CN105372640A - Multilayer plane wave decomposition-based one-dimensional single-station RCS (radar cross section) near-to-far field transformation method - Google Patents

Abstract

The invention relates to a multilayer plane wave decomposition-based one-dimensional single-station RCS (radar cross section) near-to-far field transformation method. The method includes the following steps that: multilayer planar waves for a target scattering near field are expanded according to the addition theorem, and the expanded multilayer planar waves are written into the integral of a transfer operator and a target reflectance pattern function on a unit angular spectrum sphere; and surface integral is simplified into circulation integral according to the flat body characteristics of a target, and the transfer operator is truncated according to precision required to be achieved by the algorithm, and matrix inversion is carried out through using a conjugate gradient method capable of rapid convergence. According to the method of the invention, near-field one-dimensional single-station scattering data are converted into far-field scattering data through a multilayer plane wave decomposition fast algorithm, and therefore, non-margin sampling can be realized. The method of the invention has the advantages of fast near-to-far field transformation, automatic antenna pattern compensation, automatic sampling position compensation and controllability in error, and can guide near-field sampling setting. The multilayer plane wave decomposition-based one-dimensional single-station RCS (radar cross section) near-to-far field transformation method is a fast and convenient method for obtaining a target RCS (radar cross section).

Description

Based on the one dimension mono-static RCS far to field transformation method of multilayer planar Wave Decomposition

Technical field

Involved in the present invention is Electromagnetic Scattering of Target and back scattering field, particularly relates to the one dimension mono-static RCS far to field transformation method of electromagnetic scattering.

Background technology

Target RCS test demand fulfillment far field condition, method comparatively ripe at present has the flat field test of ground, far field and Compact Range test.But test for Electrically large size object RCS, ground, far field flat field needs huge test site support, and Compact Range needs expensive reflecting surface Facilities Construction.The RCS near-field test technology that development in recent years is active, tests in the near field not meeting far field condition, then obtains target RCS by far to field transformation, have cheap feature easily.Far to field transformation method is the key of above-mentioned near-field test.

In the document that the open both at home and abroad and limited range retrieved is delivered, there are paper and patent (CN201410432104) introduction based on the far to field transformation method of Near-Field Radar Imaging, have no the far to field transformation method based on multilayer planar Wave Decomposition.Separately have external paper multilayer planar Wave Decomposition far to field transformation method, but the method can not be used for one dimension mono-static RCS far to field transformation.In sum, the unexposed one dimension mono-static RCS far to field transformation method based on multilayer planar Wave Decomposition of prior art.

Summary of the invention

The object of the invention is to propose a kind of one dimension mono-static RCS far to field transformation method based on multilayer planar Wave Decomposition, reach the sampling of non-surplus, features such as there is quick far to field transformation, automatic antenna directional diagram compensates, sampling location compensates automatically, error is controlled, near field can be instructed to sample arrange, thus provide one method quickly and easily for obtaining target RCS (RCS).

The invention provides a kind of one dimension mono-static RCS far to field transformation method based on multilayer planar Wave Decomposition, it comprises:

Step 1: determine near-far scatter data sample plane, be the center of circle on this plane with target's center, in nearest radius and the determined annulus of outermost radius, use any antenna to sample in the optional position of this annulus, record antenna receiver voltage and the sampling point position of each sampled point;

Step 2: based on the multilayer planar Wave Decomposition formula of near-field scattering, namely according to the precision that parameter and the system of near field sampled data will reach, accounting equation constant coefficient and matrix size;

Step 3: calculate gained matrix size according to step 2, by the spectrum of plane waves uniform discrete on unit circumference, fills near field transition matrix element one by one, completes the foundation of matrix equation;

Step 4: with the method for conjugate gradient solution matrix equation of steepest descent, obtain target reflectivity directional diagram when iteration convergence;

Step 5: obtain target RCS according to the relation between RCS and target reflectivity directional diagram.

One dimension list station, near field scattering data, by a kind of multilayer planar Wave Decomposition fast algorithm, is converted to Far Field Scattering data by the present invention, thus obtains target RCS.Known based on preferred embodiment, one dimension mono-static RCS far to field transformation method based on multilayer planar Wave Decomposition of the present invention, according to addition theorem by target scattering near field multilayer planar wave spread, write as transition operator and the integration of target reflectivity pattern function on unit angular spectrum ball; According to target bluff body feature, surface integral is reduced to circulation integral, blocks transition operator according to the precision reached required for algorithm, and use and the method for conjugate gradient of Fast Convergent can carry out matrix inversion.

The present invention brings following beneficial effect:

The present invention proposes a kind of far to field transformation algorithm carrying out the sampling of near field, one dimension list station in the horizontal plane, it is consistent that its advantage is that near field hits and pattern block exponent number, reach the sampling of non-surplus, and with the precision that algorithm will reach, there is clear and definite relation, make error controlled; The impact that antenna radiation pattern and sampling location cause has been it often fully compensated in iteration inversion process, make can select any antenna during near-field test, can planar random site sampling, avoid the use of the positioning equipment such as turntable or scanning support, very big abbreviation near field test system.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the one dimension mono-static RCS far to field transformation algorithm based on multilayer planar Wave Decomposition in the present invention.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment of the present invention is described.

Be illustrated in figure 1 the one dimension mono-static RCS far to field transformation algorithm flow chart based on multilayer planar Wave Decomposition in the present invention.Computing method principle of the present invention is as follows:

Based on single order Born, approximate and setting of singly standing, sets up the radiation reflective model of incident field and scattered field; According to the bluff body feature of addition theorem and target, by above-mentioned radiation reflective model multilayer planar wave spread, convert the integration of spectrum of plane waves on unit circumference to; Use method of conjugate gradient to carry out matrix equation to solve.

Calculating concrete steps are as follows:

Step 1: determine near-far scatter data sample plane, be the center of circle on this plane with target's center, recently and in the determined annulus of outermost radius, use any antenna to sample in the optional position of this annulus, record antenna receiver voltage and the sampling point position of each sampled point; If sampling number is M.

Step 2: based on the multilayer planar Wave Decomposition formula of near-field scattering, namely according to the precision that parameters and the system of near field sampled data will reach, accounting equation constant coefficient and matrix size; The multilayer planar Wave Decomposition formula of near-field scattering is:

for incident wave vector, k and be wave number and wave vector direction respectively, Z is the wave impedance in free space, U _iincident voltage, sampling point position, t _ltransition operator, η _sbe the factor irrelevant with distance, expression formula is

${\mathrm{\η}}_s\left(\stackrel{\→}{k}\right)=W\left(\hat{k}\right)S\left(2\stackrel{\→}{k}\right)W\left(\hat{k}\right)---\left(9\right)$

antenna radiation pattern, the function relevant with target.

The coefficient of calculating formula (8) is needed at pretreatment stage with one dimension circulation integral integration to count K _l

K _L＝2(L+1)(10)

L is transition operator T _lblock exponent number, it chooses the following condition of demand fulfillment

L＝kd+αlog(π+kd)(11)

D is the distance of test antenna and target, and α=-log ε, ε is the precision that algorithm will reach.Integrating step 1, the size obtaining transition operator matrix is M × K _l.

Step 3: calculate gained matrix size according to step 2, by the spectrum of plane waves uniform discrete on unit circumference, fills near field transition operator matrix element one by one, completes the foundation of matrix equation; Described matrix equation is the discrete form of formula (8)

$U_{M\×1}=-\frac{k^2{Z}^2{U}_i}{4^2{\mathrm{\π}}^2}{C}_{M\×K_L}\·H_{K_L\×1}---\left(12\right)$

The size of subscript representing matrix.The element of transition operator Matrix C is

$\frac{T_L(2{\stackrel{\→}{k}}_l,{\stackrel{\→}{r}}_m)}{\left|{\stackrel{\→}{r}}_m\right|}=-\frac{jk}{4{\mathrm{\πr}}_m}{\Σ}_{l=1}^{K_l}{(-j)}^l(2l+1)h_l^{\left(2\right)}\left(2k_l{r}_m\right)P_l({\hat{k}}_l\·{\hat{r}}_m)---\left(13\right)$

equations of The Second Kind ball Hankel function, it is Legendre polynomial.

Step 4: with steepest descent method of conjugate gradient solution matrix equation (12), obtain the H matrix comprising target reflectivity directional diagram when iteration convergence;

Step 5: obtain target RCS according to the relation between RCS and target reflectivity directional diagram.

$\mathrm{\σ}=\underset{r_A\→\mathrm{\∞}}{\lim }4{{\mathrm{\πr}}_A}^2\frac{|U_m{|}^2}{|U_i{|}^2}=\frac{k^2{Z}^2}{4\mathrm{\π}}|{\mathrm{\η}}_s\left(\stackrel{\→}{k}\right){|}^2---\left(14\right)$

In sum, radiating scattering model is set up based on single order Born is approximate with list station setting in the present invention, use addition theorem that near-field scattering is used multilayer planar Wave Decomposition, and for bluff body target, the plane wave integration in unit sphere has been tapered on unit circumference, achieve the lower quick far to field transformation method of one dimension mono-static RCS of any antenna optional position non-surplus sampling, solve and carry out cheap convenient test in target scattering near field and the needs obtaining the controlled RCS of error.

Although content of the present invention has done detailed introduction by above preferred embodiment, will be appreciated that above-mentioned description should not be considered to limitation of the present invention.After those skilled in the art have read foregoing, for multiple amendment of the present invention and substitute will be all apparent.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (4)

1., based on an one dimension mono-static RCS far to field transformation method for multilayer planar Wave Decomposition, it is characterized in that,

Described conversion method, comprises:

Step 1: determine near-far scatter data sample plane, be the center of circle on this plane with target's center, in nearest radius and the determined annulus of outermost radius, use any antenna to sample in the optional position of this annulus, record antenna receiver voltage and the sampling point position of each sampled point;

Step 2: based on the multilayer planar Wave Decomposition formula of near-field scattering, namely according to the precision that parameter and the system of near field sampled data will reach, accounting equation constant coefficient and matrix size;

Step 3: calculate gained matrix size according to step 2, by the spectrum of plane waves uniform discrete on unit circumference, fills near field transition matrix element one by one, completes the foundation of matrix equation;

Step 4: with the method for conjugate gradient solution matrix equation of steepest descent, obtain target reflectivity directional diagram when iteration convergence;

Step 5: obtain target RCS according to the relation between RCS and target reflectivity directional diagram.

2. conversion method as claimed in claim 1, is characterized in that,

Sampling number in step 1 is M;

In step 2, the multilayer planar Wave Decomposition formula of near-field scattering is:

Wherein, for incident wave vector, k and be wave number and wave vector direction respectively, Z is the wave impedance in free space, U _iincident voltage, sampling point position, t _ltransition operator, η _sbe the factor irrelevant with distance, expression formula is

${\mathrm{\η}}_s\left(\stackrel{\→}{k}\right)=W\left(\hat{k}\right)S\left(2\stackrel{\→}{k}\right)W\left(\hat{k}\right)---\left(2\right)$

antenna radiation pattern, the function relevant with target;

The coefficient of calculating formula (1) is needed at pretreatment stage with one dimension circulation integral integration to count K _l

K _L＝2(L+1)(3)

L is transition operator T _lblock exponent number, it chooses the following condition of demand fulfillment

L＝kd+αlog(π+kd)(4)

D is the distance of test antenna and target, and α=-log ε, ε is the precision that algorithm will reach;

Integrating step 1, the size obtaining transition operator matrix is M × K _l.

3. conversion method as claimed in claim 2, is characterized in that,

The matrix equation set up in step 3 is the discrete form of formula (1)

$U_{M\×1}=-\frac{k^2{Z}^2{U}_i}{4^2{\mathrm{\π}}^2}{C}_{M\×K_L}\·H_{K_L\×1}---\left(5\right)$

The size of subscript representing matrix; The element of transition operator Matrix C is

$\frac{T_L(2{\stackrel{\→}{k}}_l,{\stackrel{\→}{r}}_m)}{\left|{\stackrel{\→}{r}}_m\right|}=-\frac{jk}{4{\mathrm{\πr}}_m}{\mathrm{\Σ}}_{l=1}^{K_l}{(-j)}^l(2l+1)h_l^{\left(2\right)}\left(2k_l{r}_m\right)P_l({\hat{k}}_l\·{\hat{r}}_m)---\left(6\right)$

equations of The Second Kind ball Hankel function, it is Legendre polynomial.

4. conversion method as claimed in claim 3, is characterized in that,

With steepest descent method of conjugate gradient solution matrix equation (5) in step 4, obtain the H matrix comprising target reflectivity directional diagram when iteration convergence;

Step 5: obtain target RCS according to the relation between RCS and target reflectivity directional diagram:

$\mathrm{\σ}=\underset{r_A\→\mathrm{\∞}}{\lim }4{{\mathrm{\πr}}_A}^2\frac{|U_m{|}^2}{|U_i{|}^2}=\frac{k^2{Z}^2}{4\mathrm{\π}}|{\mathrm{\η}}_s\left(\stackrel{\→}{k}\right){|}^2---\left(7\right).$