CN103353587B - Interference angle-measuring method based on improved self-adaptive DBF (digital beam forming) - Google Patents

Abstract

The invention discloses an interference angle-measuring method based on improved self-adaptive DBF (digital beam forming), and mainly solves problems that self-adaptive DBF is large in computation amount and is difficult to satisfy real-time performance of an angle measuring system in the prior art. The interference angle-measuring method comprises realization steps of 1) dividing a centrosymmetric array into four sub-arrays, namely an upper sub-array, a lower sub-array, a left sub-array and a right sub-array; 2) calculating a beam forming weight vector of any of the sub-arrays; 3) calculating beam forming weight vectors of the other sub-arrays; 4) weighting sampling data of every sub-array by using the obtained beam forming weight vector of every sub-array and performing beam enhancement; and 5) calculating a pitch angle and an azimuth angle by selecting weighted data of every sub-array according to a range gate where the maximum value of the data output after the beam enhancement is located. The interference angle-measuring method reduces the calculation amount of the self-adaptive DBF and improves real-time performance of the angle measuring system without affecting the angle measurement accuracy, and can be used for extracting target information.

Description

Based on the interference angle-measuring method of the self-adaptive numerical integration algorithm improved

Technical field

The invention belongs to signal processing technology field, the interference angle-measuring method particularly in a kind of Radar Signal Processing, can be used for target information and extract.

Background technology

Signal transacting the signal be recorded on certain media will be processed, to extract the process of useful information, for different purposes and method, signal transacting has now developed into a lot of branch, as intelligent signal processing, Speech processing, Array Signal Processing etc.

Array Signal Processing is as an important branch in signal transacting field, and its application relates to the multiple applications such as radar, sonar, communication.The object of Array Signal Processing is that the signal received by pair array is processed, and the useful signal required for enhancing, suppresses useless interference and noise, and extracts useful signal characteristic.The topmost research contents of Array Signal Processing comprises direction of arrival DOA and estimates and digital beam froming DBF.

In existing Wave arrival direction estimating method, interferometric method be the most simply, the class methods that the most easily realize, be used widely in electronic warfare with high, the fireballing feature of its precision.Interferometric method angle measurement essence be exactly utilize radiation signal to be formed on receiving antenna phase differential to determine the direction of radiation source.

Digital beam froming is on the basis of original analog beam formation basic theory, the new technology set up after introducing digital signal processing method, signal in all for array array element is weighted merging by a certain way, to detect the signal arrived from a special angle, can think to define a wave beam.Self-adaptive numerical integration algorithm is that change is environmentally weighted reception data in an adaptive way.

Interference angle-measuring method based on traditional self-adaptive numerical integration algorithm is that an array is divided into several submatrix, each submatrix carries out self-adaptive numerical integration algorithm respectively, then utilizes interferometric method to carry out angle measurement according to the phase differential of the displaced phase center of each submatrix.Because each submatrix will carry out self-adaptive numerical integration algorithm respectively, algorithm that repeatedly realization matrix is inverted or the computational complexity such as Eigenvalue Decomposition is very high, thus under the prerequisite not increasing hardware cost, be difficult to the requirement meeting angle measuring system real-time.

Summary of the invention

The object of the invention is to the deficiency for the interference angle-measuring method based on existing self-adaptive numerical integration algorithm, a kind of interference angle-measuring method of the self-adaptive numerical integration algorithm based on improving is proposed, to reduce the operand of self-adaptive numerical integration algorithm, improve the real-time of angle measuring system.

For achieving the above object, the present invention is based on the interference angle-measuring method of the self-adaptive numerical integration algorithm of improvement, comprise the steps:

(1) by centrosymmetric array partition be four submatrix U, D, L, R up and down, contained by each submatrix, array number is identical;

(2) the Wave beam forming weighted vector of any one submatrix is calculated;

(3) the Wave beam forming weighted vector of other three submatrixs is calculated:

(3a) according to the geometric relationship between submatrix, the weights transformation matrix between other three submatrixs and the submatrix selected by step (2) is calculated respectively;

(3b) be multiplied with the Wave beam forming weighted vector of the submatrix selected by step (2) by the weights transformation matrix that each submatrix in these three submatrixs is corresponding, obtain the Wave beam forming weighted vector of each submatrix in these three submatrixs;

(4) respectively the sampled data of each submatrix is up and down weighted, and the output data after each submatrix weighting is directly added by same distance door, obtain wave beam strengthen after a circuit-switched data;

(5) maximizing in the individual pulse data of Hou mono-road is strengthened at wave beam, the range gate that record maximal value is corresponding, output valve y after the weighting of each up and down submatrix before the wave beam then finding this range gate corresponding respectively strengthens _u, y _d, y _land y _r, substitute into following interferometric method angle measurement formula and obtain angle measurement result, i.e. the angle of pitch with position angle

Wherein, arcsin () represents arcsin function, and phase angle function is got in phase () expression, represent that pitching points to slope to normal, represent that slope is pointed to normal, L in orientation _ywith L _xrepresent the distance of displaced phase center to true origin of upper submatrix U and right submatrix R respectively, θ _bwith represent the angle of pitch and the position angle of beam position respectively.

Compared with prior art, tool has the following advantages in the present invention:

The present invention is owing to only needing to utilize the Wave beam forming weighted vector of sampled data to a submatrix in four of centrosymmetric array submatrixs to calculate, then according to the geometric relationship between submatrix, obtain other three submatrixs respectively and ask the weights transformation matrix between submatrix, being followed by each weights transformation matrix asks the Wave beam forming weighted vector of submatrix to be directly multiplied again, obtain the Wave beam forming weighted vector of these three submatrixs respectively, thus the repeatedly realization of the high algorithm of the computational complexity such as matrix inversion or Eigenvalues Decomposition is avoided, reduce the operand of self-adaptive numerical integration algorithm, improve the real-time of angle measuring system, be beneficial to hardware implementing.

Accompanying drawing explanation

Fig. 1 of the present inventionly realizes general flow chart;

Fig. 2 is the array arrangement, array element numbering and the coordinate system that use in the present invention;

Fig. 3 is the sub-process figure calculating a sub-array beamforming weighted vector in the present invention.

Embodiment

With reference to Fig. 1, the present invention provides following four kinds of embodiments:

Each embodiment all uses array as shown in Figure 2 and coordinate system, and array element distance is the half of carrier wavelength; A target is set, the angle of pitch be 3 °, azimuth angle theta is 2 °; A Deceiving interference is set again, the angle of pitch is 40 °, position angle is 30 °; The angle of pitch of beam position is 3 °, position angle is 2 °; Signal to noise ratio snr=20dB, dry making an uproar compares INR=30dB.

Embodiment 1

Step 1. divides submatrix.

By the array element that the Central Symmetry array partition shown in Fig. 2 is upper submatrix U, lower submatrix D, left submatrix L, right submatrix R, these four submatrix common center positions, each submatrix includes 6 array elements, and the known upper submatrix of array element numbering comprises array element { 1,2 as shown in Figure 2,3,4,5,6}, lower submatrix comprises array element { 6,7,8,9,10,11}, left submatrix comprises array element { 12,13,14,15,16,6}, right submatrix comprises array element { 6,17,18,19,20,21}.

Step 2. calculates the Wave beam forming weighted vector of upper submatrix U.

With reference to Fig. 3, being implemented as follows of this step:

(2.1) carry out 512 snap samplings to upper submatrix U, forming sampled data matrix Xu is:

$X_u=[x_u^1,x_u^2,\·\·\·,x_u^{512}],---\left[1\right]$

Wherein, i-th snap sampled data, 1≤i≤512, then calculating sampling covariance matrix S _ufor:

$S_u=X_u\·X_u^H/512,---\left[2\right]$

Wherein, H represents conjugate transpose;

(2.2) to sample covariance matrix S _ucarry out Eigenvalues Decomposition, obtain

$S_u=Q_u{\mathrm{\Λ}}_u{Q}_u^H,---\left[3\right]$

Wherein, by sample covariance matrix S _u6 eigenvectors the matrix formed, Λ _uby sample covariance matrix S _u6 eigenwerts the diagonal matrix formed;

(2.3) be Deceiving interference according to interference, and number is 1, dryly makes an uproar than INR=30dB, these prior imformations of signal to noise ratio snr=20dB, at sample covariance matrix S _u6 eigenvectors in, selecting the eigenvector forming interference space is sample covariance matrix S _u6 eigenwerts middle maximal value characteristic of correspondence vector, is assumed to be

(2.4) according to the eigenvector of the formation interference space selected calculate interference space matrix J _ufor:

$J_u=v_u^1\·{\left(v_u^1\right)}^H\text{;---}\left[4\right]$

(2.5) according to interference space matrix J _u, calculate the orthogonal complement space matrix of interference space for:

$J_u^{\⊥}=I-J_u,---\left[5\right]$

Wherein I is the unit matrix of 6 dimensions;

(2.6) { coordinate of 1,2,3,4,5,6} is respectively p to establish the array element of submatrix U ₁, p ₂, p ₃, p ₄, p ₅, p ₆, the steering vector a of submatrix U in calculating _ufor:

$a_u={\left[\begin{array}{cccccc}{e}^{-j{k}^T{p}_1}& e^{-j{k}^T{p}_2}& e^{-j{k}^T{p}_3}& e^{-j{k}^T{p}_4}& e^{-j{k}^T{p}_5}& e^{-j{k}^T{p}_6}\end{array}\right]}^T,---\left[6\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

(2.7) according to the orthogonal complement space matrix of interference space with steering vector a _u, the Wave beam forming weighted vector w of submatrix U in calculating _ufor:

$w_u=J_u^{\⊥}\·a_u.---\left[7\right]$

Step 3. calculates the Wave beam forming weighted vector of lower submatrix D, left submatrix L, right submatrix R respectively.

(3.1) { coordinate of 6,7,8,9,10,11} is respectively p to set the array element of submatrix D ₆, p ₇, p ₈, p ₉, p ₁₀, p ₁₁, { coordinate of 12,13,14,15,16,6} is respectively p to the array element of left submatrix L ₁₂, p ₁₃, p ₁₄, p ₁₅, p ₁₆, p ₆, { coordinate of 6,17,18,19,20,21} is respectively p to the array element of right submatrix R ₆, p ₁₇, p ₁₈, p ₁₉, p ₂₀, p ₂₁;

(3.2) the Wave beam forming weighted vector w of lower submatrix D is calculated _d:

(3.2.1) coordinate difference between each array element of lower submatrix D and the corresponding array element of upper submatrix U is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{16}=p_6-p_1\\ \mathrm{\Δ}{p}_{27}=p_7-p_2\\ \mathrm{\Δ}{p}_{38}=p_8-p_3\\ \mathrm{\Δ}{p}_{49}=p_9-p_4\\ \mathrm{\Δ}{p}_{\mathrm{5,10}}=p_{10}-p_5\\ \mathrm{\Δ}{p}_{\mathrm{6,11}}=p_{11}-p_6\end{array}\right.;---\left[8\right]$

(3.2.2) lower weights transformation matrix C between submatrix D and upper submatrix U is calculated _dufor:

$C_{\mathrm{du}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{16}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{27}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{38}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{49}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{5,10}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,11}}}\end{array}\right],\left[9\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

(3.2.3) according to the weights transformation matrix C between lower submatrix D and upper submatrix U _duwith the Wave beam forming weighted vector w of upper submatrix U _u, calculate the Wave beam forming weighted vector w of lower submatrix D _dfor:

w _d=C _du·w _u； [10]

(3.3) the Wave beam forming weighted vector w of left submatrix L is calculated _l:

(3.3.1) coordinate difference between each array element of left submatrix L and the corresponding array element of upper submatrix U is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{1,12}}=p_{12}-p_1\\ \mathrm{\Δ}{p}_{\mathrm{2,13}}=p_{13}-p_2\\ \mathrm{\Δ}{p}_{\mathrm{3,14}}=p_{14}-p_3\\ \mathrm{\Δ}{p}_{\mathrm{4,15}}=p_{15}-p_4\\ \mathrm{\Δ}{p}_{\mathrm{5,16}}=p_{16}-p_5\\ \mathrm{\Δ}{p}_{66}=p_6-p_6\end{array}\right.;---\left[11\right]$

(3.3.2) the weights transformation matrix C between left submatrix L and upper submatrix U is calculated _lufor:

$C_{\mathrm{lu}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{1,12}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{2,13}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{3,14}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{4,15}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{5,16}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{66}}\end{array}\right];---\left[12\right]$

(3.3.3) according to the weights transformation matrix C between left submatrix L and upper submatrix U _luwith the Wave beam forming weighted vector w of upper submatrix U _u, calculate the Wave beam forming weighted vector w of left submatrix L _lfor:

w _l=C _lu·w _u； [13]

(3.4) the Wave beam forming weighted vector w of right submatrix R is calculated _r:

(3.4.1) coordinate difference between each array element of right submatrix R and the corresponding array element of upper submatrix U is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{16}=p_6-p_1\\ \mathrm{\Δ}{p}_{\mathrm{2,17}}=p_{17}-p_2\\ \mathrm{\Δ}{p}_{\mathrm{3,18}}=p_{18}-p_3\\ \mathrm{\Δ}{p}_{\mathrm{4,19}}=p_{19}-p_4\\ \mathrm{\Δ}{p}_{\mathrm{5,20}}=p_{20}-p_5\\ \mathrm{\Δ}{p}_{\mathrm{6,21}}=p_{21}-p_6\end{array}\right.;---\left[14\right]$

(3.4.2) the weights transformation matrix C between right submatrix R and upper submatrix U is calculated _rufor:

$C_{\mathrm{ru}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{16}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{2,17}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{3,18}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{4,19}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{5,20}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,21}}}\end{array}\right];---\left[15\right]$

(3.4.3) according to the weights transformation matrix C between right submatrix R and upper submatrix U _ruwith the Wave beam forming weighted vector w of upper submatrix U _u, calculate the Wave beam forming weighted vector w of right submatrix R _rfor:

w _r=C _ru·w _u。[16]

Step 4. weighting and wave beam strengthen.

(4.1) according to the Wave beam forming weighted vector w of each submatrix of trying to achieve _u, w _d, w _l, w _r, respectively to upper submatrix sampled data matrix X _u, lower submatrix sampled data matrix X _d, left submatrix sampled data matrix X _l, right submatrix sampled data matrix X _rbe weighted, obtain the output data vector Y after each submatrix weighting _u, Y _d, Y _l, Y _rbe respectively:

$\left\{\begin{array}{c}{Y}_u=w_u^H\·X_u\\ Y_d=w_d^H\·X_d\\ Y_l=w_l^H\·X_l\\ Y_r=w_r^H\·X_r\end{array}\right.,---\left[17\right]$

Wherein, H represents conjugate transpose, Y _ufor the output data vector after upper submatrix weighting, Y _dfor the output data vector after lower submatrix weighting, Y _lfor the output data vector after left submatrix weighting, Y _rfor the output data vector after right submatrix weighting;

(4.2) by the output data vector Y after each submatrix weighting _u, Y _d, Y _l, Y _rbe added synthesis one circuit-switched data, data vector Y after being enhanced _enfor:

Y _en=Y _u+Y _d+Y _l+Y _r； [18]

Suppose the output data vector Y after each submatrix weighting _u, Y _d, Y _l, Y _rbe respectively:

$\left\{\begin{array}{c}{Y}_u=[y_u^1,y_u^2,\·\·\·,y_u^{512}]\\ Y_d=[y_d^1,y_d^2,\·\·\·,y_d^{512}]\\ Y_l=[y_l^1,y_l^2,\·\·\·,y_l^{512}]\\ Y_r=[y_r^1,y_r^2,\·\·\·,y_r^{512}]\end{array}\right.,---\left[19\right]$

Data vector Y after then strengthening _enfor:

$Y_{\mathrm{en}}=\left[\begin{array}{cccc}{y}_u^1+y_d^1+y_l^1+y_r^1,& y_u^2+y_d^2+y_l^2+y_r^2,& \·\·\·,& y_u^{512}+y_d^{512}+y_l^{512}+y_r^{512}\end{array}\right].---\left[20\right]$

The angle measurement of step 5. interferometric method.

(5.1) the rear data vector Y of enhancing is found _enthe maximal value y of middle all elements _max, suppose y _maxdata vector Y after strengthening _ent element, 1≤t≤512;

(5.2) after the weighting of each submatrix, data vector Y is exported _u, Y _d, Y _l, Y _rin, export data vector Y after finding submatrix weighting respectively _ut element y _u, export data vector Y after lower submatrix weighting _dt element y _d, export data vector Y after left submatrix weighting _lt element y _ldata vector Y is exported with after right submatrix weighting _rt element y _r;

(5.3) according to each element value y that (5.2) obtain _u, y _d, y _l, y _r, try to achieve the angle of pitch and position angle

Wherein, arcsin () represents arcsin function, and phase angle function is got in phase () expression, and pitching points to slope k to normal _y0=2.5 π, slope k is pointed to normal in orientation _x0=2.5 π, θ _bwith represent the angle of pitch and the position angle of beam position respectively.

Embodiment 2

Steps A. identical with the step 1 of embodiment 1.

Step B. calculates the Wave beam forming weighted vector of lower submatrix D.

With reference to Fig. 3, being implemented as follows of this step:

(B1) 512 snap samplings are carried out to lower submatrix D, form sampled data matrix X _dfor:

$X_d=[x_d^1,x_d^2,\·\·\·,x_d^{512}],---\left[22\right]$

Wherein, i-th snap sampled data, 1≤i≤512, then calculating sampling covariance matrix S _dfor:

$S_d=X_d\·X_d^H/512,---\left[23\right]$

Wherein, H represents conjugate transpose;

(B2) to sample covariance matrix S _dcarry out Eigenvalues Decomposition, obtain

$S_d=Q_d{\mathrm{\Λ}}_d{Q}_d^H,---\left[24\right]$

Wherein, by sample covariance matrix S _d6 eigenvectors the matrix formed, Λ _dby sample covariance matrix S _d6 eigenwerts the diagonal matrix formed;

(B3) be Deceiving interference according to interference, and number is 1, dryly makes an uproar than INR=30dB, these prior imformations of signal to noise ratio snr=20dB, at sample covariance matrix S _d6 eigenvectors in, selecting the eigenvector forming interference space is sample covariance matrix S _d6 eigenwerts middle maximal value characteristic of correspondence vector, is assumed to be

(B4) according to the eigenvector of the formation interference space selected calculate interference space matrix J _dfor:

$J_d=v_d^1\·{\left(v_d^1\right)}^H;---\left[25\right]$

(B5) according to interference space matrix J _d, calculate the orthogonal complement space matrix of interference space for:

$J_d^{\⊥}=I-J_d,---\left[26\right]$

Wherein I is the unit matrix of 6 dimensions;

(B6) { coordinate of 6,7,8,9,10,11} is respectively p to set the array element of submatrix D ₁₂, p ₁₃, p ₁₄, p ₁₅, p ₁₆, p ₆, calculate the steering vector a of lower submatrix D _dfor:,

$a_d={\left[\begin{array}{cccccc}{e}^{-j{k}^T{p}_6}& e^{-j{k}^T{p}_7}& e^{-j{k}^T{p}_8}& e^{-j{k}^T{p}_9}& e^{-j{k}^T{p}_{10}}& e^{-j{k}^T{p}_{11}}\end{array}\right]}^T,---\left[27\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

(B7) according to the orthogonal complement space matrix of interference space with steering vector a _d, calculate the Wave beam forming weighted vector w of lower submatrix D _dfor:

$w_d=J_d^{\⊥}\·a_d.---\left[28\right]$

Step C. calculates the Wave beam forming weighted vector of submatrix U, left submatrix L, right submatrix R respectively.

(C1) { coordinate of 1,2,3,4,5,6} is respectively p to establish the array element of submatrix U ₁, p ₂, p ₃, p ₄, p ₅, p ₆, { coordinate of 12,13,14,15,16,6} is respectively p to the array element of left submatrix L ₁₂, p ₁₃, p ₁₄, p ₁₅, p ₁₆, p ₆, { coordinate of 6,17,18,19,20,21} is respectively p to the array element of right submatrix R ₆, p ₁₇, p ₁₈, p ₁₉, p ₂₀, p ₂₁;

(C2) the Wave beam forming weighted vector w of submatrix U in calculating _u:

(C2-1) coordinate difference in calculating between each array element of submatrix U and the corresponding array element of lower submatrix D:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{6,1}}=p_1-p_6\\ \mathrm{\Δ}{p}_{\mathrm{7,2}}=p_2-p_7\\ \mathrm{\Δ}{p}_{\mathrm{8,3}}=p_3-p_8\\ \mathrm{\Δ}{p}_{\mathrm{9,4}}=p_4-p_9\\ \mathrm{\Δ}{p}_{10,5}=p_5-p_{10}\\ \mathrm{\Δ}{p}_{11,6}=p_6-p_{11}\end{array}\right.;---\left[29\right]$

(C2-2) the weights transformation matrix C in calculating between submatrix U and lower submatrix D _udfor:

$C_{\mathrm{ud}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,1}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{7,2}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{8,3}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{9,4}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{10,5}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{11,6}}}\end{array}\right];---\left[30\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

(C2-3) according to the weights transformation matrix C between upper submatrix U and lower submatrix D _udwith the Wave beam forming weighted vector w of lower submatrix D _d, the Wave beam forming weighted vector w of submatrix U in calculating _ufor:

w _u=C _ud·w _d； [31]

(C3) the Wave beam forming weighted vector w of left submatrix L is calculated _l:

(C3-1) coordinate difference between each array element of left submatrix L and the corresponding array element of lower submatrix D is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{6,12}}=p_{12}-p_6\\ \mathrm{\Δ}{p}_{\mathrm{7,13}}=p_{13}-p_7\\ \mathrm{\Δ}{p}_{\mathrm{8,14}}=p_{14}-p_8\\ \mathrm{\Δ}{p}_{\mathrm{9,15}}=p_{15}-p_9\\ \mathrm{\Δ}{p}_{10,16}=p_{16}-p_{10}\\ \mathrm{\Δ}{p}_{11,6}=p_6-p_{11}\end{array}\right.;---\left[32\right]$

(C3-2) the weights transformation matrix C between left submatrix L and lower submatrix D is calculated _ldfor:

$C_{\mathrm{ld}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,12}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{7,13}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{8,14}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{9,15}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{10,16}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{11,6}}}\end{array}\right];---\left[33\right]$

(C3-3) according to the weights transformation matrix C between left submatrix L and lower submatrix D _ldwith the Wave beam forming weighted vector w of lower submatrix D _d, calculate the Wave beam forming weighted vector w of left submatrix L _lfor:

w _l=C _ld·w _d； [34]

(C4) the Wave beam forming weighted vector w of right submatrix R is calculated _r:

(C4-1) coordinate difference between each array element of right submatrix R and the corresponding array element of lower submatrix D is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{66}=p_6-p_6\\ \mathrm{\Δ}{p}_{\mathrm{7,17}}=p_{17}-p_7\\ \mathrm{\Δ}{p}_{\mathrm{8,18}}=p_{18}-p_8\\ \mathrm{\Δ}{p}_{\mathrm{9,19}}=p_{19}-p_9\\ \mathrm{\Δ}{p}_{\mathrm{10,20}}=p_{20}-p_{10}\\ \mathrm{\Δ}{p}_{\mathrm{11,21}}=p_{21}-p_{11}\end{array}\right.;---\left[35\right]$

(C4-2) the weights transformation matrix C between right submatrix R and lower submatrix D is calculated _rdfor:

$C_{\mathrm{rd}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{66}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{7,17}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{8,18}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{9,19}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{10,20}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{11,21}}}\end{array}\right];---\left[36\right]$

(C4-3) according to the weights transformation matrix C between right submatrix R and lower submatrix D _rdwith the Wave beam forming weighted vector w of lower submatrix D _d, calculate the Wave beam forming weighted vector w of right submatrix R _rfor:

w _r=C _rd·w _d。[37]

Step D. is identical with the step 4 of embodiment 1.

Step e. identical with the step 5 of embodiment 1.

Embodiment 3

Step one. identical with the step 1 of embodiment 1.

Step 2. calculate the Wave beam forming weighted vector of left submatrix L.

With reference to Fig. 3, being implemented as follows of this step:

2.1) 512 snap samplings are carried out to left submatrix L, form sampled data matrix X _lfor:

$X_l=[x_l^1,x_l^2,\·\·\·,x_l^{512}],---\left[38\right]$

Wherein, i-th snap sampled data, 1≤i≤512, then calculating sampling covariance matrix S _lfor:

$S_l=X_l\·X_l^H/512,---\left[39\right]$

Wherein, H represents conjugate transpose;

2.2) to sample covariance matrix S _lcarry out Eigenvalues Decomposition, obtain

$S_l=Q_l{\mathrm{\Λ}}_l{Q}_l^H,---\left[40\right]$

Wherein, by sample covariance matrix S _l6 eigenvectors the matrix formed, Λ _lby sample covariance matrix S _l6 eigenwerts the diagonal matrix formed;

2.3) be Deceiving interference according to interference, and number is 1, dryly makes an uproar than INR=30dB, these prior imformations of signal to noise ratio snr=20dB, at sample covariance matrix S _l6 eigenvectors in, selecting the eigenvector forming interference space is sample covariance matrix S _l6 eigenwerts middle maximal value characteristic of correspondence vector, is assumed to be

2.4) according to the eigenvector of the formation interference space selected calculate interference space matrix J _lfor:

$J_l=v_l^1\·{\left(v_l^1\right)}^H;---\left[41\right]$

2.5) according to interference space matrix J _l, calculate the orthogonal complement space matrix of interference space for:

$J_l^{\⊥}=I-J_l,---\left[42\right]$

Wherein I is the unit matrix of 6 dimensions;

2.6) { coordinate of 12,13,14,15,16,6} is respectively p to establish the array element of left submatrix L ₁₂, p ₁₃, p ₁₄, p ₁₅, p ₁₆, p ₆, calculate the steering vector a of left submatrix L _lfor:

$a_l={\left[\begin{array}{cccccc}{e}^{-j{k}^T{p}_{12}}& e^{-j{k}^T{p}_{13}}& e^{-j{k}^T{p}_{14}}& e^{-j{k}^T{p}_{15}}& e^{-j{k}^T{p}_{16}}& e^{-j{k}^T{p}_6}\end{array}\right]}^T,---\left[43\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

2.7) according to the orthogonal complement space matrix of interference space with steering vector a _l, calculate the Wave beam forming weighted vector w of left submatrix L _lfor:

$w_l=J_l^{\⊥}\·a_l.---\left[44\right]$

Step 3. calculate the Wave beam forming weighted vector of upper submatrix U, lower submatrix D, right submatrix R respectively.

3.1) { coordinate of 1,2,3,4,5,6} is respectively p to establish the array element of submatrix U ₁, p ₂, p ₃, p ₄, p ₅, p ₆, { coordinate of 6,7,8,9,10,11} is respectively p to the array element of lower submatrix D ₆, p ₇, p ₈, p ₉, p ₁₀, p ₁₁, { coordinate of 6,17,18,19,20,21} is respectively p to the array element of right submatrix R ₆, p ₁₇, p ₁₈, p ₁₉, p ₂₀, p ₂₁;

3.2) the Wave beam forming weighted vector w of submatrix U in calculating _u:

3.2.1) coordinate difference in calculating between each array element of submatrix U and the corresponding array element of left submatrix L:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{12,1}}=p_1-p_{12}\\ \mathrm{\Δ}{p}_{\mathrm{13,2}}=p_2-p_{13}\\ \mathrm{\Δ}{p}_{14,3}=p_3-p_{14}\\ \mathrm{\Δ}{p}_{\mathrm{15,4}}=p_4-p_{15}\\ \mathrm{\Δ}{p}_{16,5}=p_5-p_{16}\\ \mathrm{\Δ}{p}_{66}=p_6-p_6\end{array}\right.;---\left[45\right]$

3.2.2) the weights transformation matrix C in calculating between submatrix U and left submatrix L _ulfor:

$C_{\mathrm{ul}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{12,1}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{13,2}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{14,3}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{15,4}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{16,5}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{66}}\end{array}\right],---\left[46\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

3.2.3) according to the weights transformation matrix C between upper submatrix U and left submatrix L _ulwith the Wave beam forming weighted vector w of left submatrix L _l, the Wave beam forming weighted vector w of submatrix U in calculating _ufor:

w _u=C _ul·w _l； [47]

3.3) the Wave beam forming weighted vector w of lower submatrix D is calculated _d:

3.3.1) coordinate difference between each array element of lower submatrix D and the corresponding array element of left submatrix L is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{12,6}}=p_6-p_{12}\\ \mathrm{\Δ}{p}_{\mathrm{13,7}}=p_7-p_{13}\\ \mathrm{\Δ}{p}_{\mathrm{14,8}}=p_8-p_{14}\\ \mathrm{\Δ}{p}_{\mathrm{15,9}}=p_9-p_{15}\\ \mathrm{\Δ}{p}_{\mathrm{16,10}}=p_{10}-p_{16}\\ \mathrm{\Δ}{p}_{\mathrm{6,11}}=p_{11}-p_6\end{array}\right.;---\left[48\right]$

3.3.2) lower weights transformation matrix C between submatrix D and left submatrix L is calculated _dlfor

$C_{\mathrm{dl}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{12,6}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{13,7}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{14,8}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{15,9}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{16,10}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,11}}}\end{array}\right];---\left[49\right]$

3.3.3) according to the weights transformation matrix C between lower submatrix D and left submatrix L _dlwith the Wave beam forming weighted vector w of left submatrix L _l, calculate the Wave beam forming weighted vector w of lower submatrix D _dfor:

w _d=C _dl·w _l； [50]

3.4) the Wave beam forming weighted vector w of right submatrix R is calculated _r:

3.4.1) coordinate difference between each array element of right submatrix R and the corresponding array element of left submatrix L is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{12,6}}=p_6-p_{12}\\ \mathrm{\Δ}{p}_{\mathrm{13,17}}=p_{17}-p_{13}\\ \mathrm{\Δ}{p}_{\mathrm{14,18}}=p_{18}-p_{14}\\ \mathrm{\Δ}{p}_{\mathrm{15,19}}=p_{19}-p_{15}\\ \mathrm{\Δ}{p}_{\mathrm{16,20}}=p_{20}-p_{16}\\ \mathrm{\Δ}{p}_{\mathrm{6,21}}=p_{21}-p_6\end{array}\right.;---\left[51\right]$

3.4.2) the weights transformation matrix C between right submatrix R and left submatrix L is calculated _rlfor:

$C_{\mathrm{rl}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{12,6}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{13,17}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{14,18}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{15,19}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{16,20}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,21}}}\end{array}\right];---\left[52\right]$

3.4.3) according to the weights transformation matrix C between right submatrix R and left submatrix L _rlwith the Wave beam forming weighted vector w of left submatrix L _l, calculate the Wave beam forming weighted vector w of right submatrix R _rfor:

w _r=C _rl·w _l。[53]

Step 4. identical with the step 4 of embodiment 1.

Step 5. identical with the step 5 of embodiment 1.

Embodiment 4

The first step. identical with the step 1 of embodiment 1.

Second step. calculate the Wave beam forming weighted vector of right submatrix R.

With reference to Fig. 3, being implemented as follows of this step:

(2a) 512 snap samplings are carried out to right submatrix R, form sampled data matrix X _rfor:

$X_r=[x_r^1,x_r^2,\·\·\·,x_r^{512}],---\left[54\right]$

Wherein, i-th snap sampled data, 1≤i≤512, then calculating sampling covariance matrix S _rfor:

$S_r=X_r\·X_r^H/512,---\left[55\right]$

Wherein, H represents conjugate transpose;

(2b) to sample covariance matrix S _rcarry out Eigenvalues Decomposition, obtain

$S_r=Q_r{\mathrm{\Λ}}_r{Q}_r^H,---\left[56\right]$

Wherein, by sample covariance matrix S _r6 eigenvectors the matrix formed, Λ _rby sample covariance matrix S _r6 eigenwerts the diagonal matrix formed;

(2c) be Deceiving interference according to interference, and number is 1, dryly makes an uproar than INR=30dB, these prior imformations of signal to noise ratio snr=20dB, at sample covariance matrix S _r6 eigenvectors in, selecting the eigenvector forming interference space is sample covariance matrix S _r6 eigenwerts middle maximal value characteristic of correspondence vector, is assumed to be

(2d) according to the eigenvector of the formation interference space selected calculate interference space matrix J _rfor:

$J_r=v_r^1\·{\left(v_r^1\right)}^H;---\left[57\right]$

(2e) according to interference space matrix J _r, calculate the orthogonal complement space matrix of interference space for:

$J_r^{\⊥}=I-J_r,---\left[58\right]$

Wherein I is the unit matrix of 6 dimensions;

(2f) { coordinate of 6,17,18,19,20,21} is respectively p to establish the array element of right submatrix R ₆, p ₁₇, p ₁₈, p ₁₉, p ₂₀, p ₂₁, calculate the steering vector a of right submatrix R _rfor:

$a_r={\left[\begin{array}{cccccc}{e}^{-j{k}^T{p}_6}& e^{-j{k}^T{p}_{17}}& e^{-j{k}^T{p}_{18}}& e^{-j{k}^T{p}_{19}}& e^{-j{k}^T{p}_{20}}& e^{-j{k}^T{p}_{21}}\end{array}\right]}^T,---\left[59\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

(2g) according to the orthogonal complement space matrix of interference space with steering vector a _r, calculate right submatrix R Wave beam forming weighted vector w _rfor:

$w_r=J_r^{\⊥}\·a_r.---\left[60\right]$

3rd step. calculate the Wave beam forming weighted vector of upper submatrix U, lower submatrix D, left submatrix L respectively.

(3a) { coordinate of 1,2,3,4,5,6} is respectively p to establish the array element of submatrix U ₁, p ₂, p ₃, p ₄, p ₅, p ₆, { coordinate of 6,7,8,9,10,11} is respectively p to the array element of lower submatrix D ₆, p ₇, p ₈, p ₉, p ₁₀, p ₁₁, { coordinate of 12,13,14,15,16,6} is respectively p to the array element of left submatrix L ₁₂, p ₁₃, p ₁₄, p ₁₅, p ₁₆, p ₆;

(3b) the Wave beam forming weighted vector w of upper submatrix U is calculated _u:

(3b1) coordinate difference between each array element of upper submatrix U and the corresponding array element of right submatrix R is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{6,1}}=p_1-p_6\\ \mathrm{\Δ}{p}_{\mathrm{17,2}}=p_2-p_{17}\\ \mathrm{\Δ}{p}_{\mathrm{18,3}}=p_3-p_{18}\\ \mathrm{\Δ}{p}_{\mathrm{19,4}}=p_4-p_{19}\\ \mathrm{\Δ}{p}_{20,5}=p_5-p_{20}\\ \mathrm{\Δ}{p}_{21,6}=p_6-p_{21}\end{array}\right.;---\left[61\right]$

(3b2) upper weights transformation matrix C between submatrix U and right submatrix R is calculated _urfor:

$C_{\mathrm{ur}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,1}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{17,2}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{18,3}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{19,4}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{20,5}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{21,6}}\end{array}\right];---\left[62\right]$

Wherein, T represents transposition, and j is imaginary unit, and k is the wave-number vector that beam position is corresponding;

(3b3) according to the weights transformation matrix C between upper submatrix U and right submatrix R _urwith right submatrix R Wave beam forming weighted vector w _r, the Wave beam forming weighted vector w of submatrix U in calculating _ufor:

w _u=C _ur·w _r； [63]

(3c) the Wave beam forming weighted vector w of lower submatrix D is calculated _d:

(3c1) coordinate difference between each array element of lower submatrix D and the corresponding array element of right submatrix R is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{66}=p_6-p_6\\ \mathrm{\Δ}{p}_{\mathrm{17,7}}=p_7-p_{17}\\ \mathrm{\Δ}{p}_{\mathrm{18,8}}=p_8-p_{18}\\ \mathrm{\Δ}{p}_{\mathrm{19,9}}=p_9-p_{19}\\ \mathrm{\Δ}{p}_{\mathrm{20,10}}=p_{10}-p_{20}\\ \mathrm{\Δ}{p}_{21,11}=p_{11}-p_{21}\end{array}\right.;---\left[64\right]$

(3c2) lower weights transformation matrix C between submatrix D and right submatrix R is calculated _drfor:

$C_{\mathrm{dr}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{66}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{17,7}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{18,8}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{19,9}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{20,10}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{21,11}}}\end{array}\right];---\left[65\right]$

(3c3) according to the weights transformation matrix C between lower submatrix D and right submatrix R _drwith right submatrix R Wave beam forming weighted vector w _r, calculate the Wave beam forming weighted vector w of lower submatrix D _dfor:

w _d=C _dr·w _r； [66]

(3d) the Wave beam forming weighted vector w of left submatrix L is calculated _l:

(3d1) coordinate difference between each array element of left submatrix L and the corresponding array element of right submatrix R is calculated:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{\mathrm{6,12}}=p_{12}-p_6\\ \mathrm{\Δ}{p}_{\mathrm{17,13}}=p_{13}-p_{17}\\ \mathrm{\Δ}{p}_{\mathrm{18,14}}=p_{14}-p_{18}\\ \mathrm{\Δ}{p}_{\mathrm{19,15}}=p_{15}-p_{19}\\ \mathrm{\Δ}{p}_{\mathrm{20,16}}=p_{16}-p_{20}\\ \mathrm{\Δ}{p}_{21,6}=p_6-p_{21}\end{array}\right.;---\left[67\right]$

(3d2) the weights transformation matrix C between left submatrix L and right submatrix R is calculated _lrfor:

$C_{\mathrm{lr}}=\left[\begin{array}{cccccc}{e}^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{6,12}}}& & & & & \\ & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{17,13}}}& & & & \\ & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{18,14}}}& & & \\ & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{19,15}}}& & \\ & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{\mathrm{20,16}}}& \\ & & & & & e^{-j{k}^T\mathrm{\Δ}{p}_{21,6}}\end{array}\right];---\left[68\right]$

(3d3) according to the weights transformation matrix C between left submatrix L and right submatrix R _lrwith right submatrix R Wave beam forming weighted vector w _r, calculate the Wave beam forming weighted vector w of left submatrix L _lfor:

w _l=C _lr·w _r。[69]

4th step. identical with the step 4 of embodiment 1.

5th step. identical with the step 5 of embodiment 1.

Effect of the present invention further illustrates by following angle measurement result and theoretical analysis:

1. angle measurement result

The angle measurement result of four kinds of embodiments and the angle measurement result of angle theoretical value and classic method are compared, comparative result is as shown in the table:

The angle measurement result of table 1 four kinds of embodiments and the angle measurement Comparative result of angle theoretical value and classic method

Comparative result is as shown in Table 1 known, and the inventive method is effective.

2. rationality proves

Suppose there is A, B two submatrixs, each submatrix includes M array element, and each array element coordinate of A submatrix is respectively p _a1, p _a2..., p _aM, each array element coordinate of B submatrix is respectively p _b1, p _b2..., p _bM, then the steering vector v of A submatrix _afor:

$v_A={\left[\begin{array}{cccc}{e}^{-j{k}^T{p}_{A1}}& e^{-j{k}^T{p}_{A2}}& \·\·\·& e^{-j{k}^T{p}_{\mathrm{AM}}}\end{array}\right]}^T,---\left[70\right]$

Wherein, j is imaginary unit, and T represents transposition, and k is wave-number vector, the steering vector v of B submatrix _bfor:

$v_B={\left[\begin{array}{cccc}{e}^{-j{k}^T{p}_{B1}}& e^{-j{k}^T{p}_{B2}}& \·\·\·& e^{-j{k}^T{p}_{\mathrm{BM}}}\end{array}\right]}^T;---\left[71\right]$

Thus can obtain

Wherein array element coordinate difference △ p _{ai, Bi}=p _bi-p _ai, i=1,2 ..., M, note

Then have

v _B=C _AB·v _A， [74]

$C_{\mathrm{AB}}\·C_{\mathrm{AB}}^H=I,---\left[75\right]$

Wherein, H represents conjugate transpose, and I is the unit matrix of M dimension;

If { r _a1, r _a2,, r _amfor forming one group of steering vector of the interference space of A submatrix, and establish matrix R _a=[r _a1, r _a2,, r _am]; Eigenvalues Decomposition is carried out to the sample covariance matrix of A submatrix, if a stack features vector { s of the sample covariance matrix of A submatrix _a1, s _a2,, s _amform the interference space of A submatrix, and establish matrix S _a=[s _a1, s _a2,, s _am], then have

$R_A\·R_A^H=S_A\·S_A^H;---\left[76\right]$

If { r _b1, r _b2,, r _bmfor forming one group of steering vector of B submatrix interference space, and establish matrix R _b=[r _b1, r _b2,, r _bm]; Eigenvalues Decomposition is carried out to the sample covariance matrix of B submatrix, if a stack features vector { s of the sample covariance matrix of B submatrix _b1, s _b2,, s _bmform the interference space of B submatrix, and establish matrix S _b=[s _b1, s _b2,, s _bm], then have

$R_B\·R_B^H=S_B\·S_B^H,---\left[77\right]$

And

R _B=C _AB·R _A； [78]

So obtain the Wave beam forming weighted vector w of B submatrix _bfor:

$w_B=(I-S_B\·S_B^H)\·v_B$

$=(I-R_B\·R_B^H)\·v_B$

$=(I-C_{\mathrm{AB}}\·R_A\·R_A^H\·C_{\mathrm{AB}}^H)\·v_B$

$(C_{\mathrm{AB}}\·C_{\mathrm{AB}}^H-C_{\mathrm{AB}}\·R_A\·R_A^H\·C_{\mathrm{AB}}^H)\·C_{\mathrm{AB}}\·v_A;---\left[79\right]$

$=C_{\mathrm{AB}}\·(I-R_A\·R_A^H)\·C_{\mathrm{AB}}^H\·C_{\mathrm{AB}}\·v_A$

$=C_{\mathrm{AB}}\·(I-R_A\·R_A^H)\·v_A$

$=C_{\mathrm{AB}}\·(I-S_A\·S_A^H)\·v_A$

$=C_{\mathrm{AB}}\·w_A$

From above formula, if try to achieve Matrix C _aB, the Wave beam forming weighted vector of B submatrix can by Matrix C _aBdirectly be multiplied with the Wave beam forming weighted vector of A submatrix and obtain, C _aBbe the weights transformation matrix between B submatrix and A submatrix, C _aBconcrete form such as formula shown in [73].

From above-mentioned proof procedure, if tried to achieve the Wave beam forming weighted vector of a submatrix of Central Symmetry array, the Wave beam forming weighted vector of other three submatrixs of computing center's symmetric array, can according to the geometric relationship between submatrix, obtain other three submatrixs respectively and ask the weights transformation matrix between submatrix, being followed by each weights transformation matrix asks the Wave beam forming weighted vector of submatrix to be directly multiplied again, obtain the Wave beam forming weighted vector of these three submatrixs, namely the inventive method is rational in theory.

3. operand analysis

Operand of the present invention can be illustrated by the multiplication number of times comprised and addition number of times, and suppose that each submatrix of four submatrixs of array used in the present invention includes M array element, its operand is analyzed as follows:

(3.1) the inventive method adds than classic method the weights transformation matrix calculating weights transformation matrix corresponding to three submatrixs, three submatrixs respectively corresponding and is multiplied with asking the Wave beam forming weighted vector of submatrix respectively, analyzes the operand of these two calculating processes of increase below respectively:

(3.1a) the weights transformation matrix calculating submatrix corresponding comprises 3M multiplication and 2M (M-1) sub-addition, and the weights transformation matrix therefore calculating three submatrixs respectively corresponding comprises 33M=9M multiplication and 32M (M-1)=6M altogether ²-6M sub-addition;

(3.1b) the weights transformation matrix that submatrix is corresponding with ask the Wave beam forming weighted vector of submatrix to be multiplied to comprise 4M multiplication and 2M sub-addition, the weights transformation matrix that therefore three submatrixs are corresponding respectively with ask the Wave beam forming weighted vector of submatrix to be multiplied to comprise 34M=12M multiplication and 32M=6M sub-addition altogether.

According to the analysis of (3.1), the operand that the inventive method increases than classic method altogether: 21M multiplication and 6M ²sub-addition.

(3.2) the inventive method than classic method decrease respectively calculate three submatrixs sample covariance matrix, respectively to the sample covariance matrix of three submatrixs carry out Eigenvalues Decomposition, respectively calculate three submatrixs interference space matrix, respectively calculate the orthogonal complement space matrix of interference space of three submatrixs, the interference space of each submatrix of three submatrixs orthogonal complement space matrix be multiplied with the steering vector of this submatrix, analyze the operand of these five calculating processes of minimizing below respectively:

(3.2a) sample covariance matrix calculating a submatrix comprises 4NM ²+ 1 multiplication and 2NM ²+ N-1 sub-addition, the sample covariance matrix therefore calculating three submatrixs respectively comprises 3 (4NM altogether ²+ 1) secondary multiplication and 3 (2NM ²+ N-1) sub-addition;

(3.2b) due to the difference of the specific algorithm of Eigenvalue Decomposition, operand is also incomplete same, and the operand order of magnitude sample covariance matrix of a submatrix being carried out to Eigenvalues Decomposition is О (M ³), suppose to comprise M ³secondary multiplication and M ³sub-addition, therefore carries out Eigenvalues Decomposition to the sample covariance matrix of three submatrixs respectively and comprises 3M altogether ³secondary multiplication and 3M ³sub-addition;

(3.2c) the interference space matrix calculating a submatrix comprises 4M ²secondary multiplication and 2M ²sub-addition, the interference space matrix therefore calculating three submatrixs respectively comprises 34M altogether ²=12M ²secondary multiplication and 32M ²=6M ²sub-addition;

(3.2d) orthogonal complement space matrix calculating the interference space of a submatrix comprises the computing of M sub-addition, and the orthogonal complement space matrix therefore calculating the interference space of three submatrixs respectively comprises the computing of 3M sub-addition altogether;

(3.2e) orthogonal complement space matrix of the interference space of a submatrix is multiplied with the steering vector of this submatrix and comprises 4M ²secondary multiplication and 2M ²+ 2M (M-1) sub-addition, therefore the orthogonal complement space matrix of the interference space of each submatrix of three submatrixs is multiplied with the steering vector of this submatrix and comprises 34M altogether ²=12M ²secondary multiplication and 3 (2M ²+ 2M (M-1))=12M ²-6M sub-addition.

According to the analysis of (3.2), the operand that the inventive method reduces than classic method altogether: 3M ³+ 12 (N+2) M ²+ 3 multiplication and 3M ³+ 6 (N+3) M ²+ 3 (N-M-1) sub-addition.

To sum up (3.1) and (3.2) are to computing quantitative analysis, the operand that the inventive method increases than classic method is negligible relative to the operand reduced, again because classic method needs to utilize sampled data to calculate the Wave beam forming weighted vector of four submatrixs respectively, and the inventive method only needs to utilize sampled data to calculate the Wave beam forming weighted vector of a submatrix, the operand of self-adaptive numerical integration algorithm be in the process of the present invention about 1/4 of the operand of the self-adaptive numerical integration algorithm of classic method.It can thus be appreciated that the inventive method significantly reduces the operand of self-adaptive numerical integration algorithm.

Claims (3)

1., based on an interference angle-measuring method for the self-adaptive numerical integration algorithm improved, comprise the steps:

(1) by centrosymmetric array partition be four submatrix U, D, L, R up and down, contained by each submatrix, array number is identical;

(2) the Wave beam forming weighted vector of any one submatrix is calculated;

(3) the Wave beam forming weighted vector of other three submatrixs is calculated:

(3a) according to the geometric relationship between submatrix, the weights transformation matrix between other three submatrixs and the submatrix selected by step (2) is calculated respectively:

(3a1) remember that the submatrix selected by step (2) is submatrix 1, other three submatrixs are respectively submatrix 2,3,4, and establish four submatrixs all to comprise M array element, and the array element coordinate of submatrix 1 is respectively p ₁₁, p ₁₂..., p _1M, the array element coordinate of submatrix 2 is respectively p ₂₁, p ₂₂..., p _2M, the array element coordinate of submatrix 3 is respectively p ₃₁, p ₃₂..., p _3M, the array element coordinate of submatrix 4 is respectively p ₄₁, p ₄₂..., p _4M;

(3a2) coordinate difference between each array element of submatrix 2 and the corresponding array element of submatrix 1 is calculated:

Δp _1i,2i＝p _2i-p _1i；

Wherein i=1,2 ..., M, then calculate the weights transformation matrix between submatrix 2 and submatrix 1:

Wherein k is the wave-number vector of beam position, and T represents transposition, and j is imaginary unit;

(3a3) coordinate difference between each array element of submatrix 3 and the corresponding array element of submatrix 1 is calculated:

Δp _1i,3i＝p _3i-p _1i；

Calculate the weights transformation matrix between submatrix 3 and submatrix 1 again:

(3a4) coordinate difference between each array element of submatrix 4 and the corresponding array element of submatrix 1 is calculated:

Δp _1i,4i＝p _4i-p _1i；

Calculate the weights transformation matrix between submatrix 4 and submatrix 1 again:

(3b) be multiplied with the Wave beam forming weighted vector of the submatrix selected by step (2) by the weights transformation matrix that each submatrix in these three submatrixs is corresponding, obtain the Wave beam forming weighted vector of each submatrix in these three submatrixs;

(4) respectively the sampled data of each submatrix is up and down weighted, and the output data after each submatrix weighting is directly added by same distance door, obtain wave beam strengthen after a circuit-switched data;

(5) maximizing in the individual pulse data of Hou mono-road is strengthened at wave beam, the range gate that record maximal value is corresponding, output valve y after the weighting of each up and down submatrix before the wave beam then finding this range gate corresponding respectively strengthens _u, y _d, y _land y _r, substitute into following interferometric method angle measurement formula and obtain angle measurement result, i.e. the angle of pitch with position angle

Wherein, arcsin () represents arcsin function, and phase angle function is got in phase () expression, represent that pitching points to slope to normal, represent that slope is pointed to normal, L in orientation _ywith L _xrepresent the distance of displaced phase center to true origin of upper submatrix U and right submatrix R respectively, θ _bwith represent the angle of pitch and the position angle of beam position respectively.

2., by method according to claim 1, it is characterized in that the Wave beam forming weighted vector of any one submatrix of calculating described in step (2), carry out as follows:

(2a) N snap sampling is carried out to selected submatrix, forms sampled data matrix X, according to this matrix X calculating sampling covariance matrix S:

S＝X·X ^H/N，

Wherein, H represents conjugate transpose;

(2b) Eigenvalues Decomposition is carried out to sample covariance matrix S, obtain

S＝QΛQ ^H，

Wherein, Q=[v ₁, v ₂..., v _m] be by the m of a sample covariance matrix S proper vector v _ithe matrix formed, Λ is by the m of a sample covariance matrix S eigenvalue λ _ithe diagonal matrix formed, m is the dimension of sample covariance matrix S, i=1,2 ..., m;

(2c) according to the type of interference, m the eigenwert { λ of intensity and these prior imformations of number and sample covariance matrix S ₁, λ ₂..., λ _mbetween magnitude relationship, at m the proper vector { v of sample covariance matrix S ₁, v ₂..., v _min select and form r eigenvector { v of interference space ₁, v ₂..., v _r, 1≤r≤m;

(2d) according to r eigenvector { v of the formation interference space selected ₁, v ₂..., v _r, calculating interference space matrix J is:

$J=\underset{i=1}{\overset{r}{\mathrm{\Σ}}}{v}_i\·v_i^H;$

(2e) according to the interference space matrix J of trying to achieve, the orthogonal complement space matrix J of interference space is calculated ^⊥for:

J ^⊥＝I-J，

Wherein, I is the unit matrix with interference space matrix J same dimension;

(2f) according to the array element coordinate of selected submatrix, p is set to ₁, p ₂..., p _m, and the wave-number vector k that beam position is corresponding, calculate the steering vector a of selected submatrix ₁for:

$a_1={\left[\begin{array}{cccc}{e}^{-j{k}^T{p}_1}& e^{-j{k}^T{p}_2}& ...& e^{-j{k}^T{p}_m}\end{array}\right]}^T,$

Wherein m is element number of array, identical with the dimension of sample covariance matrix S;

(2g) according to the orthogonal complement space matrix J of the interference space of trying to achieve ^⊥with steering vector a ₁, calculate the Wave beam forming weighted vector w of selected submatrix ₁for:

w ₁＝J ^⊥·a ₁。

3. by method according to claim 1, it is characterized in that the respectively sampled data of each submatrix is up and down weighted described in step (4), be multiplied with the sampled data of each submatrix again after respectively the Wave beam forming weighted vector that each submatrix is tried to achieve being got conjugate transpose, namely

$\left\{\begin{array}{c}{\mathrm{Data}}_{\mathrm{up}\_\mathrm{out}}=w_{\mathrm{up}}^H\·{\mathrm{Data}}_{\mathrm{up}\_\mathrm{in}}\\ {\mathrm{Data}}_{\mathrm{down}\_\mathrm{out}}=w_{\mathrm{down}}^H\·{\mathrm{Data}}_{\mathrm{down}\_\mathrm{in}}\\ {\mathrm{Data}}_{\mathrm{left}\_\mathrm{out}}=w_{\mathrm{left}}^H\·{\mathrm{Data}}_{\mathrm{left}\_\mathrm{in}}\\ {\mathrm{Data}}_{\mathrm{right}\_\mathrm{out}}=w_{\mathrm{right}}^H\·{\mathrm{Data}}_{\mathrm{right}\_\mathrm{in}}\end{array}\right.,$

Wherein Data _{up_in}, Data _{down_in}, Data _{left_in}, Data _{right_in}the sampled data of each submatrix up and down respectively, w _up, w _down, w _left, w _rightthe Wave beam forming weighted vector of each submatrix up and down respectively, Data _{up_out}, Data _{down_out}, Data _{left_out}, Data _{right_out}the output data after each submatrix weighting up and down respectively.