sensing is that a signal to be reconstructed is sparsely represented, sampling can be performed at a frequency lower than the signal bandwidth under a certain condition, and high-probability reconstruction or approximation of the signal can be realized only by a small amount of observation data, so that system resources are greatly saved. The DOA estimation method based on sparse representation is not affected by coherent signals and an array structure any more, the sampling number of the signals, the cost of data transmission, storage and processing are reduced, and the estimation performance of parameters is improved. The sparse signal reconstruction algorithm is used for space spectrum estimation, and a sparse reconstruction array signal parameter estimation method is explored by combining the sparsity of the array signal in the airspace, so that the practicability of the algorithm is improved, and the method has important theoretical value and development prospect.
Disclosure of Invention
The existing DOA estimation algorithm mainly has the defects of overlarge calculated amount, insufficient solving precision and the like, and in order to overcome the defects of the technology, the RSS algorithm based on the compressed sensing theory is provided, so that the calculated amount of the algorithm is reduced, and the anti-noise interference capability is improved.
In order to achieve the above object, the present invention comprises the steps of:
1) estimating the incoming wave direction of the signal by using a conventional low-resolution algorithm to obtain a DOA initial estimation set theta, and simultaneously determining a reference frequency point f0。
2) Constructing an array flow pattern matrix A (f) of all sub-bands according to the initial value theta of DOAjθ) to obtain a focus transform matrix T (f) for all sub-bandsj)；
3) Using a focus transform array T (f)j) Receiving data X (f) from the array on the corresponding sub-bandj) Converting to a focusing frequency point to obtain array output data Y (f) at the frequency pointj) And a correlation matrix Ry(fj)；
4) Correlating the transformed data with an array R by frequency domain smoothingy(fj) Constructing a uniform array correlation matrix R on reference frequency pointsY；
5) Obtaining a final estimated value of the DOA by utilizing an L1-SVD algorithm based on compressed sensing;
the invention combines the compressed sensing theory and the traditional DOA estimation to achieve the following beneficial effects:
1. the traditional Nyquist sampling theorem states that in order to avoid signal distortion, the sampling frequency of a band-limited signal must be more than twice its bandwidth, however, as the signal bandwidth becomes wider and wider with increasing current information demand, a large amount of acquired data needs to be compressed, stored and transmitted, all of which pose higher challenges to signal processing hardware systems; the invention can sample the signal at a rate far lower than the Nyquist sampling theorem without losing information, and can completely recover the signal. The presence of compressed sensing allows the signal to be sampled at a rate well below that required by the Nyquist sampling theorem, while allowing the signal to be fully recovered, while ensuring that no information is lost.
2. In the focus change CSSM-like algorithms, such as ISSM, TCT, and MTLS-CSSM, it is not possible to avoid first obtaining a pre-estimated value of the source bearing angle before focusing, and then calculating the necessary focus matrix for the focusing operation. When the deviation between the predicted value and the true value of the focusing matrix in the selected area is large, the azimuth estimation error is easily caused, and the improved algorithm realizes 'sharing' of data at each frequency point and data at a reference frequency point, so that the azimuth prediction is avoided, and the estimation precision is improved.
3. The compressed sensing theory and DOA estimation are combined, the focus idea is utilized to divide the broadband signals into the narrowband signals, the narrowband idea is utilized to solve, and the huge calculation amount of the original broadband estimation is greatly reduced. The estimation accuracy is improved on the premise of the same sampling.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention
FIG. 2 compressed sensing measurement Process 1
FIG. 3 compressed sensing measurement Process 2
FIG. 4 is a graph showing the variation of success rate according to the variation of signal-to-noise ratio
FIG. 5 is a graph showing the variation of the root mean square error with the variation of the signal-to-noise ratio
FIG. 6 is a graph showing the variation of the success rate of the algorithm with the variation of the number of snapshots
FIG. 7 is a graph showing the variation of root mean square error with the variation of snapshot count
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative only and should not be construed as limiting the invention.
FIG. 1 shows a flow chart of the present invention: estimating the incoming wave direction of the signal by using a conventional low-resolution algorithm to obtain a DOA initial estimation set theta, and simultaneously determining a reference frequency point f0. The specific method comprises the following steps: and establishing constraint between the focused direction matrix and the direction matrix on the focusing frequency, focusing the sub-band signals except the focusing frequency in the bandwidth on the reference frequency under the condition of ensuring the minimum focusing construction error, and finally performing spatial spectrum estimation on the focused overall frequency domain signal. Assuming that the frequency domain array receives the signal as follows, T (f)j) And Y (f)j) Respectively representing a center frequency of fjAnd a signal direction matrix A (f) of the corresponding frequencyjθ) multiplication of the signals to a focus frequency f0The method comprises the following steps:
T(fj)Y(fj)＝T(fj)A(fj,θ)S(fj)＝A(f0)S(fj) (1)
wherein A (f)jθ) and A (f)0Theta) are respectively the frequency points fjAnd a reference frequency point f0Array prevalence matrix of (d), S (f)j) Is fjThe source data of (1).
Considering the case of selecting the optimal condition, the equation (1) is converted into a fitting form of the F-norm:
Figure BDA0002131191500000041
in the focusing matrix
Figure BDA0002131191500000042
In the case of satisfying the unitary matrix, that is:
Figure BDA0002131191500000043
wherein I is an identity matrix
Figure BDA0002131191500000044
Is composed of
Figure BDA0002131191500000045
The transpose matrix of (2) is combined to obtain the optimal optimization equation set:
Figure BDA0002131191500000046
where J is a natural number to solve one solution of equation set (3):
T(fj)＝V(fj)UH(fj) (4)
in the formula V (f)j)、U(fj) Are respectively A (f)j,θ)AH(fjLeft and right singular vectors U of θ)H(fj) Is U (f)j) The transposing of (1). At a focusing frequency f0From the viewpoint of focusing accuracy, the frequency having the smallest focusing error as a whole is selected as the focusing frequency, and the method obtains the focusing error epsilon of the whole broadband according to the formula (4):
Figure BDA0002131191500000047
where Re { tr } represents the ordering of the matrix, where | · |. does not calculationFExpressed as the Frobenius norm, can be reduced to the constant MK, where K is a constant representing the constraint on signal sparsity and M is the matrix dimension.
Figure BDA0002131191500000048
Bringing formula (6) into formula (5) can yield:
Figure BDA0002131191500000049
wherein J is the number of effective frequency points, lambdak[A(f0,θ)AH(fj,θ)]Is A (f)0,θ)AH(fjTheta) singular value ofH(f0Theta) is A (f)0θ). In the case where the first polynomial expression in the expression (7) is constant, if epsilon is to be secured to a minimum value close to zero, it is necessary that the second polynomial expression can be satisfied when the second polynomial expression is maximized. Is provided with
Figure BDA0002131191500000051
In the case where K is less than M thousandths, δ satisfies the inequality (8) where λkThe characteristic value is represented.
Figure BDA0002131191500000052
Order to
Figure BDA0002131191500000053
Then
Figure BDA0002131191500000054
By processing the narrow-band data on the corresponding sub-band using the focusing matrix, the following can be obtained:
Y(fj)＝T(fj)X(fj)＝A(f0,θ)S(fj)+T(fj)N(fj) (10)
the direct use of the focus transformation criterion in equation (10) to solve the focus matrix presents two problems, one is that no noise-free source data can be obtained directly
Figure BDA0002131191500000055
And S (f)0) (ii) a Secondly, an orientation pre-estimated value is needed to carry out array flow pattern matrix
Figure BDA0002131191500000056
And A (f)0And theta) is estimated. By utilizing the arrays among different frequency points to receive mutual information and self information of data, the problems can be avoided. For this purpose, two matrix variables, a cross-correlation matrix R (f), are introducedj,f0) And a noise-free covariance matrix P (f)0) Respectively for characterizing mutual information and self-information:
R(fj,f0)＝A(fj,θ)S(fj)·SH(f0)AH(f0)/L (11)
P(f0)＝A(f0,θ)S(f0)SH(f0)AH(f0)/L (12)
wherein R (f)j,f0)∈CM×MRepresenting frequency point fjAt and reference frequency f0Process data X (f)j) And X (f)0) Cross covariance matrix between; p (f)0)∈CM×MThen this indicates that reference frequency f is referred to0Process data X (f)0) The noise-free covariance matrix of (a). Transform equation (10) by multiplying both sides by SH(f0)AH(f0) L, obtaining:
T(fj)A(fj,θ)S(fj)SH(f0)AH(f0)/L＝A(f0,θ)S(f0)SH(f0)AH(f0)/L (13)
substituting equations (11) and (12) into equation (13) above yields:
T(fj)·Ρ(fj,f0)＝P(f0) (14)
equation (14) is an equivalent focus transformation criterion to equation (10) in which the focus matrix is constructed without the need for an azimuth estimate by using the autocorrelation and cross-correlation information of the array received signals. We use equation (14) with a matrix:
P(fj)＝A(fj,θ)S(fj)SH(fj)AH(fj,θ)＝A(fj,θ)R(fj)AH(fj,θ) (15)
solving the focusing transformation, then solving the arithmetic mean value of the data cross-correlation matrix on each sub-frequency band after the transformation, namely realizing frequency domain smoothing, and obtaining the transformed data correlation matrix RY：
Figure BDA0002131191500000061
Wherein R isY∈CM×MThe covariance matrix of the array samples after the focusing smoothing process is called the total sample covariance matrix. As can be seen from the flowchart in FIG. 1, the focused overall sample covariance matrix R should be estimated next using the high-resolution spatial spectrum estimation algorithm of the narrow-band spatial classYProcessing to obtain a sample covariance matrix RYObtaining a final estimation value of the DOA by using a classic L1-SVD algorithm based on a compressive sensing theory;
the compressed sensing theory process is shown in fig. 2 and 3, and utilizes M × N (M)<<Directly multiplying the N) -dimensional observation matrix phi by the signals to obtain M non-adaptive linear projection measurement values y ═ y (1),. y (M)]T,M<<N, K represents that the number of the measurement samples is far smaller than the dimension of the signal (far smaller than the dimension representing that the two differ by more than one hundred times, which is the case without special description in the whole text), and K is satisfied<M, M is more than or equal to cK log (N/K), c is an infinite constant tending to zero, and the mathematical expression is as follows:
y＝Φx (17)
for one RNOne dimensional time-scattered signal x of space, assuming that there are M N-dimensional basis vectors
Figure BDA0002131191500000062
Forming an nxn dimensional basis matrix Ψ, signal x can be represented as:
Figure BDA0002131191500000063
where s contains only K (K < < N) non-zero values, signal x is said to be compressible. Observing the compressible signal by using an M multiplied by N (M < < N) observation matrix phi, wherein the expression is as follows:
y＝Φx＝ΦΨs＝Θs (19)
the matrix measurement procedure is as shown, where Φ ═ RM×NFor the measurement matrix, Ψ ═ RN×NFor sparse representation matrices of signals, s ═ RN×1For sparse representation of coefficients, y ═ RM×1For the measurement matrix, Θ ═ RM×NFor a dictionary consisting of measurement matrices and sparse representation matrices, Θ must satisfy the finite equidistant Property (RIP) Property, i.e. select an observation matrix Φ that is not related to the exchange basis Ψ.
In order to prove the effectiveness of the algorithm, a classical MUSIC algorithm, an RSS algorithm and the algorithm are selected for comparison. Firstly, comparing the success rate change and the root mean square error change of the three algorithms when the signal-to-noise ratio changes, wherein the number of snapshots is set as 100 and is kept constant in the experiment, and the signal-to-noise ratio changes from-10 dB to 10dB at an interval of 2 dB. In order to ensure the accuracy of the test, 20 experiments are carried out for each fast beat, and the experimental results are shown in fig. 4 and fig. 5. The success rate of the three algorithms is increased and the root mean square error is reduced when the signal-to-noise ratio is increased, and the longitudinal comparison shows that the algorithm performance of the invention is superior to that of the other two algorithms in the success rate and the root mean square error.
Secondly, the success rate change of the three algorithms along with the change of the fast beat number is compared with the success rate change of the three algorithms along with the change of the fast beat number, the signal-to-noise ratio in a root-mean-square error change test is set to be 10dB and kept constant, and the fast beat number is changed at 10 intervals from 20 to 200. In order to ensure the accuracy of the test, 20 experiments are carried out for each fast beat, and the experimental results are shown in fig. 5 and fig. 6. The success rate of the three algorithms is increased and the root mean square error is reduced when the number of snapshots is increased through a result graph, and the longitudinal comparison shows that the performance of the algorithm is superior to that of the other two algorithms in the success rate and the root mean square error.

Claims (2)

1. The broadband DOA estimation algorithm based on the RSS algorithm under the compressed sensing theory is characterized in that:
1) estimating the incoming wave direction of the signal by using a low-resolution algorithm to obtain a DOA initial estimation set theta, and simultaneously determining a reference frequency point f0；
2) Constructing an array flow pattern matrix A (f) of all sub-bands according to the initial value theta of DOAjθ) to obtain a focus transform matrix T (f) for all sub-bandsj)；
3) Using a focus transform array T (f)j) Receiving data X (f) from the array on the corresponding sub-bandj) Converting to a focusing frequency point to obtain array output data Y (f) at the frequency pointj) And a correlation matrix Ry(fj)；
4) Correlating the transformed data with an array R by frequency domain smoothingy(fj) Constructing an overall sample covariance matrix R on reference frequency pointsY；
5) And obtaining a final estimated value of the DOA by utilizing an L1-SVD algorithm based on compressed sensing.
2. The algorithm of claim 1, wherein:
estimating the incoming wave direction of the signal by using a low-resolution algorithm to obtain a DOA initial estimation set theta, and simultaneously determining a reference frequency point f0(ii) a The specific method comprises the following steps: establishing constraint between the focused direction matrix and the direction matrix on the focusing frequency, focusing sub-band signals except the focusing frequency in a bandwidth on a reference frequency under the condition of ensuring the minimum focusing construction error, and finally performing spatial spectrum estimation on the focused overall frequency domain signal; assuming that the frequency domain array receives the signal as follows, T (f)j) And Y (f)j) Respectively representing a center frequency of fjAnd a signal direction matrix A (f) of the corresponding frequencyjTheta) multiplication, mapping the signal to a reference frequency point f0The method comprises the following steps:
T(fj)Y(fj)＝T(fj)A(fj,θ)S(fj)＝A(f0)S(fj) (1)
wherein A (f)jθ) and A (f)0Theta) are eachFrequency point fjAnd a reference frequency point f0Array prevalence matrix of (d), S (f)j) Is fjSource data of the site;
considering the case of selecting the optimal condition, the equation (1) is converted into a fitting form of the F-norm:
Figure FDA0003102663320000011
in the focusing matrix
Figure FDA0003102663320000021
In the case of satisfying the unitary matrix, that is:
Figure FDA0003102663320000022
wherein I is an identity matrix
Figure FDA0003102663320000023
Is composed of
Figure FDA0003102663320000024
The transpose matrix of (2) is combined to obtain the optimal optimization equation set:
Figure FDA0003102663320000025
where J is a natural number to solve one solution of equation set (3):
T(fj)＝V(fj)UH(fj) (4)
in the formula V (f)j)、U(fj) Are respectively A (f)j,θ)AH(fjLeft and right singular vectors U of θ)H(fj) Is U (f)j) Transposing; at reference frequency point f0From the viewpoint of focusing accuracy, the frequency having the smallest focusing error as a whole is selected as the focusing frequency, and the method obtains the focusing error of the whole broadband according to the formula (4)ε：
Figure FDA0003102663320000026
Where Re { tr } represents the ordering of the matrix, where | · |. does not calculationFExpressed as Frobenius norm, simplified to constant MK, where K is a constant and expresses the constraint on signal sparsity, and M is the matrix dimension;
Figure FDA0003102663320000027
wherein, a (f)j，θk) Denotes fjAnd (3) carrying formula (6) into formula (5) to obtain a steering vector at the frequency point:
Figure FDA0003102663320000028
wherein J is the number of effective frequency points, lambdak[A(f0,θ)AH(fj,θ)]Is A (f)0,θ)AH(fjTheta) singular value ofH(f0Theta) is A (f)0θ) transposing; in the case where the first polynomial in equation (7) is constant, if epsilon is to be guaranteed to be a minimum value tending to zero, it is necessary that the second polynomial can be satisfied if the second polynomial is maximized; is provided with
Figure FDA0003102663320000029
In the case where K is less than M thousandths, δ satisfies the inequality (8) where λkRepresenting a characteristic value;
Figure FDA0003102663320000031
order to
Figure FDA0003102663320000032
Then
Figure FDA0003102663320000033
Applying the focusing matrix to process narrow-band data on corresponding sub-bands to obtain:
Y(fj)＝T(fj)X(fj)＝A(f0,θ)S(fj)+T(fj)N(fj) (10)
wherein N (f)j) Representing a matrix of noisy data, now incorporating two matrix variables, a cross-correlation matrix R (f)j,f0) And a noise-free covariance matrix P (f)0) Respectively for characterizing mutual information and self-information:
R(fj,f0)＝A(fj,θ)S(fj)·SH(f0)AH(f0)/L (11)
P(f0)＝A(f0,θ)S(f0)SH(f0)AH(f0)/L (12)
wherein R (f)j,f0)∈CM×MRepresenting frequency point fjPosition and reference frequency point f0Process data X (f)j) And X (f)0) Cross covariance matrix between; p (f)0)∈CM×MThen it indicates that the reference frequency point f is concerned0Process data X (f)0) A noise-free covariance matrix of (a); l represents the number of array elements; a (f)0) Denotes f0The array at the frequency point is a popular matrix. Transform equation (10) by multiplying both sides by SH(f0)AH(f0) L, obtaining:
T(fj)A(fj,θ)S(fj)SH(f0)AH(f0)/L＝A(f0,θ)S(f0)SH(f0)AH(f0)/L (13)
substituting equations (11) and (12) into equation (13) above yields:
T(fj)·Ρ(fj,f0)＝P(f0) (14)
equation (14) is a focus transformation criterion equivalent to equation (10), under which a focus matrix can be constructed without an azimuth estimate by using autocorrelation and cross-correlation information of array received signals; equation (14) is used with a matrix:
P(fj)＝A(fj,θ)S(fj)SH(fj)AH(fj,θ)＝A(fj,θ)R(fj)AH(fj,θ) (15)
wherein R (f)j) Denotes fjCross correlation matrix at frequency points.
Solving the focusing transformation, and then solving the arithmetic mean value of the data cross-correlation matrix on each sub-frequency band after transformation, namely realizing frequency domain smoothing and obtaining RY：
Figure FDA0003102663320000041
Wherein R isY∈CM×MRepresenting an overall sample covariance matrix;
Figure FDA0003102663320000042
denotes fjAn estimate of the noise covariance matrix at the frequency point. Next, a high-resolution spatial spectrum estimation algorithm of narrow-band spatial class is used for RYProcessing is carried out, and a final estimation value of the broadband signal DOA is obtained by utilizing a classic L1-SVD algorithm based on a compressive sensing theory;
using M.times.N (M)<<Directly multiplying the N) -dimensional measurement matrix phi by the signals to obtain M non-adaptive linear projection measurement values y ═ y (1),. y (M)]T,M<<N, K represents that the number of measurement samples is far less than the dimension of the signal and satisfies K<M, M ≧ cKlog (N/K), c is an infinite constant tending to zero, and the mathematical expression is:
y＝Φx (17)
for oneRNOne dimensional time-scattered signal x of space, assuming that there are M N-dimensional basis vectors
Figure FDA0003102663320000043
An NxN-dimensional basis matrix Ψ is constructed, with signal x represented as:
Figure FDA0003102663320000044
where s contains only K (K < < N) non-zero values, signal x is said to be compressible; the compressible signal is observed by using an M multiplied by N (M < < N) measurement matrix phi, and the expression is as follows:
y＝Φx＝ΦΨs＝Θs (19)
wherein Φ ═ RM×NFor the measurement matrix, Ψ ═ RN×NFor sparse representation matrices of signals, s ═ RN×1For sparse representation of coefficients, y ═ RM×1For the measurement matrix, Θ ═ RM×NFor a dictionary consisting of measurement matrices and sparse representation matrices, Θ has to satisfy a finite equidistant distance, i.e. a measurement matrix Φ is chosen that is not related to the switch base Ψ.
CN201910638851.1A 2019-07-16 2019-07-16 Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory Active CN110412499B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910638851.1A CN110412499B (en) 2019-07-16 2019-07-16 Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910638851.1A CN110412499B (en) 2019-07-16 2019-07-16 Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory

Publications (2)

Publication Number Publication Date
CN110412499A CN110412499A (en) 2019-11-05
CN110412499B true CN110412499B (en) 2021-08-13

Family

ID=68361549

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910638851.1A Active CN110412499B (en) 2019-07-16 2019-07-16 Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory

Country Status (1)

Country Link
CN (1) CN110412499B (en)

Families Citing this family (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112272064B (en) * 2020-09-29 2021-07-06 电子科技大学 Detection probability and mutual information calculation method of cooperative MIMO radar
CN113987733A (en) * 2020-11-27 2022-01-28 猪草微(深圳)电子有限公司 Information source direction robust positioning algorithm based on linear prediction
CN112929303A (en) * 2021-01-21 2021-06-08 哈尔滨工程大学 Broadband compressed sensing direction-finding method of double-chain quantum charged system search mechanism
CN112946577B (en) * 2021-02-01 2023-12-22 东南大学 Ultra-short baseline underwater sound source positioning method based on broadband compressed sensing
CN114157538B (en) * 2021-11-22 2023-06-06 清华大学 Wireless signal arrival angle estimation method and system based on dual-channel receiver
CN116450993B (en) * 2023-04-24 2023-12-12 哈尔滨工业大学 Multi-measurement vector satellite data processing method, electronic equipment and storage medium

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106772226A (en) * 2016-12-26 2017-05-31 西安电子科技大学 DOA estimation method based on compressed sensing time-modulation array
CN107544051A (en) * 2017-09-08 2018-01-05 哈尔滨工业大学 Wave arrival direction estimating method of the nested array based on K R subspaces
WO2018035097A1 (en) * 2016-08-16 2018-02-22 Lockheed Martin Corporation Determination system for the direction of arrival of a signal and for electronic attack
CN109581277A (en) * 2018-11-29 2019-04-05 电子科技大学 A kind of four-dimensional antenna array DOA estimation method based on compressive sensing theory

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018035097A1 (en) * 2016-08-16 2018-02-22 Lockheed Martin Corporation Determination system for the direction of arrival of a signal and for electronic attack
CN106772226A (en) * 2016-12-26 2017-05-31 西安电子科技大学 DOA estimation method based on compressed sensing time-modulation array
CN107544051A (en) * 2017-09-08 2018-01-05 哈尔滨工业大学 Wave arrival direction estimating method of the nested array based on K R subspaces
CN109581277A (en) * 2018-11-29 2019-04-05 电子科技大学 A kind of four-dimensional antenna array DOA estimation method based on compressive sensing theory

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Compressed Sensing for DOA Estimation with Fewer Receivers than Sensors;Jian-Feng Gu et al.;《2011 IEEE》;20111231;第1752-1755页 *
基于压缩感知的宽频段二维DOA估计算法;沈志博等;《电子与信息学报》;20141231;第36卷(第12期);第2935-2941页 *

Also Published As

Publication number Publication date
CN110412499A (en) 2019-11-05

Similar Documents

Publication Publication Date Title
CN110412499B (en) Broadband DOA estimation algorithm based on RSS algorithm under compressed sensing theory
CN110109051B (en) Frequency control array-based cross coupling array DOA estimation method
CN107037392B (en) Degree-of-freedom increased type co-prime array direction-of-arrival estimation method based on compressed sensing
CN111123192B (en) Two-dimensional DOA positioning method based on circular array and virtual extension
CN104020439B (en) Direction of arrival angular estimation method based on space smoothing covariance matrix rarefaction representation
CN107817465A (en) The DOA estimation method based on mesh free compressed sensing under super-Gaussian noise background
CN107493106B (en) Frequency and angle joint estimation method based on compressed sensing
CN110398732B (en) Target direction detection method for low-calculation-quantity self-adaptive step size iterative search
Ahmad et al. Wideband DOA estimation based on incoherent signal subspace method
Zhang et al. An ℓ p-norm based method for off-grid doa estimation
Dakulagi et al. Smart antenna system for DOA estimation using single snapshot
CN114884841A (en) Underdetermined parameter joint estimation method based on high-order statistics and non-uniform array
CN113253192B (en) Inter-mass-array cascading DOA estimation method for non-circular signals
Dakulagi Single snapshot 2D-DOA estimation in wireless location system
Li et al. Direction estimation under compressive sensing framework: A review and experimental results
CN113567913A (en) Two-dimensional plane DOA estimation method based on iteration reweighting dimension reduction
Al-Sadoon et al. A more efficient AOA method for 2D and 3D direction estimation with arbitrary antenna array geometry
CN109507634B (en) Blind far-field signal direction-of-arrival estimation method based on propagation operator under any sensor array
Li et al. Sparse representation-based DOA estimation of coherent wideband LFM signals in FRFT domain
CN115236589B (en) Polar region under-ice DOA estimation method based on covariance matrix correction
CN115329261A (en) MIMO radar low elevation angle estimation method based on space smooth sparse reconstruction
CN110058192A (en) Atom norm mutual coupling DOA estimation method based on auxiliary array element
Yang et al. FRFT based method to estimate DOA for wideband signal
Luo et al. A novel aliasing-free subband information fusion approach for wideband sparse spectral estimation
CN108957386B (en) Incoherent direction of arrival estimation method under phase error

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