An off-grid DOA estimation method

Abstract

The invention discloses an off-grid DOA estimation method. Firstly, a signal model is constructed. Secondly, a probability model based on a Dirichlet process prior is established. According to the probability model, a joint probability density function is solved and a factor graph is designed. Then, an update formula of each parameter in the probability model is obtained by using a message passing method of a joint belief propagation and a mean field rule. Initial values ​​are assigned to unknown parameters in the probability model. The received data is processed and iteratively updated to obtain estimated values ​​of the probability model parameters. Finally, an estimated value of DOA is calculated according to the obtained parameter estimated values.

Description

Technical Field

[0001] The present invention relates to the technical field of DOA estimation methods, and in particular to an off-grid DOA estimation method. Background Art

[0002] DOA estimation is an important branch of array signal processing, playing a key role in wireless communication, positioning, radar, sonar and other fields. In the past few decades, researchers have studied this topic from different perspectives and achieved fruitful results. Subspace-based MUSIC (Multiple Signal Classification), ESPRIT (Rotation Invariant Subspace Method), ML (Maximum Likelihood Method) and their improved algorithms are relatively successful methods in the early stage, but the performance will drop sharply in a noisy environment, and the complexity will be higher when the number of snapshots is large. The emergence of compressed sensing has reduced the computational complexity. For example, OMP (Orthogonal Matching Pursuit) and norm-based algorithms are greatly affected by SNR (Signal-to-Noise Ratio). However, SBL (Sparse Bayesian Learning) algorithms are not easily affected by SNR and have good performance under low complexity conditions. SBL algorithms can be divided into two categories: on-grid and off-grid. The performance of on-grid algorithms is limited by the grid resolution, while off-grid algorithms often have higher accuracy. The OGSBI algorithm (Z. Yang, L. Xie, and C. Zhang, “Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference,” IEEE Trans. Signal Process., vol. 61, no. 1, pp. 38–43, Jan. 2013.) is the first off-grid DOA estimation algorithm based on the SBL framework. However, the algorithm assumes that all signal sources occupy the same frequency band, which affects the estimation accuracy. Summary of the invention

[0003] In order to solve the above problems, the present invention provides an off-grid DOA estimation method.

[0004] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0005] An off-grid DOA estimation method, comprising:

[0006] Step 1: Construct a signal model to construct a sparse signal model for receiving antenna array data, as follows:

[0007] A uniform linear array is used to receive far-field signals. The number of array elements is M, and the array element spacing is Δd. The signal is divided into F sub-bands. The array output data Y = [y1,…,y f] is an M×F dimensional matrix; then the angle grid is evenly divided, and the range [0°, 180°] is evenly divided into N grids, and the angle grid point set Θ = [θ1,…,θ N ]; define X = [x1,…,x f ] is a sparse signal matrix of N×F; define the noise signal W=[w1,…,w f ] is an M×F dimensional matrix; define an overcomplete approximate dictionary is an M×N dimensional matrix; the signal model of the receiving antenna array output matrix Y is established as:

[0008]

[0009] in,

[0010]

[0011] in,

[0012]

[0013] In the formula, α f (θ i ), i=1,…,N means the incident angle is θ i The guiding vector at the time, λ is the wavelength. f =[b f (θ1),b f (θ2),…,b f (θ N )],b f (θ i ) is a f (θ i ) about θ i The derivative of Δ f =diag(β f ) is the diagonal matrix of angle deviation from the grid, β f is the difference between the incident angle and the nearest grid angle, and diag(·) represents the vector matrix.

[0014] Step 2: Construct a probability model based on DP prior. The details are as follows:

[0015] Assuming that the additive noise obeys a complex Gaussian distribution with a mean of 0 and an accuracy of α0 to Gam(a,b), Gam(·) represents a Gamma distribution, then the fth column vector in the received antenna array data Y satisfies represents complex Gaussian distribution, I M represents the M-dimensional identity matrix;

[0016] Assume that the fth column vector x in the sparse signal matrix X is fThe mean is 0 and the precision is A complex Gaussian distribution, where K represents the number of categories, then x f The probability density function of is:

[0017]

[0018] in, 1[z f =k] means when z f = k, the value is 1, otherwise the value is 0; f is the distribution vector, subject to the parameters {ω k} k＝1,…,K The multinomial distribution of is the weight of the “stick-cutting” theorem; π k ~Beta(1,γ) is the length of the “cut stick” theorem; γ~Gam(e,h) is the scaling parameter of the Dirichlet process.

[0019] Step 3: According to the probability model, solve the joint probability density function and design the factor graph. The specific contents are as follows:

[0020] The joint probability density function is:

[0021]

[0022] in, Represents a collection of hidden variables.

[0023] Step 4: Use the message passing method of the joint BP-MF (belief propagation-mean field rule) to obtain the update formula of each parameter in the probability model, as follows:

[0024] The fth column vector x of the sparse signal matrix X f ,f=1,…,the mean value μ of F f and the precision matrix Γ f The update formula is:

[0025]

[0026]

[0027] In the formula, <·> represents expectation; (·) H represents the conjugate transpose, Will update later.

[0028] parameter The update formula is:

[0029]

[0030] In the formula, for The nth value of f,n μ f The nth value of ; for The nth diagonal value;

[0031] Assign variable z f The update formula is:

[0032]

[0033] in,

[0034]

[0035] The stick theorem variable π k The update formula is:

[0036]

[0037] In the formula,

[0038] The update formula of the scale parameter γ is:

[0039]

[0040] Among them, Ψ(·) is the Digamma function;

[0041] The update formula of noise accuracy α0 is:

[0042] in,

[0043]

[0044] Where tr(·) represents the trace of the matrix;

[0045] Angular deviation from grid β k The update formula is:

[0046]

[0047] in,

[0048]

[0049]

[0050] in, It means taking the real part of a complex number.

[0051] Step 5: Process the data Y according to the obtained parameter update formula to obtain the estimated values ​​of the probability model parameters. The specific contents are as follows:

[0052] For the parameter z in the probability model f , γ is given an initial value, and the data Y of the receiving antenna array is substituted into the update formula of step 4, and the update is continuously iterated until the preset threshold is reached or the preset maximum number of iterations is reached, and the update is stopped to obtain the final parameter estimation value;

[0053] Step 6: Calculate the estimated value of DOA based on the obtained parameter estimates. The details are as follows:

[0054] Calculate the fth column vector x of the sparse signal matrix X f , find the estimated value of The position of the maximum value, the sum of the angle of the grid corresponding to this position and the angle deviation from the grid is the DOA estimation value.

[0055] The present invention has the following beneficial effects:

[0056] The present invention first establishes a sparse signal model, then constructs a probability model based on the Dirichlet process prior for each variable in the model, and then uses the message passing method to obtain the update formula of the unknown parameters in the probability model. After assigning the initial value of the unknown parameters in the probability model, the data received by the receiving antenna array is processed in an iterative update manner, and the estimated values ​​of the model parameters are iteratively calculated to finally obtain the estimated value of DOA. The method proposed by the present invention obtains an estimation performance that is superior to the traditional DOA estimation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Schematic diagram of the receiving antenna array of the present invention

[0058] Figure 2 It is a schematic diagram of the factor graph model DETAILED DESCRIPTION

[0059] The present invention is further described in detail below in conjunction with specific embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0060] The technical solution adopted by the off-grid DOA estimation method provided by the present invention is divided into the following 6 steps:

[0061] Step 1: Use a uniform linear array with M elements and a spacing of Δd, such as Figure 1 As shown, the far-field signal is received and divided into F sub-bands to obtain an M×F dimensional array output data Y=[y1,…,y f ], the data Y contains incident signal information and noise information.

[0062] Step 2: Establish a sparse signal model for receiving antenna array output data:

[0063] Divide the angle grid uniformly, divide the range [0°, 180°] into N grids, and get the angle grid point set Θ = [θ1,…,θ N ]; define the N×F dimensional sparse signal matrix X = [x1,…,x f ]; define the M×F dimensional noise signal matrix W = [w1,…,w f ]; define an overcomplete approximate dictionary is an M×N dimensional matrix, and the sparse signal model is:

[0064]

[0065] in,

[0066]

[0067] in,

[0068]

[0069] In the formula, a f (θ i ), i=1,…,N means the incident angle is θ i The guiding vector at the time, λ is the wavelength. f =[b f (θ1),b f (θ2),…,b f (θ N )],b f (θ i ) is a f (θ i ) about θ i The derivative of Δ f =diag(β f ) is the diagonal matrix of angle deviation from the grid, β f is the difference between the incident angle and the nearest grid angle, and diag(·) represents the vector matrix.

[0070] Step 3: Construct a probability model based on DP prior. The details are as follows:

[0071] Assuming that the additive noise obeys a complex Gaussian distribution with a mean of 0 and an accuracy of α0 to Gam(a,b), Gam(·) represents a Gamma distribution, then the fth column vector in the received antenna array data Y satisfies represents complex Gaussian distribution, I M represents the M-dimensional identity matrix;

[0072] Assume that the fth column vector x in the sparse signal matrix X is f The mean is 0 and the precision is A complex Gaussian distribution, where K represents the number of categories, then x f The probability density function of is:

[0073]

[0074] in, Indicates when z f = k, the value is 1, otherwise the value is 0; f is the distribution vector, subject to the parameters {ω k} k＝1,…,K The multinomial distribution of is the weight of the “stick-cutting” theorem; π k ~Beta(1,γ) is the length of the “cut stick” theorem; γ~Gam(e,h) is the scaling parameter of the Dirichlet process.

[0075] Step 4: According to the probability model, solve the joint probability density function and design the factor graph. The specific contents are as follows:

[0076] The joint probability density function is:

[0077]

[0078] in, represents the set of hidden variables. Figure 2 shown.

[0079] Step 5: Use the message passing method of the joint BP-MF (belief propagation-mean field rule) to infer the hidden variables in the factor graph as follows:

[0080] The fth column vector x of the sparse signal matrix X f ,f=1,…,the mean value μ of F f and the precision matrix Γ f ,parameter z f , π k , γ, noise accuracy a0, angle deviation from the grid β k The calculation formulas are:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Among them, <·> indicates expectation; (·) H represents the conjugate transpose, diag(·) indicates vector matrixization; for The nth value of f,n μ f The nth value of ; for The nth diagonal value; Ψ(·) is the Digamma function; tr(·) represents the trace of the matrix; It means taking the real part of a complex number.

[0090] For the parameter z in the probability model f , γ is given an initial value, and the data Y of the receiving antenna array is substituted into the update formula of step 5, and the update is continuously iterated until the preset threshold is reached or the preset maximum number of iterations is reached, and the update is stopped to obtain the final parameter estimation value;

[0091] Step 6: Calculate the estimated value of DOA based on the obtained parameter estimates. The details are as follows:

[0092] Calculate the fth column vector x of the sparse signal matrix X f , find the estimated value of The position of the maximum value, the sum of the angle of the grid corresponding to this position and the angle deviation from the grid is the DOA estimation value.

[0093] The above are only preferred embodiments of the present invention. It should be noted that the above preferred embodiments should not be regarded as limiting the present invention. Any simple modification made to the above embodiments according to the technical essence of the present invention belongs to the scope of the present invention. The protection scope of the present invention shall be based on the scope defined by the claims.

Claims

1. An off-grid DOA estimation method, characterized in that: include: Step 1: Construct a signal model to construct a sparse signal model for receiving antenna array data, as follows: A uniform linear array is used to receive far-field signals. The number of array elements is M, and the array element spacing is Δd. The signal is divided into F sub-bands. The array output data Y = [y1,…,y f ] is an M×F dimensional matrix; then the angle grid is evenly divided, and the range [0°, 180°] is evenly divided into N grids, and the angle grid point set Θ = [θ1,…,θ N ]; define X = [x1,…,x f ] is a sparse signal matrix of N×F; define the noise signal W=[w1,…,w f ] is an M×F dimensional matrix; define an overcomplete approximate dictionary is an M×N dimensional matrix; the signal model of the receiving antenna array output matrix Y is established as: in, in, In the formula, a f (θ i ), i=1,…,N means the incident angle is θ i The guiding vector at the time, λ is the wavelength, B f =[b f (θ1),b f (θ2),…,b f (θ N ), b f (θ i ) is a f (θ i ) about θ i The derivative of f =diag(β f ) is the diagonal matrix of angle deviation from the grid, β f is the difference between the incident angle and the nearest grid angle, diag(·) represents the vector matrix; Step 2: Construct a probability model based on the Dirichlet process prior, as follows: Assuming that the additive noise obeys a complex Gaussian distribution with a mean of 0 and an accuracy of α0 to Gam(a,b), Gam(·) represents a Gamma distribution, then the fth column vector in the received antenna array data Y satisfies represents complex Gaussian distribution, I M represents the M-dimensional identity matrix; Assume that the fth column vector x in the sparse signal matrix X is f The mean is 0 and the precision is A complex Gaussian distribution, where K represents the number of categories, then x f The probability density function of is: in, 1[z f = k] means when z f = k, the value is 1, otherwise the value is 0; f is the distribution vector, subject to the parameters {ω k } k＝1,…,K The multinomial distribution of is the weight of the "stick-cutting" theorem; π k ~Beta(1,γ) is the length of the "stick" theorem; γ~Gam(e,h) is the scaling parameter of the Dirichlet process; Step 3: According to the probability model, solve the joint probability density function and design the factor graph. The joint probability density function is: in, represents a set of hidden variables; Step 4: Use the message passing method of the joint BP-MF (belief propagation-mean field rule) to obtain the update formula of each parameter in the probability model, as follows: The fth column vector x of the sparse signal matrix X f ,f=1,…,the mean value μ of F f and the precision matrix Γ f The update formula is: In the formula, <·> represents expectation; (·) H represents the conjugate transpose, Will be updated later; parameter The update formula is: In the formula, for The nth value of f,n μ f The nth value of ; for The nth diagonal value; Assign variable z f The update formula is: in, The stick theorem variable π k The update formula is: In the formula, The update formula of the scale parameter γ is: Among them, Ψ(·) is the Digamma function; The update formula of noise accuracy α0 is: in, Where tr(·) represents the trace of the matrix; Angular deviation from grid β k The update formula is: in, in, It means taking the real part of a complex number; Step 5: Parameter z in the probability model f , γ is given an initial value, and the data Y of the receiving antenna array is substituted into the update formula of step 4, and the update is continuously iterated until the preset threshold is reached or the preset maximum number of iterations is reached, and the update is stopped to obtain the final parameter estimation value; Step 6: Based on the obtained parameter estimates, calculate the estimated value of DOA.

2. The off-grid DOA estimation method according to claim 1, characterized in that: The step 6 comprises: Calculate the fth column vector x of the sparse signal matrix X f , find the estimated value of The position of the maximum value, the sum of the angle of the grid corresponding to this position and the angle deviation from the grid is the DOA estimation value.

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