A circular array two-dimensional DOA estimation method based on graph signal processing

Abstract

The application belongs to the technical field of array direction finding, and particularly relates to a circular array two-dimensional DOA estimation method based on graph signal processing. The method projects the measurement signal by constructing a directed graph between array elements and using an adjacency matrix thereof, and finally constructs a residual matrix to obtain the azimuth and elevation of the target signal. The application has good effects in various signal-to-noise ratio environments, and can accurately estimate the azimuth of the target and is simple and practical.

Description

Technical Field

[0001] This invention belongs to the field of array direction finding technology, specifically relating to a two-dimensional DOA estimation method for circular arrays based on graph signal processing. Background Technology

[0002] Array direction finding involves setting up multiple sensors at different locations in space to form a sensor array. This array is then used to receive (multi-point parallel sampling) and process spatial signal fields, extracting the signals received by the array and their characteristic information (parameters). At the same time, interference, noise, or information of no interest are suppressed. The location of the radiation source is calculated by using the time difference or phase difference of the signals measured at the positions of multiple array elements. Summary of the Invention

[0003] This invention proposes a novel DOA estimation method for circular arrays. Based on a circular array, the method projects the received signal onto a graph domain for processing by constructing an adjacency matrix, builds a residual matrix, and finally minimizes the residual to obtain the spectral peak. The angle corresponding to the peak is the desired azimuth angle of the radiation source. Compared to graph Fourier transform methods, this method avoids multiple eigenvalue calculations of the matrix, significantly improving computational speed in two-dimensional search, improving resolution, and also enhancing accuracy compared to traditional music algorithms.

[0004] The technical solution adopted in this invention is:

[0005] A two-dimensional DOA estimation method for circular arrays based on graph signal processing is proposed. A single-source signal is incident on a uniform circular array from an unknown angle. The array antenna consists of M array elements, and the number of array elements equals the number of channels. After receiving the signal, each array element sends it to the processor through its own transmission channel. The algorithm proposed in this paper includes the following steps:

[0006] S1. Obtain the received signal matrix X = [x[1], x[2], ..., x[L]], with a total of L snapshots. The received data at the l-th snapshot is x[l] = A(θ)s[l] + n[l], where s[l] and n[l] are the received signal and noise, respectively. For an M×1 dimensional uniform circular array manifold, its expression is:

[0007]

[0008] In the formula θ and These are the incident azimuth and elevation angles, respectively, and the array radius r is set to 1 / 2 of the incident wavelength λ.

[0009] S2. Construct the graph adjacency matrix B of the array, such that Assuming that each element is connected only to its adjacent elements, the adjacency matrix B is set in the following form:

[0010]

[0011] in And construct the array spatial graph according to the adjacency matrix form, such as Figure 1 As shown, the array is set up according to the spatial domain diagram.

[0012] S3. Construct the residual ε = BX - X = (BI)n, and under the background of additive Gaussian white noise, obtain the covariance matrix of ε using the properties of Gaussian random vectors. Finally, the probability density function of ε is obtained as follows:

[0013] S4. Perform maximum likelihood estimation on the residual ε to obtain its estimator as x. H (BI)Q -1 (BI)x.

[0014] S5. Transform the estimator into the form trace(x) H (BI)Q -1 (BI)x), and perform a two-dimensional spectral peak search to find the incident parameters that minimize the residual, i.e.

[0015]

[0016] Obtain DOA estimation results

[0017] The beneficial effects of this invention are that it can accurately estimate the incident parameters of the radiation source, namely the azimuth and elevation angles. Compared with the graphical Fourier transform method, it eliminates the need to calculate eigenvalues ​​multiple times in a two-dimensional search, significantly reducing computation time. The accuracy is also improved compared to the traditional music algorithm. The method is simple and effective. Attached Figure Description

[0018] Figure 1 The spatial domain graph of the array constructed based on the adjacency matrix;

[0019] Figure 2 To estimate the peak diagram of DOA for a uniform circular array under a fixed signal-to-noise ratio and number of snapshots;

[0020] Figure 3 A comparison chart of DOA estimation performance for a uniform circular array under different signal-to-noise ratios;

[0021] Figure 4 A comparison chart of DOA estimation performance of a uniform circular array in a 10dB signal-to-noise ratio environment under different snapshot numbers;

[0022] Figure 5 A comparison chart of DOA estimation performance of a uniform circular array in a 5dB signal-to-noise ratio environment under different snapshot numbers;

[0023] Figure 6 A comparison of DOA estimation performance for a uniform circular array in a 0dB signal-to-noise ratio environment under different snapshot numbers;

[0024] Figure 7 The graph shows a comparison of DOA estimation performance for a uniform circular array in an environment with a signal-to-noise ratio of -10dB under different snapshot numbers. Detailed Implementation

[0025] The present invention will now be described in detail with reference to embodiments:

[0026] Assuming the uniform circular array has 8 elements, 10 snapshots, and a signal-to-noise ratio of 10dB, using... A two-dimensional search was performed on the azimuth and elevation angles, resulting in the spectral peak diagram shown below. Figure 2 As shown. Next, 100 Monte Carlo simulations were performed to model some scenarios. First, DOA estimation was conducted under different signal-to-noise ratios with a fixed number of 8 array elements and 10 snapshots. The root mean square error (RMSE) was used to measure the accuracy of the DOA estimation, i.e.:

[0027]

[0028] Where θ i and These measures the azimuth and elevation angles, θ and θ, respectively. These are the azimuth and elevation angles, respectively. The simulation results are as follows: Figure 3 As shown. Then, with a fixed number of array elements of 8 and a fixed signal-to-noise ratio of 10dB, DOA estimation was performed under different snapshot numbers to verify the algorithm performance, as shown. Figure 4 As shown. Keeping the number of array elements constant and the signal-to-noise ratio fixed at 5dB, DOA estimation is performed under different snapshot numbers to verify the algorithm performance, as shown below. Figure 5 As shown. Keeping the number of array elements constant and the signal-to-noise ratio fixed at 0dB, DOA estimation is performed under different snapshot numbers to verify the algorithm performance, as shown below. Figure 6 As shown. Keeping the number of array elements constant and the signal-to-noise ratio fixed at -10dB, DOA estimation is performed under different snapshot numbers to verify the algorithm performance, as shown below. Figure 7 As shown.

[0029] Direction finding results:

[0030] To verify the effectiveness of the DOA estimation algorithm, we observed its performance by changing the signal-to-noise ratio and the number of snapshots. Figures 1-6 It can be observed that as the signal-to-noise ratio, number of snapshots, etc. change, the estimation error is almost always lower than or equal to that of the traditional music algorithm, which confirms the effectiveness of the novel uniform circular array DOA estimation algorithm proposed in this invention.

Claims

1. A two-dimensional DOA estimation method for a circular array based on graph signal processing, comprising a circular array of M elements receiving a single-source signal transmitted from an unknown angle, wherein the number of elements is defined as equal to the number of channels, and each element performs DOA estimation after receiving the signal, characterized in that... Includes the following steps: S1. Define the obtained received signal matrix as follows: The total number of snapshots is L, and the received data at the l-th snapshot is In the formula and These are the received signal and noise, respectively. For an M×1 dimensional uniform circular array manifold, the expression is: ， In the formula and These are the incident azimuth and elevation angles, respectively, and the array radius r is set to the incident wavelength. 1 / 2; S2. Construct the graph adjacency matrix of the array. , making And set each array element to connect only to its adjacent array elements, and set the adjacency matrix. Set it to the following format: ， in , Construct the array spatial graph based on the adjacency matrix form; S3, Construction Residual Against an additive white Gaussian noise background, by complex Gaussian random Find the properties of vectors covariance matrix Finally, we got The probability density function is: ; S4, Regarding residuals Performing maximum likelihood estimation, we obtain its estimator as follows: ; S5. Transform the estimator into the following form: And perform a two-dimensional spectral peak search to find the incident parameters that minimize the residual, i.e. ， Obtain DOA estimation results .

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