A DOA Estimation Method for Wideband Signals Based on Dirichlet Process Prior

Abstract

The present invention discloses a method for estimating the DOA of broadband signals based on the Dirichlet process prior. First, a broadband signal model is established, and a sparse signal model of the received antenna array data is constructed. Secondly, a probability model based on the Dirichlet process prior is established, and then a message passing method combining belief propagation and mean field rules is used to obtain the update formula for the unknown parameters in the probability model. Initial values are assigned to the unknown parameters in the probability model, the received data of the array antennas are processed, and the estimated values of the model parameters are obtained through iterative updates. Finally, the DOA estimated value is calculated based on the parameter estimated value. The DOA estimated value obtained by this method is relatively accurate, and the error between it and the true DOA is small.

Description

Technical Field

[0001] The present invention relates to the technical field of DOA estimation methods, and specifically to a broadband signal DOA estimation method based on a Dirichlet process prior. Background Art

[0002] DOA estimation is an important research direction in the field of array signal processing, and is widely applied to fields such as radar, sonar, exploration, and positioning, covering various aspects of production, life, and military affairs. Currently, relatively mature DOA estimation methods mainly include the MUSIC (Multiple Signal Classification) method and the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method based on subspace decomposition. These methods can solve the problem of high-resolution DOA estimation, but the accuracy of DOA estimation is easily affected by factors such as the number of snapshots, signal-to-noise ratio, and system complexity.

[0003] Sparse Bayesian learning-based estimation methods are currently a hot topic in the research of DOA estimation methods. The basic principle is to convert the DOA estimation problem into a sparse signal reconstruction problem for solution. First, a sparse signal model is established on the divided angular grid, and then a probability model is constructed according to the statistical characteristics of the signals received by the array antennas. Then, the variational inference method is used to obtain the estimated values of the unknown parameters in the probability model. Some parameters in the probability model correspond one-to-one with the preset grid points, and the angular grid points corresponding to the extreme value points of the selected parameters are the DOA estimation values. The patent with the application publication number CN112924924A discloses a DOA estimation method for wideband signals based on l1-norm sparse representation. This method determines the weighting matrix by optimizing the orthogonality of the subspace and uses the weighted l1-norm as the objective function to be minimized to increase the sparsity of the signals. This algorithm does not introduce prior information of the signal sources. The patent with the application publication number CN109901148A discloses a DOA estimation method for wideband signals based on the sparse representation of the covariance matrix, the patent with the application publication number CN112487703A discloses a DOA estimation method for underdetermined wideband signals based on sparse Bayesian in an unknown noise field, and the patent with the application publication number CN106324558A discloses a DOA estimation method for wideband signals based on a coprime array construct a sparse model for the signal covariance matrix instead of the signal. The DOA estimation method based on the Dirichlet process (DP) prior (L. Wang, L. Zhao, G. Bi, C. Wan, L. Zhang, and H. Zhang, Novel wideband DOA estimation based on sparse Bayesian learning with Dirichlet process priors, IEEE Trans. Signal Process., 2016; 64(2): 275–289) constructs a sparse model based on the signal, introduces the concept of clustering, and uses the mean field rule to solve the approximate posterior, showing good estimation performance in wideband signals. However, this method converges slowly. How to improve the convergence speed while enhancing the performance of the DOA estimation method is an urgent problem to be solved. Summary of the Invention

[0004] To solve the above problems, the present invention provides a DOA estimation method for wideband signals based on the Dirichlet process prior, which uses a message passing method combining belief propagation and the mean field rule to improve the estimation accuracy and convergence speed.

[0005] The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] A DOA estimation method for wideband signals based on the Dirichlet process prior, comprising:

[0007] Step 1: Establish a broadband signal model and construct a sparse signal model for the received antenna array data as follows:

[0008] Use element uniform linear array to receive far-field broadband signals, divide the broadband signals into narrowband signals, and the array output data is dimensional matrix; the spacing between the elements of the receiving antenna is ; then evenly divide the angular grid, and divide the range evenly into grids to obtain the angular grid point set ; define as sparse signal matrix, which contains broadband signal information; define the noise signal as dimensional matrix; define the overcomplete dictionary as dimensional matrix; establish the signal model of the receiving antenna array output matrix as:

[0009] ;

[0010] where,

[0011] ;

[0012] In the formula, represents the steering vector when the incident angle is , and is the wavelength.

[0013] Step 2: Establish a probability model based on the DP prior, the specific content is as follows:

[0014] Assume that the additive noise follows a complex Gaussian distribution with a mean of 0 and a precision of , represents the Gamma distribution, then the th column vector in the received antenna array data satisfies represents the complex Gaussian distribution, represents dimensional identity matrix;

[0015] Assume that the th column vector in the sparse signal matrix follows a complex Gaussian distribution with a mean of 0 and a precision of Denotes the number of classifications, Denotes vector matrixization, then The probability density function of is:

[0016] ;

[0017] Wherein, ; ; Denotes that when the value is 1, and 0 otherwise; Is the allocation vector, following the multinomial distribution with parameter ; Is the weight of the "truncated stick" theorem; Is the length of the "truncated stick" theorem; Is the scale parameter of the Dirichlet process.

[0018] Step 3: Use the message passing method of joint belief propagation and mean field rules to obtain the update formulas for each parameter in the probability model, specifically as follows:

[0019] For the sparse signal matrix The mean and precision matrix of the -th column vector of are updated as follows:

[0020] ;

[0021] ;

[0022] In the formula, Denotes the expectation; Denotes the conjugate transpose.

[0023] The noise precision is updated as follows:

[0024] ;

[0025] In the formula, Denotes the trace of the matrix;

[0026] The parameter is updated as follows:

[0027] ;

[0028] In the formula, is the -th value of; is the -th value of; is the -th value of; is the th diagonal value;

[0029] Updating formula for the variable of the stick theorem is as follows:

[0030] ;

[0031] In the formula, ; ;

[0032] The updating formula for the scaling parameter is as follows:

[0033] ;

[0034] Among them, is the Digamma function;

[0035] Updating formula for the allocation variable is as follows:

[0036] .

[0037] Step 4: Process the data according to the obtained parameter update formula to obtain the estimated values of the probability model parameters, and the specific content is as follows:

[0038] For the parameters , , in the probability model, assign initial values, and substitute the data of the receiving antenna array into the update formula in Step 3, and continuously iterate and update until the preset threshold is reached or the preset maximum number of iterations is reached, and then stop the update to obtain the final parameter estimated values;

[0039] Step 5: Calculate the estimated value of DOA according to the obtained parameter estimated values, and the specific content is as follows:

[0040] Calculate the estimated value of the th column vector of the sparse signal matrix , and find the position of the maximum value of . The angle of the grid corresponding to this position is the estimated value of DOA.

[0041] The present invention has the following beneficial effects:

[0042] The present invention first establishes a sparse signal model according to the characteristics of the incident signal, secondly constructs a probability model based on the Dirichlet process prior for each variable in the model, then uses the message passing method to obtain the update formula of the unknown parameters in the probability model, and after assigning initial values to the unknown parameters in the probability model, processes the data received by the receiving antenna array in an iterative update manner, iteratively calculates the estimated values of the model parameters, and finally obtains the estimated value of the DOA. The method proposed by the present invention obtains better estimation performance than the traditional DOA estimation method.

[0043] The basic principle and implementation scheme of the present invention have been verified by computer numerical simulation, and the results show that the proposed method has good DOA estimation performance. Brief Description of the Drawings

[0044] Figure 1 is a schematic flow chart of a broadband signal DOA estimation method based on the Dirichlet process prior provided by the present invention;

[0045] Figure 2 is a schematic diagram of the receiving antenna array of the present invention;

[0046] Figure 3 is a simulation result diagram of different signal sources of a broadband signal DOA estimation method based on the Dirichlet process prior provided by the present invention under the same signal-to-noise ratio;

[0047] Figure 4 is a simulation result diagram of the same signal source of a broadband signal DOA estimation method based on the Dirichlet process prior provided by the present invention under different signal-to-noise ratios. Detailed Embodiments

[0048] The following further describes the present invention in detail with reference to specific embodiments and drawings, but the implementation manners of the present invention are not limited thereto.

[0049] A schematic flow chart of a broadband signal DOA estimation method based on the Dirichlet process prior provided by the present invention is as Figure 1 shown, and the technical solution adopted is divided into the following 5 steps:

[0050] Step 1: Use a uniform linear array with array elements and a spacing of , as Figure 2 shown, to receive far-field broadband signals, divide the broadband signals into narrowband signals, and obtain -dimensional array output data . The data contains incident signal information and noise information.

[0051] Step 2: Establish a sparse signal model for the output data of the receiving antenna array:

[0052] Evenly divide the angular grid, and the range is evenly divided into grids to obtain the angular grid point set ; Define -dimensional sparse signal matrix , which contains broadband signal information; Define -dimensional noise signal matrix ; Define -dimensional over-complete dictionary matrix , and the sparse signal model is:

[0053] ;

[0054] Among them,

[0055] ;

[0056] In the formula, represents the steering vector when the incident angle is , and is the wavelength.

[0057] Step 3: According to the sparse signal model established above, establish a probability model based on the DP prior, and the specific content is as follows:

[0058] First, assume that the additive noise follows a complex Gaussian distribution with a mean of 0 and a precision of , represents the Gamma distribution, then the th column vector in the received antenna array data satisfies , represents the complex Gaussian distribution, and represents the

[0059] -dimensional identity matrix; Then, assume that the th column vector in the sparse signal matrix follows a complex Gaussian distribution with a mean of 0 and a precision of , where represents the number of classifications, and

[0060] ;

[0061] Among them, ; ; represents when The value is 1 when [condition], and 0 otherwise; is the allocation vector, following a polynomial distribution with parameter ; is the weight of the "truncated stick" theorem; is the length of the "truncated stick" theorem; is the scale parameter of the Dirichlet process.

[0062] Step 4: Use the message passing method of joint belief propagation and mean field rules to obtain the update formulas for the parameters in the probability model, and obtain the estimated values of the parameters:

[0063] The mean of the -th column vector of the sparse signal matrix , the precision matrix , the noise precision , the parameter , , , are calculated by the following formulas respectively:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] where denotes the expectation; denotes the trace of the matrix; denotes the conjugate transpose; is the -th value of ; is the -th value of ; is the -th value on the diagonal of ; ; ; is the Digamma function.

[0072] For the parameters in the probability model , , Assign an initial value, and substitute the data of the receiving antenna array into the update formula in Step 3, and continuously iterate and update until reaching the preset threshold or the preset maximum number of iterations, and then stop the update to obtain the final parameter estimation value;

[0073] Step 5: According to the parameter estimation value obtained in Step 4, calculate the estimated value of DOA, and the specific content is as follows:

[0074] Calculate the sparse signal matrix of the column vector estimated value , and find out the position of the maximum value, and the angle of the grid corresponding to this position is the DOA estimated value.

[0075] Use a computer to perform numerical simulation to verify the estimation performance of the method proposed in the present invention. The number of array elements of the uniform linear array of receiving antennas used in the simulation is 10, and the element spacing is half of the wavelength of the incident signal. With an interval of 1°, the angle range is evenly divided into 181 grids to obtain an angle grid point set. In order to verify the effectiveness of the method proposed in this paper, DOA estimation is performed under different simulation conditions, and a simulation experiment result graph is drawn. Figure 3 is the simulation result graph of a broadband signal DOA estimation method based on Dirichlet process prior provided by the present invention for different signal sources under the same signal-to-noise ratio. The number of signal sources in each experiment is 2, the signal source angles are randomly generated, and the signal-to-noise ratio is 0 dB.

[0076] Figure 3 are the simulation result graphs of 3 experiments. The angles in the first experiment are 40.26°, 112.08°; the angles in the second experiment are 22.43°, 155.71°; the angles in the third experiment are 28.99°, 123.37°. Figure 3 In the three graphs in

[0077] Figure 4 the horizontal axis is the angle, the vertical axis is the power, the circles are the true angles, and the crosses are the estimated angles. It can be found that the DOA estimated value is close to the true value, and the grid where the true value of DOA is located can be accurately estimated. Figure 4 is the simulation result graph of a broadband signal DOA estimation method based on Dirichlet process prior provided by the present invention for the same signal source under different signal-to-noise ratios. The number of signal sources in each experiment is 2, and the signal source angles are randomly generated 65.22°, 132.97°, Figure 4In the three figures, the horizontal axis represents the angle, the vertical axis represents the power, the circles represent the true angles, and the crosses represent the estimated angles. It can be found that under different signal-to-noise ratios, the DOA estimation values are still very close to the true values, and the grid where the true DOA value is located can be accurately estimated.

[0078] The above are only the 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 modifications made to the above embodiments based on the technical essence of the present invention all fall within the scope of the present invention. The protection scope of the present invention should be subject to the scope defined by the claims.

Claims

1. A method for estimating the DOA of broadband signals based on the Dirichlet process prior, characterized in that Including: Step 1: Establish a broadband signal model and construct a sparse signal model for the received antenna array data; The said Step 1 includes: Use a uniform linear array to receive far-field broadband signals, divide the broadband signals into narrowband signals, and the array output signal is a matrix of dimension; the spacing between the elements of the receiving antenna is ; then evenly divide the angular grid, and evenly divide the range into grids to obtain the angular grid point set ; define as the sparse signal matrix of, which contains broadband signal information; define the noise signal as a matrix of dimension; define the over-complete dictionary as a matrix of dimension; establish the signal model of the receiving antenna array output matrix as: ； Wherein, ； In the formula, represents the steering vector when the incident angle is , is the wavelength; Step 2: Establish a probability model based on the Dirichlet process prior; The said Step 2 includes: Assume that the additive noise follows a complex Gaussian distribution with a mean of 0 and a precision of , denotes the Gamma distribution, then the th column vector in the received antenna array data satisfies , denotes the complex Gaussian distribution, denotes the Assume the sparse signal matrix The column vector in it follows a complex Gaussian distribution with mean 0 and precision , where represents the number of classifications, represents vector matrixization, then The probability density function of is: ； Among them, ; ; represents that the value is 1 when , and the value is 0 in other cases; is the allocation vector, following the polynomial distribution with parameter ; is the weight of the "broken stick" theorem; is the length of the "broken stick" theorem; is the scale parameter of the Dirichlet process; Step 3: Use the message passing method combining belief propagation and mean field rules to obtain the update formulas for the parameters in the probability model; The said Step 3 includes: Sparse signal matrix The column vector mean value and the precision matrix The update formula is as follows: ， ， In the formula, denotes expectation; denotes conjugate transpose; Noise precision The update formula is as follows: ； In the formula, represents the trace of the matrix; Parameter The update formula is as follows: ； In the formula, is 's th value, is 's th value; is 's th diagonal value; Nunchaku Theorem Variables The update formula is as follows: ； In the formula, ; ; Scaling parameter The update formula is as follows: ； wherein, is the Digamma function; Allocated variable The update formula is as follows: ； Step 4: Process the received antenna array data according to the obtained parameter update formula, assign initial values to the unknown parameters, and then iteratively update to obtain the estimated values of the probability model parameters; ​ Step 5: Calculate the estimated value of DOA according to the obtained parameter estimated values.

2. The broadband signal DOA estimation method based on the Dirichlet process prior according to claim 1, characterized in that The said Step 4 includes: For the parameters in the probability model , , assign initial values, substitute the data of the receiving antenna array into the update formula in Step 3 above, and continuously iterate and update until reaching a preset threshold or a preset maximum number of iterations, at which point the update stops to obtain the final parameter estimate value.

3. A broadband signal DOA estimation method based on the Dirichlet process prior according to claim 2, characterized in that, The said Step 5 includes: Calculate the sparse signal matrix of the column vector estimate , find out the position of the maximum value. The angle of the grid corresponding to this position is the DOA estimation value.

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