A line spectrum estimation method for two-dimensional blind source compressed signals

Abstract

The application provides a line spectrum estimation method for a two-dimensional blind source compressed signal. The blind source is reflected in that the number of effective signal sources is unknown, the azimuth angle is unknown, and the signal complex amplitude is also unknown. Signal data is obtained by a sensor and then compressed and added with noise to obtain detection data. According to the detection data, an approximate message passing method on a factor graph is used to respectively estimate the activated factor sequence and the approximate posterior probability of the signal complex amplitude, the signal angle value is obtained by using a positioning module, and then the estimation value of the signal source number and the signal complex amplitude is obtained according to the signal source number and the approximate posterior probability of the signal complex amplitude. Compared with the prior art, the advantages of the present application are as follows: first, compared with BIG-AMP, the algorithm has the advantage of not needing the prior distribution of the signal azimuth angle; second, compared with ESPRIT, the algorithm has the advantage of also providing an estimation of the signal complex amplitude; and third, compared with the AMP+ESPRIT algorithm, the algorithm has the advantage of allowing the signal source number to be unknown.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of compressed sensing and line spectrum estimation, and particularly relates to compressed sensing and line spectrum estimation of blind source compressed signals. BACKGROUND

[0002] Compressed sensing, also known as compressive sling or sparse sling, is a technology for finding a sparse solution of an underdetermined linear system, and is applied to electronic engineering, especially signal processing, for acquiring and reconstructing a sparse or compressible signal. Line spectrum estimation is a technology for signal processing, and is mainly used for estimating frequency components of a signal from data quantized by a noise-affected or low-precision quantizer.

[0003] In the problem of compressed sensing and line spectrum estimation, an original signal of N complex sinusoidal superpositions is compressed and added with noise by M sensors and L shots to obtain detection data Y, and the composition can be represented as:

[0004]

[0005] wherein represents an azimuth angle of a signal source, represents a vector composed of complex exponential functions of frequencies, represents a matrix composed of complex amplitudes, is a known conversion matrix, and represents noise influence

[0006] Compressed sensing is used for acquiring and reconstructing a sparse or compressible signal, and methods for solving the compressed sensing problem include OMP, CoSAMP, BP, ISTA and AMP (Approximate Message Passing). For greedy algorithms such as OMP and CoSAMP, their calculation efficiency is high, and they are suitable for signals with high sparsity, but they are sensitive to noise and need to set the sparsity in advance. For convex optimization algorithms such as BP and ISTA, a global optimal solution can be found, and they are suitable for large-scale problems, but the calculation complexity is high and they are sensitive to noise. Compared with other algorithms, the iteration number of the AMP algorithm is usually less, and a high reconstruction accuracy can be achieved in a small number of iterations.

[0007] Line spectrum estimation problem involves solving the original signal number, frequency and complex amplitude, the method for solving line spectrum estimation problem has periodogram method, MUSIC algorithm, ESPRIT algorithm and VALSE and MVALSE algorithm based on variational inference, for ESPRIT and MUSIC algorithm, under the condition that the number of signal sources N is known, the number of sensors is greater than the number of signal sources and the signal-to-noise ratio is high, but if the number of signal sources is unknown, it cannot be used.For VALSE and MVALSE algorithm, the accuracy of the estimated value of signal frequency and signal complex amplitude is poor, and the algorithm performance will decrease when the number of signal sources N increases. SUMMARY

[0008] The present application is to solve the problem that the prior art cannot accurately estimate the signal angle, complex amplitude and the number of signal sources under the condition that the detected data is interfered by noise, the number of signal sources is unknown, the azimuth angle is unknown, and the transmitted signal amplitude is also unknown, and provides a line spectrum estimation method for two-dimensional blind source compressed signal.

[0009] To achieve the purpose of the present application, the present application adopts the following technical solutions:

[0010] A line spectrum estimation method for two-dimensional blind source compressed signal, comprising the following steps:

[0011] S1, according to the given dimensional observation matrix and dimensional compression matrix , the following line spectrum estimation model about is constructed:

[0012] , , (1)

[0013] Among them, is the dimensional observation matrix, is the dimensional compression matrix, is the dimensional signal matrix to be compressed. and are the noise matrixes of dimension and dimension respectively, both of which are subject to independent Gaussian distribution with zero mean, wherein the variance of each element of the matrix is , the variance of each element of the matrix is . is the array manifold matrix of dimension with fixed structure, and the first element of the matrix is listed as and let

[0014] , (2)

[0015] wherein is the imaginary unit, is the natural constant. is a complex matrix of dimension

[0016] , (3)

[0017] wherein is a diagonal matrix of dimension with the activation factors as main diagonal elements, used to characterize the activation status of each potential signal source. is a complex amplitude matrix of dimension of all potential signal sources. is a column vector of dimension composed of activation factors, defined as Each activation factor is modeled as being independently subject to a Bernoulli binomial distribution with parameter , i.e.

[0018] (4)

[0019] denote the element of the complex matrix in the row and the column, modeled as being subject to a Gaussian-Bernoulli distribution with parameter , i.e. is subject to the following distribution

[0020] (5)

[0021] wherein denotes the Gaussian probability density function with mean 0 and variance , and denotes the Dirac impulse function.

[0022] S2, set the maximum number of iterations , let the iteration variable , assign initial values to the intermediate variables and ;

[0023] S3, add one to the iteration variable , i.e.​​ ;

[0024] S4, with and As input, the outer decompression module is called to obtain the first... The next iteration 3D matrix ;

[0025] S5, Order ,by and As input, the positioning module is invoked to calculate the angle. The estimated value And according to formula (2), use Alternative Constructing a matrix The estimated value ;

[0026] S6, with and As input, the inner decompression module is invoked to calculate matrix elements. With activators posterior probability estimate and And calculate as follows The estimated value

[0027] ;

[0028] S7, to ,calculate

[0029] (6)

[0030] in, express exist The value at time. If Let the value be greater than or equal to 0, and let estimator Set to 1; if the value is less than 0, let Set to 0. Equal to activation sequence The number of non-zero elements in the array. Calculate.

[0031] (7)

[0032] S8. Repeat steps S3 to S7 until the iteration variable is reached. Output angle estimate Signal complex amplitude estimation value and the estimated number of signal sources ;

[0033] As an improvement of the present application, in the step S4, an outer decompression module is called to eliminate the dependence of the algorithm on the observation matrix , specifically:

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] wherein, represents the element in the i-th row and the j-th column of the matrix , represents the element in the i-th row and the j-th column of the matrix , , , , , , , , are intermediate variables generated in iteration, the subscript = , the subscript = , and the subscript = . The initial value of the module is:

[0039] , , , ,

[0040] Let the output of the module be a matrix , and let the element in the i-th row and the j-th column of the matrix be ; The derivation of the algorithm uses a factor graph, and the specific derivation process is as follows:

[0041] S4.11, according to the attached

[0042] factor graph, the message from the factor node Figure 2 to the variable node is approximated to a Gaussian distribution using the message passing method of expectation propagation; ;

[0043] S4.12, according to the attached Figure 2 , the message from the variable node​ The message from the left source is represented as ;

[0044] S4.13, Based on variable nodes The messages from the left and the messages from the right will The approximate posterior probability is expressed as ;

[0045] S4.14, Taking the probability distribution mean constitute An equivalent model can be obtained based on the SE equation. ;

[0046] Among them, let The Line 1 Column elements are , Let x be the true prior distribution. Let represent the mean and variance of the Gaussian distribution, respectively. The noise matrix follows a Gaussian distribution.

[0047] As an improvement to the present invention, in step S5, based on the obtained equivalent data and the preset number of signal sources By calling the positioning module, an estimated value of the signal angle can be obtained, which in turn yields the array manifold matrix. Specifically:

[0048] S5.11 Calculate the covariance matrix The superscript * indicates taking the conjugate transpose of the matrix;

[0049] S5.12, For the matrix Perform eigenvalue decomposition, then sort the eigenvalues, and take... The eigenvectors corresponding to the largest eigenvalues ​​are arranged to form a matrix. ;

[0050] S5.13, take respectively The former Line and after line formation and ;

[0051] S5.14, Calculation superscript This represents finding the inverse of a matrix.

[0052] S5.15, to Perform eigenvalue decomposition to obtain eigenvalues wherein ;

[0053] S5.16, take the argument of as the value of ;

[0054] S5.17, let the array manifold matrix be the matrix whose column vectors are:

[0055] ;

[0056] wherein represents the vector composed of the complex exponential functions of the estimated values of the signal angles ;

[0057] Preferably, after obtaining the manifold matrix , the equivalent model can be converted into and known, in step S6, according to the factor graph in the appendix Figure 3 , call the inner decompression module with and as inputs to obtain the estimated values of the signal complex amplitudes by the message passing method, and finally obtain the matrix . Specifically:

[0058] S6.11, use to represent the message from the factor node to the variable node , and use to represent the message in the opposite direction, and the forms of the two are respectively:

[0059] ∝ d

[0060] ∝

[0061] wherein represents the message from the node to , = ;

[0062] S6.12, according to the belief propagation rule, the sum of the messages from the left side of the node is:

[0063] d ​

[0064] And according to the factor graph, using message passing algorithm can get the message of nodes The message sum of right side source is approximately Gaussian distribution ;

[0065] S6.13、According to the message of left and right side, the approximate posterior probability of is represented as , and we have:

[0066]

[0067] Where is the random distribution of , represent the mean and variance of Gaussian distribution respectively;

[0068] S6.14、According to Figure 3 , using belief propagation rule to calculate the approximate posterior probability of variable node :

[0069] = ∝

[0070] Where represents the message from factor node to variable node in the message passing process

[0071] In S6 step, according to and the approximate posterior probability of active factor , we get and the estimated value of signal source number, which is:

[0072] S6.21、Set the maximum iteration number , let the iteration variable , and initialize ;

[0073] S6.22、Add one to the iteration variable , that is ;

[0074] S6.23、Calculate:

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] wherein, denotes the element of the matrix in the i-th row and j-th column, denotes the element of the matrix in the i-th row and j-th column. , , , denotes the element of the matrix , , , denotes an intermediate variable of the iteration process, the superscript denotes the iteration number of the inner decompression module, , the subscript , the subscript , the subscript .

[0082] S6.24, repeat steps S6.22 to S6.23 until the iteration variable , the estimated value of the signal complex amplitude is equal to .

[0083] Preferably, in step S7, a log-likelihood ratio is defined according to the approximate posterior probability is expressed as:

[0084] for , calculate

[0085]

[0086] wherein, denotes the value of at . If the value of is greater than or equal to 0, let the estimated value of be 1; if the value is less than 0, let be 0. Let equal the number of elements in the activation sequence that are not 0. And update the hidden parameter in S7:

[0087] ;

[0088] Compared with the prior art, the technical scheme of the present application has the advantages that:​

[0089] Compared to the BIG-AMP algorithm, this algorithm does not need to know the prior distribution of the signal angle. This is because when estimating the signal angle, this algorithm first presets the number of signal sources and continuously updates the number of signal sources during operation. The input of the signal source number is then fed into the positioning module to directly solve for the signal angle.

[0090] Compared to the ESPRIT algorithm, the advantage of this algorithm is that it can solve for the signal angle while providing estimates of the complex amplitude of the signal and the number of signal sources when the number of signal sources is unknown;

[0091] Compared to the AMP+ESPRIT algorithm, the advantage of this algorithm is that it can handle an unknown number of signal sources. This is because the number of signal sources is initialized, and the number of signal sources is updated using the log-likelihood ratio (LLR), and the activation sequence is updated in each iteration. implicit parameters It can estimate relevant information about blind sources more accurately;

[0092] This invention eliminates the observation matrix The compressed data is easier to process and more accurate due to the influence of various factors. Furthermore, a message passing method based on expectation propagation is used to transform matrix inversion and other operations into scalar operations, reducing computational complexity. For the line spectrum estimation problem, this invention uses a combination of inner and outer decompression modules and a positioning module, ensuring accurate signal angle estimation while also providing stable and precise estimation of the signal's complex amplitude. Attached Figure Description

[0093] Figure 1 This is a diagram illustrating the steps of the method of the present invention.

[0094] Figure 2 Factor diagram of the outer decompression module of the method of the present invention

[0095] Figure 3 Factor diagram of the inner decompression module of the method of the present invention

[0096] Figure 4 This is a schematic diagram illustrating the application of an example.

[0097] Figure 5 This is a comparison chart of the estimated signal angle and the actual signal angle in the embodiment.

[0098] Figure 6 This is a comparison chart of signal complex amplitude estimation in the examples. Detailed Implementation

[0099] In order that the present application can be more clearly understood, further detailed description will be made to the present application in conjunction with the accompanying drawings and specific embodiments. It should be noted that the terms used in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the scope of the present application. The present application is not limited to the embodiments in the drawings.

[0100] The present embodiment is to verify the feasibility and effectiveness of the method of the present application, which is specifically as follows:

[0101] Application in solving the problem of direction of arrival: such as Figure 4 As shown in the schematic diagram, it is assumed that there are multiple aircrafts as blind sources in space, which emit narrowband signals outward from different azimuth angles to a uniform linear sensor array, and the incident angle of the signal emitted by the same blind source on each sensor is the same due to sufficient distance, and the sensor signal is compressed and noise is added to generate detection data , the signal angle, signal complex amplitude and signal source number of the blind source need to be solved. The signal-to-noise ratio is set to 15dB, the signal source number , the number of sensors , the number of snapshots , the observation data dimension , the true angles of the signals are -77, -70, -65, -64, -63, -3, 2, 41, 67, 75 and a certain amount of random deviation is added.

[0102] For the estimation of the signal angle, Figure 5 The true signal angle is represented by the solid cross in the figure, and the signal angle estimated by the present algorithm is represented by the dashed hollow circle. The signal source number obtained by the present algorithm is consistent with the original signal source number, and the MSE between the signal angle and the true signal angle can reach .

[0103] For the estimation of the signal complex amplitude, Figure 6 The MSE of the estimation of the signal complex amplitude by the present algorithm is represented by the solid pentagram in the figure, and the MSE of the estimation of the signal complex amplitude by the BIGAMP algorithm is represented by the dashed hollow circle. As can be seen from Figure 6 , the signal complex amplitude obtained by the present algorithm is more accurate than that obtained by the BIGAMP algorithm in the problem of two-dimensional blind source line spectrum estimation.

[0104] The terms in the drawings are only used for illustration, and the above examples are only embodiments of the present application and cannot be understood as limitations of the present patent. Any equivalent structure or equivalent process transformation made by using the contents of the specification and drawings, or direct or indirect application in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A line spectrum estimation method for a two-dimensional blind source compressed signal, characterized in that, The method comprises the following steps: S1, according to the given... dimensional observation matrix and Compression matrix of dimension Construct the following about Line spectrum estimation model: ， ， (1) wherein, is an observation matrix of dimension is a compression matrix of dimension is a signal matrix of dimension and are are are noise matrices of dimension with zero mean and independent Gaussian distribution, where , is , is an array manifold matrix of dimension with fixed structure, denoted as is and let ， (2) wherein is the imaginary unit, is the natural constant, is a complex matrix of dimension n x n, whose expression is: , (3) wherein is a diagonal matrix of dimension with the main diagonal elements representing the activation of each potential signal source, is a diagonal matrix of dimension representing the complex amplitudes of the signals emitted by all potential signal sources, is a diagonal matrix of dimension consisting of the activation factors defined by are modeled as independent Bernoulli binomial distributed with parameters , i.e. are distributed according to (4) The composite matrix of the first row and the first column is , modeling as a Gaussian-Bernoulli distribution with parameters , i.e. is distributed according to (5) wherein, represents a Gaussian probability density function with mean 0 and variance represents a Dirac impulse function,​ S2, set the maximum number of iterations , let the iteration variable be an intermediate variable and assign initial values; S3, to the iteration variable add one, i.e. ; S4, to and As input, call outer decompression module, get the first iteration of dimensional matrix ; S5, let with and as input, call the localization module, calculate the angle estimate and, according to formula (2), replace with , construct the matrix estimate ; S6. To and As input, the inner decompression module is called, which computes the matrix elements and the posterior probability estimate of the activation factor and and computes the estimate of ； S7, to , compute (6) wherein, denotes in the value of if the value of is greater than or equal to 0, let be 1; if the value is less than 0, let be 0, let equal the number of elements in the activation sequence that are not 0, calculate ； (7) S8, repeat steps S3 to S7 until iteration variable , output angle estimate , signal complex amplitude estimate , and signal source number estimate .

2. The line spectrum estimation method for a two-dimensional blind source compressed signal according to claim 1, characterized in that, The outer layer decompression module in the step S4 is specifically: ； ； ； ； wherein denotes the element of the matrix in the i-th row and j-th column, denotes the element of the matrix in the i-th row and j-th column, denotes the element of the matrix in the i-th row and j-th column, denotes the element of the matrix in the i-th row and j-th column, , , , are intermediate variables generated iteratively, the index , the index , the index , initialized with the values of the module ， ， ， ， The output result of the module is a matrix , let the element in the i-th row and the j-th column of the matrix take value . .

3. The method of line spectrum estimation for a two-dimensional blind source compressed signal according to claim 1, wherein, The positioning module in the step S5 is specifically: S5.11, compute the covariance matrix The superscript * indicates taking the conjugate transpose of a matrix. S5.12, matrix Eigenvalue decomposition is performed, and the eigenvalues are sorted, and the eigenvectors corresponding to the largest eigenvalues are taken, and arranged to form a matrix ;​ S5.13, respectively taking the front row and the back row form with ; S5.14, compute where the superscript denotes matrix inversion; S5.15, to perform eigenvalue decomposition to obtain eigenvalues where ; S5.16, take the argument of as the value of S5.17, let the array manifold matrix of the first column vector is: 。 4. The method of line spectrum estimation for a two-dimensional blind source compressed signal according to claim 1, characterized in that The inner layer decompression module algorithm in the step S6 is expressed as: S6.11, set the maximum number of iterations Let the iteration variable Initialize ; S6.12, to the iteration variable add one, i.e. ; S6.13, calculating: ； ； ； ； ； ； wherein denotes the matrix the row the column element, denotes the matrix the row the column element, , , , denote intermediate variables of the iteration process, the superscript denotes the number of iterations of the inner decompression module, , the subscript , the subscript , the subscript , S6.14, the steps S6.12 to S6.13 are repeatedly performed until the iteration variable is equal to , the estimate of the signal complex amplitude is equal to , The posterior probability estimate calculation expression is: Activation factor The posterior probability estimate of the activation factor is calculated by the expression 。

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