A non-common baseline distributed uniform array and a method for obtaining target position thereof

Abstract

The present invention relates to a non-common baseline distributed uniform array and a method for obtaining a target azimuth thereof, belonging to the field of array signal processing and antenna technology. In order to solve the shortcomings of the prior art that the common baseline distributed array is inflexible in arrangement, seriously affected by geographical factors such as terrain and rivers, and has many restrictions, the non-common baseline distributed uniform array includes two identical linear uniform arrays, the number of array elements and the array element spacing of the two linear uniform arrays are the same, they are parallel to each other and not colinear, and the non-common baseline distributed uniform array can better adapt to the actual geographical environment while improving the accuracy of the target azimuth estimation.

Description

Technical Field

[0001] The invention relates to a non-common baseline distributed uniform array and a method for acquiring a target orientation thereof, belonging to the technical field of array signal processing and antennas. Background Art

[0002] Direction of Arrival (DOA) estimation is a key issue in array signal processing and is widely used in radar, sonar, wireless communications and other fields. The performance of DOA estimation is closely related to the array aperture. The larger the effective aperture of the array, the higher the angular resolution and DOA estimation accuracy of the array. For linear uniform arrays, the array aperture is only linearly related to the number of antenna elements. In order to increase the effective aperture of the array, the number of antenna elements needs to be increased proportionally, which will lead to an increase in the system hardware cost and the computational complexity of the angle measurement algorithm.

[0003] Nowadays, non-uniform sparse arrays, such as minimum redundant arrays, coprime arrays, nested arrays, etc., have become a hot topic of research because they have achieved improvements in the effective aperture and degrees of freedom of the array. However, these arrays have limited advantages in expanding the array aperture. Distributed arrays are another form of sparse arrays, consisting of multiple dispersed subarrays with a large baseline length between the subarrays, which can greatly improve the effective aperture of the array. A large number of studies have been carried out at home and abroad on distributed arrays with common baselines, and the subspace algorithm has been applied to greatly improve the accuracy of DOA estimation. However, in the context of actual applications, due to the influence of geographical factors such as terrain and rivers, it is impossible to arrange distributed antenna arrays on the same baseline, which greatly limits the application of distributed antenna arrays in actual radar systems.

[0004] In 2001, Swindlehurst proposed the concept of non-co-baseline distributed array. However, compared with co-baseline distributed array, non-co-baseline distributed array is more complex, and it needs more complex angle measurement algorithm to obtain high-precision DOA estimation. At present, there are few related studies on non-co-baseline distributed array at home and abroad. In order to make distributed array easier to apply to actual radar systems, it is urgent to solve the problems of inflexible array layout, great influence of terrain and river factors, and many restrictions. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the prior art that the common baseline distributed array is inflexible in layout, is seriously affected by geographical factors such as terrain and rivers, and has many restrictions, and to provide a non-common baseline distributed uniform array and a method for obtaining the target azimuth thereof. The non-common baseline distributed uniform array can better adapt to the actual geographical environment while improving the accuracy of azimuth estimation of the target.

[0006] In order to solve the above problems, the present application is implemented through the following technical solutions:

[0007] A non-co-baseline distributed uniform array, which is special in that it includes two identical linear uniform arrays, the number of array elements and the array element spacing of the two linear uniform arrays are the same, they are parallel to each other and not co-linear; the two identical linear uniform arrays are respectively and Indicates that all array elements are distributed on the x-y plane, and and They are all parallel to the x-axis, and the origin of the coordinate system is (0,0);

[0008] The linear uniform array The coordinates of the array element position in the x-y plane are ,in, , d represents the unit element spacing, N is a uniform linear array The number of array elements in ;

[0009] The linear uniform array The coordinates of the array element position in the x-y plane are ,

[0010] in, express and The length of the baseline along the x-axis, express and The length of the baseline along the y-axis, Much larger than the aperture of a uniform linear array, and The baseline length between .

[0011] Furthermore, the total number of array elements of the non-common baseline distributed uniform array is ;

[0012] Furthermore, the array element antenna is a dipole antenna.

[0013] The method for obtaining the target position based on the non-common baseline distributed uniform array is special in that it includes the following steps:

[0014] Step 1: Obtain the received signal of the non-common baseline distributed uniform array at time t as echo data;

[0015] Step 2: Calculate the covariance matrix R of the echo data in step 1 and decompose its eigenvalues ​​to obtain the signal subspace ;

[0016] Step 3: Use the signal subspace obtained in step 2 Solve the rotation invariant relationship matrix between the unambiguous rough estimate and the fine estimate and ;

[0017] Step 4: For the and Perform eigenvalue decomposition to get a rough estimate of the direction cosines and precise estimation ;

[0018] Step 5: The precise estimate obtained in step 4 Obtaining accurate estimates of unambiguous direction cosines using a dual-scale deambiguation method ;

[0019] Step 6: Accurately estimate the unambiguous direction cosines according to step 5 Calculate the unambiguous DOA of the incident source signal and accurately estimate the azimuth ;

[0020] Depend on , have to .

[0021] Furthermore, the step 1 is specifically as follows:

[0022] K far-field narrowband signal sources with unknown angles are incident on the non-common baseline distributed uniform array, that is, the incident angles of the K far-field narrowband signal sources are all located in the xy plane. represents the incident angle of the kth signal source, , then the direction cosines of the x-axis and y-axis are and ;

[0023] by The first array element in is the reference array element. As the reference array, the received signal of the non-common baseline distributed uniform array at time t, i.e., the echo data, is expressed as: X ( t ) = [ X 1 ( t ) X 2 ( t ) ] = A S ( t ) + N ( t ) ∈ ℂ 2 N × 1 ,

[0024] Where: The received signal vector is X 1 ( t ) = [ x 11 ( t ) , x 12 ( t ) , ⋯ , x 1 N ( t ) ] T ∈ ℂ N × 1 , for The received signal of the nth array element is, ;

[0025] The received signal vector is X 2 ( t ) = [ x 21 ( t ) , x 22 ( t ) , ⋯ , x 2 N ( t ) ] T ∈ ℂ N × 1 , for The received signal of the nth array element is, ;

[0026] The signal vector is , ⋯ , s K ( t ) ] T ∈ ℂ K × 1 ,

[0027] Where: represents the kth source signal;

[0028] Zero-mean additive white Gaussian noise is N ( t ) = [ n 11 ( t ) , ⋯ , n 1 N ( t ) , n 21 ( t ) , ⋯ , n 2 N ( t ) ] T ∈ ℂ 2 N × 1 ,

[0029] Where: and They are and Gaussian white noise of the nth array element;

[0030] is the array steering vector matrix, A = [ A s A s Φ ] ,

[0031] Where: for The array-guided vector matrix, A s = [ a ( θ 1 ) , a ( θ 2 ) , ⋯ , a ( θ K ) ] ∈ ℂ N × K ,

[0032] Where: a ( θ k ) = [ z 1 k , z 2 k , ⋯ ,z N k ] T , ;

[0033] for and The phase shift matrix between

[0034] ,

[0035] Where: is the angle between the two sub-arrays, ,

[0036] Where: express and The length of the baseline along the x-axis, express and The length of the baseline along the y-axis.

[0037] Furthermore, the step 2 is specifically as follows:

[0038] The received echo data is multiplied by its own conjugate transpose and the mathematical expectation is calculated to obtain the covariance matrix R of the echo data: ,

[0039] Where: represents the noise power, is the covariance matrix of the signal source vector. The signal sources are independent of each other. ,in represents the power of the kth signal source; Indicates that the dimension is equal to The identity matrix of

[0040] Covariance matrix Perform eigenvalue decomposition to obtain the signal subspace ,Right now ,

[0041] Where: , U s = [ x 00 x 10 ⋯ x ( K − 1 ) 0 x 01 x 11 ⋯ x ( K − 1 ) 1 ⋮ ⋮ ⋱ ⋮ x 0 ( 2 N − 1 ) x 1 ( 2 N − 1 ) ⋯ x ( K − 1 ) ( 2 N − 1 ) ] 2 N × K ,

[0042] Where: represents the eigenvalue matrix, , , …, is the covariance matrix The characteristic value of is the signal subspace, , , …, represents the numerical value of the signal subspace;

[0043] The space and signal subspace formed by the array steering vector matrix is the same space, there must be a unique non-singular matrix satisfy .

[0044] Furthermore, the step 3 is specifically as follows:

[0045] Step 3.1, select the linear uniform array S 1 and S 2 The subarray in the rotation invariant relation equation is determined by selecting S 1 and S 2 The first N-1 array elements of form subarray C1, select S 1 and S 2 The last N-1 array elements form subarray C2. The spatial translation between subarray C1 and subarray C2 is d.

[0046] The rotation invariant relationship equation is expressed as: ,

[0047] Where: W C 1 = I ( 2 ) ⊗ [ I ( N − 1 ) 0 ( N − 1 ) × 1 ] is the selection matrix of sub-matrix C1; I ( N − 1 ) ] is the selection matrix of sub-matrix C2; represents the 2nd-order unit matrix, represents the (N-1)-order unit matrix, To roughly estimate the rotation invariant relationship matrix, represents a (N-1)×1 dimensional zero vector, represents a diagonal matrix, represents a rough estimate of the complex value, represents direction cosines, represents the azimuth of the kth target;

[0048] Step 3.2: Linear uniform array S 1 and S 2 The rotation invariant relationship equation expression of the linear uniform array S 1 and S 2 There is a spatial translation invariance with a translation amount of L on the x-y plane, and the rotation invariance relationship equation is expressed as: ,

[0049] In the formula, W F 1 = [ I N 0 N ] and W F 2 = [ 0 N I N ] S 1 and S 2 The selection matrix; To accurately estimate the rotation invariant relationship matrix, represents the exact estimate of the complex value, To include The direction cosines of ; L represents the baseline length between arrays, Indicates the signal wavelength;

[0050] Step 3.3: Use the signal subspace obtained in step 2 Obtain the rotation invariant relationship matrix between the rough estimate and the fine estimate and :

[0051] The signal subspace Substitute and , can be obtained , ,

[0052] Where: and are the coarse estimation and fine estimation rotation invariant relationship matrices respectively; and Respectively and is a similarity matrix;

[0053] Step 3.4: Use the rough estimate and fine estimate rotation invariant relationship matrix obtained in step 3.3 and Obtain the rotation invariant relationship matrix between the unambiguous estimate and the precise estimate and :

[0054] Apply the least squares criterion to solve the equations separately , , we can get the rotation invariant relationship matrix and equal: Ω ^ C = [ ( W C 1 U ^ s ) H ( W C 1 U ^ s ) ] − 1 ( W C 1 U ^ s ) H ( W C 2 U ^ s ) , Ω ^ F = [ ( W F 1 U ^ s ) H ( W F 1 U ^ s ) ] − 1 ( W F 1 U ^ s ) H ( W F 2 U ^ s ) .

[0055] Furthermore, the step 4 is specifically as follows: respectively and Perform eigenvalue decomposition and use the pairing algorithm to pair the eigenvalues ​​corresponding to the same source signal, that is, , ; , ,

[0056] In the formula, represents the rough estimated eigenvalue matrix, To roughly estimate the complex value, is the signal subspace, represents the precise estimated eigenvalue matrix, is an accurate estimate of the complex value;

[0057] According to the relationship between direction cosine and eigenvalue complex phase , , a rough estimate of the direction cosines of the incident source signal , and accurate estimation They are , ,

[0058] Where: Indicates acquisition The phase angle, d represents the array element spacing, represents the wavelength of the signal, and L represents the distance between the two sub-arrays.

[0059] Further, the step 5 is specifically as follows: The defuzzification cycle is as follows:

[0060] Based on the rough estimation of direction cosines Constructing a rough estimate without fuzziness ,Right now ,

[0061] Where: is the angle between the two sub-arrays;

[0062] Unambiguous Direction Cosines Estimation With precise estimation The following relationship exists: ,

[0063] Where: for The number of ambiguity cycles of the phase is For the cycle, ,

[0064] Where: The value range is , Indicates rounding towards negative infinity and positive infinity.

[0065] The non-co-baseline distributed uniform array of the present application is composed of dispersed non-co-baseline sub-arrays, which can greatly improve the effective aperture of the array, and at the same time has the advantages of flexible array arrangement, little influence by geographical factors such as terrain and rivers, and few restrictions, and can be better applied to actual radar systems;

[0066] When the traditional two-scale ESPRIT algorithm is used to solve the model, the coarse estimate obtained is the direction cosine containing the incident angle of the signal source, and the fine estimate obtained is the direction cosine containing the incident angle of the signal source and the angle between the two uniform linear arrays. The ambiguity period of the fine estimate cannot be solved by referring to the coarse estimate. Therefore, the traditional two-scale ESPRIT algorithm is not suitable for non-common baseline distributed uniform arrays. Therefore, the present invention proposes a new two-scale deambiguation algorithm. Based on the parameter construction method, the coarse estimate obtained by the two-scale ESPRIT algorithm is used to construct coarse estimation parameters with the same form as the fine estimation. The constructed coarse estimation parameters are free of ambiguity but have low estimation accuracy. The constructed coarse estimation parameters are then used as a reference to solve the ambiguity period of the fine estimation, so that a high-precision and unambiguous direction cosine estimate can be obtained. Since the solved direction cosine fine estimate contains the incident angle of the signal source and the angle between the two uniform linear arrays, the known angle between the two uniform linear arrays is finally removed to obtain a high-precision DOA estimate of the signal source incident angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a non-co-baseline distributed uniform array structure model;

[0068] Figure 2 Sub-array division for non-common baseline distributed uniform array;

[0069] Figure 3 Processing flow chart for obtaining direction of arrival for non-common baseline distributed uniform array;

[0070] Figure 4Schematic diagram of the change of root mean square error with SNR;

[0071] Figure 5 Schematic diagram of the change of root mean square error with the number of snapshots;

[0072] Figure 6 Schematic diagram of the change of successful estimation probability with SNR. DETAILED DESCRIPTION

[0073] The following is a specific implementation of the present invention with reference to the accompanying drawings to further illustrate the composition of the present invention.

[0074] Example 1. A non-common baseline distributed uniform array, such as Figure 1-Figure 2 As shown, it includes two identical linear uniform arrays, the number of array elements and the array element spacing of the two linear uniform arrays are the same, and they are parallel to each other and not collinear;

[0075] The two identical linear uniform arrays are respectively and Indicates that all array elements are distributed on the x-y plane, and and They are all parallel to the x-axis, and the origin of the coordinate system is (0,0);

[0076] The linear uniform array The coordinates of the array element position in the x-y plane are ,in, , d represents the unit element spacing, N is a uniform linear array The number of array elements in ;

[0077] The linear uniform array The coordinates of the array element position in the x-y plane are ,

[0078] in, express and The length of the baseline along the x-axis, express and The length of the baseline along the y-axis, Much larger than the aperture of a uniform linear array, and The baseline length between ;

[0079] The total number of array elements of the non-common baseline distributed uniform array is ;

[0080] Among them, the array element antenna selects a dipole antenna.

[0081] Embodiment 2. A method for acquiring target position based on a non-common baseline distributed uniform array, the process of which is as follows: Figure 3 As shown, the following steps are included:

[0082] Step 1: Obtain the received signal of the non-common baseline distributed uniform array at time t as echo data;

[0083] Step 2: Calculate the covariance matrix R of the echo data in step 1 and decompose its eigenvalues ​​to obtain the signal subspace ;

[0084] Step 3: Use the signal subspace obtained in step 2 Solve the rotation invariant relationship matrix between the unambiguous rough estimate and the fine estimate and ;

[0085] Step 4: For the and Perform eigenvalue decomposition to get a rough estimate of the direction cosines and precise estimation ;

[0086] Step 5: The precise estimate obtained in step 4 Obtaining accurate estimates of unambiguous direction cosines using a dual-scale deambiguation method ;

[0087] Step 6: Accurately estimate the unambiguous direction cosines according to step 5 Calculate the unambiguous DOA of the incident source signal and accurately estimate the azimuth :

[0088] Depend on , have to .

[0089] The step 1 is specifically as follows: K far-field narrowband signal sources with unknown angles are incident on a non-common baseline distributed uniform array, that is, the incident angles of the K far-field narrowband signal sources are all located in the xy plane, represents the incident angle of the kth signal source, , then the direction cosines of the x-axis and y-axis are and ;

[0090] by The first array element in is the reference array element. As the reference array, the received signal of the non-common baseline distributed uniform array at time t, i.e., the echo data, is expressed as: X ( t ) = [ X 1 ( t ) X 2 ( t ) ] = A S ( t ) + N ( t ) ∈ ℂ 2 N × 1 ,

[0091] Where: The received signal vector is X 1 ( t ) = [ x 11 ( t ) , x 12 ( t ) , ⋯ , x 1 N ( t ) ] T ∈ ℂ N × 1 , for The received signal of the nth array element is, ;

[0092] The received signal vector is X 2 ( t ) = [ x 21 ( t ) , x 22 ( t ) , ⋯ , x 2 N ( t ) ] T ∈ ℂ N × 1 , for The received signal of the nth array element is, ;

[0093] The signal vector is , ⋯ , s K ( t ) ] T ∈ ℂ K × 1 ,

[0094] Where: represents the kth source signal;

[0095] Zero-mean additive white Gaussian noise is N ( t ) = [ n 11 ( t ) , ⋯ , n 1 N ( t ) , n 21 ( t ) , ⋯ , n 2 N ( t ) ] T ∈ ℂ 2 N × 1 ,

[0096] Where: and They are and Gaussian white noise of the nth array element;

[0097] is the array steering vector matrix, A = [ A s A s Φ ] ,

[0098] Where: for The array-guided vector matrix, A s = [ a ( θ 1 ) , a ( θ 2 ) , ⋯ , a ( θ K ) ] ∈ ℂ N × K ,

[0099] Where: a ( θ k ) = [ z 1 k , z 2 k , ⋯ ,z N k ] T , ;

[0100] for and The phase shift matrix between

[0101] ,

[0102] Where: is the angle between the two sub-arrays, ,

[0103] Where: express and The length of the baseline along the x-axis, express and The length of the baseline along the y-axis.

[0104] The specific step 2 is as follows: multiply the received echo data by its own conjugate transpose and calculate the mathematical expectation to obtain the covariance matrix R of the echo data: ,

[0105] Where: represents the noise power, is the covariance matrix of the signal source vector. If the signal sources are independent of each other, then ,in represents the power of the kth signal source; Indicates that the dimension is equal to The identity matrix of

[0106] Covariance matrix Perform eigenvalue decomposition to obtain the signal subspace ,Right now ,

[0107] Where: , U s = [ x 00 x 10 ⋯ x ( K − 1 ) 0 x 01 x 11 ⋯ x ( K − 1 ) 1 ⋮ ⋮ ⋱ ⋮ x 0 ( 2 N − 1 ) x 1 ( 2 N − 1 ) ⋯ x ( K − 1 ) ( 2 N − 1 ) ] 2 N × K ,

[0108] in, represents the eigenvalue matrix, , , …, is the covariance matrix The characteristic value of is the signal subspace, , , …, Represents the value of the signal subspace; the space formed by the array steering vector matrix is ​​the same as the signal subspace is the same space, there must be a unique non-singular matrix satisfy .

[0109] The specific details of step 3 are as follows: Step 3.1: Select a linear uniform array S 1 and S 2 The subarray in the rotation invariant relation equation is determined by selecting S 1 and S 2 The first N-1 array elements of form subarray C1, select S 1 and S 2 The last N-1 array elements form subarray C2. The spatial translation between subarray C1 and subarray C2 is d.

[0110] The rotation invariant relationship equation is expressed as: ,

[0111] Where: W C 1 = I ( 2 ) ⊗ [ I ( N − 1 ) 0 ( N − 1 ) × 1 ] is the selection matrix of sub-matrix C1;

[0112] I ( N − 1 ) ] is the selection matrix of sub-matrix C2; where, represents the 2nd-order unit matrix, represents the (N-1)-order unit matrix, To roughly estimate the rotation invariant relationship matrix, represents a (N-1)×1 dimensional zero vector, represents a diagonal matrix, represents a rough estimate of the complex value, represents direction cosines, represents the azimuth of the kth target;

[0113] Step 3.2: Linear uniform array S 1 and S 2 The rotation invariant relationship equation expression of the linear uniform array S 1 and S 2 There is a spatial translation invariance with a translation amount of L on the x-y plane, and the rotation invariance relationship equation is expressed as: ,

[0114] In the formula, W F 1 = [ I N 0 N ] and W F 2 = [ 0 N I N ] S 1 and S 2 The selection matrix; To accurately estimate the rotation invariant relationship matrix, represents the exact estimate of the complex value, To include The direction cosines of ; L represents the baseline length between arrays, Represents the signal wavelength; Step 3.3, use the signal subspace obtained in step 2 Obtain the rotation invariant relationship matrix between the rough estimate and the fine estimate and :

[0115] The signal subspace Substitute and , can be obtained , ,

[0116] Where: and are the coarse estimation and fine estimation rotation invariant relationship matrices respectively; and Respectively and is a similarity matrix;

[0117] Step 3.4: Use the rough estimate and fine estimate rotation invariant relationship matrix obtained in step 3.3 and Obtain the rotation invariant relationship matrix between the unambiguous estimate and the precise estimate and :

[0118] Apply the least squares criterion to solve the equations separately , , we can get the rotation invariant relationship matrix and equal:

[0119] Ω ^ C = [ ( W C 1 U ^ s ) H ( W C 1 U ^ s ) ] − 1 ( W C 1 U ^ s ) H ( W C 2 U ^ s ) , Ω ^ F = [ ( W F 1 U ^ s ) H ( W F 1 U ^ s ) ] − 1 ( W F 1 U ^ s ) H ( W F 2 U ^ s ) .

[0120] The step 4 is as follows: and Perform eigenvalue decomposition and use the pairing algorithm to pair the eigenvalues ​​corresponding to the same source signal, that is, , ; , ,

[0121] in, represents the rough estimated eigenvalue matrix, To roughly estimate the complex value, is the signal subspace, represents the precise estimated eigenvalue matrix, is an accurate estimate of the complex value;

[0122] According to the relationship between direction cosine and eigenvalue complex phase , , a rough estimate of the direction cosines of the incident source signal , and accurate estimation They are , ,

[0123] Where: Indicates acquisition The phase angle, d represents the array element spacing, represents the wavelength of the signal, and L represents the distance between the two sub-arrays.

[0124] Wherein, the step 5 is specifically as follows: The defuzzification period is as follows: Based on the rough estimate of direction cosines Constructing a rough estimate without fuzziness ,Right now ,

[0125] Where: is the angle between the two sub-arrays;

[0126] Unambiguous Direction Cosines Estimation With precise estimation The following relationship exists: ,

[0127] Unambiguous precise estimation This means that there is a fuzzy estimate of Plus phase blur , this is common sense; a rough estimate Unambiguous rough estimate They are all direction cosine estimates with low estimation accuracy but no ambiguity. Substitute them into the formula: The fuzzy period number can be obtained from ,

[0128] Where: for The number of ambiguity cycles of the phase is For the cycle, ,

[0129] Where: The value range is , Indicates rounding towards negative infinity and positive infinity.

[0130] Example 3. This section uses simulation experiments to evaluate the DOA estimation performance of the designed array and the new deambiguation algorithm. In the simulation experiment, the DOA estimation performance of the common baseline distributed uniform array and the uniform linear array with equal array elements is compared, and the Cramer-Rao bounds of the non-common baseline distributed uniform array, the common baseline distributed uniform array and the uniform linear array are given as references.

[0131] like Figure 1 The non-common baseline distributed uniform array model shown in the figure, in the simulation, the total number of array elements is set to be 28, and the signal wavelength is m, the length of the baseline in the x-axis direction , the baseline length in the y-axis direction , unit element spacing m. Angle of incidence They are equal to 21° and 32° respectively, the successful estimation probability threshold is 0.08°, and 2 000 Monte Carlo tests are performed.

[0132] Figure 4 The results of the RMS error and SNR variation when the number of snapshots is 500 are given. Figure 5 The results of the change of the root mean square error with the number of snapshots when the SNR is equal to 0dB are given. From the simulation results, it can be seen that with the increase of SNR and the number of snapshots, the root mean square error gradually decreases. When the SNR is greater than 0dB, the non-co-baseline distributed uniform array and the co-baseline distributed uniform array designed in this paper can greatly improve the DOA estimation accuracy, and their estimation accuracy is basically the same, which is very close to the Cramer-Rao bound. However, when the SNR is less than 0dB, the non-co-baseline distributed uniform array has the best DOA estimation characteristics, and its estimation accuracy is better than the co-baseline distributed uniform array and uniform linear array with the same number of array elements. This is because the non-co-baseline distributed uniform array increases the effective aperture of the array, thereby improving the DOA estimation accuracy. In addition, compared with the co-baseline distributed uniform array, the non-co-baseline distributed uniform array is more flexible in array arrangement, less affected by geographical factors, and has relatively fewer restrictions. It can better adapt to the needs of the actual background, which is another advantage of the array designed in this paper.

[0133] On this basis, the success estimation probabilities of non-common baseline distributed uniform array, common baseline distributed uniform array and uniform linear array under different SNRs are compared. Figure 6 As shown in the simulation results, when the SNR is greater than -4dB, the non-common baseline distributed uniform array can successfully estimate the incident angle of the signal source under the threshold value of 0.08°, while the common baseline distributed uniform array and uniform linear array with equal array elements can successfully estimate the incident angle of the signal source with the SNR thresholds of 0 dB and 16 dB respectively. Figure 6 The simulation results further illustrate the advantages of the designed non-common-baseline distributed uniform array DOA estimation performance.

[0134] The array element spacing d of the non-common baseline distributed uniform array proposed by the present invention can be set to half a wavelength, and the array element antenna selects a dipole antenna. Figure 1 The antenna elements are placed in the array structure shown in the figure. The flowchart for DOA estimation using this array is as follows Figure 3 shown.

Claims

1. A method for acquiring target position based on a non-common baseline distributed uniform array, characterized in that: The non-co-baseline distributed uniform array comprises two identical linear uniform arrays, the number of array elements and the array element spacing of the two linear uniform arrays are the same, and the two linear uniform arrays are parallel to each other and not co-linear; the two identical linear uniform arrays are respectively and Indicates that all array elements are distributed on the x-y plane, and and are parallel to the x-axis, with the origin of the coordinate system being (0,0); the linear uniform array The coordinates of the array element position in the x-y plane are ,in, , d represents the unit element spacing, N is a uniform linear array The number of array elements in ; The linear uniform array The coordinates of the array element position in the x-y plane are , in, express and The length of the baseline along the x-axis, express and The length of the baseline along the y-axis, Much larger than the aperture of a uniform linear array, and The baseline length between ; The following steps are involved: Step 1: Obtain the received signal of the non-common baseline distributed uniform array at time t as echo data; Step 2: Calculate the covariance matrix R of the echo data in step 1 and decompose its eigenvalues ​​to obtain the signal subspace ; Step 3: Use the signal subspace obtained in step 2 Solve the rotation invariant relationship matrix between the unambiguous rough estimate and the fine estimate and ; Step 4: For the and Perform eigenvalue decomposition to get a rough estimate of the direction cosines and precise estimation ; Step 5: The precise estimate obtained in step 4 Obtaining accurate estimates of unambiguous direction cosines using a dual-scale deambiguation method :Estimation of precision The defuzzification period is as follows: Based on the rough estimate of direction cosines Constructing a rough estimate without fuzziness ,Right now ， Where: is the angle between the two sub-arrays; Unambiguous Direction Cosines Estimation With precise estimation The following relationship exists: , Where: for The number of ambiguity cycles of the phase is For the cycle, , Where: The value range is , Indicates rounding towards negative infinity and positive infinity; Step 6: Accurately estimate the unambiguous direction cosines according to step 5 Calculate the unambiguous incident source signal DOA accurate estimation azimuth ; Depend on , have to ; Where: is the angle between the two sub-arrays.

2. The method for acquiring target position based on non-common baseline distributed uniform array according to claim 1, characterized in that: The total number of array elements of the non-common baseline distributed uniform array is .

3. The method for acquiring target position based on non-common baseline distributed uniform array according to claim 1, characterized in that: The step 1 is specifically as follows: K far-field narrowband signal sources of unknown angles are incident on a non-common baseline distributed uniform array, that is, the incident angles of the K far-field narrowband signal sources are all located in the xy plane, represents the incident angle of the kth signal source, , then the direction cosines of the x-axis and y-axis are and ; by The first array element in is the reference array element. As the reference array, the received signal of the non-common baseline distributed uniform array at time t, i.e., the echo data, is expressed as: , Where: The received signal vector is , for The received signal of the nth array element is ; The received signal vector is , for The received signal of the nth array element is ; The signal vector is , Where: represents the kth source signal; Zero-mean additive white Gaussian noise is , Where: and They are and Gaussian white noise of the nth array element; is the array steering vector matrix, , Where: for The array-guided vector matrix, , Where: , ; for and The phase shift matrix between , Where: is the angle between the two sub-arrays, , Where: express and The length of the baseline along the x-axis, express and The length of the baseline along the y-axis.

4. The method for acquiring target position based on non-common baseline distributed uniform array according to claim 1, characterized in that: The step 2 is specifically as follows: multiply the received echo data by its own conjugate transpose and calculate the mathematical expectation to obtain the covariance matrix R of the echo data: , Where: represents the noise power, is the covariance matrix of the signal source vector. If the signal sources are independent of each other, then ,in represents the power of the kth signal source; Indicates that the dimension is equal to The identity matrix of Covariance matrix Perform eigenvalue decomposition to obtain the signal subspace ,Right now , Where: , , in, represents the eigenvalue matrix, , , …, is the covariance matrix The characteristic value of is the signal subspace, , , …, Represents the numerical value of the signal subspace; The space and signal subspace formed by the array steering vector matrix is the same space, there must be a unique non-singular matrix satisfy .

5. The method for acquiring target position based on non-common baseline distributed uniform array according to claim 1, characterized in that: The step 3 is as follows: Step 3.1, select subarrays in the linear uniform arrays S1 and S2, and determine the expression of the rotation invariant relationship equation: select the first N-1 array elements of S1 and S2 to form subarray C1, select the last N-1 array elements of S1 and S2 to form subarray C2, and the spatial translation between subarray C1 and subarray C2 is d, The rotation invariant relationship equation is expressed as: , Where: is the selection matrix of sub-matrix C1; is the selection matrix of sub-matrix C2; represents the 2nd-order unit matrix, represents the (N-1)-order unit matrix, To roughly estimate the rotation invariant relationship matrix, represents a (N-1)×1 dimensional zero vector, represents a diagonal matrix, represents a rough estimate of the complex value, represents direction cosines, represents the azimuth of the kth target; Step 3.2, the rotation invariance relationship equation expression of the linear uniform arrays S1 and S2: The linear uniform arrays S1 and S2 have spatial translation invariance with a translation amount of L on the x-y plane, and the rotation invariance relationship equation is expressed as: , In the formula, and are the selection matrices for S1 and S2 respectively; To accurately estimate the rotation invariant relationship matrix, represents the exact estimate of the complex value, To include The direction cosines of ; L represents the baseline length between arrays, Represents the signal wavelength; Step 3.3, use the signal subspace obtained in step 2 Obtain the rotation invariant relationship matrix between the rough estimate and the fine estimate and : The signal subspace Substitute and , can be obtained , , Where: and are the coarse estimation and fine estimation rotation invariant relationship matrices respectively; and Respectively and is a similarity matrix; Step 3.4: Use the rough estimate and fine estimate rotation invariant relationship matrix obtained in step 3.3 and Obtain the rotation invariant relationship matrix between the unambiguous estimate and the precise estimate and : Apply the least squares criterion to solve the equations separately , , we can get the rotation invariant relationship matrix and equal: , .

6. The method for acquiring target position based on non-common baseline distributed uniform array according to claim 1, characterized in that: The step 4 is specifically as follows: For the matrix and Perform eigenvalue decomposition and use the pairing algorithm to pair the eigenvalues ​​corresponding to the same source signal, that is, , ; , , Where: represents the rough estimated eigenvalue matrix, To roughly estimate the complex value, is the signal subspace, represents the precise estimated eigenvalue matrix, is an accurate estimate of the complex value; According to the relationship between direction cosine and eigenvalue complex phase , , a rough estimate of the direction cosines of the incident source signal , and accurate estimation They are , , Where: Indicates acquisition The phase angle, d represents the array element spacing, represents the wavelength of the signal, and L represents the distance between the two sub-arrays.

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