Radar Direction of Arrival Estimation Method Based on Alternating Descent OG-IAA

Abstract

The present invention discloses a radar direction-of-arrival estimation method based on alternating descent (OG-IAA). The method constructs an auxiliary dictionary matrix, uses a first-order Taylor expansion to approximate the steering vector of the direction of arrival that deviates from a predefined angular grid point, and uses IAA iteration to obtain the spatial amplitude spectrum and the angular offset of the DOA, and then updates the reconstruction dictionary matrix. The present invention uses a single snapshot echo signal and a dictionary matrix to estimate the initial spatial power spectrum. The spatial amplitude spectrum and the angular offset of the direction of arrival are then alternately optimized during the IAA iteration process, and the reconstruction dictionary matrix is ​​continuously updated. This process forms the alternating descent (OG-IAA). The method can estimate the direction of arrival that deviates from a predefined angular grid point, using only a single IAA estimation to alternately optimize the spatial amplitude spectrum and the angular offset, reducing the algorithm's computational complexity and facilitating engineering implementation.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and more specifically to a radar direction-of-arrival (DOA) estimation method based on an alternating descent off-grid iterative adaptive approach (OG-IAA) in the field of radar parameter estimation. The present invention can be used to estimate the direction of arrival (DOA) of an array radar echo signal. Background Art

[0002] Direction of arrival estimation is an important component of array signal processing and plays a vital role in radar, communications, electronic countermeasures, biomedicine and other fields. The direction of arrival estimation method based on alternating descent requires the selection of a sparse metric to reconstruct the signal on a predefined discrete dictionary grid. The iterative adaptive algorithm IAA (Iterative Adaptive Approach) as a DOA estimation method has attracted widespread attention due to its excellent performance. The algorithm uses weighted least squares as the cost function, which is similar to finding a linear unbiased estimator. It only requires a single snapshot echo signal to estimate the signal covariance matrix, and continuously iteratively updates the signal amplitude and power. It has high accuracy even when processing coherent sources. However, the algorithm can only accurately estimate the sources located at the predefined angle grid points, and will produce large errors for sources deviating from the angle grid points.

[0003] Beijing University of Science and Technology and Chengdu University of Information Technology jointly applied for a patent document "High-resolution narrowband DOA estimation algorithm and implementation method for wireless signals" (application number: CN 202110573650.5, application date: 2021.05.25, authorization announcement number: CN 113420411 B). A high-resolution narrowband DOA estimation algorithm and implementation method for wireless signals are disclosed. The implementation steps of this method are as follows: first, a two-dimensional antenna array data model is established. In the two-dimensional uniform rectangular array model, the received signal exists only within the echo direction range of the plane angle pitch angle, and the range is evenly divided into different angle grid points; secondly, the two-dimensional IAA algorithm is used to obtain the signal power spectrum and determine the echo direction range of the received signal; finally, the Gram-Schmidt orthogonal decomposition and 2-DFFT method are used to reduce the computational complexity of the fast iterative adaptive algorithm SIAA (Swift Iterative Adaptive Approach) to complete the direction of arrival estimation. However, this method still has the disadvantage that it cannot estimate the direction of arrival that deviates from the predefined angle grid points. In reality, the direction of arrival is random and does not necessarily exist at the predefined angle grid points, so accurate DOA estimation cannot be achieved.

[0004] Jie Yunkang et al. proposed an off-grid DOA estimation method based on a modified iterative adaptive power spectrum algorithm in their paper "A method for off-grid DOA estimation based on iterative adaptation" (Journal of Electronics and Information Technology, 2023, 45(10): 3805-3811) to address the large error in the direction of arrival estimation caused by the mismatch between the true source position and the dictionary grid. The implementation steps of this method are as follows: first, the signal power spectrum is obtained by a modified iterative adaptive algorithm, and the corresponding grid angle of the power peak is read as a rough estimation result; second, the square error cost function is used to expand the cost function by the second order Taylor and minimize it to obtain the initial offset; third, the power component and the offset are alternately optimized to achieve high-precision off-grid DOA estimation. The method still has the disadvantage that its alternating optimization process requires multiple IAA estimates, and it requires multiple snapshots to accurately estimate the noise power, which significantly increases the amount of calculation and operation time, and the real-time performance of the engineering implementation is poor. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a radar direction of arrival estimation method based on alternating descent OG-IAA, which is used to solve the problem that the fast iterative adaptive algorithm in the prior art cannot estimate the direction of arrival of points that deviate from the predefined angle grid and cannot achieve accurate DOA estimation, and the problem that the alternating optimization process in the off-grid DOA estimation method based on iterative adaptation requires multiple IAA estimations and multiple snapshots to accurately estimate the noise power, resulting in increased calculation amount and operation time.

[0006] To achieve the above objectives, the present invention is based on the following principles: A single-snapshot echo signal and a dictionary matrix are used to simply estimate the initial spatial power spectrum. An auxiliary dictionary matrix is ​​constructed, and a first-order Taylor expansion is used to approximate the steering vector of the direction of arrival (DOA) that deviates from a predefined angular grid point. The angular offset of the DOA is calculated and the reconstructed dictionary matrix is ​​updated. This solves the problem of fast iterative adaptive algorithms being unable to estimate the DOA that deviates from the predefined angular grid point, resulting in an inability to achieve accurate DOA estimation, thus facilitating engineering implementation. The present invention alternately optimizes the spatial amplitude spectrum and the angular offset of the DOA, continuously updates the reconstructed dictionary matrix, and reaches a stable convergence state. This avoids the problem of multiple IAA estimations and snapshots required for accurate noise power estimation in off-grid DOA estimation methods based on iterative adaptive methods during the alternating optimization process, reducing the computational complexity and operation time, thereby improving the performance of the DOA estimation method. Using single-snapshot echo data and the dictionary matrix, the initial spatial power spectrum is estimated. Then, during the IAA iteration, the spatial amplitude spectrum and the angular offset of the DOA are alternately optimized, and the reconstructed dictionary matrix is ​​continuously updated. This process forms an alternating descending OG-IAA for DOA estimation.

[0007] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0008] Step 1: Divide the space into uniform angle grid points, construct a dictionary matrix, and obtain a single snapshot echo signal;

[0009] Step 2, estimate the initial spatial power spectrum;

[0010] Step 3: Perform IAA iteration to obtain the spatial amplitude spectrum and spatial power spectrum after the current iteration;

[0011] Step 4: construct an auxiliary dictionary matrix and use a first-order Taylor expansion to approximate the steering vector of the direction of arrival that deviates from the predefined angle grid point;

[0012] Step 5: Calculate the angle offset of the direction of arrival and update the reconstruction dictionary matrix;

[0013] Step 6: Determine whether the current offset meets the termination condition. If so, execute step 7; otherwise, execute step 3.

[0014] Step 7, As a result of the direction of arrival estimation, θ l Indicates the direction of arrival at the lth angle grid point in the space where the radar receives the echo signal during the current iteration, δ l Indicates the angular offset of the direction of arrival at the lth angle grid point in the current iteration.

[0015] Compared with the prior art, the present invention has the following advantages:

[0016] First, the auxiliary dictionary matrix constructed by the present invention uses a first-order Taylor expansion to approximate the steering vector of the direction of arrival that deviates from the predefined angle grid point, solves the angular offset of the direction of arrival and updates the reconstructed dictionary matrix, thereby solving the problem that the fast iterative adaptive algorithm of the prior art cannot estimate the direction of arrival that deviates from the predefined angle grid point and cannot achieve accurate DOA estimation, making the present invention convenient for handling actual engineering situations.

[0017] Second, since the present invention alternately optimizes the spatial amplitude spectrum and the angular offset of the wave arrival direction, continuously updates the reconstructed dictionary matrix and reaches a stable convergence state, it avoids the problem that the alternating optimization process in the off-grid DOA estimation method based on iterative adaptation in the prior art requires multiple IAA estimates and multiple snapshots to accurately estimate the noise power. This reduces the amount of algorithm calculation in the present invention, thereby improving the performance and efficiency of the DOA estimation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the present invention;

[0019] Figure 2 It is a simulation diagram of the present invention. DETAILED DESCRIPTION

[0020] The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0021] Reference Figure 1 The specific implementation steps of the present invention are further described in detail in the following embodiments.

[0022] Step 1: Divide the space into uniform angle grid points, construct a dictionary matrix, and obtain a single snapshot echo signal.

[0023] Step 1.1: Based on the basic parameters of the radar array and the concept of spatial sparsity, the space where the radar receives the echo signal is divided into M angular grid points with equal intervals r, where r is a positive number less than or equal to 5, and M is

[0024] In the embodiment of the present invention, the interval r is set to 2, and the radar receives the echo signal after spatial equidivision, and then divides it into 90 angular grid points.

[0025] Step 1.2, construct the dictionary matrix according to the following formula:

[0026] A(θ)=[a(θ1),a(θ2),…,a(θ l ),...,a(θ L )]

[0027] Where A(θ) represents a dictionary matrix composed of the steering vectors of all angular grid points in the space where the radar receives the echo signal. The matrix size is N×L, where N represents the total number of elements in the matrix rows, and the value of N is equal to the number of radar array elements. L represents the total number of elements in the matrix columns, and the value of L is equal to the total number of angular grid points M. a(θ l ) represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l The steering vector is l=1,2,...,L.

[0028] The a(θ l ) is obtained by the following formula:

[0029]

[0030] Among them, e (·) represents the exponential operation with the natural constant e as the base, j represents the imaginary unit symbol, π represents the ratio of circumference to circumference, d represents the spacing between radar array elements, λ represents the wavelength, Q represents the total number of radar array elements, (·) T In the embodiment of the present invention, the total number of radar array elements Q = 10, the wavelength λ = 1m, and the spacing between radar array elements

[0031] Step 1.3: At a certain moment, obtain the single snapshot echo data y, y = A(θ)s + n, where s represents the spatial complex amplitude vector of the radar received echo signal, s = [s1, s2, ..., s l …,s L ] T , s l Represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l The complex amplitude of the signal source, s l ∈s,l=1,2,...,L,n means the mean is 0 and the variance is σ 2 , additive Gaussian white noise with covariance matrix Q.

[0032] Step 2: Estimate the initial spatial power spectrum.

[0033] Step 2.1: Estimate the initialization source amplitude according to the following formula:

[0034]

[0035] in, Represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l The initialization amplitude, (·) H represents the conjugate transpose operation, and y represents the single snapshot echo signal.

[0036] Step 2.2: Estimate the initial source power according to the following formula:

[0037]

[0038] in, Represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l The initialization power of , |·| represents the absolute value operation.

[0039] In step 2.3, the spatial power spectrum is initialized by combining the initialization power of the direction of arrival at all angle grid points in the space where the radar receives the echo signal according to the following formula:

[0040]

[0041] in, Represents the initialization of the spatial power spectrum.

[0042] Step 3: Perform IAA iteration to obtain the spatial amplitude spectrum and spatial power spectrum after the current iteration.

[0043] In step 3.1, estimate the covariance matrix of the single snapshot echo signal according to the following formula:

[0044]

[0045] Where R represents the covariance matrix of the single snapshot echo signal, diag(·) represents the operation of forming a diagonal matrix with the vector in the brackets as the main diagonal element, Represents the spatial power spectrum of the current iteration process. In the first iteration The value of

[0046] Step 3.2, estimate the source amplitude in the current iteration according to the following formula:

[0047]

[0048] in, Indicates the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal during the current iteration l The amplitude of (·) -1 Indicates the inverse operation.

[0049] In step 3.3, the spatial amplitude spectrum is formed by the amplitude of the direction of arrival at all angle grid points in the space where the radar receives the echo signal during the current iteration according to the following formula:

[0050]

[0051] in, Represents the spatial amplitude spectrum of the current iteration process.

[0052] Step 3.4, based on the relationship between amplitude and power: According to the following formula, the spatial power spectrum of the current iteration process is obtained:

[0053]

[0054] in, It represents the spatial power spectrum of the radar received echo signal in the space composed of the power of the wave arrival direction at all angle grid points in the current iteration process.

[0055] Step 4: construct an auxiliary dictionary matrix and use a first-order Taylor expansion to approximate the steering vector of the direction of arrival that deviates from the predefined angle grid point.

[0056] Step 4.1: According to the following formula, solve the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal: l The steering vector a(θ l )’s first-order derivative b(θ l ):

[0057]

[0058] Where n represents the array element position vector, n = [0, 1, ..., N-1] T , ○ represents the Hadamard product operation.

[0059] In step 4.2, the first-order derivatives of the direction-of-arrival steering vectors at all angular grid points in the space where the radar receives the echo signal are formed into an auxiliary dictionary matrix.

[0060] In step 4.3, to address the issue of the fast iterative adaptive algorithm being unable to estimate the direction of arrival (DOA) for points that deviate from the predefined angle grid, and thus failing to achieve accurate DOA estimation, a first-order Taylor expansion is used to approximate the steering vector for the direction of arrival for points that deviate from the predefined angle grid, as shown in the following equation:

[0061]

[0062] in, represents the true direction of arrival from a predefined angle grid point, Indicates the true direction of arrival from a predefined angle grid point The steering vector, θ l Indicates the distance to the direction of arrival The nearest angular grid point, θ l ∈{θ1,θ2,...,θ L}.

[0063] Step 5: Calculate the angle offset of the direction of arrival and update the reconstruction dictionary matrix.

[0064] Step 5.1: Calculate the angle offset of the direction of arrival according to the following formula:

[0065]

[0066] Where δ represents the angular offset of the direction of arrival, δ=[δ1,δ2,...,δ l ,…,δ L ] T , Represents a pseudo-inverse operation.

[0067] Step 5.2, update the reconstruction dictionary matrix according to the following formula:

[0068]

[0069] Among them, B(θ) represents the auxiliary dictionary matrix, B(θ)=[b(θ1),b(θ2),…,b(θ L )].

[0070] Step 6: Determine whether the current offset meets the termination condition. If so, execute step 7; otherwise, execute step 3.

[0071] The termination condition refers to the situation where one of the following conditions is met:

[0072] Condition 1: The difference in the angle offset between the two arrival directions is less than or equal to 10 -4 ;

[0073] Condition 2: The maximum number of iterations set according to the DOA estimation accuracy requirement is reached, which is 3N.

[0074] Since the alternating optimization process in the iterative adaptive off-grid DOA estimation method requires multiple IAA estimates and multiple snapshots are needed to accurately estimate the noise power, the computational complexity and operation time increase significantly, and the real-time performance of the engineering implementation is poor.

[0075] The embodiment of the present invention repeats steps 3, 4, and 5 to alternately optimize the spatial amplitude spectrum. And the angle offset δ of the wave direction, and update the reconstruction dictionary matrix every iteration The termination condition is that the difference in the angle offset between the two arrival directions is less than or equal to 10 -4 , or reaching the maximum number of iterations (3N) set according to the DOA estimation accuracy requirement. This method uses only the echo data of a single snapshot to achieve high-precision DOA estimation, eliminating the need to solve for noise power and performing only one IAA estimation. This reduces the algorithm's computational effort and system complexity, facilitating engineering implementation.

[0076] Step 7, As a result of the direction of arrival estimation, θ l Indicates the direction of arrival at the lth angle grid point in the space where the radar receives the echo signal during the current iteration, δ l Indicates the angular offset of the direction of arrival at the lth angle grid point in the current iteration.

[0077] The effects of the present invention are further described below in conjunction with simulation experiments:

[0078] 1. Simulation experiment conditions:

[0079] The hardware platform of the simulation experiment of the present invention is: the processor is Intel (R) Core (TM) i5-7300HQ CPU, the main frequency is 2.50GHz, and the memory is 4.00GB.

[0080] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system and MATLAB R2016b.

[0081] 2. Simulation content and results analysis:

[0082] The simulation experiment of the present invention adopts the method and iterative adaptive algorithm of the present invention. The coarse grid interval in the iterative adaptive algorithm is 2° and the fine grid interval is 0.1°. In an environment where the number of radar array elements is 10, the true direction of arrival deviating from the predefined angle grid point is 22.5° and 54.8°. The detection signal-to-noise ratio changes from -10dB to 30dB in steps of 5dB. 500 Monte Carlo experiments are performed to obtain the estimated value of the direction of arrival. The resolution probability of the direction of arrival estimation and the root mean square error of the estimated value in the 500 experiments are statistically calculated, and a curve is plotted as shown below. Figure 2 shown.

[0083] The following combination Figure 2 The simulation result diagram of the present invention is further described.

[0084] Figure 2 The figure shows the estimated values ​​of the direction of arrival obtained by the method of the present invention and the iterative adaptive algorithm under the same simulation conditions. In an environment where the number of radar array elements is 10, the resolution probability of the direction of arrival estimation and the root mean square error of the estimated value are compared.

[0085] Figure 2 The comparison chart is obtained when the detection signal-to-noise ratio changes from -10dB to 30dB in 5dB steps. Figure 2 The curve marked with “○” in the figure represents the result curve of fine grid simulation using iterative adaptive algorithm. Figure 2 The curve marked with “●” in the figure represents the result curve of the coarse grid simulation using the iterative adaptive algorithm. Figure 2 The curve marked with "*" in FIG. 1 represents the result curve of simulation using the method of the present invention.

[0086] Figure 2 The horizontal axis in (a) represents the detection signal-to-noise ratio in dB, and the vertical axis represents the resolution probability of the direction of arrival estimation.

[0087] Figure 2 The horizontal axis in (b) represents the detection signal-to-noise ratio in dB, and the vertical axis represents the root mean square error of the direction of arrival estimate.

[0088] Depend on Figure 2Comparison of the three curves in (a) shows that when the detection signal-to-noise ratio is -10dB, -5dB, 0dB, 5dB, 10dB, 15dB, 20dB, 25dB and 30dB, the resolution probabilities of DOA estimation obtained by the method of the present invention are 5.00%, 26.80%, 77.80%, 97.60%, 99.60%, 100%, 100%, 100% and 100%, respectively. When the iterative adaptive algorithm is used in the case of fine grid, the resolution probabilities of DOA estimation obtained are 5.00%, 29.20%, 81.00%, 97.60%, 99.80%, 100%, 100%, 100% and 100%, respectively. Using the iterative adaptive algorithm in the case of coarse grid, the resolution probabilities of DOA estimation obtained are: 6.80%, 28.60%, 77.80%, 95.60%, 99.60%, 100%, 100%, 100% and 100%. Figure 2 Comparison of the three curves in (a) shows that, in an environment with 10 radar elements and the same detection signal-to-noise ratio, the resolution probabilities of the method of the present invention and the iterative adaptive algorithm in the coarse and fine grid conditions are not much different. Both increase with the increase of the detection signal-to-noise ratio and can reach over 90% in a high signal-to-noise ratio environment.

[0089] Depend on Figure 2Comparison of the three curves in (b) shows that when the detection signal-to-noise ratio is -10dB, -5dB, 0dB, 5dB, 10dB, 15dB, 20dB, 25dB, and 30dB, the root mean square errors of the DOA estimates obtained using the method of the present invention are 2.4675°, 2.3994°, 1.9560°, 1.2739°, 0.7504°, 0.4170°, 0.2355°, 0.1398°, and 0.0841°, respectively. Using the iterative adaptive algorithm in the case of a fine grid, the root mean square errors of the DOA estimates are 2.8870°, 2.4624°, 2.1139°, 1.4928°, 0.9874°, 0.5547°, 0.2979°, 0.1826°, and 0.1059°, respectively. The RMS errors of the DOA estimates obtained using the iterative adaptive algorithm for a coarse grid are 3.0857°, 2.2816°, 1.9758°, 1.4792°, 1.1104°, 0.8512°, 0.8041°, 0.7870°, and 0.7474°, respectively. This indicates that, in an environment with 10 radar elements and the same detection signal-to-noise ratio (SNR), the RMS errors of the DOA estimates obtained using both the method of the present invention and the iterative adaptive algorithm for both coarse and fine grids decrease as the detection SNR increases. The RMS errors of the DOA estimates obtained using both the method of the present invention and the iterative adaptive algorithm for fine grids are significantly lower than those obtained using the coarse grid when the detection SNR is high. However, the RMS errors of the DOA estimates obtained using the method of the present invention and the iterative adaptive algorithm for fine grids are not significantly different. It is proved that in an environment with 10 radar array elements, the method of the present invention achieves the DOA estimation performance of the iterative adaptive algorithm in the fine grid condition, and can accurately estimate the direction of arrival of the grid point that deviates from the predefined angle; the computational complexity of each iteration of IAA is O(N 2 L), the value of L in the method of the present invention is significantly smaller than the value of L in the iterative adaptive algorithm in the case of fine grids, so the computational complexity of the implementation process is greatly reduced, the computational complexity is reduced, the performance of DOA estimation is improved, and it is convenient for engineering applications.

Claims

1. A radar direction of arrival estimation method based on alternating descent (OG-IAA), characterized in that: A first-order Taylor expansion is used to approximate the steering vector of the direction of arrival (DOA) that deviates from a predefined angle grid point. An iterative adaptive algorithm is applied to alternately optimize the spatial amplitude spectrum and the offset. The reconstructed dictionary matrix is ​​continuously updated until it stabilizes and the DOA estimation result is output. The specific steps of this DOA estimation method include the following: Step 1: Divide the space into uniform angle grid points, construct a dictionary matrix, and obtain a single snapshot echo signal; Step 2, estimate the initial spatial power spectrum; Step 3: Perform IAA iteration to obtain the spatial amplitude spectrum and spatial power spectrum after the current iteration; Step 4: construct an auxiliary dictionary matrix and use a first-order Taylor expansion to approximate the steering vector of the direction of arrival that deviates from the predefined angle grid point; The steps of constructing the auxiliary dictionary matrix are as follows: The first step is to solve the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal according to the following formula: l The steering vector a(θ l )’s first-order derivative b(θ l ): Where n represents the array element position vector, n = [0, 1, ..., N-1] T , Represents the Hadamard product operation; The second step is to form an auxiliary dictionary matrix with the first-order derivatives of the direction-of-arrival steering vector at all angular grid points in the space where the radar receives the echo signal; Step 5: Calculate the angle offset of the direction of arrival and update the reconstruction dictionary matrix; Step 6: Determine whether the angular offset of the current direction of arrival satisfies the termination condition. If so, proceed to step 7; otherwise, proceed to step 3. Step 7, As the result of the direction of arrival estimation, θ l Indicates the direction of arrival at the lth angle grid point in the space where the radar receives the echo signal during the current iteration, δ l Indicates the angular offset of the direction of arrival at the lth angle grid point in the current iteration.

2. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 1, characterized in that: The division of space into uniform angular grid points in step 1 means that, based on the basic parameters of the radar array and the concept of spatial sparsity, the space where the radar receives the echo signal is divided into M angular grid points at equal intervals r, where r is a positive number less than or equal to 5, and M is 3. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 2, characterized in that: The dictionary matrix described in step 1 is as follows: A(θ)=[a(θ1),a(θ2),…,a(θ l ),...,a(θ L )] Where A(θ) represents a dictionary matrix composed of the steering vectors of all angular grid points in the space where the radar receives the echo signal. The matrix size is N×L, where N represents the total number of elements in the matrix rows, and the value of N is equal to the number of radar array elements. L represents the total number of elements in the matrix columns, and the value of L is equal to the total number of angular grid points M. a(θ l ) represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l Steering vector, l = 1, 2, ..., L; a(θ l ) can be obtained by the following formula: Among them, e (·) represents the exponential operation with the natural constant e as the base, j represents the imaginary unit symbol, π represents the ratio of circumference to circumference, d represents the spacing between radar array elements, λ represents the wavelength, Q represents the total number of radar array elements, (·) T Represents a transpose operation.

4. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 3, characterized in that: The steps for estimating the initial spatial power spectrum described in step 2 are as follows: The first step is to estimate the initialization source amplitude according to the following formula: in, Represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l The initialization amplitude, (·) H represents the conjugate transpose operation, and y represents the single snapshot echo signal; The second step is to estimate the initial source power according to the following formula: in, Represents the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal l Initialization power, |·| represents the absolute value operation; The third step is to initialize the spatial power spectrum by combining the initialization power of the wave arrival direction at all angle grid points in the space where the radar receives the echo signal according to the following formula: in, Represents the initialization of the spatial power spectrum.

5. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 4, characterized in that: The steps for obtaining the spatial amplitude spectrum and spatial power spectrum described in step 3 are as follows: The first step is to estimate the covariance matrix of the single snapshot echo signal according to the following formula: Where R represents the covariance matrix of the single snapshot echo signal, diag(·) represents the operation of forming a diagonal matrix with the vector in the brackets as the main diagonal element, Represents the spatial power spectrum of the current iteration process. In the first iteration The value of The second step is to estimate the source amplitude in the current iteration process according to the following formula: in, Indicates the direction of arrival θ at the lth angle grid point in the space where the radar receives the echo signal during the current iteration l The amplitude of (·) -1 Indicates the inverse operation; In the third step, the spatial amplitude spectrum is formed by the amplitude of the direction of arrival at all angle grid points in the space where the radar receives the echo signal during the current iteration according to the following formula: in, Represents the spatial amplitude spectrum of the current iteration process; The fourth step is based on the relationship between amplitude and power: According to the following formula, the spatial power spectrum of the current iteration process is obtained: in, It represents the spatial power spectrum of the radar received echo signal in the space composed of the power of the wave arrival direction at all angle grid points in the current iteration process.

6. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 5, characterized in that: The steering vector of the direction of arrival that deviates from the predefined angle grid point using the first-order Taylor expansion described in step 4 is completed by the following formula: in, represents the true direction of arrival from a predefined angle grid point, Indicates the true direction of arrival from a predefined angle grid point The steering vector, θ l Indicates the distance to the direction of arrival The nearest angular grid point, θ l ∈{θ1,θ2,...,θ L }.

7. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 6, characterized in that: The angle offset of the direction of arrival described in step 5 is obtained by the following formula: Where δ represents the angular offset of the direction of arrival, δ=[δ1,δ2,...,δ l ,...,δ L ] T , Represents a pseudo-inverse operation.

8. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 7, characterized in that: The reconstructed dictionary matrix described in step 5 is obtained as follows: Among them, B(θ) represents the auxiliary dictionary matrix, B(θ)=[b(θ1),b(θ2),...,b(θ L )].

9. The radar direction of arrival estimation method based on alternating descent (OG-IAA) according to claim 8, characterized in that: The termination condition described in step 6 refers to the situation where one of the following conditions is met: Condition 1: The difference in the angle offset between the two arrival directions is less than or equal to 10 -4 ; Condition 2: The maximum number of iterations set according to the DOA estimation accuracy requirement is reached, which is 3N.

Images