CN106772221A - Conformal array amplitude and phase error correction method based on wing deformation fitting - Google Patents

Abstract

The present invention proposes a kind of conformal array amplitude and phase error correction method based on wing deformation fitting, and for solving, existence and stability in the conformal array amplitude and phase error correction method of existing wing is low, poor real technical problem, realizes that step is：Covariance matrix is calculated by reception data and carry out feature decomposition, calculate white noise acoustical power and noise subspace；The range error matrix of conformal array is calculated by covariance matrix；Go out wing deformation curve using range error matrix fitting；The phase error matrix of conformal array is calculated using wing deformation curve, and combines the conformal array response matrix of range error matrix computations, search MUSIC spectrums obtain Mutual coupling angle；Calculation cost function, finally output meets the Mutual coupling result during condition of convergence.The present invention a small number of accurately need not correct array element, be prevented effectively from the more systematic errors of generation, and stability is high, and using direction of arrival as optimized variable, calculating speed is fast, and real-time is good.

Description

Conformal array amplitude and phase error correction method based on wing deformation fitting

Technical field

The invention belongs to signal processing technology field, it is related to the vibration error bearing calibration of even linear array, and in particular to one The conformal array amplitude and phase error correction method based on wing deformation fitting is planted, can be used for wing when plane airfoil vibrates conformal Array carries out Mutual coupling.

Background technology

Conformal array antenna is attached to above on-plane surface carrier for array element, forms the dexterous covering on carrier.Compare Traditional face battle array, conformal array has excellent aerodynamic performance, broader beam scanning scope and smaller radar The characteristics such as scattering area, and it is widely used in guided missile, rocket, aircraft and naval vessel etc..Because carrier structure is unstable and installs mistake Difference influence, array element can occur position skew, produce array amplitude phase error, cause the property such as conformal array train wave beam width, gain Can degradation.To ensure conformal array normal work, it is necessary to be corrected to the amplitude phase error of conformal array, common correction Method includes two kinds of automatic correcting method and active correction method.Active correction method needs signal source known to orientation, but real Often there is certain deviation in the signal source known orientation in the work of border, cause correction stability undesirable with actual value, and should Method can not be corrected to the amplitude phase error that orientation is relied on.Automatic correcting method typically by Combined estimator array error parameter and Aspect realizes correction, it is not necessary to the orientation of known signal source, it is possible to achieve the amplitude phase error that orientation is relied on is corrected.

When carrier is aerofoil surface, due to being influenceed by itself or extraneous factor, body structure surface can occur vibration deformation, The array amplitude phase error for causing orientation to rely on.The conformal array amplitude phase error caused by wing flutter has the characteristics that：

1. wing deformation is larger, easily produces 2 π to obscure, and array element is more remote apart from airfoil root, and amplitude phase error is bigger.

2. array position changes, and can produce phase error；If array element is directional aerial, when array element beam position hair Raw skew, because the gain of array element different directions is different, will produce range error.

For the conformal array amplitude phase error caused by wing flutter, it is common to use automatic correcting method is corrected.Self-correcting Correction method can be generally divided into two classes：One class method is using by several accurate array elements for having corrected and not correcting array element and constitute portion The positive array in branch school realizes the correction to amplitude phase error, and this partial correction array approach under all situations it cannot be guaranteed that all may be used With pre-set it is several accurately corrected array element, when having corrected array element and having there is error, the calibration result of the method will it is serious under Drop, so stability is not high.Another kind of automatic correcting method uses Combined estimator array error parametric technique, with amplitude phase error vector Used as optimized variable, the shortcoming that space to be optimized is big, convergence rate is slow causes the real-time of algorithm poor.

The content of the invention

It is an object of the invention to the defect for overcoming above-mentioned prior art to exist, it is proposed that a kind of based on wing deformation fitting Conformal array amplitude and phase error correction method, for solving to have stabilization in the conformal array amplitude and phase error correction method of existing wing Property low and poor real technical problem.

Technical thought of the invention is：Covariance matrix is calculated first and feature decomposition is carried out, and secondly calculates white noise work( Rate and noise subspace, the range error matrix of array element in conformal array are calculated by covariance matrix, by range error matrix Wing deformation curve is fitted, and calculates the phase error matrix that conformal array is present, be total in conjunction with range error matrix Shape array response matrix, so that searching for MUSIC spectrums obtains Mutual coupling angle, calculation cost function, finally output meets Mutual coupling result during the condition of convergence.

According to above-mentioned thinking, realize that the technical scheme that the object of the invention is taken comprises the following steps：

(1) assume that signal number N is 1, the deviation angle φ of conformal array reference unit in search coverage₁It is zero or Know, covariance matrix R is calculated using data are received, and feature decomposition is carried out to covariance matrix R, obtain white noise acoustical power σ² With noise subspace U_N, the expression formula of wherein covariance matrix is：

Wherein, K is the fast umber of beats for receiving data, and x (t) is the t times reception data of snap, ()^HTo receive data square Battle array takes conjugate transposition；

(2) covariance matrix R and white noise acoustical power σ is utilized², calculate the relative received strength of array element in conformal arrayAnd by the relative received strength of array element in the conformal array that is calculatedBuild diagonalization square Battle array, the matrix is the relative amplitude errors matrix of conformal array

(3) Mutual coupling angle, θ in setting iteration ordinal number variable j, iteration j_jWith cost function J_j, and to sequence Number variable j, Mutual coupling angle, θ_jAnd cost function J_jInitialized, made j=1, θ₁=0, J₁=0；

(4) by Mutual coupling angle, θ_jThe absolute receiving intensity F (1) of conformal array reference array element is calculated, is recycled The absolute receiving intensity F (1) of conformal array reference array element calculates the absolute amplitude error matrix F of conformal array, and using conformal The absolute amplitude error matrix F of array calculates the deviation angle φ of array element in conformal array₁,φ₂,…,φ_M；

(5) using the deviation angle φ of array element in conformal array₁,φ₂,…,φ_M, calculate the skew of array element in conformal array Slope ρ₁ρ₂…ρ_M, and according to the skew slope ρ of array element in the conformal array for calculating₁ρ₂…ρ_M, using polynomial curve fitting Algorithm fits slope curve f (x) of conformal array, then slope curve f (x) of the conformal array to fitting is integrated, Deformation curve F (x) of conformal array is obtained, deformation curve F (x) of the conformal array for finally being obtained using integration is calculated conformal The side-play amount vector y of array element in array；

(6) according to the side-play amount vector y of array element in the conformal array for calculating, the phase error matrix of conformal array is calculated W, and according to the phase error matrix W of conformal array, the response matrix Γ (θ of conformal array after being deformed_j)A(θ_j), this is rung Answer matrix Γ (θ_j)A(θ_j) MUSIC spectral functions are substituted into, search MUSIC spectrums obtain Mutual coupling angle, θ_j+1；

(7) Mutual coupling angle, θ is utilized_j+1Calculation cost function, the condition of convergence is substituted into by the value of cost function, is sentenced Whether the disconnected condition of convergence meets, if so, then represent conformal array amplitude and phase error correction completing, exports Mutual coupling angle θ_j+1；Otherwise, j=j+1 is made, step (4) is performed.

The present invention relative to prior art, with advantages below：

1) the range error information that the present invention is produced using mono signal source in receiving terminal, the form for fitting array deformation is bent Line, so as to the amplitude phase error to conformal array is corrected, it is not necessary to which minority has accurately corrected array element, is prevented effectively from generation more Systematic error, with existing conformal array amplitude and phase error correction technology in by some self-correctings of array elements for precisely having corrected Method is compared, and improves the stability of amplitude and phase error correction.

2) present invention uses curve-fitting method, conformal with existing using Mutual coupling angle as optimized variable The automatic correcting method of Combined estimator array error parameter is compared in array amplitude and phase error correction technology, and space to be optimized is small, convergence Number of times is few, therefore calculating speed is fast, and real-time is good.

3) present invention uses curve-fitting method, using Mutual coupling angle as optimized variable to conformal array width phase Error correction, and in last output Mutual coupling angle, the present invention can be by analyzing the estimated accuracy pair of direction of arrival Conformal array amplitude and phase error correction effect is judged, from Simulation results as can be seen that in different distortion form, different ripples Up in the case of direction, the Mutual coupling angular error that the inventive method is obtained is typically maintained in the range of 0.2 °, thus this Invention has good calibration result to conformal array amplitude and phase error correction, greatly improves ripple when there is amplitude phase error and reaches side To estimated accuracy.

Brief description of the drawings

Fig. 1 realizes FB(flow block) for of the invention；

Fig. 2 is the Mutual coupling analogous diagram of present invention different signal source incident direction within a vibration period；

Fig. 3 is that the present invention carries out 300 Mutual coupling analogous diagrams of Monte Carlo Experiment.

Specific embodiment：

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Reference picture 1, it is of the invention to realize that step is as follows：

Step 1, calculates covariance matrix R and feature decomposition is carried out to covariance matrix R, calculates white noise acoustical power σ²With make an uproar Phonon space U_N。

Step 1a assumes that signal number N is 1, conformal array reference unit deviation angle φ in search coverage₁It is zero or Know, using receiving data estimation covariance matrix R, and feature decomposition is carried out to covariance matrix R, obtain the white of reception system Noise power σ²With noise subspace U_N, the expression formula of wherein covariance matrix is：

Wherein, K is the fast umber of beats for receiving data, and x (t) is the t times reception data of snap, ()^HExpression takes conjugation and turns Put；

Step 1b carries out feature decomposition to covariance matrix R, and resolves into the cumulative form of eigen vector, will Characteristic value is arranged from big to small：

Wherein M is array number, λ_iIt is the characteristic value of covariance matrix R, α_iIt is the eigenvalue λ in covariance matrix_iIt is corresponding Characteristic vector.

Step 1c is due to number of sources N=1, the eigenvalue λ of covariance matrix R₂,λ₃,…λ_MCorrespondence covariance matrix R Spatial noise in system white noise acoustical power.Use eigenvalue λ₂,λ₃,…λ_MArithmetic mean of instantaneous value represent white noise acoustical power σ²：

σ²=(λ₂+λ₃…+λ_M)/(M-1) <4>

Step 1d defines the eigenvalue λ of covariance matrix R₂,λ₃,…λ_MCorresponding characteristic vector opens into subspace for noise Subspace U_N=[α₂,α₃,…α_M]。

Step 2, using covariance matrix R and white noise acoustical power σ²Calculate the absolute amplitude error moments of array element in conformal array Battle array.

Step 2a is using covariance matrix R and white noise acoustical power σ², calculate the relative received strength of array element in conformal arrayComputing formula is：

Wherein, R_i,iIt is i-th diagonal element of covariance matrix R, M is conformal array elements number；

Step 2c is by the relative received strength of array element in conformal arrayConformal array is built by following formula Relative amplitude errors matrix

Wherein, diag () is represented by sequence construct diagonalizable matrix.

Step 3, initializes to iteration ordinal number with Mutual coupling angle.

Mutual coupling angle, θ in setting iteration ordinal number variable j, iteration j_jWith cost function J_j, and ordinal number is become Amount j, Mutual coupling angle, θ_jAnd cost function J_jInitialized, made j=1, θ₁=0, J₁=0；

Step 4, calculates the deviation angle φ of array element in conformal array₁,φ₂,…,φ_M。

Step 4a utilizes Mutual coupling angle, θ_j, calculate the absolute receiving intensity F (1) of conformal array reference array element：

F (1)=f (θ_j+φ₁),<7>

Wherein, φ₁It is the deviation angle of conformal array reference array element；

Step 4b is using the absolute receiving intensity F (1) of conformal array reference array element and the relative amplitude errors of conformal array MatrixAccording toCalculate the absolute amplitude error matrix F of conformal array；

Step 4c calculates signal source relative to array element in conformal array using the absolute amplitude error matrix F of conformal array Weighting vector η₁,η₂,…η_M：

η_i=f^-1(F_i,i), i=1,2 ..., M,<8>

Wherein, F_i,iI-th diagonal element of the absolute amplitude error matrix F of conformal array is represented, f (θ) is conformal array The pattern function of element antenna, ()^-1The inverse function of direction figure function is represented, if F_i,i>=1, then force to set f^-1 (F_i,i) it is 0；

Step 4d assumes that the array element in conformal array is arranged in order towards X-axis positive direction, with reference to actual conditions, in conformal array The deviation angle of array element meets condition：

Wherein, θ is weighting vector of the signal source relative to array, φ_iIt is i-th angle of array element deviation X-axis, takes conformal The deviation angle φ of array element in array_iAngle is for just during deflection Y-axis positive direction；There are different deformation forms in conformal array, and η is corresponded to respectively₁,η₂,…η_MDifferent increase and decrease situations, therefore according to η₁,η₂,…η_MIncrease and decrease situation calculate array element in conformal array Deviation angle φ₁,φ₂,…,φ_M：

(1) if η₁,η₂,…η_MDescending series, then in conformal array array element deviation angle：

φ_i=η_i-θ_j, i=1,2 ... M；<10>

(2) if η₁,η₂,…η_MBe incremented by sequence, then in conformal array array element deviation angle：

φ_i=θ_j-η_i, i=1,2 ... M；<11>

(3) if η₁,η₂,…η_MIt is decreasing order row after first increasing, it assumes that η₁,η₂,…η_pIt is increasing sequence,

η_p+1,η_p+2,…η_MIt is descending series, then the deviation angle of array element in preceding p conformal array：

φ_i=θ_j-η_i, i=1,2 ... p；<12>

Afterwards in the conformal array of (M-p) item array element deviation angle：

φ_i=η_i-θ_j, i=p+1, p+2 ... M.<13>

Step 5, using the deviation angle of conformal array elements, using different array elements in the approximating method conformal array of calculating Side-play amount.

Step 5a utilizes the deviation angle φ of array element in conformal array₁,φ₂,…,φ_M, array element in the conformal array of calculating Skew slope ρ₁,ρ₂,…,ρ_M：

ρ_i=tan (φ_i) i=1,2 ..., M；<14>

Step 5b assumes the skew slope ρ of array element in conformal array₁,ρ₂,…,ρ_MMeet with X-axis coordinate variable as independent variable (M-1) rank multinomial curve：

F (x)=a₁x^M-1+a₁x^M-2+…+a_M-1x+a_M,<15>

Wherein, a_iIt is the coefficient of the polynomial curve, i=1,2 ... M, x are the X-axis coordinate variable of array element, and claim this many Item formula curve f (x) is the slope curve of conformal array, by the X-axis coordinate points x of conformal array elements₁,x₂,…,x_MSubstitute into above Slope curve f (x) of conformal array, obtains relational expression：

Wherein, [x₁,x₂,…,x_M]^TIt is the X-axis coordinate point vector of array element in conformal array, ()^TRepresent transposition computing, ρ =[ρ₁ ρ₂…ρ_M]^TIt is the skew slope vector of array element in conformal array, by relational expression<11>It is reduced to

aX₁=ρ<17>

Wherein, a=[a₁ a₂…a_M]^TIt is the coefficient vector of slope curve f (x) of conformal array,The generalized circular matrix with the X-axis coordinate points of array element in conformal array as element is represented, By formula<17>The both sides right side multiplies matrixObtain the expression formula of the coefficient vector a of slope curve f (x) for calculating conformal array：

Wherein,It is matrix X₁Inverse matrix, and using skew slope vector ρ, the square of the formula and array element in conformal array Battle arrayCalculate the coefficient vector a of slope curve f (x) of conformal array；

Step 5c is integrated to slope curve f (x) of conformal array, obtains the polynomial table of conformal array deformation curve Up to formula：

F (x)=b₁x^M+b₂x^M-1+…+b_Mx+b_M+1 <19>

Wherein, b_iIt is the coefficient of deformation curve F (x) of conformal array, i=1,2 ... M+1 take constant b_M+1=0, by altogether Deformation curve F (x) of shape array is obtained with the relation of slope curve f (x) of conformal array：

Wherein, () ' represents the deformation curve differentiation to conformal array, contrast<15>With formula<20>In coefficient, Obtain

Wherein, b=[b₁,b₂,…,b_M]^TIt is the coefficient vector of deformation curve F (x) of conformal array,It is matrix Hadamard is accumulated, by formula<21>Simplify, obtain the expression formula of the coefficient vector b of deformation curve F (x) for calculating conformal array：

Wherein,And using the formula and vector n, slope curve f (x) of conformal array Coefficient vector a calculates the coefficient vector b of conformal array deformation curve F (x)；

Step 5d utilizes the coefficient vector b and formula of conformal array deformation curve F (x)<19>, calculate array element in conformal array Side-play amount vector y：

Y=bX₂,<23>

Wherein, y=[y₁ y₂…y_M]^T,

Step 5e subsequent simulation results show the polynomial fitting method when matrix number is less, and fitting effect is accurate enough Really, and calculate simple, thinking is clear and definite；In calculating process, initial X-coordinate is, it is known that matrix X₁And X₂Can calculate in advance, as Numerical tabular is placed on the data field of the program of realization, reduces amount of calculation, improves calculating speed, it is ensured that algorithm can in real time to conformal array Amplitude phase error be corrected.

Step 6, the side-play amount vector y according to array element in the conformal array for calculating calculates Mutual coupling angle, θ_j+1。

Step 6a is obtained in conformal array due to array element position using the side-play amount vector y of array element in the conformal array that calculates Put the phase error W of the conformal array that skew causes：

K is propagation constant, k=2 π/λ, y_iIt is the side-play amount of different array elements, i=1,2 ... M；

Step 6b utilizes the phase error W, the amplitude phase error vector Γ of array after being deformed of the conformal array for obtaining (θ_j)：

Wherein, vecd () represents that extracting matrix diagonals elements constitutes column vector, then MUSIC spectral functions are：

Wherein,A (θ)=[1, e^jksin(θ)/2,e^2jksin(θ)/2... e^{(M-1)jksin(θ)/2}]^T, A (θ) represents the steering vector of conformal array；

Step 6c can obtain new Mutual coupling angle, θ by searching for MUSIC spectrums_j+1：

Wherein, arg () is to take plural argument,To take θ angles when transition formula evaluation is minimum in bracket.

Step 7, calculation cost function judges whether to meet the condition of convergence.

Step 7a passes through Mutual coupling angle, θ_j+1Calculation cost function, cost function is：

J_j+1=(C (θ_j+1)U_N)(C(θ_j+1)U_N)^H,<28>

Wherein,A(θ_j+1) represent signal source Mutual coupling angle be θ_j+1 When conformal array steering vector,

If 0≤J of step 7b_j-J_j+1<ε or j >=j_max, then it represents that meet the condition of convergence, conformal array amplitude and phase error correction Complete, stop iteration and export Mutual coupling angle, θ_j+1, wherein, j_maxIt is the maximum iteration of setting；

The sufficient condition of convergence otherwise with thumb down, performs：

θ_j+1=θ_j+ ν * τ,<29>

Wherein, ν is random digit, and value is -1 or 1, τ are angle searching step-length, iteration ordinal number j=j+1 and return to step 4；

Step 7c is set to 0.02 ° according to experiment simulation experience, general τ, and ε is set to 1.

Below in conjunction with emulation experiment, technique effect of the invention is described in detail：

1st, experimental situation and condition

Experimental situation：Experiment uses the half-wavelength uniform line-array of array number M=8, and linear array is installed along aerofoil surface, analog machine The conformal antenna of wing surface.

Simulated conditions：Wing flutter data are obtained using a kind of wing flutter model of parsing, and by wing flutter data For in subsequent simulation, the wing flutter model of the parsing to be as follows：

Z (x, t)=Z₀(x)+a(t)+q₁(t)Z₁(x),<23>

The model is divided into three parts, Part I Z₀X () is：

Wherein,The material coefficient of replicating machine wing scale is represented, L is zig, and h is substrate thickness, Z₀X () represents The static deformation that wing occurs when being influenceed by gravity and other static forces；

Part II：

A (t)=ω₀Cos (ω t),<25>

ω₀To add the amplitude of vibration, ω is the vibration angular frequency for adding, and it is array that a (t) is represented by airfoil root Forced vibration is added at origin, simulation fuselage and air force are added in the forced vibration on wing；

Part III：

Wherein, Z₁Bending die of (x) representative model substrate under the first mode of oscillation, Q₁Representative formula<25>In pressure Vibrate the influence to the first mode of oscillation：

G represents carrier board damping, a=ω/ω₁, ω₁Substrate the first mode of oscillation natural angular frequency is represented, as a=1, Resonance will be caused.

Take wing length L=1m, thickness h=0.004m；First vibration modal frequency f₁=5Hz, i.e. ω₁=2 π f₁=10 π rad；z₁=3.785；Assuming that wing is aluminium,The damped coefficient of substrate is G=0.03m；What is added is strong Damping dynamic frequency f is 4Hz, i.e. ω=2 π f=8 π rad, forced vibration amplitude ω₀=0.1m.

2nd, experiment content and interpretation of result

Experiment 1, the signal to noise ratio snr=20dB of signal source, direction of arrival is respectively 15 °, 25 °, 35 °, 45 °, 55 °, 65 °, Fast umber of beats K=200, maximum iteration j_max=5, respectively for 15 °, 25 °, 35 °, 45 °, 55 °, 65 ° of direction of arrival, use Different distortion data in one [0,0.25s] time vibration period, direction of arrival is carried out using the present invention respectively with MUSIC algorithms Estimate, shown in simulation result such as Fig. 2 (a) to Fig. 2 (f).The present invention is by the Mutual coupling after analysis correction amplitude phase error Precision, and contrast and obtain Mutual coupling angle using MUSIC algorithms, conformal array amplitude and phase error correction effect is sentenced It is disconnected.From Simulation results as can be seen that in the case of different distortion form, different direction of arrival, what the inventive method was obtained Mutual coupling angular error is maintained in the range of 0.2 °, thus the present invention have to conformal array amplitude and phase error correction it is fine Calibration result, greatly improve Mutual coupling precision when there is amplitude phase error.

Experiment 2, the signal to noise ratio snr=20dB of signal source, direction of arrival is 45 °, fast umber of beats K=200, maximum iteration j_max=5, the array deformation data in 0.03s moment points are taken, and carry out respectively 300 times using inventive algorithm and MUSIC algorithms Monte Carlo Experiment, estimates direction of arrival, as shown in Figure 3.As can be seen that the present invention carries out 300 from simulation result The Mutual coupling angular error that secondary Monte Carlo Experiment is obtained all is maintained in the range of 0.1 °, it is contemplated that method sweeping in itself Retouch the systematic error scopes about [- 0.06 °, 0.06 °] such as step-length, convergence step-length, it can be seen that the inventive method can be stablized To high-precision Mutual coupling angle, the effectively amplitude phase error to conformal array is corrected, with good stability.

Claims (4)

1. a kind of conformal array amplitude and phase error correction method based on wing deformation fitting, comprises the following steps：

(1) assume that signal number N is 1, the deviation angle φ of conformal array reference unit in search coverage₁It is zero or, it is known that utilization Receive data and calculate covariance matrix R, and feature decomposition is carried out to covariance matrix R, obtain white noise acoustical power σ²And noise Subspace U_N, the expression formula of wherein covariance matrix is：

$R=\frac{1}{K}\underset{t=1}{\overset{K}{\&Sigma;}}x\left(t\right)x{\left(t\right)}^H,$

Wherein, K is the fast umber of beats for receiving data, and x (t) is the t times reception data of snap, ()^HTaken altogether to receive data matrix Yoke transposition；

(2) covariance matrix R and white noise acoustical power σ is utilized², calculate the relative received strength of each array element in conformal arrayAnd by the relative received strength of each array element in the conformal array that is calculatedBuild diagonalization Matrix, the matrix is the relative amplitude errors matrix of conformal array

(3) Mutual coupling angle, θ in setting iteration ordinal number variable j, iteration j_jWith cost function J_j, and ordinal number is become Amount j, Mutual coupling angle, θ_jAnd cost function J_jInitialized, made j=1, θ₁=0, J₁=0；

(4) by Mutual coupling angle, θ_jThe absolute receiving intensity F (1) of conformal array reference array element is calculated, conformal array is recycled The absolute receiving intensity F (1) of row reference array element calculates the absolute amplitude error matrix F of conformal array, and using conformal array Absolute amplitude error matrix F calculates the deviation angle φ of each array element in conformal array₁,φ₂,…,φ_M；

(5) using the deviation angle φ of each array element in conformal array₁,φ₂,…,φ_M, calculate the skew of each array element in conformal array Slope ρ₁ ρ₂ … ρ_M, and according to the skew slope ρ of each array element in the conformal array for calculating₁ ρ₂ … ρ_M, using multinomial Curve fitting algorithm fits slope curve f (x) of conformal array, then slope curve f (x) of the conformal array to fitting enters Row integration, obtains deformation curve F (x) of conformal array, deformation curve F (x) of the conformal array for finally being obtained using integration, meter Calculate the side-play amount vector y of array element in conformal array；

(6) according to the side-play amount vector y of array element in the conformal array for calculating, the phase error matrix W of conformal array is calculated, and Phase error matrix W according to conformal array, the response matrix Γ (θ of conformal array after being deformed_j)A(θ_j), by the response square Battle array Γ (θ_j)A(θ_j) MUSIC spectral functions are substituted into, search MUSIC spectrums obtain Mutual coupling angle, θ_j+1；

(7) Mutual coupling angle, θ is utilized_j+1Calculation cost function, the condition of convergence is substituted into by the value of cost function, judges to receive Hold back whether condition meets, if so, then represent conformal array amplitude and phase error correction completing, export Mutual coupling angle, θ_j+1；It is no Then, j=j+1 is made, step (4) is performed.

2. the conformal array amplitude and phase error correction method based on wing deformation fitting according to claim 1, its feature exists In the relative amplitude errors matrix of the conformal array described in step (2)Its obtaining step is：

2a) using covariance matrix R and white noise acoustical power σ², calculate the relative received strength of each array element in conformal arrayComputing formula is：

${\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_i=\sqrt{\frac{R_{i,i}-{\mathrm{\&sigma;}}^2}{R_{1,1}-{\mathrm{\&sigma;}}^2}},i=1,2,...,M---<1>$

Wherein, R_i,iIt is i-th diagonal element of covariance matrix R, M is conformal array elements number；

2b) by the relative received strength of each array element in conformal arrayThe relative of conformal array is built by following formula Range error matrix

$\hat{F}=diag({\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_1,{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_2,...{\stackrel{\&OverBar;}{\mathrm{\&alpha;}}}_M)---<2>$

Wherein, diag () is represented by sequence construct diagonalizable matrix.

3. the conformal array amplitude and phase error correction method based on wing deformation fitting according to claim 1, its feature exists In the deviation angle φ of each array element in the conformal array of calculating described in step (4)₁,φ₂,…,φ_M, implementation step is：

4a) utilize Mutual coupling angle, θ_j, calculate the absolute receiving intensity F (1) of conformal array reference array element：

F (1)=f (θ_j+φ₁),<3>

Wherein, φ₁It is the deviation angle of conformal array reference array element；

4b) the absolute receiving intensity F (1) using conformal array reference array element and the relative amplitude errors matrix of conformal arrayRoot According toCalculate the absolute amplitude error matrix F of conformal array；

4c) using the absolute amplitude error matrix F of conformal array, calculate signal source and reached relative to the ripple of each array element in conformal array Direction η₁,η₂,…η_M, its computing formula is：

η_i=f^-1(F_i,i), i=1,2 ..., M,<4>

Wherein, F_i,iI-th diagonal element of the absolute amplitude error matrix F of conformal array is represented, f (θ) is conformal array element The pattern function of antenna, ()^-1The inverse function of direction figure function is represented, if F_i,i>=1, then force to set f^-1(F_i,i) It is 0；

Each array element is arranged in order along X-axis positive direction in 4d) taking conformal array, according to direction of arrival η₁,η₂,…η_MIncrease and decrease situation, Calculate the deviation angle φ of each array element in conformal array₁,φ₂,…φ_i…,φ_M, wherein, φ_iIt is i-th array element in conformal array Deviate the angle of X-axis, and deviation angle φ_iAngle is for just during deflection Y-axis positive direction：

(1) if η₁,η₂,…η_MArrangement of successively decreasing, then in conformal array each array element deviation angle：

φ_i=η_i-θ_j, i=1,2 ... M；<6>

(2) if η₁,η₂,…η_MBe incremented by arrangement, then in conformal array each array element deviation angle：

φ_i=θ_j-η_i, i=1,2 ... M；<7>

(3) if η₁,η₂,…η_MIt is emission reduction row after first increasing, takes η₁,η₂,…η_pTo be incremented by arrangement, η_p+1,η_p+2,…η_MIt is the row that successively decreases Row, then in preceding p conformal array each array element deviation angle：

φ_i=θ_j-η_i, i=1,2 ... p；<8>

Afterwards in the conformal array of (M-p) item each array element deviation angle：

φ_i=η_i-θ_j, i=p+1, p+2 ... M,<9>

4. the conformal array amplitude and phase error correction method based on wing deformation fitting according to claim 1, its feature exists In, the side-play amount vector y of array element in the conformal array of calculating described in step (5), implementation step is：

5a) using the deviation angle φ of each array element in conformal array₁,φ₂,…,φ_M, calculate the skew of each array element in conformal array Slope ρ₁,ρ₂,…,ρ_M：

ρ_i=tan (φ_i) i=1,2 ..., M；<9>

5b) take the skew slope ρ of each array element in conformal array₁,ρ₂,…,ρ_MMeet (M-1) with X-axis coordinate variable as independent variable Rank multinomial curve, i.e., the slope curve of conformal array：

F (x)=a₁x^M-1+a₂x^M-2+…+a_M-1x+a_M,<10>

Wherein, a₁,a₂,…a_MIt is constant, x is the X-axis coordinate variable of array element；By the X-axis coordinate points x of conformal array elements₁, x₂,…,x_MSubstitution formula<10>In, obtain relational expression：

Wherein, [x₁,x₂,…,x_M]^TIt is the X-axis coordinate point vector of array element in conformal array, ()^TRepresent transposition computing, ρ=[ρ₁ ρ₂ … ρ_M]^TIt is the skew slope vector of array element in conformal array；By relational expression<11>It is reduced to

aX₁=ρ<12>

Wherein, a=[a₁ a₂ … a_M]^TIt is the coefficient vector of slope curve f (x) of conformal array,Represent the generalized circular matrix with the X-axis coordinate points of array element in conformal array as element； By formula<12>The both sides right side multiplies matrixObtain the expression formula of the coefficient vector a of slope curve f (x) for calculating conformal array：

$a={\mathrm{\&rho;X}}_1^{-1},---<13>$

Wherein,It is matrix X₁Inverse matrix, and using skew slope vector ρ, the matrix of the formula and array element in conformal array Calculate the coefficient vector a of slope curve f (x) of conformal array；

5c) conformal array deformation curve F (x) meets M rank multinomials：

F (x)=b₁x^M+b₂x^M-1+…+b_Mx+b_M+1 <14>

Wherein, b₁,…b_M,b_M+1It is the coefficient of deformation curve F (x) of conformal array, takes constant b_M+1=0, by the change of conformal array Shape curve F (x) is obtained with the integral relation of slope curve f (x) of conformal array：

$\begin{array}{c}{F}^{\&prime;}\left(x\right)=f\left(x\right)\\ =b_1{\mathrm{Mx}}^{M-1}+b_2(M-1)x^{M-2}+\mathrm{...}+b_M\end{array}---<15>$

Wherein, () ' represents the deformation curve differentiation to conformal array, contrast<10>With formula<15>In coefficient, obtain

A=b ⊕ [M, M-1 ..., 1]^T <16>

Wherein, b=[b₁,b₂,…,b_M]^TIt is the coefficient vector of deformation curve F (x) of conformal array, ⊕ is the Hadamard of matrix Product, by formula<16>Simplify, obtain the expression formula of the coefficient vector b of deformation curve F (x) for calculating conformal array：

B=a ⊕ n,<17>

Wherein,And using the formula and vector n, the coefficient of slope curve f (x) of conformal array Vector a calculates the coefficient vector b of conformal array deformation curve F (x)；

5d) using the coefficient vector b and formula of conformal array deformation curve F (x)<14>, calculate the side-play amount of array element in conformal array Vector y：

Y=bX₂,<18>

Wherein, y=[y₁ y₂ … y_M]^T,