阅读说明：本技术 基于联合约束的自适应单脉冲测向方法 (Self-adaptive monopulse direction finding method based on joint constraint ) 是由 谢菊兰 程方昊 唐思晴 何勤 李会勇 于 2019-08-19 设计创作，主要内容包括：本发明公开了一种基于联合约束的情况下自适应单脉冲测向方法,属于自适应阵列信号处理领域的单脉冲测向技术。本发明可以有效的避免在自适应干扰抑制过程中,由于干扰存在的情况下单脉冲估计性能下降的问题,从而改善单脉冲的性能。基于本发明的处理过程,使得在通过扩维度进行求解最优权向量的同时,改善了计算时间的复杂度,与常规的线性约束条件相当,并且性能还优于常规的线性约束条件。且本发明方法与常规的静态单脉冲比十分接近,有效的改善了单脉冲性能。此外,本发明通过充分利用了对窄带信号进行整体处理的方式,相比于传统的单脉冲测角方法,具有信噪比小、时间复杂度低精度高、更加稳健的优点。因此,本发明具有较强的工程实用性。(The invention discloses a self-adaptive monopulse direction finding method based on joint constraint, and belongs to the monopulse direction finding technology in the field of self-adaptive array signal processing. The invention can effectively avoid the problem of the performance reduction of the single-pulse estimation under the condition of the existence of the interference in the self-adaptive interference suppression process, thereby improving the performance of the single pulse. Based on the processing procedure of the invention, the complexity of the calculation time is improved while the optimal weight vector is solved by expanding the dimensionality, the method is equivalent to the conventional linear constraint condition, and the performance is better than the conventional linear constraint condition. And the method is very close to the conventional static single pulse ratio, and the single pulse performance is effectively improved. In addition, the method makes full use of the mode of integrally processing the narrow-band signal, and has the advantages of small signal-to-noise ratio, low time complexity, high precision and more stability compared with the traditional single-pulse angle measurement method. Therefore, the invention has stronger engineering practicability.)

1. An adaptive monopulse direction finding method based on joint constraint is characterized by comprising the following steps:

step 1: obtaining received data x of narrowband interfering signals by uniform array_i(n) and by the formulaObtaining the covariance matrix R of the array_X；

Step 2: based on the covariance matrix R that is obtained_XAnd a predetermined angle-identifying slope k₁Calculating the beam weight vector

Wherein the content of the first and second substances,

P＝[1 0]；

I₁＝[I 0]，I₂＝[0 I]；

H＝[a(θ₀-Δθ) a(θ₀) a(θ₀+Δθ)]，ρ＝[-k₁Δθ 0 k₁Δθ]；

a (-) denotes a steering vector, θ₀Representing the incoming wave direction of the target signal, delta theta representing the deviation angle and I representing an identity matrix;

and step 3: for weight vector w_optSplitting to obtain

Thereby obtaining a weight vector w of a sum beam and a difference beam of the received signal_∑、w_Δ；

And 4, step 4: carrying out sum and difference amplitude comparison processing on received data:

using x (n) to represent the signal matrix of the received data, and based on the sum and difference beam weight vector w obtained in step 3_∑、w_ΔObtaining a sum beamDifferential beamThereby obtaining the sum and difference amplitude of the received data as real (y)_diff./y_sum) Wherein real (·) represents the real part of the complex; a/represents each number in the vector by a dot division;

and 5: according to the formulaCalculating to obtain the angle of the single pulse angle measurement

2. The method of claim 1, wherein in step 2, the angularity slope k is set₁Is 1.

3. The method of claim 1, wherein, in step 2,the solving method specifically comprises the following steps:

wherein, U_JRepresenting the interference eigenvector matrix by fitting the covariance matrix R_XThe singular value of (2) is decomposed to obtain;

to R_XSingular value decomposition is carried out to obtain:

wherein λ is_iRepresents R_XAnd the eigenvalues are arranged in descending order, u_iRepresenting the corresponding eigenvalue λ_iThe feature vector of (2);

Λ_Jdiagonal matrices formed for the first J largest eigenvalues, i.e.' A_J＝diag{λ₁…λ_J}；

Interference eigenvector matrix U_JComprises the following steps: u shape_J＝[u₁…u_J]。

Technical Field

The invention relates to a monopulse direction finding technology in the field of adaptive array signal processing, in particular to an adaptive monopulse angle finding technology adopting joint constraint aiming at narrow-band monopulse.

Background

Detection and parameter estimation of targets are the most important tasks in tracking radar. The most typical of these are Monopulse techniques (see in particular the documents T.Vu, A new type of high-performance Monopulse feed, U.N.. The single-pulse technique can realize high-precision real-time angle estimation, and is superior to the cone scanning technique in the conditions of signal-to-noise ratio (SNR) and target fluctuation. Today's Monopulse technology has successfully achieved digitized sum and difference beam angle measurements by the design of arrays in the field of phased arrays (see in particular the documents: Z. Yu, A Broadband Planar Monopulse Array of C-Band and direct estimation for two beam targets in Monopulse). However, in the presence of interference in the received signal, the conventional monopulse technique is distorted due to beam adaptation, which may cause an angle error.

According to the method for extracting the angle information of the target from the echo signal, the single-pulse angle measurement is divided into an amplitude comparison method and a phase comparison method, and the conventional method is the amplitude comparison method. The traditional self-adaptive monopulse algorithm can work well on narrow-band signals, and the principle of the method is as follows:

consider an N-dimensional far-field narrow-band signal with an array element number M. Let the incoming wave direction of the target signal be theta₀The direction of the incoming wave of the interference signal is theta₁,θ₂,…,θ_K. Ideally, the received interference signal x at time n_i(n) is:

x_i(n)＝A(θ)s_i(n)+e(n),n＝1,2,…,N

wherein a (θ) ═ a (θ)₁),a(θ₂),…,a(θ_K)]Is a steering matrix of interference signals with size of M × K, K is the number of interference signals, and a (theta) ═ 1e^{-j(2π/λ)dsinθ}…e^{-j(2π/λ)(M-1)dsinθ}]D is the spacing of the array elements, λ is the wavelength, s_i(n)＝[s₁(n),s₂(n),…,s_K(n)]^TIs the complex envelope of the interfering signal at n times, e (n) is zero mean, varianceOf the noise vector, sign (·)^TIndicating transposition.

There are four single pulse and difference angle measuring modes, including half-array method, direct and difference method, double-direction method and beam symmetrical inversion method. For conventional non-interference conventional static monopulse angle measurement, a half-array method is often adopted. From the basic principle of the half-array method, the linear relation of the monopulse ratio with respect to the deviation angle can be obtained as follows:

wherein, a_∑(θ₀) For static sum beams, a_∑(θ₀)＝a(θ₀)，a_Δ(θ₀) For the static difference beam, it can be expressed as:

wherein, the "-" indicates a Hadamard product.

For the above-mentioned single pulse ratio f_eRegarding the deviation angle Δ θ, it can be approximately converted into: f. of_e＝k₁A, where,k₁is the correlation coefficient of the conventional single-pulse angle identification curve.

From the above formula, it can be seen that the single pulse ratio f_eCan be approximated as a linear function with respect to Δ θ. Fig. 1 shows the static single-pulse angle plots of the conventional theoretical derivation and the above formula, respectively. From fig. 1, it can be seen that in the case of very small deviation angles, the deviation angle is dependent on f_e＝k₁Delta theta can be well fitted to the monopulse ratio f_e。

Due to the single pulse ratio f_eThe method is obtained under the condition of static self-adaptive monopulse angle measurement, and if the signal model has interference, the static monopulse algorithm will fail, so that the error of the estimated monopulse angle is large.

In order to solve the problem of Angle measurement precision reduction, a document of Angle estimation with adaptive arrays in external noise fields utilizes a Maximum Likelihood (ML) theory to derive three different monopulse expressions for a uniform linear array; the document Overview of generated monopulse estimation proposes that the less computationally intensive monopulse algorithm is a first order Taylor approximation of the ML estimation. The essence of the problem of the above algorithm is to solve for the weights of the sum and difference beams. Therefore, the Constrained Adaptive Monopulse (CAM) scheme proposed in the literature "Statistical Performance Prediction of Generalized Monopulse Estimation" imposes constraints on the Monopulse ratio. The method can effectively eliminate interference, and simultaneously keeps the distortion-free of the self-adaptive beam pattern; on the basis, Zhulin et al put forward a Combined Constrained Adaptive Monopulse (CCAM) method for convex optimization solution (see the literature, "Combined Constrained Adaptive Sum and difference Beamforming in Monopulse Angle Estimation"), different from the most advanced Adaptive Monopulse method at present, the algorithm firstly performs joint optimization on the weights of Sum and difference beams, and designs an optimization problem including three-channel output power minimization, Monopulse curve constraint and array gain in order to fully utilize the degrees of freedom of the Sum and difference beams. Compared with the CAM algorithm, the CCAM algorithm can obtain higher single-pulse curve performance and anti-interference capability. However, the time complexity of the algorithm is very high. The document Sum and difference beamforming for angle-dependent radars proposes a Sum-difference monopulse algorithm using space-time adaptive processing, which incorporates a number of constraints (including amplitude and phase constraints, derivative constraints and zero point constraints) into the angular doppler plane. The document "Adaptive monopulse acquisition with joint linear constraints for planar array subarray level" estimates the sum beam and the difference beam respectively, thereby realizing single-pulse angle measurement. The above algorithms all further reduce the complexity of the algorithm. It is not universal, but requires distribution of desired and interfering signals.

Disclosure of Invention

The invention aims to: aiming at the condition of interference, the invention discloses a self-adaptive monopulse direction finding method based on joint constraint, which comprises the following steps:

step 1: obtaining received data x of narrowband interfering signals by uniform array_i(n) of (a). By the formulaObtaining the covariance matrix R of the array_X；

Step 2: setting the angle-identifying slope k₁Using the covariance matrix R of the array_XCalculating the beam weight vector

Wherein the content of the first and second substances,

I₁＝[I 0]，I₂＝[0 I]；

H＝[a(θ₀-Δθ)a(θ₀)a(θ₀+Δθ)]，ρ＝[-k₁Δθ 0 k₁Δθ]；

a (-) denotes a steering vector, θ₀Representing the incoming wave direction of the target signal, [ Delta ] theta represents the deviation angle, I represents the identity matrix, superscript "H" represents the matrix conjugate, [ ·]_iAn ith column representing a corresponding matrix;

in order to further reduce the problem of computational complexity brought by the dimensionality of the invention, the inventionThe solution of (2) can be solved in the following way:

wherein, the interference eigenvector matrix U_JCan be passed through R_XIs obtained by singular value decomposition, i.e.

Wherein the characteristic value lambda_iArranged in descending order, u_i(i ═ 1,2, …, J) is the corresponding eigenvector, Λ_JDiagonal matrix corresponding to J large eigenvalues, i.e.' A_J＝diag{λ₁…λ_J}; interference eigenvector matrix U_JIs U_J＝[u₁…u_J]；

And step 3: the weight vector w obtained above_optSplitting according to the structural form to obtain the weight vector w of the sum beam and the difference beam of the received signal_∑、w_Δ；

The expression of the constructed weight vector isThen splitting w_optObtain the corresponding weight vector w_∑、w_Δ(ii) a And 4, step 4: carrying out sum and difference amplitude comparison processing on the received data;

using x (n) to represent the signal matrix of the received data, and based on the sum and difference beam weight vector w obtained in step 3_∑、w_ΔObtaining a sum beamDifferential beamThereby obtaining the sum and difference amplitude of the received data as real (y)_diff./y_sum) Wherein real (·) represents the complex number practiceA section; the expression is used to divide each number in the vector by a dot.

And 5: according to the formulaCalculating to obtain the angle of the single pulse angle measurement

In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:

1. when the pulse signal is a narrow band and has narrow-band interference, the single-pulse angle measurement processing method provided by the invention can effectively inhibit the narrow-band interference and simultaneously carry out single-pulse angle measurement;

2. the method provided by the invention can still carry out effective angle measurement under the condition of main lobe interference;

3. the method provided by the invention can still realize effective angle measurement under the condition of low signal-to-noise ratio;

4. the method provided by the invention fully utilizes the characteristic of integral processing of the narrow-band signal, and has the advantages of small signal-to-noise ratio, low time complexity, high precision and more stability compared with the traditional single-pulse angle measurement method.

Drawings

FIG. 1 static conventional single pulse ratio angle plot

Fig. 2 sum beam in case of non-coherent signal

Poor beam in the case of the signal incoherence of fig. 3

Phase discrimination plot for the signal incoherent case of fig. 4

FIG. 5 shows the variation of RMSE with SNR for the case of signal incoherence

FIG. 6 shows the variation of RMSE with snapshot number in the case of incoherent signal

Fig. 7 a case where an interference signal exists in the main lobe range

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings.

The invention provides a self-adaptive monopulse method for carrying out combined beam making, which aims to make the method approach to a conventional static monopulse angle discrimination curve as much as possible. In order to further reduce the time complexity during processing, the invention utilizes the special form of the constructed covariance matrix to carry out dimension division processing, thereby obtaining an execution scheme which is more convenient and has lower algorithm complexity. The steps executed by each part are as follows:

(1) the self-adaptive monopulse technology based on joint constraint:

through the received data of the array, the covariance matrix of the array can be obtained as:

wherein E {. denotes mathematical expectation. In the presence of clutter interference, the conventional adaptive monopulse approach will distort the monopulse. Aiming at the problem of monopulse ratio distortion, the invention adopts a multi-point constraint mode to establish the following joint constraint conditions

Wherein the constraint matrix H and the response matrix ρ are:

to simplify the above formula, let I₁＝[I 0]，Wherein the content of the first and second substances,thereby, it is possible to obtain: w is a_∑＝I₁w,w_Δ＝I₂w；

For the minimization condition, there are

Wherein the content of the first and second substances,

for constraint conditionsIs provided with

For constraint conditionsFor each element [ rho ] in rho]_iIs provided with

Wherein [ H ]]_iRepresenting the ith column of matrix H. Thus, for all elements in ρ, there are

w^HR_e＝0

Wherein the content of the first and second substances,

furthermore, the above constraint problem is simplified to obtain

Wherein the content of the first and second substances,P＝[1 0]。

by using the lagrange multiplier method, the optimal weight vector can be obtained as follows:

will w_optAnd splitting is carried out, so that corresponding sum beam weight vectors and difference beam weight vectors can be obtained, and further, the angle can be conveniently estimated.

Namely, the implementation steps of the invention comprise:

step 1: obtaining received data x of narrowband signals by uniform array_i(n) of (a). By the formulaObtaining a covariance matrix of the array;

step 2: setting the angle-identifying slope k₁(it can be set to 1 in general), based on the covariance matrix R_XCalculating the beam weight vector

And step 3: the weight vector w obtained above_optSplitting according to the structural form to obtain the weight vector w of the sum beam and the difference beam of the received signal_∑、w_Δ；

And 4, step 4: according to the single pulse ratio f_eAnd obtaining the final single pulse angle according to the relation of the sum and difference beam weight vectors.

(2) The invention aims at the inverse processing of the covariance matrix.

In the implementation process of the invention, there is an operation of covariance matrix inversion, and since the invention performs dimensional expansion on the covariance matrix during processing, the operation of covariance matrix inversion brings a large operation dimension.

And for matrix R_XXDue to the fact that

Recombination ofIs described in (1). Can obtain

For the diagonal matrix, the inverse matrix is:

i.e. in solving forWhen it is determinedCan be easily obtainedTherefore, the present invention solves the problem in the following mannerThereby further reducing the computational complexity of the present invention.

By taking the inverse theorem of the sampling matrix, the covariance matrix of the interference and the noise can be obtained as

Therein, sigma_JIn order to be a matrix of the power of the interfering signals,i is the identity matrix.

In view ofAnd the number of the first and second electrodes,the result is a constant, which only affects the magnitude of the weight vector, but not the change of the system itself, and the constant coefficient can be normalized, so as to obtain:

if the steering matrix a (θ) of the interference signal is directly obtained by DOA estimation, there are inevitably a lot of problems with the operation of DOA estimation, and an estimation error may occur. Taking into account the interference eigenvector matrix U_JIn relation to A (theta), there is a J-dimensional invertible matrix T having A (theta) equal to U_JT, then

Wherein, U_JCan be passed through R_XIs obtained by singular value decomposition, i.e.

Wherein the characteristic value lambda_iArranged in descending order, u_i(i ═ 1,2, …, J) is the corresponding eigenvector, Λ_JDiagonal matrix corresponding to J large eigenvalues, i.e.' A_J＝diag{λ₁…λ_J}; interference eigenvector matrix U_JIs U_J＝[u₁…u_J]；

By the above-mentioned relationCan be easily obtainedAnd then can obtain

Substituting it into the optimal weight vector w obtained in the above formula_optThen, w is_optAnd splitting to obtain corresponding sum beam weight vector and difference beam weight vector. Through the operation of the algorithm, the single-pulse angle measurement can be performed more conveniently, and the time complexity of calculation is further reduced.

In order to make the purpose, technical scheme and technical effect of the invention clearer, the invention is further described in detail through simulation experiments.

In the simulation experiment, the snapshot number is 1000, the SNR is 0dB, the INR is 10dB, the angle of the desired signal is 10 °, the angle of the interference signal is-10 °, 30 °, the signals are incoherent, Δ θ is 4 °, k is 4 °, and k is not particularly described in the experimental conditions₁0.1. Firstly, time complexity comparison is carried out on the method and other methods, and then performance analysis is carried out on the algorithm and other algorithms under the condition that the simulation signals do not have coherence and signal coherence.

Simulation experiment conditions I: in order to display the time performance advantage of the algorithm, the number of the adopted array elements is 100, and the final simulation time is obtained by performing averaging after 100 times of simulation in an experiment. The simulation results are as follows:

from the above data, it can be clearly found that the cost of the adaptive monopulse technology based on compressed sensing is far higher than that of any other algorithm, which is related to the performance of the compressed sensing algorithm itself. The self-adaptive monopulse technology based on compressed sensing solves a Q matrix related to a joint weight vector, the dimension of the Q matrix is large and far exceeds other algorithm dimensions, so that the difficulty is brought to a cvx tool box (a convex optimization tool) to search an optimal solution, and when the number of arrays reaches a certain number (for example, the number of arrays exceeds 200), an adopted simulation tool reports an abnormal condition of insufficient memory, which is inapplicable in actual engineering. By adopting the method of the invention: a specific expression is given by the combined constrained adaptive monopulse technology, so that the optimal solution is solved without auxiliary tools such as a cvx tool box and the like, and the time complexity of the algorithm is greatly reduced. Due to the joint solution of the algorithm, the array dimension related by the invention is inevitably increased in operation time compared with the algorithm of separate solution, but because the constructed joint covariance matrix has a certain special form, the method of the invention comprises the following steps: the self-adaptive monopulse technology of the combined constraint of the matrix inversion further reduces the complexity of the algorithm, and the algorithm with the reduced algorithm complexity and the algorithm for separately solving are both in a power series, so that the performance is not burdened.

Simulation experiment conditions II: in order to analyze the performance of the algorithm, the number of array elements of the uniform line array adopted in the experiment is 16. When the situation that Root Mean Square Error (RMSE) changes along with Signal-to-noise ratio (SNR) is simulated, the number of snapshots is 1000; when the RMSE variation with fast beat number (snapshot) is simulated, the SNR is 10. In order to eliminate the influence of the random test on the simulation result, the number of monte carlo experiments in the experiment is 500. Wherein the mean square error is expressed as

Wherein, M is the number of times of the test,and theta is the estimated value of the angle at the m time, and theta is the real value of the signal angle. The results of the simulation experiments are shown in fig. 2-6.

From fig. 2-4, it can be seen that the proposed algorithm can fit well to the sum and difference beam patterns of the uncorrelated signals; 5-6, the algorithm can be well performed, not only has good performance in time complexity, but also is superior to the linear constrained adaptive monopulse technique and the compressed sensing-based adaptive monopulse technique.

And (3) simulation experiment conditions are as follows: when the angle of the expected signal has angle mismatch, the number of array elements of the uniform line array adopted in the experiment is 16 in order to analyze the performance of the algorithm. The angle of the desired signal is 10 deg., the angle of the interfering signal is 30 deg., and the signals are incoherent. In the case of angular mismatch of the desired signal angles, the mismatch range of the desired signal is [ -2 °:0.2 °:2 ° ].

From fig. 7, it can be clearly seen that in the case of angular mismatch of the angle of the desired signal, the RMSE of the single-pulse angle estimated by the present invention in the mismatch interval is very small, and the performance of the present invention is superior to the linear constrained adaptive single-pulse technique, the compressed sensing-based adaptive single-pulse technique.

In conclusion, the invention can effectively avoid the problem of performance degradation of single-pulse estimation under the condition of clutter interference in the self-adaptive interference suppression process, well improve the performance of single pulse, and is superior to other existing methods. In addition, the method provided by the invention fully utilizes the characteristic of carrying out integral processing on the narrow-band signal, and has the advantages of small signal-to-noise ratio, low time complexity, high precision and more stability compared with the traditional single-pulse angle measurement method.

While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except mutually exclusive features and/or steps.