CN105928448A - Insect dimension measurement method based on Rayleigh region analysis scattering modeling - Google Patents

Abstract

The invention discloses an insect dimension measurement method based on Rayleigh region analysis scattering modeling, and the method comprises the steps: carrying out the Rayleigh region scattering modeling of an insect through employing a rotational symmetry dielectric ellipsoid; measuring the three-dimensional axon direction, body length and width of the insect through at least two radars, thereby achieving the further inversion of the mass and the body length to body width ratio of the insect. Compared with a conventional insect radar dimension inversion method, the method can greatly increase the amount of obtained information, so the method can improve the insect type recognition capability of the insect radars.

Description

A kind of insecticide dimension measurement method resolving scattering modeling based on Rayleigh region

Technical field

The invention belongs to entomological radar technical field, be specifically related to a kind of insecticide chi resolving scattering modeling based on Rayleigh region Very little measuring method.

Background technology

Entomological radar is by launching the insecticide that a branch of electromagnetic wave directive migrates in the air, and insect body (has similar to raindrop Character) can cause electromagnetic signal to surrounding reflect, partially reflective signal returns to radar and is received by radar in direction, utilizes thunder The direction finding and ranging character reached, can calculate insect communities orientation, highly, the parameter such as moving direction and density, for obtaining Behavioristics's parameter of insecticide high-altitude flight provides brand-new research means, has promoted Migrating Insects by qualitative investigation to quantitatively The great-leap-forward development analyzed, fly way and immigration pattern to insecticide have had new knowledge, have expanded Migrating Insects research neck The breadth and depth in territory.The U.S., Australia and Britain have been owned by the entomological radar system of oneself at present, and China is also on mountain The many places such as east, Henan, Liaoning are configured with entomological radar system.

Tradition entomological radar is limited by factors such as working system, systemic-function, algorithm and indexs, it is impossible to accurately obtain elder brother Worm biological parameter.The entomological radar scattering resonance state being typically only capable to obtain radar surveying is compared with empirical value, thus pushes away Calculate the quality of insecticide, and further according to quality inverting build or classify.Even if owing to insecticide kind is identical, individual body constitution Amount difference is the most obvious, therefore carries out classification only by quality and there is bigger ambiguity, can only be to insecticide in big class Make a distinction.In addition to quality, the actually size of insecticide also includes body long body width ratio, and this there is also between different types of insecticide Notable difference, if body long body width ratio and the quality of insecticide can be recorded simultaneously, then can be greatly improved entomological radar to insecticide kind The precision of class identification.

Summary of the invention

In view of this, it is an object of the invention to provide a kind of insecticide dimensional measurement side resolving scattering modeling based on Rayleigh region Method, it is possible to use rotationally symmetrical dielectric ellipsoid carries out Rayleigh region scattering modeling to insecticide, and records insecticide by least 2 radars Said three-dimensional body axle point to, the biological parameter such as body length and body width, significant to entomological radar target recognition and classification.

A kind of insecticide dimension measurement method resolving scattering modeling based on Rayleigh region, comprises the steps:

Step one, at least 2 radars of employing, observe insecticide, it is thus achieved that the said three-dimensional body axle of insecticide points to from different perspectives:

I-th radar observation to insecticide Complete polarimetry matrix be:

$S_i=\left[\begin{array}{cc}{S}_{hh}^i& S_{hv}^i\\ S_{vh}^i& S_{vv}^i\end{array}\right]---\left(4\right)$

Wherein, i=1,2 ..., M, M represent the quantity of radar；For horizontal polarized components,For perpendicular polarisation components,WithFor cross polar component；

Rotationally symmetrical body insecticide is hadThen insect bodies axial projection and the folder of i-th radar horizon polarised direction Angle α_iIt is given by:

${\mathrm{\α}}_i=\frac{1}{2}arctan\[\frac{2\left|S_{vh}^i\right|\left(\right|S_{hh}^i|{\mathrm{cos\γ}}_i+|S_{vv}^i\left|cos\right({\mathrm{\γ}}_i-{\mathrm{\ψ}}_i))}{|S_{hh}^i-S_{vv}^i|}\]---\left(5\right)$

Wherein γ_iRepresentWithBetween phase contrast, ψ_iRepresentWithBetween phase contrast；

The unit direction vector of the intersecting lens of the vertical plane of insect bodies axle and polarization radar planeIt is written as:

${\hat{d}}_i={\hat{h}}_i{\mathrm{sin\α}}_i-{\hat{v}}_i{\mathrm{cos\α}}_i---\left(6\right)$

Wherein,Represent radar horizon polarised direction vector,Represent radar vertical polarization directions vector；

Then insect bodies axle unit direction vectorInversion formula be:

$\hat{e}=e_x\hat{x}+e_y\hat{y}+e_z\hat{z}=\frac{1}{M}\underset{i,j=1,...,M,i\≠j}{\Σ}{\hat{d}}_i\×{\hat{d}}_j---\left(7\right)$

Wherein,WithRepresent the unit vector along each coordinate axes, e under overall situation rectangular coordinate system respectively_x、e_yAnd e_z Represent respectivelyThe size of projection components on each coordinate axes, "×" represents trivector multiplication cross computing；

The azimuth that then insect bodies axle points toPitching angle theta is expressed as:

$\mathrm{\θ}={\cos }^{-1}\left(\frac{e_z}{\sqrt{e_x^2+e_z^2+e_z^2}}\right)---\left(8\right)$

Step 2, it is thus achieved that insect bodies length and the ratio of body width:

Try to achieve the angle theta of the insect bodies axle under i-th radar local coordinate system and this radar line of sight_i:

${\mathrm{\θ}}_i=arccos(\hat{e}\·({\hat{h}}_i\×{\hat{v}}_i\left)\right)---\left(9\right)$

Then radar maximum reception polarization intensity is:

$S_{\max i}=\frac{1}{2}\left(\right|S_{hh}^i+S_{vv}^i|+\sqrt{|S_{hh}^i-S_{vv}^i{|}^2+4|S_{vh}^i|})---\left(10\right)$

The reception polarization strength S that then measurement of M portion radar obtains_max1,S_max2,...,S_maxMIt is expressed as:

$\left[\begin{array}{c}{S}_{\max 1}\\ S_{\max 2}\\ S_{\max 3}\\ \mathrm{...}\\ S_{\max M}\end{array}\right]=\left[\begin{array}{c}\begin{array}{cc}{\sin }^2{\mathrm{\θ}}_1& {\cos }^2{\mathrm{\θ}}_1\end{array}\\ \begin{array}{cc}{\sin }^2{\mathrm{\θ}}_2& {\cos }^2{\mathrm{\θ}}_2\end{array}\\ \begin{array}{cc}{\sin }^2{\mathrm{\θ}}_3& {\cos }^2{\mathrm{\θ}}_3\end{array}\\ \mathrm{...........}\\ \begin{array}{cc}{\sin }^2{\mathrm{\θ}}_M& {\cos }^2{\mathrm{\θ}}_M\end{array}\end{array}\right]\left[\begin{array}{c}{C}_1\\ C_2\end{array}\right]---\left(11\right)$

Wherein,

K=2 π/λ represents wave number, and λ is wavelength, ε_rIt is the multiple relative dielectric constant of insect body, V=4 π/3 ab²For elder brother Polypide amasss, and a is the half of insect bodies length, and b is the half that insect bodies is wide, L₁,L₂It it is the ginseng determined by the ratio of insect bodies length with body width Number, is expressed as:

$g=\sqrt{1-{(a/b)}^{-2}}$

$L_1=\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})---\left(12\right)$

$L_2=\frac{1}{2g^2}(2g^2-1+\frac{1-g^2}{2g}ln\frac{1+g}{1-g})$

(11) formula is carried out Matrix Calculating pseudoinverse and then solves C₁,C₂, again due to L₂=(1-L₁)/2, based on (12) formula by L₁Solve Go out:

$L_1=\frac{1+({\mathrm{\ϵ}}_r-1)/2-C_1/C_2}{(C_1/C_2+1/2)({\mathrm{\ϵ}}_r-1)}---\left(12\right)$

Wherein L₁Uniquely determined by b/a；

By θ_i(11) and (12) formula of substitution, obtains the ratio a/b of insect bodies length and body width:

$a/b=\frac{1}{1.7327L_1^2+2.1478L_1+0.0755}---\left(13\right)$

Step 3, it is thus achieved that insect bodies length, body width, volume and quality:

By ratio a/b substitution (2) formula of insect bodies length and body width:

$S_{\max i}=\frac{k^{2}V}{\sqrt{4\mathrm{\π}}}\{({\mathrm{\ϵ}}_r-1)\[\frac{{\sin }^2{\mathrm{\θ}}_i}{1+L_1({\mathrm{\ϵ}}_r-1)}+\frac{{\cos }^2{\mathrm{\θ}}_i}{1+L_2({\mathrm{\ϵ}}_r-1)}\]\}---\left(2\right)$

Then obtain insecticide volume:

$V=S_{max}\frac{\sqrt{4\mathrm{\π}}}{k^2}\frac{\frac{{\mathrm{\ϵ}}_r+1}{{\mathrm{\ϵ}}_r-1}+{\mathrm{\ϵ}}_r\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\]+({\mathrm{\ϵ}}_r-1){\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\]}^2}{2+({\mathrm{\ϵ}}_r-1){\sin }^2{\mathrm{\θ}}_i+({\mathrm{\ϵ}}_r-1)\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\](2{\cos }^2{\mathrm{\θ}}_i-{\sin }^2{\mathrm{\θ}}_i)}---\left(14\right)$

The long 2a of insect bodies and body width 2b is calculated by following formula respectively:

$2b={\[\frac{3V}{2\mathrm{\π}}{\left(\frac{a}{b}\right)}^{-1}\]}^{1/3}---\left(15\right)$

$2a=2b\left(\frac{a}{b}\right)$

Insect density ρ is measured by experiment and obtains, and its quality m is:

M=ρ V (16).

There is advantages that

A kind of insecticide dimension measurement method resolving scattering modeling based on Rayleigh region of the present invention, the method can be surveyed simultaneously The said three-dimensional body axle of insecticide point to, body length and body width, based on this can the quality of inverting insecticide and body long body width ratio further, this Method can be obtained with quantity of information and is greatly increased compared with traditional entomological radar size inversion method, therefore also enhances insecticide The radar ability to caste identification.

Accompanying drawing explanation

Fig. 1 is three entomological radar multi-angle observation geometric representation.

Fig. 2 is that list portion radar is to insecticide observation model.

Fig. 3 is radar observation insect body scattering strength figure.

Fig. 4 is three radar multi-angle observation insecticide schematic vector diagram.

Fig. 5 is that complete polarization ratio of extreme values compares curve linear relationship with body axle.

Fig. 6 is insecticide target CST model.

Fig. 7 is emulation multi-angle observation insecticide geometrical relationship.

Fig. 8 is radar 1 multiband polarised direction figure comparative result.

Fig. 9 is radar 2 multiband polarised direction figure comparative result.

Figure 10 is radar 3 multiband polarised direction figure comparative result.

Detailed description of the invention

Develop simultaneously embodiment below in conjunction with the accompanying drawings, describes the present invention.

For typical case high-altitude Migrating Insects, such as planthopper (body length 2.7～3.5mm) and aphid (1.5～4.9mm), X and Ku The wavelength of wave band is more than five times of body length, it can be considered that its scattering is in Rayleigh region.With rotationally symmetrical dielectric ellipsoid mould Insecticide is modeled by type, and based on rotationally symmetrical dielectric ellipsoid model the scattering formula of Rayleigh region carry out towards with size inverting.

Insecticide observed from different perspectives by three radars, as shown in Figure 1.If insect bodies axle points to the side under global coordinate system Parallactic anglePitching angle theta, the unit direction vector of body axle is expressed as:

As in figure 2 it is shown, set insect bodies axle under the LOS coordinate system of i-th radar with radar line of sight direction vectorAngle For θ_i, insect bodies axle is in radar antenna polarization reception planeInterior projection and radar horizon polarised direction vector's Angle is α_i, radar vertical polarization directions vector representation is

Insecticide scattering is simulated at the scattering model of Rayleigh region with rotationally symmetrical dielectric ellipsoid.According to this model, single During portion's radar observation flying insect, radar receives insect bodies scattering strength to be changed in dumbbell shape curve with polarization radar, such as Fig. 3 Shown in.The maximum polarised direction that receives is along insect bodies axle projecting direction in polarization plane, and the minimum polarised direction that receives is perpendicular to Body axle projecting direction in polarization plane.

To i-th radar, its maximum polarization intensity that receives is:

$S_{\max i}=\frac{k^{2}V}{\sqrt{4\mathrm{\π}}}\{({\mathrm{\ϵ}}_r-1)\[\frac{{\sin }^2{\mathrm{\θ}}_i}{1+L_1({\mathrm{\ϵ}}_r-1)}+\frac{{\cos }^2{\mathrm{\θ}}_i}{1+L_2({\mathrm{\ϵ}}_r-1)}\]\}---\left(2\right)$

Wherein k=2 π/λ represents wave number, and λ is wavelength, ε_rIt is the multiple relative dielectric constant of insect body (approximating with water), V =4 π/3 ab²For ellipsoid volume, a is ellipsoid semimajor axis length (i.e. the half of insect bodies length), and b is ellipsoid semi-minor axis length (half that i.e. insect bodies is wide), L₁,L₂It is the parameter only determined than a/b (i.e. insect bodies long body width ratio) by the short axle of ellipsoid major axis, It is expressed as:

$g=\sqrt{1-{(a/b)}^{-2}}$

$L_1=\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})$

$L_2=\frac{1}{2g^2}(2g^2-1+\frac{1-g^2}{2g}ln\frac{1+g}{1-g})---\left(3\right)$

Therefore, the invention provides a kind of insecticide size inversion method resolving scattering modeling based on Rayleigh region, including such as Lower step.

Step one, uses at least 2 radars, observes insecticide from different perspectives, it is thus achieved that the said three-dimensional body axle of insecticide points to:

By Fig. 3 it is known that insect bodies axle overlaps with radar maximum polarization reception direction in polarization plane inner projection direction.And thunder Reaching maximum polarization reception direction can be by radar Complete polarimetry inverse matrix.

I-th radar observation to insecticide Complete polarimetry matrix be:

$S_i=\left[\begin{array}{cc}{S}_{hh}^i& S_{hv}^i\\ S_{vh}^i& S_{vv}^i\end{array}\right]---\left(4\right)$

For horizontal polarized components,For perpendicular polarisation components,WithFor cross polar component；

Rotationally symmetrical body insecticide is hadThen insect bodies axial projection and the angle α of radar horizon polarised direction_i It is given by:

${\mathrm{\α}}_i=\frac{1}{2}arctan\[\frac{2\left|S_{vh}^i\right|\left(\right|S_{hh}^i|{\mathrm{cos\γ}}_i+|S_{vv}^i\left|cos\right({\mathrm{\γ}}_i-{\mathrm{\ψ}}_i))}{|S_{hh}^i-S_{vv}^i|}\]---\left(5\right)$

Wherein γ_iRepresentWithBetween phase contrast, ψ_iRepresentWithBetween phase contrast.

Utilize space geometry relation, easily provide the unit side of the vertical plane of insect bodies axle and the intersecting lens of polarization radar plane To vectorIt is written as:

${\hat{d}}_i={\hat{h}}_i{\mathrm{sin\α}}_i-{\hat{v}}_i{\mathrm{cos\α}}_i---\left(6\right)$

According to vector multiplication cross rule, insect bodies axle unit direction vectorInversion formula be:

$\hat{e}=e_x\hat{x}+e_y\hat{y}+e_z\hat{z}=\frac{1}{M}\underset{i,j=1,...,M,i\≠j}{\Σ}{\hat{d}}_i\×{\hat{d}}_j---\left(7\right)$

Wherein,Represent the unit vector along each coordinate axes, e under overall situation rectangular coordinate system respectively_x、e_y、e_z Represent respectivelyThe size of projection components on each coordinate axes；M represents the quantity of radar, and "×" represents that trivector multiplication cross is transported Calculate, geometrical relationship such as Fig. 4.

The azimuth that then body axle points toPitching angle theta can be expressed as:

$\mathrm{\θ}={\cos }^{-1}\left(\frac{e_z}{\sqrt{e_x^2+e_z^2+e_z^2}}\right)---\left(8\right)$

Step 2, it is thus achieved that insect bodies length and the ratio of body width:

By three-dimensional obtain towards inverting insect bodies axle at global coordinate system under parameterAfter, can be in the hope of Insect bodies axle under i-th radar local coordinate system and the angle theta of this radar line of sight_i:

${\mathrm{\θ}}_i=arccos(\hat{e}\·(\hat{h}\×{\hat{v}}_i\left)\right)---\left(9\right)$

Assuming the polarization response matrix such as (4) formula that this radar Polarimetry obtains, rotationally symmetrical body insecticide hasThen radar maximum reception polarization intensity can be calculated as:

$S_{\max i}=\frac{1}{2}\left(\right|S_{hh}^i+S_{vv}^i|+\sqrt{|S_{hh}^i-S_{vv}^i{|}^2+4|S_{vh}^i|})---\left(10\right)$

The reception polarization strength S that the measurement of M portion radar obtains is understood according to (2) formula_max1,S_max2,...,S_maxMCan represent For:

$\left[\begin{array}{c}{S}_{\max 1}\\ S_{\max 2}\\ S_{\max 3}\\ \mathrm{...}\\ S_{\max M}\end{array}\right]=\left[\begin{array}{c}\begin{array}{cc}{\sin }^2{\mathrm{\θ}}_1& {\cos }^2{\mathrm{\θ}}_1\end{array}\\ \begin{array}{cc}{\sin }^2{\mathrm{\θ}}_2& {\cos }^2{\mathrm{\θ}}_2\end{array}\\ \begin{array}{cc}{\sin }^2{\mathrm{\θ}}_3& {\cos }^2{\mathrm{\θ}}_3\end{array}\\ \mathrm{...........}\\ \begin{array}{cc}{\sin }^2{\mathrm{\θ}}_M& {\cos }^2{\mathrm{\θ}}_M\end{array}\end{array}\right]\left[\begin{array}{c}{C}_1\\ C_2\end{array}\right]---\left(11\right)$

Wherein(11) formula is carried out Matrix Calculating pseudo- Against solving C₁,C₂, L again₂=(1-L₁)/2, so can solve L1 based on following formula:

$L_1=\frac{1+({\mathrm{\ϵ}}_r-1)/2-C_1/C_2}{(C_1/C_2+1/2)({\mathrm{\ϵ}}_r-1)}---\left(12\right)$

Wherein L₁Uniquely being determined by b/a, this functional relationship can approximate with quadratic function, as shown in (12) formula.By θ_iAs Knowing that parameter substitutes into (11) (12) formula, the ratio a/b of insect bodies length and body width can use L₁Quadratic function approximate inversion, to bent in Fig. 5 Line is:

$a/b=\frac{1}{1.7327L_1^2+2.1478L_1+0.0755}---\left(13\right)$

Step 3, it is thus achieved that insect bodies length, body width, volume and quality:

So a/b being substituted into (2) formula, insecticide volume V can be calculated by following formula:

$V=S_{max}\frac{\sqrt{4\mathrm{\π}}}{k^2}\frac{\frac{{\mathrm{\ϵ}}_r+1}{{\mathrm{\ϵ}}_r-1}+{\mathrm{\ϵ}}_r\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\]+({\mathrm{\ϵ}}_r-1){\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\]}^2}{2+({\mathrm{\ϵ}}_r-1){\sin }^2{\mathrm{\θ}}_i+({\mathrm{\ϵ}}_r-1)\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\](2{\cos }^2{\mathrm{\θ}}_i-{\sin }^2{\mathrm{\θ}}_i)}---\left(14\right)$

The long 2a of insect bodies and body width 2b can be calculated by following formula:

$2b={\[\frac{3V}{2\mathrm{\π}}{\left(\frac{a}{b}\right)}^{-1}\]}^{1/3}---\left(15\right)$

$2a=2b\left(\frac{a}{b}\right)$

Insect density ρ is measured by experiment and obtains, and its quality m can also be tried to achieve:

M=ρ V (16)

Embodiment:

CST simulation result is utilized to compare with theoretical formula method result, checking modeling accuracy and parametric inversion effect, Emulator is moment method.With rotationally symmetrical dielectric ellipsoid model, insecticide is modeled, the typical case a length of a of Migrating Insects (such as plant hopper) semiaxis =1.5mm, b=0.5mm, CST phantom is as shown in Figure 6.

Three radar fixs are respectively (500,0,0), (0,500,0), (-500,0,0), and insecticide coordinate is (100,100) 9,0 lists 0 are rice, and insect bodies axle is θ=60 ° towards the angular dimensions in global coordinate system,Geometrical relationship is illustrated such as Fig. 7.

Provide the complete polarization RCS directional diagram (red dotted line) of three radars of CST emulation and according to complete polarization RCS formula meter Complete polarization RCS directional diagram (blue solid lines) obtained compares, as shown in Fig. 8～Figure 10.

Use a kind of insecticide size inversion method resolving scattering modeling based on Rayleigh region of the present invention, complete this ginseng Insecticide size inverting emulation under several, idiographic flow is as follows:

Step one, carries out said three-dimensional body axle towards inverting according to polarization scattering matrix

Utilizing aforementioned dimensions inversion method, the Complete polarimetry data emulated by CST substitute into (5) formula and can calculate respectively To α₁=25.0372, α₂=42.3937, α₃=45.6855, unit is degree.By α₁,α₂,α₃(6) formula of substitution can solveBy d₁,d₂,d₃Substitute into (7) formula can solveWill(8) formula of substitution can solve θ=59.94,Unit is degree.

Step 2, by θ,(9) formula of substitution can solve θ₁=78.7399, θ₂=69.1841, θ₃= 29.7292, unit is degree；Can solve according to CST emulation data By θ₁,θ₂,θ₃ And S_max1,S_max2,S_max3(11) formula of substitution can solve C₁/C₂=4.7745-0.8806j；By C₁/C₂DIELECTRIC CONSTANT ε with water_r =49.942637-36.510517j substitutes into (12) formula can solve L₁=0.0808；By L₁(13) formula of substitution can solve proper length Body width compares a/b=3.8401.

Step 3, can solve insecticide volume V=1.3085 × 10 by a/b substitution (14) formula^-9m³, and then according to (15) formula Can solve proper a length of 3.32mm, a width of 0.86mm of body, it is assumed that insect density is worked as with aqueous phase, then the quality that inverting obtains is about 1.31mg。

Can be concluded that based on above-mentioned simulation result

Either CST simulation result or result of calculation, RCS maximum direction all overlaps with body direction of principal axis, and permissible Preferably the three-dimensional of invertomer axle towards and size.

Be can be seen that by simulation result and utilize this high efficiency based on parsing scattering modeling method and effectiveness.Utilize This method can realize the target size inverting of entomological radar.

In sum, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention. All within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included in the present invention's Within protection domain.

Claims (1)

1. the insecticide dimension measurement method resolving scattering modeling based on Rayleigh region, it is characterised in that comprise the steps:

Step one, at least 2 radars of employing, observe insecticide, it is thus achieved that the said three-dimensional body axle of insecticide points to from different perspectives:

I-th radar observation to insecticide Complete polarimetry matrix be:

$S_i=\left[\begin{array}{cc}{S}_{hh}^i& S_{hv}^i\\ S_{vh}^i& S_{vv}^i\end{array}\right]---\left(4\right)$

Wherein, i=1,2 ..., M, M represent the quantity of radar；For horizontal polarized components,For perpendicular polarisation components,WithFor cross polar component；

Rotationally symmetrical body insecticide is hadThen insect bodies axial projection and the angle α of i-th radar horizon polarised direction_i It is given by:

${\mathrm{\α}}_i=\frac{1}{2}\arctan \[\frac{2\left|S_{vh}^i\right|\left(\right|S_{hh}^i|{\mathrm{cos\γ}}_i+|S_{vv}^i\left|cos\right({\mathrm{\γ}}_i-{\mathrm{\ψ}}_i\left)\right)}{|S_{hh}^i-S_{vv}^i|}\]---\left(5\right)$

Wherein γ_iRepresentWithBetween phase contrast, ψ_iRepresentWithBetween phase contrast；

The unit direction vector of the intersecting lens of the vertical plane of insect bodies axle and polarization radar planeIt is written as:

${\hat{d}}_i={\hat{h}}_i{\mathrm{sin\α}}_i-{\hat{v}}_i{\mathrm{cos\α}}_i---\left(6\right)$

Wherein,Represent radar horizon polarised direction vector,Represent radar vertical polarization directions vector；

Then insect bodies axle unit direction vectorInversion formula be:

$\hat{e}=e_x\hat{x}+e_y\hat{y}+e_z\hat{z}=\frac{1}{M}\underset{i,j=1,...,M,i\≠j}{\Σ}{\hat{d}}_i\×{\hat{d}}_j---\left(7\right)$

Wherein,WithRepresent the unit vector along each coordinate axes, e under overall situation rectangular coordinate system respectively_x、e_yAnd e_zRespectively RepresentThe size of projection components on each coordinate axes, "×" represents trivector multiplication cross computing；

The azimuth that then insect bodies axle points toPitching angle theta is expressed as:

$\mathrm{\θ}={\cos }^{-1}\left(\frac{e_z}{\sqrt{e_x^2+e_z^2+e_z^2}}\right)---\left(8\right)$

Step 2, it is thus achieved that insect bodies length and the ratio of body width:

Try to achieve the angle theta of the insect bodies axle under i-th radar local coordinate system and this radar line of sight_i:

${\mathrm{\θ}}_i=\arccos (\hat{e}\·({\hat{h}}_i\×{\hat{v}}_i\left)\right)---\left(9\right)$

Then radar maximum reception polarization intensity is:

$S_{\max i}=\frac{1}{2}\left(\right|S_{hh}^i+S_{vv}^i|+\sqrt{|S_{hh}^i-S_{vv}^i{|}^2+4|S_{vh}^i|})---\left(10\right)$

The reception polarization strength S that then measurement of M portion radar obtains_max1,S_max2,...,S_maxMIt is expressed as:

Wherein,

K=2 π/λ represents wave number, and λ is wavelength, ε_rIt is the multiple relative dielectric constant of insect body, V=4 π/3 ab²For insect bodies Long-pending, a is the half of insect bodies length, and b is the half that insect bodies is wide, L₁,L₂It is the parameter determined by the ratio of insect bodies length with body width, It is expressed as:

$\begin{array}{c}g=\sqrt{1-{\left(a/b\right)}^{-2}}\\ L_1=\frac{1-g^2}{g^2}\left(-1+\frac{1}{2g}\ln \frac{1+g}{1-g}\right)\\ L_2=\frac{1}{2g^2}\left(2g^2-1+\frac{1-g^2}{2g}\ln \frac{1+g}{1-g}\right)\end{array}---\left(11\right),$

(11) formula is carried out Matrix Calculating pseudoinverse and then solves C₁,C₂, again due to L₂=(1-L₁)/2, based on (12) formula by L₁Solve:

$L_1=\frac{1+({\mathrm{\ϵ}}_r-1)/2-C_1/C_2}{(C_1/C_2+1/2)({\mathrm{\ϵ}}_r-1)}---\left(12\right)$

Wherein L₁Uniquely determined by b/a；

By θ_i(11) and (12) formula of substitution, obtains the ratio a/b of insect bodies length and body width:

$a/b=\frac{1}{1.7327L_1^2+2.1478L_1+0.0755}---\left(13\right)$

Step 3, it is thus achieved that insect bodies length, body width, volume and quality:

By ratio a/b substitution (2) formula of insect bodies length and body width:

$S_{\max i}=\frac{k^{2}V}{\sqrt{4\mathrm{\π}}}\{({\mathrm{\ϵ}}_r-1)\[\frac{{\sin }^2{\mathrm{\θ}}_i}{1+L_1({\mathrm{\ϵ}}_r-1)}+\frac{{\cos }^2{\mathrm{\θ}}_i}{1+L_2({\mathrm{\ϵ}}_r-1)}\]\}---\left(2\right)$

Then obtain insecticide volume:

$V=S_{max}\frac{\sqrt{4\mathrm{\π}}}{k^2}\frac{\frac{{\mathrm{\ϵ}}_r+1}{{\mathrm{\ϵ}}_r-1}+{\mathrm{\ϵ}}_r\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\]+({\mathrm{\ϵ}}_r-1){\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\]}^2}{2+({\mathrm{\ϵ}}_r-1){\sin }^2{\mathrm{\θ}}_i+({\mathrm{\ϵ}}_r-1)\[\frac{1-g^2}{g^2}(-1+\frac{1}{2g}ln\frac{1+g}{1-g})\](2{\cos }^2{\mathrm{\θ}}_i-{\sin }^2{\mathrm{\θ}}_i)}---\left(14\right)$

The long 2a of insect bodies and body width 2b is calculated by following formula respectively:

$\begin{array}{c}2b={\[\frac{3V}{2\mathrm{\π}}{\left(\frac{a}{b}\right)}^{-1}\]}^{1/3}\\ 2a=2b\left(\frac{a}{b}\right)\end{array}---\left(15\right)$

Insect density ρ is measured by experiment and obtains, and its quality m is:

M=ρ V (16).