Two-dimensional DOA estimation method based on extended array motion sampling

Abstract

The invention relates to a two-dimensional DOA estimation method based on extended array motion sampling, and the method comprises the following steps: determining the initial array structure of each sub-array based on the total number of array elements, and obtaining array parameters including the array spacing, the motion direction, the motion rate and the sampling interval; based on the array parameters, the array manifold of each sub-array is determined in combination with the relative positions of different sub-arrays; determining a receiving signal model of each sub-array based on the array manifold in combination with dynamic sub-array characteristics; determining a received signal covariance matrix based on the received signal model of each sub-array in combination with motion sampling and array characteristics; deducing a multi-dimensional parameter estimation algorithm based on ESPRIT according to the virtual array structure based on the received signal covariance matrix; based on a fuzzy phase estimated by a multi-dimensional parameter estimation algorithm, a unique solution is obtained by deblurring by utilizing array characteristics and an angle relation and is used as a final estimated two-dimensional DOA parameter. Compared with the prior art, the method has the advantages that the calculation amount is low while high-precision DOA estimation is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of antenna array signal processing, and in particular to a two-dimensional DOA estimation method based on extended array motion sampling. Background Art

[0002] In recent decades, with the gradual adoption of phased arrays in communications, radar, voice, and navigation systems, array signal processing has garnered widespread attention and in-depth research. Compared to traditional one-dimensional direction of arrival (DOA) estimation, two-dimensional DOA estimation for target signals provides three-dimensional spatial information about the target, effectively improving the ability to locate the target signal. Therefore, it has always been a research hotspot and a challenge in array signal processing.

[0003] However, conventional planar arrays (such as parallel arrays and L-shaped arrays) consume significant hardware resources to achieve high-precision 2D DOA estimation. Furthermore, conventional planar arrays are susceptible to strong inter-element coupling, resulting in limited improvement in direction-finding accuracy. Furthermore, traditional multidimensional parameter estimation methods often impose significant computational complexity for 2D DOA estimation, making them difficult to meet the real-time processing requirements of real-world scenarios. These issues are crucial for 2D DOA estimation based on multidimensional arrays and should be addressed.

[0004] CN114487990A discloses a two-dimensional DOA estimation method, apparatus, device, and medium based on parallel nested arrays. The method includes: calculating the received signal of each subarray in three parallel nested arrays; calculating the covariance matrix of each subarray based on the received signal of each subarray, and expanding the covariance matrix to obtain a virtual covariance matrix; calculating the mutual covariance matrix between subarrays based on the received signal of each subarray, and expanding the mutual covariance matrix to obtain a virtual mutual covariance matrix; constructing a DOA estimation matrix based on the virtual covariance matrix and the virtual mutual covariance matrix; performing eigenvalue decomposition on the DOA estimation matrix, and calculating the angle between the incident signal and the X-axis and the angle between the incident signal and the Y-axis based on the decomposed eigenvalues. This DOA estimation method not only achieves two-dimensional angle balance estimation with low complexity, but also greatly improves the estimation accuracy.

[0005] However, this method has the following limitations: first, its array configuration must satisfy a three-parallel nested structure, resulting in a strict arrangement of array elements and a high array cost; second, since the spacing between some array elements in the nested array is small, a strong mutual coupling effect will be introduced, resulting in a decrease in DOA estimation performance. Summary of the Invention

[0006] The purpose of the present invention is to provide a two-dimensional DOA estimation method based on extended array motion sampling.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A two-dimensional DOA estimation method based on extended array motion sampling includes the following steps:

[0009] Step 1: Determine the initial array structure of each sub-array based on the total number of array elements, and obtain array parameters including array spacing, motion direction, motion rate, and sampling interval;

[0010] Step 2: Based on the array parameters and the relative positions of different sub-arrays, determine the array manifold of each sub-array;

[0011] Step 3: Based on the array manifold and combined with the dynamic sub-array characteristics, determine the received signal model of each sub-array;

[0012] Step 4: Determine the received signal covariance matrix based on the received signal model of each sub-array, combined with motion sampling and array characteristics;

[0013] Step 5: Based on the received signal covariance matrix, derive a multi-dimensional parameter estimation algorithm based on ESPRIT according to the virtual array structure;

[0014] Step 6: Based on the ambiguous phase estimated by the multidimensional parameter estimation algorithm, the array characteristics and the angle relationship are used to deambiguate and obtain a unique solution as the final estimated two-dimensional DOA parameter.

[0015] The array is a planar array structure, consisting of sub-array 1 and sub-array 2. Sub-array 1 is a sparse uniform linear array with a total of M array elements. The array element spacing is D1d, where d = λ / 2, and λ represents the wavelength of the signal. Sub-array 2 has only two array elements, which are located at a distance of D2d from the first and last array elements of sub-array 1.

[0016] A Cartesian coordinate system is established with the array as the yoz coordinate plane. The array moves in a uniform linear motion at a speed v in the x-axis direction, and is sampled at an interval τ, where vτ=D3d. The position of sub-array 1 at the time of sampling after time τ is recorded as sub-array 3. Where D1, D2, and D3 are all integers greater than 1 and are mutually prime.

[0017] The array position of the sub-array 1 is expressed as:

[0018] L1=[(0,0,0),(0,D1d,0),(0,2D1d,0),…,(0,(M-1)D1d,0)]

[0019] The array position of the sub-array 2 is expressed as:

[0020] L2=[(0,0,D2d),(0,(M-1)D1d,D2d)]

[0021] Sampling at time τ, the array position of the sub-array 3 is expressed as:

[0022] L3=[(D3A,0,0),(D3d,D1d,0),…,(D3d,(M-1)D1d,0)].

[0023] The array manifolds of the sub-arrays are:

[0024] The array manifold A1 of subarray 1 is:

[0025]

[0026] in, 1≤k≤K, K represents the number of signal sources, θ k represents the pitch angle of k signals measured from the positive direction of the z-axis, Represents the azimuth of k directions measured from the positive direction of the x-axis;

[0027] Combined with the relative position relationship between the arrays, the array manifold A2 of subarray 2 is determined as:

[0028]

[0029] in, β k =cosθ k ; The planes where subarrays 1 and 2 are located are always parallel to the yoz plane and have the same azimuth angle;

[0030] The array manifold d3 of the sub-array 3 sampled at time τ is:

[0031]

[0032] in, The planes where sub-arrays 1 and 3 are located are always parallel to the xoy plane, and have the same elevation angles.

[0033] The receiving signal models of the sub-arrays are:

[0034] The received signal model of subarray 1 is: y1(t)=A1*s(t)+n1(t);

[0035] The received signal model of subarray 2 is: y2(t)=A2*s(t)+n2(t);

[0036] The received signal model of subarray 3 is: y3(t) = A3*s(t+τ) + n1(t+τ); assuming that the incident signal sources are all far-field narrowband signals, then y3(t) = A3*s(t) + n1(t);

[0037] in, represents the incident signal source model of K signals, n1(t) is the noise vector of sub-array 1, and n2(t) is the noise vector of sub-array 2.

[0038] The received signal covariance matrix is ​​specifically:

[0039] The first received signal covariance matrix calculated based on the received signal model of subarray 1 and subarray 2 is:

[0040]

[0041] in,

[0042]

[0043]

[0044] Array manifold corresponding to the first received signal covariance matrix Right now It is equivalent to the covariance matrix of the received signal of 2M array elements, where R S represents the covariance matrix of the source signal, σ 2 represents the noise power, I 2M is a 2M×2M identity matrix defined as:

[0045]

[0046] The second received signal covariance matrix calculated based on the received signal model of subarray 1 and subarray 3 is:

[0047]

[0048] in,

[0049] The second received signal covariance matrix The corresponding array manifold Right now in,

[0050] The ESPRIT-based multidimensional parameter estimation algorithm is used to estimate the pitch angle θ and azimuth angle The specific steps include:

[0051] Perform eigenvalue decomposition on the covariance matrix of the received signal to obtain the signal subspace;

[0052] separating the virtual array into two identical overlapping sub-arrays based on the signal subspace;

[0053] Derived the phases between adjacent array elements based on the overlapping sub-arrays and calculated the average value, and performed fuzzy estimation based on the phase average value to obtain multiple groups of estimated values;

[0054] Based on the estimated values ​​and the coprime relationship between D1, D2, and D3, the pitch angle and the azimuth angle are estimated.

[0055] The phase between adjacent array elements in the y-axis direction derived based on the first received signal covariance matrix and α k Related to D1, it is expressed as:

[0056]

[0057]

[0058] in, is the matrix derived based on overlapping submatrices The estimated value of

[0059] Taking the phase average, the phase mean is:

[0060]

[0061] Depend on To α k Make an estimate and get the first set of fuzzy estimates The number of fuzzy estimates is equal to D1, l1 satisfies the condition l1∈[1,D1];

[0062] The phase ∈ between adjacent array elements in the z-axis direction derived based on the first received signal covariance matrix i,j,k and β k Related to D2, it is expressed as:

[0063]

[0064] in, is the estimated value of the matrix A1′ derived based on the overlapping sub-matrices,

[0065] Taking the phase average value k=1,2,…,K,

[0066] Depend on β k Make an estimate and get the second set of fuzzy estimates The number of fuzzy estimates is equal to D2, l2 satisfies the condition l2∈[1,D2].

[0067] The phase between adjacent array elements in the x-axis direction derived based on the second received signal covariance matrix and γk and is related to D3, expressed as:

[0068]

[0069] Taking the phase average, we get

[0070]

[0071] Depend on γ k Make an estimate and get the third set of fuzzy estimates The number of fuzzy estimates is equal to D3, l3 satisfies the condition l3∈[1,D3].

[0072] The step 6 is specifically as follows:

[0073] The following optimization problem is solved to deblur the image and find a unique solution for the elevation and azimuth angles:

[0074]

[0075] stl1∈[1,D1],l2∈[1,D2],l3∈[1,D3]

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] The array design of the present invention significantly increases the degree of freedom by expanding the virtual aperture, effectively reduces the hardware cost through array motion sampling, and at the same time, the sparse and uniform distribution of array elements has high arrangement flexibility and can greatly alleviate the mutual coupling effect between array elements. Based on this array structure, the present invention uses the joint construction of the covariance matrix to further reduce the mutual coupling effect and improve the estimation accuracy. At the algorithm level, through the efficient division of the signal subspace and the closed-form phase difference calculation, multi-dimensional search is avoided and the computational complexity is controlled within (where L represents the number of snapshots), which has advantages over traditional methods in terms of speed and stability, and is suitable for real-time direction of arrival estimation in multi-target and low signal-to-noise ratio scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 is a flow chart of the method of the present invention;

[0079] Figure 2 A schematic diagram of a three-dimensional array based on extended array motion sampling in one embodiment;

[0080] Figure 3 2D DOA estimation scatter plot based on extended array motion sampling in one embodiment, where (3a) represents the pitch angle estimation and (3b) represents the azimuth angle estimation;

[0081] Figure 4 2D DOA estimation root mean square error changes with signal-to-noise ratio in one embodiment;

[0082] Figure 5 FIG. 4 shows how the root mean square error of two-dimensional DOA estimation varies with the number of snapshots in one embodiment. DETAILED DESCRIPTION

[0083] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0084] This embodiment provides a two-dimensional Direction of Arrival (DOA) estimation method based on extended array motion sampling. This method leverages the unique structure and motion characteristics of dynamic subarrays to achieve high-precision two-dimensional spatial localization of target signals. First, the physical structure, element spacing, motion parameters (such as direction and velocity), and sampling interval of each subarray are determined based on the total number of array elements. This process considers the relative positional relationships between subarrays to optimize the array manifold design. Next, the array manifolds of each subarray are constructed using these parameters, and the received signal model is derived based on this. Subsequently, the received data covariance matrix is ​​obtained based on the array characteristics of each subarray and the motion sampling data. Based on this covariance matrix, a multidimensional parameter estimation method based on the ESPRIT algorithm is used to estimate parameters to determine the azimuth and elevation angles of the signal source. To address angular ambiguity, this method also introduces a deambiguation strategy that leverages the coprime of element spacings along different array dimensions and the two-dimensional angular mutual coupling relationship to determine a unique solution. Finally, a theoretical complexity analysis of the proposed two-dimensional DOA estimation method demonstrates that it achieves high-precision estimation while maintaining low computational complexity. Compared with existing direction-finding technologies, the proposed method not only reduces the mutual coupling effect, but also expands the array aperture and degrees of freedom, while effectively achieving high-precision two-dimensional DOA estimation with low complexity.

[0085] Specifically, such as Figure 1 As shown, the method includes the following steps:

[0086] Step 1: Determine the initial array structure of each sub-array based on the total number of array elements, and obtain array parameters including array spacing, motion direction, motion rate, and sampling interval.

[0087] The array mentioned in this embodiment is a planar array structure, such as Figure 2 As shown, it consists of sub-array 1 and sub-array 2. Sub-array 1 is a sparse uniform linear array with a total of M array elements. The array element spacing is D1d, where d = λ / 2, λ represents the wavelength of the signal, and D1>>1; sub-array 2 has only two array elements, located at a distance of D2d from the first and last array elements of sub-array 1, where D2>>1.

[0088] A Cartesian coordinate system is established with the array as the yoz coordinate plane. The array is subjected to uniform linear motion along the x-axis at a velocity v, sampled at intervals τ, where vτ = D3d, where D3>>1. The position of subarray 1 at the time of sampling after τ is denoted as subarray 3. D1, D2, and D3 are all integers greater than 1 and mutually prime.

[0089] Then, the array position of subarray 1 is expressed as:

[0090] L1=[(0,0,0),(0,D1d,0),(0,2D1d,0),…,(0,(M-1)D1d,0)]

[0091] The array position of subarray 2 is expressed as:

[0092] L2=[(0,0,D2d),(0,(M-1)D1d,D2d)]

[0093] Sampling at time τ, the array position of subarray 3 is expressed as:

[0094] L3=[(D3d,0,0),(D3d,D1d,0),…,(D3d,(M-1)D1d,0)]

[0095] Step 2: Based on the array parameters and the relative positions of different sub-arrays, determine the array manifold of each sub-array.

[0096] The array manifold A1 of subarray 1 is:

[0097]

[0098] in, 1≤k≤K, K represents the number of signal sources, θ k represents the pitch angle of k signals measured from the positive direction of the z-axis, Represents the azimuth of k directions measured from the positive direction of the x-axis;

[0099] Combined with the relative position relationship between the arrays, the array manifold A2 of subarray 2 is determined as:

[0100]

[0101] in, The planes where subarrays 1 and 2 are located are always parallel to the yoz plane and have the same azimuth angle.

[0102] The array manifold d3 of sub-matrix 3 sampled at time v is:

[0103]

[0104] in, The planes where sub-arrays 1 and 3 are located are always parallel to the xoy plane, and have the same elevation angles.

[0105] Step 3: Based on the array manifold and combined with the dynamic sub-array characteristics, determine the received signal model of each sub-array.

[0106] According to the above array manifold, the received signal model of each sub-array can be obtained:

[0107] The received signal model of subarray 1 is: y1(t)=A1*s(t)+n1(t);

[0108] The received signal model of subarray 2 is: y2(t)=A2*s(t)+n2(t);

[0109] The received signal model of subarray 3 is: y3(t) = A3*s(t+τ) + n1(t+τ); assuming that the incident signal sources are all far-field narrowband signals, then y3(t) = A3*s(t) + n1(t);

[0110] in, represents the incident signal source model of K signals, n1(t) is the noise vector of sub-array 1, and n2(t) is the noise vector of sub-array 2.

[0111] Based on the received signal model of subarray 1 and subarray 2, we can get:

[0112]

[0113] Step 4: Based on the received signal model of each sub-array, combined with motion sampling and array characteristics, determine the received signal covariance matrix.

[0114] The first received signal covariance matrix is ​​derived based on the received signal models of subarray 1 and subarray 2. The derivation process is as follows:

[0115]

[0116] in,

[0117]

[0118] From the knowledge of dynamic sub-array characteristics and correlation matrix reconstruction, we can get [R 12 ] 1,1 =[R 12 ] M,2 , R 11 =R 22 According to the Toeplitz structure of the matrix, we can get

[0119]

[0120] Then R 11 and A 2M×2M symmetric Toeplitz matrix can be constructed, which is the first received signal covariance matrix:

[0121]

[0122] The covariance matrix can be considered as the covariance matrix of a virtual array composed of two sparse uniform linear arrays, and its corresponding array manifold is Right now It can be equivalently regarded as the covariance matrix of the received signal of 2M array elements. S represents the covariance matrix of the source signal, σ 2 represents the noise power, i 2M is an identity matrix of size -2M×2M, defined as:

[0123]

[0124] Similarly, the second received signal covariance matrix calculated based on the received signal models of subarrays 1 and 3 is:

[0125]

[0126] in, No refactoring required.

[0127] It can be considered as the covariance matrix of a virtual array composed of two sparse uniform linear arrays, and the corresponding array manifold is Right now in,

[0128] Step 5: Based on the received signal covariance matrix and the virtual array structure, a multi-dimensional parameter estimation algorithm based on ESPRIT is derived. The target's pitch angle θ and azimuth angle are jointly estimated by signal subspace decomposition and rotation invariance principle.

[0129] The multi-dimensional parameter estimation algorithm based on ESPRIT is used to estimate the pitch angle θ and azimuth angle The specific steps include:

[0130] Step 51: performing eigenvalue decomposition on the received signal covariance matrix to obtain a signal subspace;

[0131] Step 52: Separate the virtual array into two identical overlapping sub-arrays based on the signal subspace;

[0132] Step 53: Derived the phases between adjacent array elements based on the overlapping sub-arrays and calculated the average value, and fuzzy estimation was performed based on the phase average value to obtain multiple groups of estimated values;

[0133] Step 54: Estimate the pitch angle and azimuth angle based on the estimated values ​​and the coprime relationship between D1, D2, and D3.

[0134] The specific process is as follows:

[0135] The covariance matrix obtained by step 4 Perform eigenvalue decomposition on it, expressed as:

[0136]

[0137] Where U is a unitary matrix whose column vectors are The eigenvectors of , Λ is a diagonal matrix whose diagonal elements are The eigenvalues ​​of are usually sorted in descending order, Λ=diag(λ1,λ2,…,λ 2M ),λ1≥λ2≥…≥λ 2M , 2M is the dimension of the received signal. The eigenvectors corresponding to the first K large eigenvalues ​​constitute the signal subspace U S , the eigenvectors corresponding to the remaining 2M-K small eigenvalues ​​constitute the noise subspace U N , that is, U=[U S U n ], you can Decomposed into two parts: signal and noise:

[0138]

[0139] Among them, U S represents the signal subspace, Λ S =diag(λ1,λ2,…,λ K ) represents the signal eigenvalue matrix, U N represents the noise subspace, Λ N =diag(λ K+1 ,λ K+2 ,…,λ 2M ) represents the noise eigenvalue matrix.

[0140] The ESPRIT concept can separate the virtual array into two identical overlapping sub-arrays U S,1 and U S,2 , which can be expressed as:

[0141] U s,1 =G1U S , U S,2 =G2U S

[0142] Where G1 and G2 are selection matrices, defined as:

[0143]

[0144] Among them, O M-1 represents a (M-1)×(M-1) dimensional all-zero matrix, G3=[I M-1 O (M-1)×1 ],G4=[O (M-1)×1 I M-1 ], I M-1 is the M-1 dimensional identity matrix, O (M-1)×1 is an (M-1)×1 dimensional all-zero matrix.

[0145] because and U S are in the same subspace, so there exists a K×K dimensional non-singular matrix T such that Select the first M-1 signal subspace vectors and the last M-1 signal subspace vectors of submatrix 1 and submatrix 2 respectively, that is, U S Further split into

[0146]

[0147] in

[0148] The displacement invariance relationship between sub-arrays U S,1 =U S,2 Ψ, derive the nonlinear mapping of the rotation matrix Ψ and the angle parameter Ψ = T -1 ΘT, then perform eigendecomposition on Ψ, and estimate Θ and transformation matrix T through its eigenvalues ​​and eigenvectors, which are recorded as and The estimated value of It can be obtained by the following formula

[0149]

[0150] Based on the first received signal covariance matrix The derived phase between adjacent array elements in the y-axis direction is k Related to D1, it is expressed as:

[0151]

[0152] Taking the phase average, the phase mean is:

[0153]

[0154] In this embodiment, integer variables l1, l2, and l3 are introduced to cover periodic phase ambiguity.

[0155] Depend on From the structure of , we can see that α k Can be It is estimated that, because D1>>1, there is phase ambiguity, so a set of fuzzy estimates is obtained, and the number of fuzzy estimates is equal to D1. The first set of fuzzy estimates is recorded as l1 satisfies the conditions l1∈[1,D1].

[0156] Similarly, the phase between adjacent array elements in the z-axis direction ∈ i,j,k and β k Related to D2, it can be expressed as

[0157]

[0158] Take the average value k=1,2,…,k,

[0159] From the above derivation, we can see that the second set of fuzzy estimates is l2 meets the conditions l2∈[1,D2]. For the covariance matrix For example, can be considered as an identical constant.

[0160] Similarly, for the second received signal covariance matrix The phase and γ between adjacent array elements in the x-axis direction can be obtained k and is related to D3, expressed as:

[0161]

[0162]

[0163] Taking the average value, we get

[0164]

[0165] Depend on γ k Make an estimate and get the third set of fuzzy estimates The number of fuzzy estimates is equal to D3, l3 satisfies the condition l3∈[1,D3].

[0166] For the kth signal source, the first set of fuzzy Contains D1 fuzzy estimates, the second group of fuzzy Contains D2 fuzzy estimates, the third group of fuzzy Contains D3 fuzzy estimates. Theoretically, since D1, D2, and D3 are mutually prime, there is a unique solution θ k and The above three formulas are satisfied at the same time.

[0167] Step 6: Based on the ambiguous phase estimated by the multidimensional parameter estimation algorithm, the array characteristics and angle relationship are used to deambiguate and obtain a unique solution as the final estimated two-dimensional DOA parameter.

[0168] Next, we use D1 and D2 to be mutually prime, and D1 and D3 to defuzzify and find the unique solution θ k and That is, solve the following optimization problem:

[0169]

[0170] stl1∈[1,D1],l2∈[1,D2],l3∈[1,D3]

[0171] in

[0172] Step 7: Calculate the theoretical complexity of the multidimensional parameter estimation algorithm.

[0173] Compared with the existing technology, the above DOA estimation method has the characteristics of low mutual coupling, high degree of freedom, and large aperture in the array design. The proposed algorithm can effectively remove the ambiguity estimation by utilizing the array characteristics. The complexity of its receiving covariance matrix is The complexity of eigenvalue decomposition using the ESPRIT algorithm twice is The complexity of closed-form operation for the angle is approximately So the total complexity is approximately

[0174] Figure 3 The scatter plot of the pitch angle and azimuth angle estimated by the method of the present invention is shown. Figure 3 It can be seen that in 100 Monte Carlo simulation experiments, the pitch angle and the azimuth angle can be accurately estimated, and the 100 estimated values ​​are approximately a straight line, indicating that the method of the present invention has strong stability. Figure 4 and Figure 5 are the estimated mean square error changes with the signal-to-noise ratio and the number of snapshots. Figure 4 It can be seen that the root mean square error of the method of the present invention is always smaller than that of the DFT-based algorithm and the SAID-based estimation method, whether in high SNR scenarios or low SNR scenarios, indicating that the method of the present invention has strong adaptability to different SNR scenarios and has high estimation accuracy. Figure 5It can be seen that the root mean square error of the method of the present invention is still smaller than that of the above two methods under different snapshot numbers, indicating that the method of the present invention has better performance than the existing methods in different snapshot number scenarios.

[0175] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A two-dimensional DOA estimation method based on extended array motion sampling, characterized in that: The following steps are involved: Step 1: Determine the initial array structure of each sub-array based on the total number of array elements, and obtain array parameters including array spacing, motion direction, motion rate, and sampling interval; Step 2: Based on the array parameters and the relative positions of different sub-arrays, determine the array manifold of each sub-array; Step 3: Based on the array manifold and combined with the dynamic sub-array characteristics, determine the received signal model of each sub-array; Step 4: Determine the received signal covariance matrix based on the received signal model of each subarray, combined with motion sampling and array characteristics; Step 5: Based on the received signal covariance matrix, derive a multi-dimensional parameter estimation algorithm based on ESPRIT according to the virtual array structure; Step 6: Based on the ambiguous phase estimated by the multidimensional parameter estimation algorithm, the array characteristics and the angle relationship are used to deambiguate and obtain a unique solution as the final estimated two-dimensional DOA parameter.

2. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 1, characterized in that: The array is a planar array structure, consisting of sub-array 1 and sub-array 2. Sub-array 1 is a sparse uniform linear array with a total of M array elements. The array element spacing is D1d, where d = λ / 2, and λ represents the wavelength of the signal. Sub-array 2 has only two array elements, which are located at a distance of D2d from the first and last array elements of sub-array 1. A Cartesian coordinate system is established with the array as the yoz coordinate plane. The array moves in a uniform linear motion at a speed v in the x-axis direction, and is sampled at an interval τ, where vτ=D3d. The position of sub-array 1 at the time of sampling after time τ is recorded as sub-array 3. Where D1, D2, and D3 are all integers greater than 1 and are mutually prime.

3. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 2, characterized in that: The array position of the sub-array 1 is expressed as: L1=[(0,0,0),(0,D1d,0),(0,2D1d,0),…,(0,(M-1)D1d,0)] The array position of the sub-array 2 is expressed as: L2=[(0,0,D2d),(0,(M-1)D1d,D2d)] Sampling at time τ, the array position of the sub-array 3 is expressed as: L3=[(D3d,0,0),(D3d,D1d,0),…,(D3d,(M-1)D1d,0)].

4. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 3, characterized in that: The array manifolds of the sub-arrays are: The array manifold A1 of subarray 1 is: in, 1≤k≤k, K represents the number of signal sources, θ k represents the pitch angle of k signals measured from the positive direction of the z-axis, Represents the azimuth of k directions measured from the positive direction of the x-axis; Combined with the relative position relationship between the arrays, the array manifold A2 of subarray 2 is determined as: in, β k =cosθ k ; The planes where subarrays 1 and 2 are located are always parallel to the yoz plane and have the same azimuth angle; The array manifold A3 of sub-array 3 sampled at time τ is: in, The planes where sub-arrays 1 and 3 are located are always parallel to the xoy plane, and have the same elevation angles.

5. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 4, characterized in that: The receiving signal models of the sub-arrays are: The received signal model of subarray 1 is: y1(t)=A1*s(t)+n1(t); The received signal model of subarray 2 is: y2(t)=A2*s(t)+n2(t); The received signal model of subarray 3 is: y3(t) = A3*s(t+τ) + n1(t+τ); assuming that the incident signal sources are all far-field narrowband signals, then y3(t) = A3*s(t) + n1(t); in, represents the incident signal source model of K signals, n1(t) is the noise vector of sub-array 1, and n2(t) is the noise vector of sub-array 2.

6. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 5, characterized in that: The received signal covariance matrix is ​​specifically: The first received signal covariance matrix calculated based on the received signal model of subarray 1 and subarray 2 is: in, Array manifold corresponding to the first received signal covariance matrix Right now It is equivalent to the covariance matrix of the received signal of 2M array elements, where R S represents the covariance matrix of the source signal, σ 2 represents the noise power, I 2M is a 2M×2M identity matrix defined as: The second received signal covariance matrix calculated based on the received signal model of subarray 1 and subarray 3 is: in, The second received signal covariance matrix The corresponding array manifold Right now in, 7. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 6, characterized in that: The ESPRIT-based multidimensional parameter estimation algorithm is used to estimate the pitch angle θ and azimuth angle The specific steps include: Perform eigenvalue decomposition on the covariance matrix of the received signal to obtain the signal subspace; separating the virtual array into two identical overlapping sub-arrays based on the signal subspace; Derived the phases between adjacent array elements based on the overlapping sub-arrays and calculated the average value, and performed fuzzy estimation based on the phase average value to obtain multiple groups of estimated values; Based on the estimated values ​​and the coprime relationship between D1, D2, and D3, the pitch angle and the azimuth angle are estimated.

8. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 7, characterized in that: The phase between adjacent array elements in the y-axis direction derived based on the first received signal covariance matrix and α k Related to D1, it is expressed as: in, is the matrix derived based on overlapping submatrices The estimated value of Taking the phase average, the phase mean is: Depend on To α k Make an estimate and get the first set of fuzzy estimates The number of fuzzy estimates is equal to D1, l1 satisfies the condition l1∈[1,D1]; The phase ∈ between adjacent array elements in the z-axis direction derived based on the first received signal covariance matrix i,j,k and β k Related to D2, it is expressed as: in, is the estimated value of the matrix A1′ derived based on the overlapping sub-matrices, Taking the phase average value k=1,2,…,K, Depend on β k Make an estimate and get the second set of fuzzy estimates The number of fuzzy estimates is equal to D2, l2 satisfies the condition l2∈[1,D2].

9. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 8, characterized in that: The phase between adjacent array elements in the x-axis direction derived based on the second received signal covariance matrix and γ k and is related to D3, expressed as: Taking the phase average, we get Depend on γ k Make an estimate and get the third set of fuzzy estimates The number of fuzzy estimates is equal to D3, l3 satisfies the condition l3∈[1,D3].

10. The two-dimensional DOA estimation method based on extended array motion sampling according to claim 9, characterized in that: The step 6 is specifically as follows: The following optimization problem is solved to deblur the image and find a unique solution for the elevation and azimuth angles: stl1∈[1,D1],l2∈[1,D2],l3∈[1,D3].

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