An array self-calibration direction finding method based on local optimization search

Abstract

The present invention provides an array self-calibration direction finding method based on local optimization search, belonging to the technical field of array signal processing. By decomposing the eigenvector of the array data covariance matrix into a signal subspace and a noise subspace, the present invention uses the orthogonality between the product of the steering vector matrix and the error matrix and the noise subspace for cyclic iteration, and improves the convergence speed and direction finding stability by introducing local optimization search, so as to achieve a better angle estimation result.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and particularly to an array self-calibration direction finding method based on local optimization search. Background Art

[0002] Array signal processing is an extremely important branch in the field of modern signal processing, and source parameter estimation has always been regarded as an important research content in the field of array signal processing. The main purpose of source parameter estimation is to estimate parameters such as the direction of arrival and distance of the radiation signal of the source. For an actual array, there are often array element position errors, which seriously affect the DOA (direction of arrival) performance. Traditional array error self-calibration algorithms have problems such as a large number of iterations, slow convergence speed, and low direction finding accuracy, which limit the engineering application of traditional array error self-calibration algorithms. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a high-precision estimation method for array non-ideal factor self-calibration DOA estimation.

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

[0005] An array self-calibration direction finding method based on local optimization search, comprising the following steps:

[0006] Step 1: Initialize the settings, let k = 0, Γ (k) = Γ0, where k is the number of iterations, and Γ (k) represents the amplitude and phase error correction matrix of the k-th iteration, and Γ0 is the initial value of the amplitude and phase error correction matrix;

[0007] Step 2: Calculate the estimated value of the source covariance matrix using the array received data, and obtain the noise subspace matrix after eigenvalue decomposition

[0008] Step 3: Construct a spatial spectrum The superscript H represents the conjugate transpose, and search for the N largest spatial peak points N is the number of sources, and these peak points correspond to N steering vectors

[0009] Step 4: Construct a cost function

[0010]

[0011] In the formula, δ (k) = [Γ (k) 11 , Γ (k)22 ,..., Γ (k) MM T ; diag represents a diagonal matrix, where the subscripts 11, 22,..., MM represent the corresponding elements in the matrix, and the superscript T represents the matrix transpose;

[0012] Step 5: Under the constraint condition δ (k)H w = 1, find the minimum value of the cost function (k) for δ while obtaining the optimal solution δ of δ at the same time: (k+1) :

[0013]

[0014] In the formula, w = [1, 0,..., 0] T ;

[0015] Step 6: Conduct local optimization search:

[0016] For any within a range of an interval of with δ as the neighborhood radius, search at a certain interval, calculate the cost values within the search range for each angle and select the angle corresponding to the minimum cost value as the angle input for the (k + 1)-th iteration:

[0017]

[0018] Step 7: Set the convergence determination value ε, judge the convergence, and the convergence condition is:

[0019]

[0020] If it does not converge, jump to Step 3 to continue the iteration, otherwise terminate the iteration to obtain the final estimated value of the source azimuth angle

[0021]

[0022] Furthermore, the initial value Γ0 of the amplitude and phase error correction matrix in Step 1 is given by an empirical value or obtained through testing of known sources.

[0023] The present invention has the following advantages compared with the prior art:

[0023] 1. The present invention has fewer iteration times and a faster convergence speed than the traditional array error self-calibration algorithm.

[0024] 2. The present invention has higher direction finding accuracy and better stability than the traditional array error self-calibration algorithm.​ Description of the Drawings

[0025] Figure 1 is the overall flowchart of the present invention.

[0026] Figure 2 is the direction-finding spatial spectrum obtained by the present invention, and the incoming wave directions are (0°, 15°) and (0°, 25°) respectively.

[0027] Figure 3 is the performance comparison result of the direction-finding results of the present invention and the traditional array error self-calibration algorithm with the number of simulation times. Detailed Embodiment

[0028] Next, the technical solution of the present invention will be further described in detail with reference to the drawings.

[0029] An array self-calibration direction-finding method based on local optimization search includes the following steps:

[0030] Step 1: Initialization setting, let k = 0, Γ (k) = Γ0, where Γ0 is the initial value of the amplitude and phase error correction matrix;

[0031] Step 2: Calculate the estimated value of the source covariance matrix using the array received data, and obtain the noise subspace matrix after eigenvalue decomposition

[0032] Step 3: Construct the spatial spectrum Search for the N (N is the number of sources) largest spatial domain peak points These peak points correspond to N steering vectors

[0033] Step 4: Construct the cost function

[0034]

[0035] In the above formula, δ (k) =[Γ (k) 11 ,Γ (k) 22 ,...,Γ (k) MM T ;

[0036] Step 5: Under the constraint condition δ (k)H w = 1, find the minimum value of the cost function (k) for δ At the same time, obtain the optimal solution δ of δ at (k+1) :​​​

[0037]

[0038] Wherein, w = [1, 0,..., 0] T ;

[0039] Step 6: Conduct local optimization search:

[0040] For any Within a small interval range of the interval, search at a certain interval, and calculate the cost values within the search range for each angle respectively, and select the angle corresponding to the minimum cost value as the angle input for the (k + 1)-th iteration:

[0041]

[0042] Step 7: Judge the convergence. The convergence condition is:

[0043]

[0044] If it does not converge, jump to Step 3 to continue the iteration; otherwise, terminate the iteration to obtain the final estimated value of the source azimuth angle

[0045] Furthermore, the initial value Γ0 of the amplitude and phase error correction matrix can be estimated by empirical values or obtained through testing with known sources

[0046] The main working process of this method includes: calculating the covariance matrix from the sampling samples of the source by the receiving array, obtaining the noise subspace matrix by decomposing the covariance matrix, generating the direction finding spatial spectrum using the noise subspace matrix and the array steering vector matrix preliminarily corrected in terms of amplitude and phase to obtain the preliminary estimated value of the direction finding angle, and then constructing a cost function and iteratively solving its minimum cost value, continuously updating the direction finding angle and the amplitude and phase error correction matrix until convergence, finally realizing the DOA estimation of the source. This method is based on the array received signals, constructs the spatial spectrum by using the orthogonality between the array steering vector corrected in terms of amplitude and phase and the noise subspace matrix, takes the output angle of the spatial spectrum as the initial value to iteratively solve the cost function and conducts local optimization search during each iteration, realizing the fast and accurate estimation of the source incoming wave direction

[0047] The following is a more specific example:

[0048] Referring to Figure 1 , an array self-calibration direction finding method based on local optimization search includes the following steps: ​

[0049] Step 1: Initialize the settings, let k = 0, Γ (k) = Γ0, where Γ0 is the initial value of the amplitude and phase error correction matrix;

[0050] Step 2: Calculate the estimated value of the source covariance matrix using the array received data, and obtain the noise subspace matrix through eigenvalue decomposition;

[0051] Step 3: Construct the spatial spectrum Search for the N (N is the number of sources) largest spatial peak points These peak points correspond to N steering vectors

[0052] Step 4: Construct the cost function

[0053]

[0054] In the above formula, δ (k) = [Γ (k) 11 , Γ (k) 22 ,..., Γ (k) MM T ;

[0055] Step 5: Under the constraint condition δ (k)H w = 1, find the minimum value of the cost function (k) for δ Meanwhile, obtain the optimal solution δ of δ at : (k+1) :

[0056]

[0057] In the formula, w = [1, 0,..., 0] T ,

[0058] Step 6: Conduct local optimization search:

[0059] For any in a small interval range of , search at a certain interval, calculate the cost values within the search range for each angle and select the angle corresponding to the minimum cost value as the angle input for the (k + 1)-th iteration:

[0060] ​​

[0061] Step 7: Judge convergence. The convergence condition is:

[0062]

[0063] If it does not converge, jump to Step 3 to continue the iteration; otherwise, terminate the iteration to obtain the final estimated value of the source azimuth angle.

[0064] Simulation verification:

[0065] Simulation conditions: Use a non-uniform linear array with 17 array elements, and the array element coordinates are:

[0066] dx = [0, 1, 2, 4, 5, 7, 8, 10, 12, 13, 14, 16, 17, 19, 21, 23, 26]' * d

[0067] where d is the half-wavelength, the signal frequencies are all 1 GHz, the channel amplitude error ≤ 3 dB, the channel phase error ≤ 20°, and the incident directions of the two sources are (0°, 15°) and (0°, 25°) respectively.

[0068] The simulation results are as Figure 2 、 Figure 3 shown.

[0069] It can be seen through Figure 2 that when the amplitude and phase errors of the channels are relatively large, accurate DOA estimation can still be achieved. It can be seen through Figure 3 that after introducing local optimization search, the direction finding accuracy has been significantly improved compared with the traditional array error self-correction algorithm.

[0070] In summary, in the present invention, by decomposing the eigenvector of the array data covariance matrix into a signal subspace and a noise subspace, using the orthogonality of the product of the steering vector matrix and the error matrix and the noise subspace for cyclic iteration, and by introducing local optimization search, the convergence speed and direction finding stability are improved, thereby achieving a better angle estimation result.

Claims

1. An array self-calibration direction finding method based on local optimization search, characterized in that, It includes the following steps: Step 1: Initialize the settings, let k = 0, Γ (k) = Γ0, where k is the number of iterations, and Γ (k) represents the amplitude and phase error correction matrix for the k-th iteration, and Γ0 is the initial value of the amplitude and phase error correction matrix; Step 2: Use the array to receive data to calculate the estimated value of the source covariance matrix, and obtain the noise subspace matrix after eigen-decomposition Step 3: Construct the spatial spectrum The superscript H represents the conjugate transpose, and search for the N largest spatial domain peak points N is the number of signal sources, and these peak points correspond to N steering vectors Step 4: Construct the cost function In the formula, δ (k) = [[Γ (k) 11 , Γ (k) 22 ,..., Γ (k) MM T ; diag represents a diagonal matrix, the subscripts 11, 22,..., MM represent the corresponding elements in the matrix, and the superscript T represents the matrix transpose;​ Step 5: Under the constraint condition δ (k)H w = 1, find the cost function (k) for δ to obtain its minimum value while also obtaining the optimal solution δ of δ at (k+1) : Wherein, Step 6: Conduct local optimization search: For any in the range of an interval of θ i (k) where δ is the neighborhood radius, search is carried out at certain intervals, and for each angle θ calculate the cost value within the search range respectively i (k) and select the angle corresponding to the minimum cost value as the angle input for the (k + 1)-th iteration: ​ Step 7: Set the convergence determination value ε and judge the convergence. The convergence condition is: If it does not converge, jump to step 3 to continue the iteration; otherwise, terminate the iteration to obtain the final estimated value of the source azimuth angle 2. The array self-calibration direction finding method based on local optimization search according to claim 1, wherein, The initial value Γ0 of the amplitude and phase error correction matrix in Step 1 is given by an empirical value or obtained through testing of a known information source.

Images