Polarization sensitive array radar high-precision angle measurement method under aperture constraint

Abstract

The invention discloses a polarization sensitive array radar high-precision angle measurement method under aperture constraint. The method is divided into an array comprehensive error correction part and a virtual aperture expansion angle measurement part, and the array comprehensive error correction part is used for carrying out joint modeling on various array errors existing in engineering implementation; and theoretically proving that a matrix bundle generated based on the actually measured steering vectors of the two different polarization correction sources is equivalent to a matrix bundle generated based on a real steering vector (having the same generalized eigenvalue), thereby realizing the accurate correction of the polarization sensitive array error. According to virtual aperture expansion angle measurement, on the basis of correction data, high-order cumulant is utilized to realize effective aperture expansion, limitation of physical aperture is broken through, and then angle measurement precision and resolution capability of the array radar are improved. The method can be applied to polarization sensitive arrays of any structures, all array errors existing in actual engineering are corrected, and the method is suitable for severe conditions with various errors and can be directly applied to engineering.

Description

Technical Field

[0001] The invention relates to the technical field of array signal processing, and in particular to a high-precision angle measurement method for a polarization-sensitive array radar under aperture constraints. Background Art

[0002] The rise and rapid development of spatial spectrum estimation technology has led to the widespread application of array radar in the field of angle measurement. Thanks to the high resolution of subspace decomposition algorithms represented by the multiple signal classification (MUSIC) algorithm and the rotationally invariant subspace (ESPRIT) algorithm, their engineering applications are also increasing. Although subspace decomposition algorithms can break through the constraints of the "Rayleigh limit", their angle measurement accuracy is still limited by the physical aperture. In scenes where the physical aperture is constrained, the angle measurement accuracy is difficult to meet the requirements, and there are many unavoidable errors in engineering implementation, such as channel amplitude and phase errors, array element position errors, mutual coupling errors, array element pattern errors, etc. The existence of errors will have a significant impact on the angle measurement performance of array radars.

[0003] In order to solve the limitation of physical aperture, many scholars at home and abroad have proposed a variety of angle measurement algorithms based on high-order cumulants. For example, in 2007, Chevalier proposed a polarization-sensitive array angle measurement algorithm based on high-order cumulants in the paper "Higher order direction finding from Arrays with diversely polarized antennas: The PD-2q-MUSIC algorithms", which realized virtual aperture expansion. However, this method did not consider the error factors in engineering implementation and did not work well in practical applications. In order to solve the influence of errors in engineering applications, many scholars have studied array error correction methods. In 2010, Wang Ding proposed an error correction method in the paper "Active Correction Algorithm for Array Errors and Its Improvement", but this method did not consider the influence of array element pattern errors and could not realize virtual aperture expansion, and its performance was poor under aperture constraints.

[0004] At present, there is no relevant research that considers both comprehensive error correction and virtual aperture expansion. Therefore, array radar has the problem of low angle measurement accuracy under harsh conditions where the physical aperture is limited and array errors exist. Summary of the invention

[0005] In view of this, the present invention provides a high-precision angle measurement method for polarization-sensitive array radar under aperture constraints, which can achieve high-precision angle measurement of array radar under working conditions where the physical aperture is limited and there are multiple array errors, and is suitable for polarization-sensitive arrays of arbitrary structures.

[0006] The high-precision angle measurement method of polarization-sensitive array radar under aperture constraint of the present invention comprises:

[0007] Step 1: Equivalent all errors to an angle-dependent comprehensive error matrix W(θ) to construct the array receiving data model; where: θ is the pitch angle, is the azimuth;

[0008] Step 2: fix the angle parameter θ, select any two correction sources with different polarizations to transmit separately in time division, and obtain the array receiving data when a single correction source is used; use the array receiving data to extract the measured steering vectors under different polarizations, and combine the measured steering vectors to obtain the correction data under the angle; traverse θ in the airspace of interest to obtain the correction data at each angle;

[0009] Step 3, calculate the fourth-order cumulant matrix of the array received data to realize virtual aperture expansion; perform eigendecomposition on the fourth-order cumulant matrix to obtain the noise subspace; construct a matrix beam based on the measured steering vector and the noise subspace, which is equivalent to the matrix beam constructed based on the real steering vector and the noise subspace; obtain the spatial spectrum by calculating the minimum generalized eigenvalue of the matrix beam at each angle θ; perform spectral peak search on the spatial spectrum to obtain the angle measurement result.

[0010] Preferably, in step 1, the true steering vector including the comprehensive error matrix is

[0011]

[0012] Where β = [cosγsinγe jη ] T , γ is the polarization auxiliary angle, η is the polarization phase difference, (·) T Represents matrix transpose; and a(θ,β) represent the real steering vector and the theoretical steering vector respectively; A 12 (θ) is the angle-dependent term in a(θ,β);

[0013] The array receiving data model is:

[0014]

[0015] where x(t)=[x1(t),...,x N (t)] T Receive data for an N×1 array, s(t)=[s1(t),...,s K (t)] T is a K×1 signal source, n(t)=[n1(t),...,n N (t)] T is an N×1 noise signal, is the true steering vector of K signal sources.

[0016] Preferably, in step 2, a signal subspace method, a Fourier transform method or a covariance matrix time-domain averaging method is used to extract the measured steering vector from the array received data, thereby obtaining correction data at the angle.

[0017] Preferably, the signal subspace method is used to extract the measured steering vector and obtain the correction data, specifically:

[0018] Calculate the covariance matrix of the received data of the two correction source arrays respectively, and perform eigendecomposition on the covariance matrix to obtain the corresponding signal subspace U s1 with U s2 , the signal subspace is the measured steering vector, which satisfies the following linear relationship with the true steering vector:

[0019]

[0020] Will U s1 with U s2 Combined together, we get the correction data at the current angle θ:

[0021]

[0022] Preferably, in step 3,

[0023] The array receives data x(t)=[x1(t),...,x N (t)] T The fourth-order cumulant is defined as

[0024]

[0025] The fourth-order cumulant matrix R4 is: R4((i1-1)N+i3,(i2-1)N+i4)=C 4x (i1,i2,i3,i4);

[0026] The steering vector after aperture expansion is:

[0027]

[0028] Perform eigendecomposition on the fourth-order cumulant matrix R4 to obtain the noise subspace U 4,n ;

[0029] According to C(θ) and U 4,n Construct the matrix:

[0030]

[0031] By traversing the angle parameter θ, the spatial spectrum is obtained:

[0032]

[0033] The angle measurement result can be obtained by searching the peak of the spatial spectrum.

[0034] Preferably, the polarization sensitive array radar is of any array configuration.

[0035] Preferably, the polarization sensitive array radar is an L-shaped array, a uniform circular array or a uniform rectangular array.

[0036] Preferably, all the errors include channel amplitude and phase errors, array element position errors, mutual coupling errors and / or array element radiation pattern errors.

[0037] Beneficial effects:

[0038] The present invention takes into account various error factors in engineering implementation, including channel amplitude and phase error, array element position error, mutual coupling error, array element pattern error, etc., and designs a set of comprehensive error correction methods to correct various errors existing in actual engineering. Then, the fourth-order cumulant is used to realize virtual aperture expansion, break through the limitation of physical aperture, and then realize high-precision angle measurement of array radar. The present invention can realize high-precision angle measurement of array radar under working conditions where the physical aperture is limited and there are various array errors.

[0039] The present invention can be applied to polarization sensitive arrays of any structure, such as L-shaped arrays, uniform circular arrays, uniform rectangular arrays, etc., and the present invention can correct all array errors existing in actual engineering (including but not limited to channel amplitude and phase errors, array element position errors, mutual coupling errors, array element radiation pattern errors, etc.), is suitable for harsh conditions with multiple errors, and can be directly applied in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the present invention.

[0041] Figure 2 Schematic diagram of an eight-element polarization-sensitive uniform circular array.

[0042] Figure 3 Schematic diagram of physical array and virtual array.

[0043] Figure 4 This is the spectrum peak diagram before and after aperture expansion and error correction.

[0044] Figure 5 is the azimuth RMSE before and after aperture expansion and error correction.

[0045] Figure 6 is the RMSE of the elevation angle before and after aperture expansion and error correction. DETAILED DESCRIPTION

[0046] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0047] The present invention provides a high-precision angle measurement method for polarization-sensitive array radar under aperture constraints, which is divided into two parts: array comprehensive error correction and virtual aperture expansion angle measurement. The array comprehensive error correction jointly models various array errors existing in engineering implementation, and theoretically proves that the matrix beam generated based on the measured steering vectors of two different polarization correction sources is equivalent to the matrix beam generated based on the real steering vector (having the same generalized eigenvalues), thereby achieving accurate correction of polarization-sensitive array errors; virtual aperture expansion angle measurement uses high-order cumulants on the basis of correction data to achieve the expansion of the effective aperture, breaking through the limitation of the physical aperture, thereby improving the angle measurement accuracy and resolution capability of the array radar. The flow chart of the method of the present invention is as follows Figure 1 As shown, the specific steps are as follows:

[0048] Step 1: Array comprehensive error correction:

[0049] Step 1.1, establish a comprehensive error model

[0050] Consider K far-field narrowband signals incident on an N-element polarization-sensitive array of arbitrary configuration, and model the channel amplitude and phase error, array element position error, mutual coupling error, and array element pattern error. Under narrowband conditions, all errors can be equivalent to an angle-dependent comprehensive error matrix W(θ). This error matrix cannot be clearly separated and analytically represented according to the error parameters. The true steering vector can be expressed as

[0051]

[0052] In the formula, Contains the pitch angle θ and azimuth angle β=[cosγsinγe jη ] T Includes polarization auxiliary angle γ and polarization phase difference η. (·) T Represents matrix transpose. and a(θ,β) represent the real steering vector and the theoretical steering vector respectively. 12 The product of (θ) and the comprehensive error matrix W(θ) is written as WA 12 (θ).

[0053] The array receiving data model at this time is:

[0054]

[0055] In the formula, x(t)=[x1(t),...,x N (t)] TReceive data for an N×1 array, s(t)=[s1(t),...,s K (t)] T is a K×1 signal source, n(t)=[n1(t),...,n N (t)] T is an N×1 noise signal, is the true steering vector of K signal sources.

[0056] Step 1.2: Obtain correction data based on two correction sources with different polarizations

[0057] The angle parameter is fixed as θ, and any two different polarization parameters β1 and β2 are selected. The two correction sources with different polarizations are transmitted separately in time division to obtain the array receiving data when a single correction source is used. In order to obtain the correction data at this angle, it is necessary to extract the measured steering vector from the array receiving data, which can be achieved through a variety of processing methods, such as the signal subspace method, Fourier transform method, covariance matrix time domain averaging method, etc. The following takes the signal subspace method as an example:

[0058] Calculate the covariance matrix of the received data of the two correction source arrays respectively, and perform eigendecomposition on the covariance matrix to obtain the corresponding signal subspace U s1 with U s2 , the signal subspace is the measured steering vector, which satisfies the following linear relationship with the true steering vector:

[0059]

[0060] Will U s1 with U s2 Combined together, we get the correction data at the current angle θ:

[0061]

[0062] Change θ and traverse the angle parameters in the spatial domain of interest to obtain the correction data at each angle.

[0063] Step 2: Virtual aperture expansion angle measurement:

[0064] Step 2.1, calculate the fourth-order cumulant matrix to achieve aperture expansion

[0065] When measuring angles, first obtain the array receiving data x(t) = [x1(t),...,x N (t)] T , whose fourth-order cumulant is defined as

[0066]

[0067] As i1, i2, i3, i4 change, there are N 4Fourth-order cumulants, these N 4 Put the value into N 2 ×N 2 In the fourth-order cumulant matrix R4, R4((i1-1)N+i3,(i2-1)N+i4)=C 4x (i1,i2,i3,i4).

[0068] The fourth-order cumulant matrix R4 is used for subsequent spatial spectrum estimation to achieve virtual aperture expansion. The steering vector after aperture expansion is

[0069]

[0070] Step 2.2, perform eigendecomposition on the fourth-order cumulant matrix to obtain the noise subspace

[0071] The characteristic decomposition of R4 can be obtained:

[0072] R4=U 4,s Λ 4,s U 4,s H +U 4,n Λ 4,n U 4,n H (7)

[0073] Where U 4,n represents the noise subspace, which is orthogonal to the extended steering vector corresponding to the target, that is:

[0074]

[0075] Substituting equation (6) into the equation, we can obtain an optimization problem that requires a four-dimensional parameter search to solve, as follows:

[0076]

[0077] In the formula

[0078]

[0079] Formula (9) is a problem of solving a generalized Rayleigh quotient, so the two-dimensional search for β can be transformed into solving the minimum generalized eigenvalue of the matrix bundle. Formula (9) can be simplified to:

[0080]

[0081] Step 2.3: Construct a matrix bundle based on the correction data and noise subspace

[0082] U in Q1(θ) and Q2(θ) 4,n Can be obtained according to the array receiving data, but WA 12(θ) cannot be obtained, so the correction data C(θ) is needed for equivalent replacement.

[0083] According to C(θ) and U 4,n Construct the matrix:

[0084]

[0085] The polarization states of the two correction sources are different. is a full rank matrix, so (T1(θ), T2(θ)) and (Q1(θ), Q2(θ)) are equivalent matrix bundles (with the same generalized eigenvalues), so the optimization problem of formula (11) can be equivalent to the following optimization problem:

[0086]

[0087] Step 2.4, traverse the angles to obtain the spatial spectrum, and perform a peak search on the spatial spectrum

[0088] The two matrices in formula (13) can be obtained based on the array received data and the correction data. By traversing the angle parameter θ and finding the minimum generalized eigenvalue at each angle, the spatial spectrum can be obtained:

[0089]

[0090] The angle parameter Containing two-dimensional angles of azimuth and elevation, high-precision angle measurement results can be obtained by searching the peak of the spatial spectrum.

[0091] In this embodiment, the array is set to be a polarization-sensitive uniform circular array composed of 8 electric oscillators tangent to the circumference, such as Figure 2 As shown, Figure 3 The virtual array corresponding to the physical array is shown, where ○ represents the physical array element and ◆ represents the virtual array element; the specific simulation parameters are shown in Table 1:

[0092] Table 1

[0093]

[0094] First, two correction sources with different polarizations are selected, and the two-dimensional angle grid is traversed to obtain the received data (500 snapshots) of the two correction sources at each angle. The correction data is obtained and stored according to the received data.

[0095] Set the signal source as shown in the table above, get the corresponding received data (100 snapshots), get the noise subspace based on the received data, and use the noise subspace and correction data to generate the spatial spectrum. The single simulation spectrum peak diagram when the signal-to-noise ratio is 25dB is as follows Figure 4 shown.

[0096] Monte Carlo simulations were performed 100 times at each angle. The azimuth and elevation angles obtained by spectral peak search were compared with the true values, and their root mean square errors (RMSE) were calculated. The azimuth RMSE before and after aperture expansion and error correction was compared. Figure 5 As shown in Figure 2, the RMSE comparison of the pitch angle before and after aperture expansion and error correction is as follows: Figure 6 shown.

[0097] The effectiveness of the high-precision angle measurement method proposed in the present invention can be clearly seen from the comparison diagram of the simulated spectrum peak diagram and the RMSE diagram, and high-precision angle measurement can be achieved under harsh conditions with limited physical aperture and array errors.

[0098] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A high-precision angle measurement method for polarization-sensitive array radar under aperture constraints, characterized in that: include: Step 1: Equivalent all errors to an angle-dependent comprehensive error matrix W(θ) to construct the array receiving data model; where: θ is the pitch angle, is the azimuth; Step 2: fix the angle parameter θ, select any two correction sources with different polarizations to transmit separately in time division, and obtain the array receiving data when a single correction source is used; use the array receiving data to extract the measured steering vectors under different polarizations, and combine the measured steering vectors to obtain the correction data under the angle; traverse θ in the airspace of interest to obtain the correction data at each angle; Step 3, calculate the fourth-order cumulant matrix of the array received data to realize virtual aperture expansion; perform eigendecomposition on the fourth-order cumulant matrix to obtain the noise subspace; construct a matrix beam based on the measured steering vector and the noise subspace, which is equivalent to the matrix beam constructed based on the real steering vector and the noise subspace; obtain the spatial spectrum by calculating the minimum generalized eigenvalue of the matrix beam at each angle θ; perform spectral peak search on the spatial spectrum to obtain the angle measurement result.

2. The method according to claim 1, characterized in that In step 1, the true steering vector including the comprehensive error matrix is Where β = [cosγsinγe jη ] T , γ is the polarization auxiliary angle, η is the polarization phase difference, (·) T Represents matrix transpose; and a(θ,β) represent the real steering vector and the theoretical steering vector respectively; A 12 (θ) is the angle-dependent term in a(θ,β); The array receiving data model is: where x(t)=[x1(t),…,x N (t)] T Receive data for an N×1 array, s(t)=[s1(t),…,s K (t)] T is a K×1 signal source, n(t)=[n1(t),…,n N (t)] T is an N×1 noise signal, is the true steering vector of K signal sources.

3. The method according to claim 1 or 2, characterized in that In step 2, a signal subspace method, a Fourier transform method or a covariance matrix time-domain averaging method is used to extract the measured steering vector from the array received data, thereby obtaining correction data at the angle.

4. The method according to claim 3, characterized in that The signal subspace method extracts the measured steering vector and obtains the correction data, which is as follows: Calculate the covariance matrix of the received data of the two correction source arrays respectively, and perform eigendecomposition on the covariance matrix to obtain the corresponding signal subspace U s1 with U s2 , the signal subspace is the measured steering vector, which satisfies the following linear relationship with the true steering vector: Will U s1 with U s2 Combined together, we get the correction data at the current angle θ:

5. The method according to claim 2, characterized in that In step 3, The array receives data x(t)=[x1(t),…,x N (t)] T The fourth-order cumulant is defined as The fourth-order cumulant matrix R4 is: R4((i1-1)N+i3,(i2-1)N+i4)=C 4x (i1,i2,i3,i4); The steering vector after aperture expansion is: Perform eigendecomposition on the fourth-order cumulant matrix R4 to obtain the noise subspace U 4,n ; According to C(θ) and U 4,n Construct the matrix: By traversing the angle parameter θ, the spatial spectrum is obtained: The angle measurement result can be obtained by searching the peak of the spatial spectrum.

6. The method according to claim 1, characterized in that The polarization sensitive array radar has an arbitrary array configuration.

7. The method according to claim 6, characterized in that The polarization sensitive array radar is an L-shaped array, a uniform circular array or a uniform rectangular array.

8. The method according to claim 1, characterized in that The all errors include channel amplitude and phase errors, array element position errors, mutual coupling errors and / or array element radiation pattern errors.

Images