High-precision angle measurement method for polarization-sensitive array radar under aperture constraint

Abstract

This invention discloses a high-precision angle measurement method for polarization-sensitive array radar under aperture constraints. The invention consists of two parts: array synthesis error correction and virtual aperture expansion angle measurement. Array synthesis error correction jointly models various array errors present in engineering implementation and theoretically proves that the matrix bundle generated based on the measured steering vectors of two different polarization correction sources is equivalent to the matrix bundle generated based on the real steering vector (having the same generalized eigenvalues), thus achieving accurate correction of polarization-sensitive array errors. Virtual aperture expansion angle measurement, based on the corrected data, utilizes higher-order cumulants to expand the effective aperture, breaking through the limitations of the physical aperture, thereby improving the angle measurement accuracy and resolution of the array radar. This invention can be applied to polarization-sensitive arrays of arbitrary structures, correcting all array errors present in actual engineering, and is suitable for harsh conditions with multiple errors, enabling direct application in engineering.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically to a high-precision angle measurement method for a polarization-sensitive array radar under aperture constraints. Background Technology

[0002] The rise and rapid development of spatial spectrum estimation technology has led to the widespread application of array radar in angle measurement. Thanks to the high resolution of subspace decomposition algorithms, such as the Multiple Signal Classification (MUSIC) algorithm and the Rotation Invariant Subspace (ESPRIT) algorithm, their engineering applications are increasing. Although subspace decomposition algorithms can overcome the Rayleigh limit, their angle measurement accuracy is still limited by the physical aperture. In scenarios with constrained physical apertures, the required angle measurement accuracy is difficult to meet, and various unavoidable errors exist in engineering implementation, such as channel amplitude and phase errors, element position errors, mutual coupling errors, and element pattern errors. These errors significantly impact the angle measurement performance of array radar.

[0003] To address the limitations of physical aperture, many scholars both domestically and internationally have proposed various angle measurement algorithms based on higher-order cumulants. For example, in 2007, Chevalier proposed a polarization-sensitive array angle measurement algorithm based on higher-order cumulants in his paper "Higher order direction finding from Arrays with diversely polarized antennas: The PD-2q-MUSIC algorithms," which achieved virtual aperture expansion. However, this method did not consider error factors in engineering implementation, resulting in poor performance in practical applications. To address the impact of errors in engineering applications, many scholars have researched array error correction methods. In 2010, Wang Ding proposed an error correction method in his paper "Active Algorithm for Array Error Correction and Its Improvement." However, this method did not consider the influence of array element pattern errors and could not achieve virtual aperture expansion, resulting in poor performance under aperture constraints.

[0004] Currently, there is no research that simultaneously considers comprehensive error correction and virtual aperture expansion. Therefore, array radar suffers from 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 realize high-precision angle measurement of array radar under working conditions where the physical aperture is limited and there are various array errors, and is applicable to polarization-sensitive arrays of arbitrary structure.

[0006] The high-precision angle measurement method for aperture-constrained polarization-sensitive array radar of the present invention includes:

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

[0008] Step 2: Fix the angle parameter θ, select any two correction sources with different polarizations and transmit them separately in a time-division manner to obtain the array received data with a single correction source; use the array received data to extract the measured steering vectors under different polarizations, and combine the measured steering vectors to obtain the correction data under that angle; traverse θ in the space of interest to obtain the correction data under each angle.

[0009] Step 3: Calculate the fourth-order cumulant matrix of the array received data to realize virtual aperture expansion; perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the noise subspace; construct a matrix bundle based on the measured steering vector and the noise subspace, which is equivalent to the matrix bundle constructed based on the real steering vector and the noise subspace; obtain the spatial spectrum by calculating the minimum generalized eigenvalue of the matrix bundle 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 containing 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 Indicates matrix transpose; Let a(θ,β) represent the actual steering vector and the theoretical steering vector, respectively; A 12 (θ) is the angle-related term in a(θ,β);

[0013] The array receiving data model is as follows:

[0014]

[0015] Where x(t)=[x1(t),...,x N (t)] T For receiving data in an N×1 array, s(t) = [s1(t),...,s...]. K (t)] T Given a K×1 signal source, n(t) = [n1(t),...,n N (t)] T For an N×1 noise signal, Let be the true steering vector of the K signal sources.

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

[0017] A preferred method is to extract the measured steering vector using the signal subspace method to obtain the correction data, specifically as follows:

[0018] Calculate the covariance matrices of the received data from the two calibration source arrays respectively, and perform eigenvalue decomposition on the covariance matrices to obtain the corresponding signal subspace U. s1 with U s2 The signal subspace is the measured steering vector, and it satisfies the following linear relationship with the true steering vector:

[0019]

[0020] Will U s1 with U s2 Combining these data yields the correction data for 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 guide vector after aperture expansion is:

[0027]

[0028] Eigenvalue decomposition of the fourth-order cumulant matrix R4 yields the noise subspace U. 4,n ;

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

[0030]

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

[0032]

[0033] The angle measurement result is obtained by searching for spectral peaks in the spatial spectrum.

[0034] Preferably, the polarization-sensitive array radar is of arbitrary 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 pattern errors.

[0037] Beneficial effects:

[0038] This invention considers various error factors in engineering implementation, including channel amplitude and phase errors, array element position errors, mutual coupling errors, and array element pattern errors. It designs a comprehensive error correction method to correct various errors present in actual engineering. Then, it utilizes fourth-order cumulants to achieve virtual aperture expansion, overcoming the limitations of physical aperture, and thus realizing high-precision angle measurement for array radar. This invention enables high-precision angle measurement of array radar under operating conditions where the physical aperture is limited and various array errors exist.

[0039] This invention can be applied to polarization-sensitive arrays of any structure, such as L-shaped arrays, uniform circular arrays, uniform rectangular arrays, etc. Furthermore, this 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 pattern errors, etc.), and is suitable for harsh conditions with multiple errors, and can be directly applied in engineering. Attached Figure Description

[0040] Figure 1 This is a flowchart of the present invention.

[0041] Figure 2 This is a schematic diagram of an octet polarization-sensitive uniform circular array.

[0042] Figure 3 This is a schematic diagram of physical arrays and virtual arrays.

[0043] Figure 4 The images show the peak patterns before and after aperture expansion and error correction.

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

[0045] Figure 6 The pitch angle RMSE is the angle before and after aperture expansion and error correction. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0047] This invention provides a high-precision angle measurement method for polarization-sensitive array radar under aperture constraints, consisting of two parts: array synthesis error correction and virtual aperture expansion angle measurement. The array synthesis error correction method jointly models various array errors present in engineering implementation and theoretically proves that the matrix bundle generated based on the measured steering vectors of two different polarization correction sources is equivalent to (having the same generalized eigenvalues) the matrix bundle generated based on the real steering vector, thus achieving accurate correction of polarization-sensitive array errors. The virtual aperture expansion angle measurement method, based on the correction data, utilizes higher-order cumulants to expand the effective aperture, overcoming the limitations of the physical aperture and thereby improving the angle measurement accuracy and resolution of the array radar. The flowchart of this invention is shown below. Figure 1 As shown, the specific steps are as follows:

[0048] Step 1, Array synthesis error correction:

[0049] Step 1.1, Establish a comprehensive error model

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

[0051]

[0052] In the formula, Includes pitch angle θ and azimuth angle β=[cosγsinγe jη ] T Includes the polarization auxiliary angle γ and the polarization phase difference η. (·) T This indicates the matrix transpose. Let a(θ,β) represent the actual steering vector and the theoretical steering vector, respectively. Let A be the angle-related term in a(θ,β). 12 The product of (θ) and the comprehensive error matrix W(θ) can be 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)] TFor receiving data in an N×1 array, s(t) = [s1(t),...,s...]. K (t)] T Given a K×1 signal source, n(t) = [n1(t),...,n N (t)] T For an N×1 noise signal, Let K be the true steering vectors of the K signal sources.

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

[0057] With a fixed angle parameter θ, two arbitrary polarization parameters β1 and β2 are selected. Two correction sources with different polarizations are transmitted separately in a time-division multiplexing manner, yielding array received data with a single correction source. To obtain the correction data at this angle, the measured steering vector needs to be extracted from the array received data. This can be achieved through various processing methods, such as the signal subspace method, the Fourier transform method, and the time-domain averaging method of the covariance matrix. The signal subspace method is used as an example below:

[0058] Calculate the covariance matrices of the received data from the two calibration source arrays respectively, and perform eigenvalue decomposition on the covariance matrices to obtain the corresponding signal subspace U. s1 with U s2 The signal subspace is the measured steering vector, and it satisfies the following linear relationship with the true steering vector:

[0059]

[0060] Will U s1 with U s2 Combining these data yields the correction data for the current angle θ:

[0061]

[0062] By changing θ and iterating through the angular parameters within the spatial domain of interest, the correction data for each angle can be obtained.

[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 acquire the array received data x(t) = [x1(t),...,x N (t)] T Its fourth-order cumulant is defined as

[0066]

[0067] As i1, i2, i3, i4 change, there are a total of N 4These N fourth-order cumulants 4 Each value is placed 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] By using the fourth-order cumulant matrix R4 for subsequent spatial spectrum estimation, virtual aperture expansion can be achieved. The steering vector after aperture expansion is:

[0069]

[0070] Step 2.2: Perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the noise subspace.

[0071] Eigenvalue decomposition of R4 yields:

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

[0073] In the formula U 4,n Let represent the noise subspace, which is orthogonal to the extended steering vector corresponding to the target, i.e.:

[0074]

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

[0076]

[0077] In the formula

[0078]

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

[0080]

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

[0082] U in Q1(θ) and Q2(θ) 4,n It can be obtained from the data received by the array, but WA 12Since (θ) is unavailable, the corrected data C(θ) is needed for an equivalent substitution.

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

[0084]

[0085] The two correction sources have different polarization states. Since it is a full-rank matrix, (T1(θ),T2(θ)) and (Q1(θ),Q2(θ)) are equivalent matrix bundles (with the same generalized eigenvalues). Therefore, the optimization problem of equation (11) can be equivalently transformed into 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 equation (13) can be obtained from the array received data and the correction data. By iterating through the angle parameter θ and finding the minimum generalized eigenvalue at each angle, the spatial spectrum can be obtained:

[0089]

[0090] In the formula, the angle parameter It includes two dimensions of angles: azimuth and elevation. High-precision angle measurement results can be obtained by searching for spectral peaks in the spatial spectrum.

[0091] In this embodiment, the array is configured as a polarization-sensitive uniform circular array composed of eight 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 a physical array element and ◆ represents a virtual array element; the specific simulation parameters are shown in Table 1:

[0092] Table 1

[0093]

[0094] First, select two calibration sources with different polarizations, traverse the two-dimensional angle grid, and acquire the received data (500 snapshots) of the two calibration sources at each angle. Then, obtain the calibration data based on the received data and store it.

[0095] The signal source is set up as shown in the table above, and the corresponding received data (100 snapshots) is obtained. The noise subspace is obtained based on the received data. A spatial spectrum is generated using the noise subspace and the correction data. The single-simulation spectrum peak diagram at a signal-to-noise ratio of 25dB is shown below. Figure 4 As shown.

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

[0097] The effectiveness of the high-precision angle measurement method proposed in this invention can be clearly seen from the comparison of the simulated peak diagram and RMSE diagram. It can achieve high-precision angle measurement under harsh conditions such as limited physical aperture and array error.

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

Claims

1. A high-precision angle measurement method for a polarization-sensitive array radar under aperture constraint, characterized in that, include: Step 1: Equivalent all errors to an angle-dependent comprehensive error matrix W(θ), constructing the array received data model; where, θ is the pitch angle. The azimuth angle is ; the true steering vector containing the comprehensive error matrix is ​​. Where β=[cosγsinγe jη ] T γ is the polarization auxiliary angle, η is the polarization phase difference, (·) T Indicates matrix transpose; Let a(θ,β) represent the actual steering vector and the theoretical steering vector, respectively; A 12 (θ) is the angle-related term in a(θ,β); The array receiving data model is as follows: Where x(t)=[x1(t),...,x N (t)] T For receiving data in an N×1 array, s(t) = [s1(t),...,s...]. K (t)] T Given a K×1 signal source, n(t) = [n1(t),...,n N (t)] T For an N×1 noise signal, The true steering vectors of the K signal sources; Step 2: Fix the angle parameter θ, select any two correction sources with different polarizations and transmit them separately in a time-division manner to obtain the array received data when using a single correction source; use the array received data to extract the measured steering vectors under different polarizations, and combine the measured steering vectors to obtain the correction data under that angle; traverse θ in the space of interest to obtain the correction data C(θ) under each angle. Step 3: Calculate the fourth-order cumulant matrix of the received array data to achieve virtual aperture expansion; perform eigenvalue decomposition on the fourth-order cumulant matrix to obtain the noise subspace; construct a matrix bundle based on the measured steering vector and the noise subspace, which is equivalent to the matrix bundle constructed based on the real steering vector and the noise subspace; obtain the spatial spectrum by calculating the minimum generalized eigenvalue of the matrix bundle at each angle θ; perform spectral peak search on the spatial spectrum to obtain the angle measurement result; specifically, 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 guide vector after aperture expansion is: Eigenvalue decomposition of the fourth-order cumulant matrix R4 yields the noise subspace U. 4,n ; According to C(θ) and U 4,n Construct the matrix: By iterating through the angle parameter θ, the spatial spectrum is obtained: The angle measurement result is obtained by searching for spectral peaks in the spatial spectrum.

2. The method as described in claim 1, characterized in that, In step 2, the measured steering vector is extracted from the array received data using the signal subspace method, Fourier transform method, or covariance matrix time-domain averaging method, thereby obtaining the correction data at that angle.

3. The method as described in claim 2, characterized in that, The signal subspace method is used to extract the measured steering vector and obtain correction data, specifically as follows: Calculate the covariance matrices of the received data from the two calibration source arrays respectively, and perform eigenvalue decomposition on the covariance matrices to obtain the corresponding signal subspace U. s1 with U s2 The signal subspace is the measured steering vector, and it satisfies the following linear relationship with the true steering vector: Will U s1 with U s2 Combining these, we obtain the correction data C(θ) at the current angle θ:

4. The method as described in claim 1, characterized in that, The polarization-sensitive array radar has an arbitrary array configuration.

5. The method as described in claim 1, characterized in that, The polarization-sensitive array radar is an L-shaped array, a uniform circular array, or a uniform rectangular array.

6. The method as described in claim 1, characterized in that, All errors include channel amplitude and phase errors, array element position errors, mutual coupling errors, and array element pattern errors.

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