Polarization sensitive array radar adaptive snapshot number angle measurement method

Abstract

The invention belongs to the technical field of array signal processing, and relates to a polarization sensitive array radar adaptive snapshot number angle measurement method. The method specifically comprises the following steps of: setting an initial azimuth angle, a Cramer-Rao Bound (CRB) of a pitch angle and an initial snapshot number; a far-field narrow-band signal is set to be incident to a polarization sensitive array of any configuration, and an array receiving data covariance matrix is calculated; performing characteristic decomposition on the covariance matrix to obtain a noise subspace; estimating a target angle and a polarization parameter by using orthogonality of a noise subspace and a target steering vector; on the basis of Cramer-Rao bound derivation of the azimuth angle and the pitch angle of the polarization sensitive array, the relation between the azimuth angle CRB and the snapshot number and the relation between the pitch angle CRB and the snapshot number are obtained, and the minimum snapshot number meeting the CRB requirement is calculated through the estimated target angle, polarization parameters and the Cramer-Rao bound of the set initial azimuth angle and pitch angle; and selecting receiving data corresponding to the snapshots according to the calculated minimum number of snapshots, and carrying out angle and polarization parameter estimation.

Description

Technical Field

[0001] The invention relates to an adaptive snapshot angle measurement method for a polarization-sensitive array radar, and in particular to an adaptive snapshot angle measurement method based on a polarization-sensitive array for a moving platform, and belongs to the technical field of array signal processing. Background Art

[0002] In the application scenarios of some moving platforms such as aircraft, the carrier space is limited and the installation structure is irregular, so it is difficult to ensure that each antenna in the array has the same polarization selection characteristics, so the polarization-sensitive array is a better choice. In addition, the polarization-sensitive array can also sense the polarization information of electromagnetic waves based on the spatial and temporal information. The use of polarization, spatial, and temporal information can improve the target recognition ability and enhance the anti-interference performance. Therefore, the angle measurement method based on the polarization-sensitive array has been widely studied.

[0003] When using MUSIC algorithms for parameter estimation in polarization-sensitive arrays, it is necessary to perform a four-dimensional parameter search including two-dimensional angle domain parameters and two-dimensional polarization domain parameters. The computational complexity is extremely high, and it is difficult to ensure real-time performance with current computing power. To solve this problem, in 2007, Chevalier et al. in the article "Higher order direction finding from Arrays with diversely polarized antennas: The PD-2q-MUSIC algorithms" equivalently regarded the angle measurement of polarization-sensitive arrays as a generalized Rayleigh quotient minimization problem, thereby achieving dimensionality reduction estimation of angle parameters. In 2017, Zeng Fuhong et al. proposed a rank-deficient MUSIC algorithm in the article "Dimensionality reduction estimation algorithm for DOA and polarization parameters of polarization-sensitive arrays" using the principle of matrix rank loss to achieve dimensionality reduction estimation of angle parameters.

[0004] Both methods achieve high-precision angle measurement based on the received data with a fixed number of snapshots. By reducing the four-dimensional search to a two-dimensional search, the amount of calculation is reduced to a certain extent, which is convenient for engineering implementation. For the angle measurement method with a fixed number of snapshots, if a small number of snapshots is selected, the angle measurement accuracy requirements cannot be met when the signal-to-noise ratio is low; if a large number of snapshots is selected, as the moving platform gradually approaches the target, the signal-to-noise ratio increases, and a small number of snapshots or even a single snapshot data can meet the system's angle measurement accuracy requirements. At this time, using multiple snapshot data to measure the angle will result in a waste of computational overhead. At present, there is no related research on the angle measurement of polarization-sensitive array radar with adaptive snapshot number. Summary of the invention

[0005] To solve the above problems, the present invention proposes a polarization-sensitive array radar adaptive snapshot number angle measurement method, which is applied to the scenario of continuous angle measurement of a moving platform. The number of snapshots required for angle measurement is adaptively changed as the signal-to-noise ratio changes, which can improve the real-time performance of the system while ensuring the angle measurement accuracy.

[0006] The technical solution for implementing the present invention is as follows:

[0007] A polarization sensitive array radar adaptive snapshot angle measurement method, the specific process is:

[0008] Step 1: Set the initial Cramer-Rao Bound (CRB) of the azimuth and elevation angles θ0 and the initial snapshot number L0;

[0009] Step 2: Assume that K far-field narrowband signals are incident on an N-element polarization sensitive array of arbitrary configuration, and calculate the array receiving data covariance matrix of L0 snapshots;

[0010] Step 3: Perform eigendecomposition on the covariance matrix to obtain the noise subspace;

[0011] Step 4: Utilize the orthogonality between the noise subspace and the target guidance vector to calculate the target angle and polarization parameter (γ,η) estimation;

[0012] Step 5: Based on the Cramer-Rao bounds of the azimuth and elevation angles of the polarization-sensitive array, obtain the relationship between the azimuth CRB, elevation CRB and the number of snapshots. Use the target angle and polarization parameters estimated in step 4 and step 1 to set the Cramer-Rao bounds of the initial azimuth and elevation angles. θ0, calculate the minimum number of snapshots that meet the CRB requirements;

[0013] Step 6: According to the calculated minimum number of snapshots L min Select the received data of the corresponding snapshot to estimate the angle and polarization parameters.

[0014] Furthermore, in step 5 of the present invention, the relationship between the azimuth angle CRB, the pitch angle CRB and the number of snapshots L is:

[0015]

[0016]

[0017] Among them, CRB(θ) is a K×K matrix, and its diagonal K elements CRB(θ) i,i (i=1,2,…,K) are the squares of the Cramer-Rao bounds of the K signal elevation angles; is a K×K matrix with K elements on its diagonal are the squares of the Cramer-Rao bounds of the K signal azimuths; ⊙ represents the Hadamard product, A θ represents the derivative of the steering vector matrix A with respect to the pitch angle θ; Represents the orientation angle of the steering vector matrix A The derivative of , A represents the steering vector matrix of K signal sources, s represents the signal source, represents the noise power, Indicates the signal power, which is obtained through the online estimation of the current signal-to-noise ratio.

[0018] Furthermore, the target angle and polarization parameters estimated by step 4 and the Cramer-Rao bounds of setting the initial azimuth and elevation angles in step 1 are used as the basis for the present invention. θ0, calculate the minimum number of snapshots that meet the CRB requirements. The specific process is:

[0019] The estimated value in step 4 Substituting into equation (15) we get the K×K matrix W θ and Set θ0, Substitute the squares into CRB(θ) and 2K diagonal elements of; according to W θ and CRB(θ) and and Each diagonal element of can get a minimum snapshot number L j , then the minimum number of snapshots required under the current signal-to-noise ratio is L min for

[0020] L min =α×max{L j ,j=1,2,…,2K} (16)

[0021] In the formula, α≥1 is the compensation factor.

[0022] Furthermore, the noise subspace U of the present invention n for:

[0023] R=U s Λ s U s H +U n Λ n U n H

[0024] Where R is the covariance matrix of the received data, U s is the N×K signal subspace, U n is the N×(NK) noise subspace, Λs is a K×K diagonal matrix, the diagonal elements are the K main eigenvalues, and the remaining elements are 0, Λ n is a (NK)×(NK) diagonal matrix with NK-order eigenvalues ​​and the rest of the elements are 0.

[0025] Furthermore, the specific process of step 4 of the present invention is:

[0026]

[0027] The minimum generalized eigenvalue is obtained by using formula (7) to replace the two-dimensional search of polarization parameters (γ, η). The target angle can be obtained by two-dimensional search According to the properties of the generalized Rayleigh quotient, the eigenvector corresponding to the minimum generalized eigenvalue is β(γ,η)=[cosγsinγe jη ] T , and then the target polarization parameters (γ, η) are obtained.

[0028] Beneficial Effects

[0029] Compared to the conventional polarization sensitive array angle measurement method with a fixed number of snapshots, the present invention can adaptively change the number of snapshots used for angle measurement according to changes in the signal-to-noise ratio. When the signal-to-noise ratio is low, the number of snapshots is adaptively increased to ensure the accuracy of angle measurement. When the signal-to-noise ratio is high, the number of snapshots is adaptively reduced to reduce the system computing overhead and improve the real-time performance of the system. In addition, the energy of the reflected wave of the moving platform carrier increases under high signal-to-noise ratios, and selecting fewer snapshots can reduce the impact of the multipath effect to a certain extent. In summary, the present invention has practical application value on moving platforms with limited computing power and high real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 It is a flow chart of the present invention.

[0032] Figure 2 Schematic diagram of an eight-element polarization-sensitive uniform circular array.

[0033] Figure 3 It is the azimuth RMSE of the present invention and the existing method.

[0034] Figure 4 It is the pitch angle RMSE of the present invention and the existing method.

[0035] Figure 5 It is the average number of snapshots of the present invention and the existing method. DETAILED DESCRIPTION

[0036] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0037] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0038] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0039] The present invention proposes a polarization sensitive array radar adaptive snapshot angle measurement method, which is mainly used for moving platforms. Under the premise that the angle measurement accuracy meets the index requirements, the snapshot number used for angle measurement can be adaptively adjusted. When the signal-to-noise ratio is low, more snapshot data is selected to ensure the angle measurement accuracy, and when the signal-to-noise ratio is high, less snapshot data is selected, so as to reduce the system operation overhead and improve the real-time performance of the system. Figure 1 As shown, the specific steps of the present invention are as follows:

[0040] Step 1: Initialization, setting the Cramer-Rao bounds for azimuth and elevation and the number of initial snapshots

[0041] Set the Cramérau bounds CRB for azimuth and elevation as θ0, and the initial number of snapshots L0 at the first estimation.

[0042] Step 2: Assume that K far-field narrowband signals are incident on an N-element polarization sensitive array of arbitrary configuration, and calculate the array received data covariance matrix of L0 snapshots:

[0043] Considering K far-field narrowband signals incident on an N-element polarization sensitive array of arbitrary configuration, the array receiving data model of L0 snapshots can be expressed as:

[0044] x(t)=As(t)+n(t) (1)

[0045] In the formula, x(t)=[x1(t),...,x N (t)] T Receive data for an N×L0 array, s(t)=[s1(t),…,s K (t)] T is a K×L0 signal source, n(t)=[n1(t),…,n N (t)] T is a noise signal of N×L0, and the noise power is σ n 2 , is the steering vector of K signal sources, and the target steering vector of the polarization sensitive array can be expressed as:

[0046]

[0047] Where θ represents the pitch angle, represents the azimuth, β(γ,η)=[cosγsinγe jη ] T It includes the polarization auxiliary angle γ and the polarization phase difference η. is an N×2 matrix representing the angle-related part of the target-oriented vector.

[0048] The covariance matrix can be obtained based on the array receiving data:

[0049]

[0050] Step 3: Perform eigendecomposition on the covariance matrix to obtain the noise subspace

[0051] Performing eigendecomposition on the covariance matrix, we can obtain:

[0052] R=U s Λ s U s H +U n Λ n U n H (4)

[0053] Where U s is the N×K signal subspace, U n is the N×(NK) noise subspace. s is a K×K diagonal matrix, the diagonal elements are the K main eigenvalues, and the remaining elements are 0, Λ n is a (NK)×(NK) diagonal matrix with NK-order eigenvalues ​​and the rest of the elements are 0.

[0054] Step 4: Utilize the orthogonality between the noise subspace and the target guidance vector (see Equation 2) to calculate the target angle and polarization parameters (γ,η) estimation

[0055] The noise subspace is orthogonal to the target guidance vector, namely:

[0056]

[0057] Substitute equation (2) to solve the target parameter The process can be equivalent to the following optimization problem:

[0058]

[0059] This optimization problem requires a four-dimensional parameter search to solve. Its structure is a generalized Rayleigh quotient minimization problem, so it can be simplified to:

[0060]

[0061] By finding the minimum generalized eigenvalue instead of the two-dimensional search of polarization parameters (γ,η), only the angle parameter The target angle can be obtained by two-dimensional search According to the properties of the generalized Rayleigh quotient, the eigenvector corresponding to the minimum generalized eigenvalue is β(γ,η)=[cosγsinγe jη ] T , and then the target polarization parameters (γ, η) are obtained.

[0062] Step 5: Utilize the estimated parameters Calculate the minimum number of snapshots required to meet CRB requirements

[0063] Firstly, the Cramer-Rao bounds of the azimuth and elevation angles of the polarization sensitive array are derived, and the relationship between the azimuth angle CRB, the elevation angle CRB and the number of snapshots is obtained respectively; secondly, based on the relationship, the minimum number of snapshots required is obtained according to the set azimuth angle CRB and elevation angle CRB.

[0064] The derivation process of the relationship between the azimuth angle CRB, the pitch angle CRB and the number of snapshots in this embodiment is:

[0065] The output signal x of the polarization sensitive array satisfies the mean value As and the variance σ n 2 N×1-dimensional Gaussian distribution of I:

[0066]

[0067]

[0068] In the formula, μ represents the unknown parameter vector, that is, Then the Fisher information matrix of the vector matrix can be defined as:

[0069]

[0070] The Fisher information matrix has the characteristics of block structure and can be expressed as

[0071]

[0072] In the formula, F θθ , is the sub-block related to the arrival angle direction, F γγ 、F ηη is the sub-block related to the polarization parameters, and the remaining sub-blocks are related to other unknown parameters and their cross terms, as shown in the following subscripts.

[0073] According to equations (9), (10), and (11), we can obtain the Cramer-Rao bound matrix CRB(u) of the signal under uniform noise, whose elements in the i-th row and j-th column satisfy

[0074]

[0075] When polarization-sensitive array radar measures angles, it mainly focuses on the azimuth angle CRB and the elevation angle CRB, which are extracted through the first 2K elements on the diagonal in the above formula. Therefore, it is only necessary to calculate the first term on the right side of the equal sign in the above formula to obtain the required CRB.

[0076] Calculating the derivative of As with respect to μ, we can obtain

[0077]

[0078] in,

[0079]

[0080] Substituting formula (14) into formula (12), the relationship between the azimuth angle CRB, the pitch angle CRB and the number of snapshots is as follows:

[0081]

[0082] Where ⊙ represents the Hadamard product, A θ represents the derivative of the steering vector matrix A with respect to the pitch angle θ; Represents the orientation angle of the steering vector matrix A The derivative of . It is represented as the steering vector of K signal sources, and s represents the signal source; represents the noise power, Indicates the signal power, which is obtained through the online estimation of the current signal-to-noise ratio.

[0083] CRB(θ) is a K×K matrix, and its diagonal K elements CRB(θ) i,i (i=1,2,…,K) are the squares of the Cramer-Rao bounds of the K signal elevation angles; is a K×K matrix with K elements on its diagonal are the squares of the Cramer-Rao bounds of the K signal azimuths, respectively. We mainly focus on the 2K elements on the diagonal of the two K×K matrices.

[0084] The estimated value in step 4 Substituting into equation (15) we get the K×K matrix W θ and Set θ0, Substitute the squares into CRB(θ) and According to W θ and CRB(θ) and and Each diagonal element of can get a minimum snapshot number L j , then the minimum number of snapshots required under the current signal-to-noise ratio is L min for

[0085] L min =α×max{L j ,j=1,2,…,2K} (16)

[0086] In the formula, α≥1 is the compensation factor.

[0087] Since the actual accuracy of parameter estimation in actual application scenarios is inconsistent with the Cramer-Rao bound of parameter estimation, the compensation factor is used to compensate for the number of snapshots so that the actual angle measurement accuracy is close to the CRB set value. This factor needs to be adjusted according to the application scenario.

[0088] Step 6: Repeat steps 2 to 5.

[0089] According to the minimum number of snapshots L obtained in step 5 min , select the received data of the corresponding snapshot, repeat steps 2, 3, and 4 to estimate the angle and polarization parameters; then substitute the estimated angle and polarization parameters into step 5 to update the minimum number of snapshots.

[0090] And so on, by repeating steps 2, 3, 4, and 5, the angle estimation of the adaptive snapshot number is completed.

[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, as shown in the attached figure. Figure 2As shown, for a single target scene, the azimuth and elevation angle measurement accuracy requirements are 0.5°, the compensation factor α=6, and the specific simulation parameters are as follows:

[0092]

[0093]

[0094] Firstly, the array received data containing 1000 initial snapshots are selected to estimate the angle parameters and polarization parameters. After obtaining the initial estimated values, the minimum number of snapshots that meets the CRB requirements is obtained according to the current estimated values ​​of the angle parameters and polarization parameters and the current signal-to-noise ratio. Then, the next parameter estimation is performed based on the obtained minimum number of snapshots, and this is repeated 500 times at each signal-to-noise ratio. The root mean square error (RMSE) of the azimuth and elevation angle estimates at each signal-to-noise ratio and the average number of snapshots of 500 Monte Carlo simulations at each signal-to-noise ratio are counted, and compared with the PD-2-MUSIC and rank-deficient MUSIC algorithms with fixed snapshot numbers.

[0095] The comparison of azimuth RMSE between the present invention and the existing method is shown in the attached figure. Figure 3 As shown in the figure, the pitch angle RMSE of the present invention and the existing method are compared as shown in the figure below. Figure 4 As shown in the figure, the average snapshot number of the present invention and the existing method is compared as shown in the figure. Figure 5 shown.

[0096] It can be seen from the simulation results that under low signal-to-noise ratio (near 0dB), the algorithm with a fixed number of snapshots cannot meet the angle measurement accuracy requirement of 0.5°. The algorithm with an adaptive number of snapshots proposed in the present invention increases the number of snapshots used for angle measurement according to the signal-to-noise ratio and meets the accuracy requirement. Under high signal-to-noise ratio, both the algorithm with a fixed number of snapshots and the algorithm with an adaptive number of snapshots proposed in the present invention can meet the accuracy requirement of 0.5°. The adaptive number of snapshots algorithm only needs single-digit snapshots near a signal-to-noise ratio of 30dB and has good real-time performance, while the algorithm with a fixed number of snapshots will cause a waste of computational overhead.

[0097] The specific advantages of the embodiments of the present application are as follows: In 2007, Chevalier in the article "Higher order direction finding from Arrays with diversely polarized antennas: The PD-2q-MUSIC algorithms" equivalently regarded the angle measurement of the polarization sensitive array as a generalized Rayleigh quotient minimization problem, thereby realizing the dimensionality reduction estimation of the angle parameters; in 2017, Zeng Fuhong et al. proposed the rank-deficient MUSIC algorithm in the article "DOA and polarization parameter dimensionality reduction estimation algorithm of polarization sensitive array" using the principle of matrix rank loss to realize the dimensionality reduction estimation of the angle parameters. Both methods are based on the received data of a fixed number of snapshots to achieve high-precision angle measurement. For the angle measurement method with a fixed number of snapshots, if a small number of snapshots is selected, the angle measurement accuracy requirement cannot be met when the signal-to-noise ratio is low; if a large number of snapshots is selected, as the moving platform gradually approaches the target, the signal-to-noise ratio increases, and a small number of snapshots or even a single snapshot data can meet the angle measurement accuracy requirement of the system. At this time, using multiple snapshot data to measure the angle will cause a waste of computational overhead.

[0098] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A polarization sensitive array radar adaptive snapshot angle measurement method, characterized in that: The specific process is: Step 1: Set the initial azimuth and elevation angles of the Cramer-Rao bounds θ0 and the initial snapshot number L0; Step 2: Assume that K far-field narrowband signals are incident on an N-element polarization sensitive array of arbitrary configuration, and calculate the array receiving data covariance matrix of L0 snapshots; Step 3: Perform eigendecomposition on the covariance matrix to obtain the noise subspace; Step 4: Utilize the orthogonality between the noise subspace and the target guidance vector to calculate the target angle and polarization parameter (γ,η) estimation; Step 5: Based on the Cramer-Rao bounds of the azimuth and elevation angles of the polarization-sensitive array, obtain the relationship between the azimuth CRB, elevation CRB and the number of snapshots. Use the target angle and polarization parameters estimated in step 4 and step 1 to set the Cramer-Rao bounds of the initial azimuth and elevation angles. θ0, calculate the minimum number of snapshots that meet the CRB requirements; Step 6: According to the calculated minimum number of snapshots L min Select the received data of the corresponding snapshot to estimate the angle and polarization parameters.

2. The method for adaptive snapshot angle measurement of polarization sensitive array radar according to claim 1, characterized in that: In step 5, the relationship between the azimuth angle CRB, the pitch angle CRB and the number of snapshots L is: Among them, CRB(θ) is a K×K matrix, and its diagonal K elements CRB(θ) i,i (i=1,2,…,K) are the squares of the Cramer-Rao bounds of the K signal elevation angles; is a K×K matrix with K elements on its diagonal are the squares of the Cramer-Rao bounds of the K signal azimuths; ⊙ represents the Hadamard product, A θ represents the derivative of the steering vector matrix A with respect to the pitch angle θ; Represents the orientation angle of the steering vector matrix A The derivative of , A represents the steering vector matrix of K signal sources, s represents the signal source, represents the noise power, Indicates the signal power.

3. The method for adaptive snapshot angle measurement of polarization sensitive array radar according to claim 2, characterized in that: The target angle and polarization parameters estimated by step 4 and the Cramer-Rao bounds of the initial azimuth and elevation angles set in step 1 are θ0, calculate the minimum number of snapshots that meet the CRB requirements. The specific process is: The estimated value in step 4 Substituting into equation (15) we get the K×K matrix W θ and Set θ0, Substitute the squares into CRB(θ) and 2K diagonal elements of; according to W θ and CRB(θ) and and Each diagonal element of can get a minimum snapshot number L j , then the minimum number of snapshots required under the current signal-to-noise ratio is L min for L min =α×max{L j ,j=1,2,…,2K} (16) In the formula, α≥1 is the compensation factor.

4. The method for adaptive snapshot angle measurement of polarization sensitive array radar according to claim 1, characterized in that: The noise subspace U n for: R=U s Λ s IN s H +U n Λ n IN n H Where R is the covariance matrix of the received data, U s is the N×K signal subspace, U n is the N×(NK) noise subspace, Λ s is a K×K diagonal matrix, the diagonal elements are the K main eigenvalues, and the remaining elements are 0, Λ n is a (NK)×(NK) diagonal matrix with NK-order eigenvalues ​​and the rest of the elements are 0.

5. The method for adaptive snapshot angle measurement of polarization sensitive array radar according to claim 1, characterized in that: The specific process of step 4 is as follows: The minimum generalized eigenvalue is obtained by using formula (7) to replace the two-dimensional search of polarization parameters (γ, η). The target angle can be obtained by two-dimensional search According to the properties of the generalized Rayleigh quotient, the eigenvector corresponding to the minimum generalized eigenvalue is β(γ,η)=[cosγsinγe jη ] T , and then the target polarization parameters (γ, η) are obtained.

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