CN102736073B - Method for computing range ambiguity of satellite-borne synthetic aperture radar (SAR) in universal mode - Google Patents

Abstract

The invention provides a method for computing the range ambiguity of a satellite-borne synthetic aperture radar (SAR) in a universal mode and belongs to the field of signal processing. The method comprises the following steps of: reading relevant parameters of a satellite-borne SAR system; acquiring range parameters in a skew state; widening a range antenna; acquiring the number of fuzzy areas; acquiring the energy of the fuzzy areas; computing the range ambiguity of a j-th position; and drawing change curves of the range ambiguity along range positions. The method has the advantages that during acquisition of skew distance between a range antenna pattern and a satellite platform as well as a target point, an earth sphere model is employed, the situation is approximate to actual situation, and a result is accurate and reliable; during acquisition of the range ambiguity, the space geometric characteristic under the condition of large scanning angle is taken into full consideration, and the result is high in reliability; and for different designs of scanning angles in system design, different change curves of the range ambiguity can be obtained, and different scanning angles can be compared and optimized by analyzing the different change curves.

Description

The satellite-borne SAR distance is to the computing method of blur level under a kind of common-mode

Technical field

The invention belongs to the signal process field, be specifically related to the distance of satellite-borne SAR under a kind of common-mode to the computing method of blur level.

Background technology

Synthetic-aperture radar (Synthetic Aperture Radar, SAR) satellite developed rapidly in the last few years, because the SAR satellite is not subjected to the restriction of factors such as weather, geography, time, can carry out the observation of round-the-clock over the ground, and have certain penetration power, thereby be widely used in aspects such as military surveillance, topographic mapping, resource detection, oceanographic observation, ecological monitoring, disaster monitoring, quick rescue.

Distance is a important indicator in the satellite-borne SAR to blur level, and it has directly reflected distance to the annoyance level of secondary lobe signal to the main lobe signal, and in system's design, when the ripple position is chosen, the range ambiguity degree is one of main performance assessment criteria.Synthetic-aperture radar adopts the pulsed operation system, its must bring the orientation to distance to fuzzy problem.Because radar horizon is far away, travelling speed is fast, the azimuth-range of synthetic-aperture radar is fuzzy more outstanding.

SAR image fuzzy is from the outer echoed signal of mapping band the interference of ripple signal to be taken back in mapping, causes image quality decrease, causes difficulty for the application of SAR image.Fuzzy problem also is a major issue that will solve in the SAR engineering design, and particularly fuzzy problem is even more important in the satellite-borne SAR design.SAR image fuzzy can be divided into distance to fuzzy and orientation to fuzzy, the orientation to fuzzy be because exomonental pulse repetition rate (PRF) is low excessively, the Doppler frequency spectrum of echoed signal is owed to sample and is caused.And distance to fuzzy be because the repetition frequency of radar transmitted pulse is too high causes, mainly be in mapping band in the useful echoed signal arrival, the pulse of launching before or after this pulse also has the echoed signal of returning from other suitable targets of distance and arrives, their energy is sneaked into and is caused range ambiguity in the target echo signal, is illustrated in figure 1 as distance to fuzzy synoptic diagram.At present, traditional distance is primarily aimed in positive side-looking situation to the computing method of blur level, and the research that the distance under the wide angle scanning situation is calculated to blur level seldom.Therefore, the present invention proposes and a kind ofly be applicable to that the distance under the general satellite-borne SAR pattern of wide angle scanning is to the meticulous algorithm of blur level, utilize the present invention can reflect accurately distance to blur level with distance to the phenomenon of change in location, realize that distance is to the optimization of blur level.

Summary of the invention

The present invention proposes distance under a kind of general satellite-borne SAR pattern to the computing method of blur level, this method is based on earth model, satellite distance geometric relationship, by analyzing confusion region and the position relation of surveying and drawing band in the earth model under the wide angle scanning situation, in conjunction with the distance to antenna radiation pattern, obtain the signal energy of confusion region signal energy and mapping band, draw distance at last to the value of blur level.

The present invention proposes distance under a kind of general satellite-borne SAR pattern to the computing method of blur level, specifically comprise following step:

Step 1: read in the correlation parameter of Spaceborne SAR System, comprise orbit altitude H, antenna distance is to size L _r, radar operation wavelength λ, radius of a ball R fifty-fifty _e, light velocity c, pulse repetition rate PRF, center of antenna view angle theta _m, initial scan angle Stop scan angle

The interscan angle

Distance is to mapping bandwidth SW_r, and distance is to chosen position number Fr.

Step 2: obtain under the stravismus state distance to parameter;

(1) set up coordinate system; True origin is the earth centre of sphere; Z-direction is to point to satellite by the earth centre of sphere; Y direction is for being starting point with the earth centre of sphere, and direction is parallel with the satellite velocities direction; X-direction perpendicular to satellite flight path direction, makes this coordinate system constitute right hand rectangular coordinate system for being starting point with the earth centre of sphere;

(2), obtain beam center view angle theta under the stravismus state _m';

θ wherein _mBe the center of antenna visual angle,

Be the interscan angle;

(3), obtain stravismus mapping band central point oblique distance R down _m

$\frac{R_e+H}{\sin {{\mathrm{\β}}_m}^{\′}}=\frac{R_e}{\sin {{\mathrm{\θ}}_m}^{\′}}---\left(2a\right)$

γ _m′＝β _m′-θ _m′ (2b)

$R_m=\sqrt{{(R_e+H)}^2+{R_e}^2-2R_e\·(R_e+H)\·\cos {{\mathrm{\γ}}_m}^{\′}}---\left(2c\right)$

Wherein, β _m' and γ _m' being incident angle and the geocentric angle of observation band central point, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state;

(4), obtain mapping band central point B coordinate (x, y, z);

z＝R _e+H-R _m·cosθ _m′ (3b)

$x=\sqrt{{R_e}^2-y^2-z^2}---\left(3c\right)$

Wherein, R _mBe with the central point oblique distance for looking side ways mapping down,

Be the interscan angle, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state, x, y and z are respectively X-axis, Y-axis and the Z axial coordinate of mapping band central point B;

(5), obtain mapping band central point B point place distance to the roundlet radius r and apart to off-axis angle α _B

$r=\sqrt{{R_e}^2-y^2}---\left(4a\right)$

$\sin {\mathrm{\γ}}_B=\frac{x}{r}---\left(4b\right)$

$\frac{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos {\mathrm{\γ}}_B}}{\sin {\mathrm{\γ}}_B}=\frac{r}{\sin {\mathrm{\α}}_B}---\left(4c\right)$

Wherein, γ _BBe the central angle of mapping band central point B point place roundlet, R _eBe the radius of a ball fifty-fifty, (x, y z) are the coordinate of mapping band central point B, and H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B.

Step 3: carry out distance to sky line width broadening;

(1), obtains distance to 3dB beam angle θ _3dB

${\mathrm{\θ}}_{3\mathrm{dB}}=\frac{0.886\mathrm{\λ}}{L_r}---\left(5\right)$

Wherein λ is the radar operation wavelength, L _rFor antenna distance to size;

(2), obtain stravismus down, distance is to beam angle α _r

${\mathrm{\γ}}_1=\frac{\mathrm{SW}\_r}{2r}---\left(6a\right)$

$R_{\max }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)+y^2}---\left(6b\right)$

$\sin {\mathrm{\α}}_{\max }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}}---\left(6c\right)$

$R_{\min }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+y^2}---\left(6d\right)$

$\sin {\mathrm{\α}}_{\min }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)}}---\left(6e\right)$

α _r＝α _max-α _min (6f)

Wherein, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, R _MaxAnd R _MinBe respectively maximum oblique distance and the minimum oblique distance of mapping band and satellite platform, α _MaxAnd α _MinBe respectively mapping band in little disk corresponding distance to maximal off-axis angles and minimal off-axis angle, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B;

(3), compare distance to beam angle α _rWith the distance to 3dB beam angle θ _3dBSize, need to judge whether broadening distance to sky line width L _r, if distance is to beam angle α _rGreater than the distance to 3dB beam angle θ _3dB, then carry out broadening, the distance behind the broadening is designated as L to the sky line width _t:

$L_t=\frac{0.886\mathrm{\λ}}{{\mathrm{\α}}_r+0.001}---\left(7\right)$

If distance is to beam angle α _rLess than the distance to 3dB beam angle θ _3dB, then do not carry out broadening, L _t=L _r

Step 4: obtain confusion region number N r;

$R_{a\max }=\sqrt{{(R_e+H)}^2-{R_e}^2}---\left(8a\right)$

$R_{a\min }=\sqrt{y^2+{(R_e+H-r)}^2}---\left(8b\right)$

$S_{\min }=-[\frac{2(R_{\min }-R_{a\min })}{c}\·\mathrm{PRE}]---\left(8c\right)$

$S_{\max }=-[\frac{2(R_{\max }-R_{a\max })}{c}\·\mathrm{PRE}]---\left(8d\right)$

Nr＝S _max-S _min (8e)

Wherein, R _{A max}And R _{A min}Be respectively confusion region oblique distance and nearest oblique distance farthest, S _MaxAnd S _MinBe respectively the maximum sequence number in confusion region and smallest sequence number, the maximum integer that is not more than x, R are got in [x] expression _eBe the radius of a ball fifty-fifty, H is orbit altitude, r for mapping band central point B point place distance to little radius of circle, c is the light velocity, PRF is pulse repetition rate, y is with the Y-axis coordinate of central point B for mapping.

Step 5: obtain confusion region energy E a;

(1), upwards evenly chooses Fr position in mapping band distance; Fr is that distance is to the chosen position number;

(2), ask for the oblique distance R that surveys and draws band apart from make progress j position and satellite platform _j

$\mathrm{\Δ\γ}=\frac{\mathrm{SW}\_r}{r\·\mathrm{Fr}}---\left(9b\right)$

$R_j=\sqrt{{(\sin ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})}^2\·r^2+y^2+{((\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})\·r-(R_e+H))}^2}---\left(9d\right)$

Wherein, Δ γ is the central angle step pitch, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place distance to little radius of circle, Fr be distance to the chosen position number, r for mapping be with central point B point place apart to little radius of circle, c, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B;

(3), ask for S _iThe oblique distance of j position and satellite platform in the confusion region

With off-axis angle α _Ij

$R_{a_{\mathrm{ij}}}=R_j+\frac{S_i\·c}{2\·\mathrm{PRE}}---\left(10a\right)$

$\cos {\mathrm{\γ}}_{\mathrm{ij}}=\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{2r\·(R_e+H)}---\left(10b\right)$

$\frac{r}{\sin {\mathrm{\α}}_{\mathrm{ij}}}=\sqrt{\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{\sin {\mathrm{\γ}}_{\mathrm{ij}}}}---\left(10c\right)$

Wherein, γ _IjBe corresponding central angle, S _iBe the confusion region sequence number, PRF is pulse repetition rate, and c is the light velocity, R _jBe the upwards oblique distance of j position and satellite platform of mapping band distance, r for mapping be with central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B;

(4), ask for S _iThe distance of j position is to antenna radiation pattern Wr in the confusion region _Ij

${\mathrm{Wr}}_{\mathrm{ij}}=\frac{{\sin }^2(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}{{(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}^2}---\left(11\right)$

α wherein _IjBe off-axis angle, λ is the radar operation wavelength, L _tFor the distance behind the broadening to sky line width, α _BFor the distance to off-axis angle;

(5), ask for S _iJ energy E that the position is returned in the confusion region _Ij

$\cos (\mathrm{\π}-{{\mathrm{\β}}_{\mathrm{ij}}}^{\′})=\frac{{R_{a_{\mathrm{ij}}}}^2+{R_e}^2-{(R_e+H)}^2}{2R_e\·R_{a_{\mathrm{ij}}}}---\left(12a\right)$

$E_{\mathrm{ij}}=\frac{{{\mathrm{Wr}}_{\mathrm{ij}}}^2\·{\mathrm{\σ}}_0}{\sin {{\mathrm{\β}}_{\mathrm{ij}}}^{\′}\·{R_{\mathrm{aij}}}^3}---\left(12b\right)$

Wherein, β _Ij' be the incident angle sequence, σ ₀Expression ground backscattering coefficient, R _eBe the radius of a ball fifty-fifty, H is orbit altitude,

Represent S _iThe oblique distance of j position and satellite platform in the confusion region;

(6), repeating step (2) is to (5), calculates the energy that all positions are returned;

(7), ask for the gross energy E that returns j position _AlljWith confusion region energy E a _j

$E_{\mathrm{allj}}=\underset{i}{\mathrm{\Σ}}{E}_{\mathrm{ij}}---\left(13a\right)$

${\mathrm{Ea}}_j=E_{\mathrm{allj}}-E_{\left(\right|S_{\min }|+1)j}---\left(13b\right)$

S wherein _MinBe confusion region smallest sequence number, E _IjBe S _iJ energy that the position is returned in the confusion region,

Be i=|s _Min|+1 o'clock S _iJ energy that the position is returned in the confusion region.

Step 6: ask for the distance of j position to blur level RASR _j;

${\mathrm{RASR}}_j=10\·\log 10\left(\frac{E{a}_j}{E_{\left(\right|S_{\min }|+1)j}}\right)---\left(14\right)$

Ea wherein _jBe confusion region energy, s _MinBe the confusion region smallest sequence number.

Step 7: draw distance to blur level with the change curve of distance to the position.

The invention has the advantages that:

(1) the present invention proposes distance under a kind of general satellite-borne SAR pattern to the blur level computing method, this precision of method height.When the present invention obtains distance to the oblique distance of antenna radiation pattern and satellite platform and impact point, employing be that ground ball model and actual conditions are more approached, so the result is more accurately and reliably.

(2) the present invention proposes distance under a kind of general satellite-borne SAR pattern to the blur level computing method, this method reliability height.In the process of carrying out system's design, distance to blur level accurately for the expansion of follow-up work with make a strategic decision significant, the present invention taken into full account the space geometry characteristic under the wide angle scanning situation, so the result has higher reliability when obtaining distance to blur level.

(3) the present invention proposes distance under a kind of general satellite-borne SAR pattern to the blur level computing method, and this method is practical.For in the system design to the different designs of scan angle, the present invention can obtain different distances to the change curve of blur level, by analyzing these different change curves, can different scan angles be compared and optimize.

(4) the present invention proposes distance under a kind of general satellite-borne SAR pattern to the blur level computing method, and this method intuitive is good.By the present invention can obtain distance to blur level with distance to the curve of change in location, therefore can reflect very intuitively that distance is to the situation of change of blur level in whole scene, therefore form of expression intuitive is strong as a result, is convenient to system designer and the decision maker makes right judgement by curve.

Description of drawings

Fig. 1 is that distance of the present invention is to fuzzy synoptic diagram;

Fig. 2 is that distance under a kind of general satellite-borne SAR pattern that proposes of the present invention is to the process flow diagram of blur level computing method;

Fig. 3 is under the calculating stravismus state of the present invention, and distance is to the process flow diagram of calculation of parameter;

Fig. 4 is that positive side-looking of the present invention is to the conversion synoptic diagram of stravismus;

Fig. 5 is under the stravismus state of the present invention, beam center visual angle synoptic diagram;

Fig. 6 is under the stravismus state of the present invention, perpendicular to the geometric relationship synoptic diagram of satellite flight path direction;

Fig. 7 is under the calculating stravismus state of the present invention, and distance is to the process flow diagram of sky line width broadening;

Fig. 8 is under the stravismus state of the present invention, the sectional view of mapping band central point B place roundlet;

Fig. 9 is the process flow diagram of calculating of the present invention confusion region energy;

Figure 10 is that emulated data of the present invention is drawn the gained distance to the curve of blur level;

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention proposes distance under a kind of general satellite-borne SAR pattern to the blur level computing method, as shown in Figure 2, comprises following step:

Step 1: read in the correlation parameter of Spaceborne SAR System, comprising: orbit altitude H, antenna distance is to size L _r, radar operation wavelength λ, radius of a ball R fifty-fifty _e, light velocity c, pulse repetition rate PRF, center of antenna view angle theta _m, initial scan angle

Stop scan angle

The interscan angle

Distance is to mapping bandwidth SW_r, and distance is to chosen position number Fr.

Step 2: obtain under the stravismus state distance to parameter, as shown in Figure 3;

(1) set up coordinate system, as shown in Figure 4, true origin is the earth centre of sphere; Z-direction is to point to satellite by the earth centre of sphere; Y direction is for being starting point with the earth centre of sphere, and direction is parallel with the satellite velocities direction; X-direction perpendicular to satellite flight path direction, makes this coordinate system constitute right hand rectangular coordinate system for being starting point with the earth centre of sphere.

(2), obtain beam center view angle theta under the stravismus state _m', as shown in Figure 5;

θ wherein _mBe the center of antenna visual angle,

Be the interscan angle.

(3), obtain stravismus mapping band central point oblique distance R down _m, as shown in Figure 6;

$\frac{R_e+H}{\sin {{\mathrm{\β}}_m}^{\′}}=\frac{R_e}{\sin {{\mathrm{\θ}}_m}^{\′}}---\left(2a\right)$

γ _m′＝β _m′-θ _m′ (2b)

$R_m=\sqrt{{(R_e+H)}^2+{R_e}^2-2R_e\·(R_e+H)\·\cos {{\mathrm{\γ}}_m}^{\′}}---\left(2c\right)$

Wherein, β _m' and γ _m' being incident angle and the geocentric angle of observation band central point, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state.

(4), obtain mapping band central point B coordinate (x, y, z), as shown in Figure 4;

z＝R _e+H-R _m·cosθ _m′ (3b)

$x=\sqrt{{R_e}^2-y^2-z^2}---\left(3c\right)$

Wherein, R _mBe with the central point oblique distance for looking side ways mapping down,

Be the interscan angle, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state, x, y and z are respectively X-axis, Y-axis and the Z axial coordinate of mapping band central point B.

(5), obtain mapping band central point B point place distance to the roundlet radius r and apart to off-axis angle α _B, as shown in Figure 4;

$r=\sqrt{{R_e}^2-y^2}---\left(4a\right)$

$\sin {\mathrm{\γ}}_B=\frac{x}{r}---\left(4b\right)$

$\frac{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos {\mathrm{\γ}}_B}}{\sin {\mathrm{\γ}}_B}=\frac{r}{\sin {\mathrm{\α}}_B}---\left(4c\right)$

Wherein, γ _BBe the central angle of mapping band central point B point place roundlet, R _eBe the radius of a ball fifty-fifty, (x, y z) are the coordinate of mapping band central point B, and H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B.

Step 3: carry out distance to sky line width broadening, as shown in Figure 7;

(1), obtains distance to 3dB beam angle θ _3dB

${\mathrm{\θ}}_{3\mathrm{dB}}=\frac{0.886\mathrm{\λ}}{L_r}---\left(5\right)$

Wherein λ is the radar operation wavelength, L _rFor antenna distance to size.

(2), obtain stravismus down, distance is to beam angle α _r, as shown in Figure 8;

${\mathrm{\γ}}_1=\frac{\mathrm{SW}\_r}{2r}---\left(6a\right)$

$R_{\max }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)+y^2}---\left(6b\right)$

$\sin {\mathrm{\α}}_{\max }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}}---\left(6c\right)$

$R_{\min }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+y^2}---\left(6d\right)$

$\sin {\mathrm{\α}}_{\min }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)}}---\left(6e\right)$

α _r＝α _max-α _min (6f)

Wherein, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, R _MaxAnd R _MinBe respectively maximum oblique distance and the minimum oblique distance of mapping band and satellite platform, α _MaxAnd α _MinBe respectively mapping band in little disk corresponding distance to maximal off-axis angles and minimal off-axis angle, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B.

(3), compare distance to beam angle α _rWith the distance to 3dB beam angle θ _3dBSize, need to judge whether broadening distance to sky line width L _rIf distance is to beam angle α _rGreater than the distance to 3dB beam angle θ _3dB, then carry out broadening, the distance behind the broadening is designated as L to the sky line width _t:

$L_t=\frac{0.886\mathrm{\λ}}{{\mathrm{\α}}_r+0.001}---\left(7\right)$

If distance is to beam angle α _rLess than the distance to 3dB beam angle θ _3dB, then do not carry out broadening, L _t=L _r

Step 4: obtain confusion region number N r;

$R_{a\max }=\sqrt{{(R_e+H)}^2-{R_e}^2}---\left(8a\right)$

$R_{a\min }=\sqrt{y^2+{(R_e+H-r)}^2}---\left(8b\right)$

$S_{\min }=-[\frac{2(R_{\min }-R_{a\min })}{c}\·\mathrm{PRE}]---\left(8c\right)$

$S_{\max }=-[\frac{2(R_{\max }-R_{a\max })}{c}\·\mathrm{PRE}]---\left(8d\right)$

Nr＝S _max-S _min (8e)

Wherein, R _{A max}And R _{A min}Be respectively confusion region oblique distance and nearest oblique distance farthest, S _MaxAnd S _MinBe respectively the maximum sequence number in confusion region and smallest sequence number, the maximum integer that is not more than x, R are got in [x] expression _eBe the radius of a ball fifty-fifty, H is orbit altitude, r for mapping band central point B point place distance to little radius of circle, c is the light velocity, PRF is pulse repetition rate, y is with the Y-axis coordinate of central point B for mapping.

Step 5: obtain confusion region energy E a, as shown in Figure 9;

(1), upwards evenly chooses Fr position in mapping band distance; Fr is that distance is to the chosen position number.

(2), ask for the oblique distance R that surveys and draws band apart from make progress j position and satellite platform _j

$\mathrm{\Δ\γ}=\frac{\mathrm{SW}\_r}{r\·\mathrm{Fr}}---\left(9b\right)$

$R_j=\sqrt{{(\sin ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})}^2\·r^2+y^2+{((\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})\·r-(R_e+H))}^2}---\left(9d\right)$

Wherein, Δ γ is circle heart angle Walk distance, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place distance to little radius of circle, Fr be distance to the chosen position number, r for survey and draw be with central point B point place apart to little radius of circle, c, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B.

(3), ask for S _iThe oblique distance of j position and satellite platform in the confusion region With off-axis angle α _Ij

$R_{a_{\mathrm{ij}}}=R_j+\frac{S_i\·c}{2\·\mathrm{PRE}}---\left(10a\right)$

$\cos {\mathrm{\γ}}_{\mathrm{ij}}=\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{2r\·(R_e+H)}---\left(10b\right)$

$\frac{r}{\sin {\mathrm{\α}}_{\mathrm{ij}}}=\sqrt{\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{\sin {\mathrm{\γ}}_{\mathrm{ij}}}}---\left(10c\right)$

Wherein, γ _IjBe corresponding central angle, S _iBe the confusion region sequence number, PRF is pulse repetition rate, and c is the light velocity, R _jBe the upwards oblique distance of j position and satellite platform of mapping band distance, r for mapping be with central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B.

(4), ask for S _iThe distance of j position is to antenna radiation pattern Wr in the confusion region _Ij

${\mathrm{Wr}}_{\mathrm{ij}}=\frac{{\sin }^2(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}{{(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}^2}---\left(11\right)$

α wherein _IjBe off-axis angle, λ is the radar operation wavelength, L _tFor the distance behind the broadening to sky line width, α _BFor the distance to off-axis angle

(5), ask for S _iJ energy E that the position is returned in the confusion region _Ij

$\cos (\mathrm{\π}-{{\mathrm{\β}}_{\mathrm{ij}}}^{\′})=\frac{{R_{a_{\mathrm{ij}}}}^2+{R_e}^2-{(R_e+H)}^2}{2R_e\·R_{a_{\mathrm{ij}}}}---\left(12a\right)$

$E_{\mathrm{ij}}=\frac{{{\mathrm{Wr}}_{\mathrm{ij}}}^2\·{\mathrm{\σ}}_0}{\sin {{\mathrm{\β}}_{\mathrm{ij}}}^{\′}\·{R_{\mathrm{aij}}}^3}---\left(12b\right)$

Wherein, β _Ij' be the incident angle sequence, σ ₀Expression ground backscattering coefficient, R _eBe the radius of a ball fifty-fifty, H is orbit altitude,

Represent S _iThe oblique distance of j position and satellite platform in the confusion region.

(6), repeating step (2) is to (5), calculates the energy that all positions are returned.

(7), ask for the gross energy E that returns j position _AlljWith confusion region energy E a _j

$E_{\mathrm{allj}}=\underset{i}{\mathrm{\Σ}}{E}_{\mathrm{ij}}---\left(13a\right)$

${\mathrm{Ea}}_j=E_{\mathrm{allj}}-E_{\left(\right|S_{\min }|+1)j}---\left(13b\right)$

S wherein _MinBe confusion region smallest sequence number, E _IjBe S _iJ energy that the position is returned in the confusion region,

Be i=|s _Min|+1 o'clock S _iJ energy that the position is returned in the confusion region.

Step 6: ask for the distance of j position to blur level RASR _j;

${\mathrm{RASR}}_j=10\·\log 10\left(\frac{E{a}_j}{E_{\left(\right|S_{\min }|+1)j}}\right)---\left(14\right)$

Ea wherein _jBe confusion region energy, s _MinBe the confusion region smallest sequence number.

Step 7: draw distance to blur level with the change curve of distance to the position.

Embodiment

Present embodiment provides distance under a kind of general satellite-borne SAR pattern to the blur level computing method, comprises following step, process flow diagram, as shown in Figure 2:

Step 1: read in the correlation parameter of Spaceborne SAR System, comprising: orbit altitude H, distance is to sky line width L _r, radar operation wavelength λ, radius of a ball R fifty-fifty _e, light velocity c, pulse repetition rate PRF, center of antenna view angle theta _m, initial scan angle Stop scan angle

The interscan angle

Distance is to mapping bandwidth SW_r, and distance is to chosen position number Fr;

Wherein, concrete parameter is in the present embodiment: H=800km, L _r=2m, λ=0.03m, R _e=6371140m, c=3 * 10 ⁸M/s, PRF=2000Hz, θ _m=30 °,

SW_r=15000m, Fr=1001;

Step 2: obtain under the stravismus state distance to parameter, process flow diagram as shown in Figure 3;

A, set up coordinate system, as shown in Figure 4;

True origin: the earth centre of sphere

Z axle: point to satellite by the earth centre of sphere

Y-axis: be starting point with the earth centre of sphere, direction is parallel with the satellite velocities direction

X-axis: be starting point with the earth centre of sphere, perpendicular to satellite flight path direction, make this coordinate system constitute right hand rectangular coordinate system

B, obtain beam center view angle theta under the stravismus state _m', as shown in Figure 5;

Method is as shown in Equation (1):

Wherein, concrete parameter is in the present embodiment: θ _m=30 °,

Obtain θ _m'=31.6942 °.

C, obtain down mapping band central point oblique distance R of stravismus _m, as shown in Figure 6;

Method as formula (shown in the 2a ~ 2c):

$\frac{R_e+H}{\sin {{\mathrm{\β}}_m}^{\′}}=\frac{R_e}{\sin {{\mathrm{\θ}}_m}^{\′}}---\left(2a\right)$

γ _m′＝β _m′-θ _m′ (2b)

$R_m=\sqrt{{(R_e+H)}^2+{R_e}^2-2R_e\·(R_e+H)\·\cos {{\mathrm{\γ}}_m}^{\′}}---\left(2c\right)$

Wherein, the concrete parameter in the present embodiment is: R _e=6371140m, H=800km, θ _m' (1) acquisition by formula obtains R _m=963.91km.

D, obtain mapping band central point B coordinate (X, Y, Z), as shown in Figure 4;

Method as formula (shown in the 3a ~ 3c):

z＝R _e+H-R _m·cosθ _m′ (3b)

$x=\sqrt{{R_e}^2-y^2-z^2}---\left(3c\right)$

Wherein, the concrete parameter in the present embodiment is:

R _e=6371140m, θ _m' (1) acquisition by formula, R _mBy formula (2a～2c) obtain obtains Y=179.58km, Z=6351km, X=473.52km.

E, obtain B point place distance to the roundlet radius r and distance to off-axis angle α _B, as shown in Figure 4;

Method as formula (shown in the 4a ~ 4c):

$r=\sqrt{{R_e}^2-y^2}---\left(4a\right)$

$\sin {\mathrm{\γ}}_B=\frac{x}{r}---\left(4b\right)$

$\frac{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos {\mathrm{\γ}}_B}}{\sin {\mathrm{\γ}}_B}=\frac{r}{\sin {\mathrm{\α}}_B}---\left(4c\right)$

Wherein, the concrete parameter in the present embodiment is: R _eBy formula (3a ~ 3c) obtain obtains r=6368.6km, α for=6371140m, H=800km, X, Y _B=30 °.

Step 3: distance is to sky line width broadening, and process flow diagram as shown in Figure 7.

A, obtain the distance to 3dB beam angle θ _3dB

Method is as shown in Equation (5):

${\mathrm{\θ}}_{3\mathrm{dB}}=\frac{0.886\mathrm{\λ}}{L_r}---\left(5\right)$

Wherein, the concrete parameter in the present embodiment is: L _r=2m, λ=0.03m obtains θ _3dB=0.0133rad.

B, obtain stravismus down, distance is to beam angle α _r, as shown in Figure 8;

Method as formula (shown in the 6a ~ 6f):

${\mathrm{\γ}}_1=\frac{\mathrm{SW}\_r}{2r}---\left(6a\right)$

$R_{\max }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)+y^2}---\left(6b\right)$

$\sin {\mathrm{\α}}_{\max }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}}---\left(6c\right)$

$R_{\min }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+y^2}---\left(6d\right)$

$\sin {\mathrm{\α}}_{\min }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)}}---\left(6e\right)$

α _r＝α _max-α _min (6f)

Wherein, the concrete parameter in the present embodiment is: R _e=6371140m, H=800km, SW_r=15000m, r by formula (4a) obtain γ _BBy formula (4b) obtains, and obtains α _r=0.0131rad.

C, comparison distance are to beam angle α _rWith the distance to 3dB beam angle θ _3dBSize, need to judge whether broadening distance to sky line width L _rIf α _rGreater than θ _3dB, then carry out broadening, the distance behind the broadening is designated as L to the sky line width _t

Method is as shown in Equation (7):

$L_t=\frac{0.886\mathrm{\λ}}{{\mathrm{\α}}_r+0.001}---\left(7\right)$

Wherein, the concrete parameter in the present embodiment is: λ=0.03m, θ _3dBBy formula (5) obtain, α _rBy formula (6a ~ 6f) obtain obtains L _t=1.8798.

Step 4: obtain confusion region number N r;

Method as formula (shown in the 8a ~ 8e):

$R_{a\max }=\sqrt{{(R_e+H)}^2-{R_e}^2}---\left(8a\right)$

$R_{a\min }=\sqrt{y^2+{(R_e+H-r)}^2}---\left(8b\right)$

$S_{\min }=-[\frac{2(R_{\min }-R_{a\min })}{c}\·\mathrm{PRE}]---\left(8c\right)$

$S_{\max }=-[\frac{2(R_{\max }-R_{a\max })}{c}\·\mathrm{PRE}]---\left(8d\right)$

Nr＝S _max-S _min (8e)

Wherein, the concrete parameter in the present embodiment is: R _e=6371140m, H=800km, PRF=2000Hz, Y by formula (3a) obtain R _MaxBy formula (6b) obtains, R _MinBy formula (6d) obtains, and obtains Nr=26.

Step 5: obtain confusion region energy E a, process flow diagram as shown in Figure 9;

A, provide following expression, upwards evenly choose Fr position in mapping band distance;

B, ask for the upwards oblique distance R of j position and satellite platform of mapping band distance _j

Method as formula (shown in the 9a ~ 9b):

$\mathrm{\Δ\γ}=\frac{\mathrm{SW}\_r}{r\·\mathrm{Fr}}---\left(9b\right)$

$R_j=\sqrt{{(\sin ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})}^2\·r^2+y^2+{((\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})\·r-(R_e+H))}^2}---\left(9d\right)$

Wherein, the concrete parameter in the present embodiment is: R _e=6371140m, H=800km, SW_r=15000m, Fr=1001, r by formula (4a) obtain, and Y by formula (3a) obtains γ _BBy formula (4b) obtains, γ ₁By formula (6a) obtains, and obtains R according to the different values of j _j

C, ask for S _iThe oblique distance Ra of j position and satellite platform in the confusion region _IjWith off-axis angle α _Ij

Method as formula (shown in the 10a ~ 10c):

$R_{a_{\mathrm{ij}}}=R_j+\frac{S_i\·c}{2\·\mathrm{PRE}}---\left(10a\right)$

$\cos {\mathrm{\γ}}_{\mathrm{ij}}=\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{2r\·(R_e+H)}---\left(10b\right)$

$\frac{r}{\sin {\mathrm{\α}}_{\mathrm{ij}}}=\sqrt{\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{\sin {\mathrm{\γ}}_{\mathrm{ij}}}}---\left(10c\right)$

Wherein, the concrete parameter in the present embodiment is: c=3 * 108m/s, R _e=6371140m, H=800km, PRF=2000Hz, r by formula (4a) obtain, and Y by formula (3a) obtains R _jBy formula (9d) obtains, according to j and S _iDifferent values obtain Ra _IjAnd α _Ij

D, ask for S _iThe distance of j position is to antenna radiation pattern Wrij in the confusion region;

Method as formula (shown in the 11a ~ 11b):

${\mathrm{Wr}}_{\mathrm{ij}}=\frac{{\sin }^2(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}{{(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}^2}---\left(11\right)$

Wherein, the concrete parameter in the present embodiment is: λ=0.03m, α _BBy formula (4a～4c) obtains, α _IjBy formula (10a ~ 10c) obtains, L _tBy formula (7) obtain, according to j and S _iDifferent values obtain Wr _Ij

E, ask for S _iJ energy E that the position is returned in the confusion region _Ij

Method as formula (shown in the 12a～12b):

$\cos (\mathrm{\π}-{{\mathrm{\β}}_{\mathrm{ij}}}^{\′})=\frac{{R_{a_{\mathrm{ij}}}}^2+{R_e}^2-{(R_e+H)}^2}{2R_e\·R_{a_{\mathrm{ij}}}}---\left(12a\right)$

$E_{\mathrm{ij}}=\frac{{{\mathrm{Wr}}_{\mathrm{ij}}}^2\·{\mathrm{\σ}}_0}{\sin {{\mathrm{\β}}_{\mathrm{ij}}}^{\′}\·{R_{\mathrm{aij}}}^3}---\left(12b\right)$

Wherein, the concrete parameter in the present embodiment is: σ ₀=1, R _e=6371140m, H=800km, Ra _IjBy formula (10a) obtains, Wr _IjBy formula (11a ~ 11b) acquisition is according to j and S _iDifferent values obtain E _Ij

F, repeating step B calculate the energy that all positions are returned to E.

G, ask for the gross energy E that returns j position _AlljWith confusion region energy E a _j

Method as formula (shown in the 13a～13b):

$E_{\mathrm{allj}}=\underset{i}{\mathrm{\Σ}}{E}_{\mathrm{ij}}---\left(13a\right)$

$E_{\mathrm{aj}}=E_{\mathrm{allj}}-E_{\left(\right|S_{\min }|+1)j}---\left(13b\right)$

Wherein, the concrete parameter in the present embodiment is: E _IjBy formula (12a～12b) obtains, and obtains E according to the different values of j _AlljAnd Ea _j

Step 6: ask for the distance of j position to blur level RASR _j;

Method is as shown in Equation (14):

${\mathrm{RASR}}_j=10\·\log 10\left(\frac{E{a}_j}{E_{\left(\right|S_{\min }|+1)j}}\right)---\left(14\right)$

Wherein, the concrete parameter in the present embodiment is: E _IjBy formula (12a～12b) obtains, Ea _jBy formula (13 ~ 13) obtain, and obtain RASR according to the different values of j _j

Step 7: draw distance to blur level with the change curve of distance to the position.

The distance that adopts the present invention to propose under a kind of general satellite-borne SAR pattern is calculated to the blur level computing method, the emulated data of the present embodiment that draws, emulated data is drawn the curve that obtains apart to blur level, as shown in figure 10, this curve reflects that intuitively distance is to the situation of change of blur level in whole scene, form of expression intuitive is strong as a result, is convenient to system designer and the decision maker makes right judgement by curve.

Claims (1)

1. the distance under the general satellite-borne SAR pattern comprises to the acquisition methods of blur level:

Step 1: read in the correlation parameter of Spaceborne SAR System, comprise orbit altitude H, antenna distance is to size L _r, radar operation wavelength λ, radius of a ball R fifty-fifty _e, light velocity c, pulse repetition rate PRF, center of antenna view angle theta _m, initial scan angle

Stop scan angle

The interscan angle

Distance is to mapping bandwidth SW_r, and distance is to chosen position number Fr;

It is characterized in that also comprising:

Step 2: obtain under the stravismus state distance to parameter;

(1) sets up coordinate system; True origin is the earth centre of sphere; Z-direction is to point to satellite by the earth centre of sphere; Y direction is for being starting point with the earth centre of sphere, and direction is parallel with the satellite velocities direction; X-direction perpendicular to satellite flight path direction, makes this coordinate system constitute right hand rectangular coordinate system for being starting point with the earth centre of sphere;

(2), obtain beam center view angle theta under the stravismus state _m';

θ wherein _mBe the center of antenna visual angle,

Be the interscan angle;

(3), obtain stravismus mapping band central point oblique distance R down _m

$\frac{R_e+H}{\sin {{\mathrm{\β}}_m}^{\′}}=\frac{R_e}{\sin {{\mathrm{\θ}}_m}^{\′}}---\left(2a\right)$

γ _m'＝β _m'-θ _m' (2b)

$R_m=\sqrt{{(R_e+H)}^2+{R_e}^2-{2R}_e\·(R_e+H)\·\cos {{\mathrm{\γ}}_m}^{\′}}---\left(2c\right)$

Wherein, β _m' and γ _m' being incident angle and the geocentric angle of observation band central point, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state;

(4), obtain mapping band central point B coordinate (x, y, z);

z＝R _e+H-R _m·cosθ _m' (3b)

$x=\sqrt{{R_e}^2-y^2-z^2}---\left(3c\right)$

Wherein, R _mBe with the central point oblique distance for looking side ways mapping down,

Be the interscan angle, H is orbit altitude, R _eBe the radius of a ball fifty-fifty, θ _m' be beam center visual angle under the stravismus state, x, y and z are respectively X-axis, Y-axis and the Z axial coordinate of mapping band central point B;

(5), obtain mapping band central point B point place distance to the roundlet radius r and apart to off-axis angle α _B

$r=\sqrt{{R_e}^2-y^2}---\left(4a\right)$

$\sin {\mathrm{\γ}}_B=\frac{x}{r}---\left(4b\right)$

$\frac{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos {\mathrm{\γ}}_B}}{\sin {\mathrm{\γ}}_B}=\frac{r}{\sin {\mathrm{\α}}_B}---\left(4c\right)$

Wherein, γ _BBe the central angle of mapping band central point B point place roundlet, R _eBe the radius of a ball fifty-fifty, (x, y z) are the coordinate of mapping band central point B, and H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B;

Step 3: carry out distance to sky line width broadening;

(1), obtains distance to 3dB beam angle θ _3dB

${\mathrm{\θ}}_{3\mathrm{dB}}=\frac{0.886\mathrm{\λ}}{L_r}---\left(5\right)$

Wherein λ is the radar operation wavelength, L _rFor antenna distance to size;

(2), obtain stravismus down, distance is to beam angle α _r

${\mathrm{\γ}}_1=\frac{\mathrm{SW}\_r}{2r}---\left(6a\right)$

$R_{\max }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)+y^2}---\left(6b\right)$

$\sin {\mathrm{\α}}_{\max }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}}---\left(6c\right)$

$R_{\min }=\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)+y^2}---\left(6d\right)$

$\sin {\mathrm{\α}}_{\min }=\frac{r\·\sin ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}{\sqrt{r^2+{(R_e+H)}^2-2r\·(R_e+H)\·\cos ({\mathrm{\γ}}_B+{\mathrm{\γ}}_1)}}---\left(6e\right)$

α _r＝α _max-α _min (6f)

Wherein, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, R _MaxAnd R _MinBe respectively maximum oblique distance and the minimum oblique distance of mapping band and satellite platform, α _MaxAnd α _MinBe respectively mapping band in little disk corresponding distance to maximal off-axis angles and minimal off-axis angle, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B;

(3), compare distance to beam angle α _rWith the distance to 3dB beam angle θ _3dBSize, need to judge whether broadening distance to sky line width L _r, if distance is to beam angle α _rGreater than the distance to 3dB beam angle θ _3dB, then carry out broadening, the distance behind the broadening is designated as L to the sky line width _t:

$L_t=\frac{0.886\mathrm{\λ}}{{\mathrm{\α}}_r+0.001}---\left(7\right)$

If distance is to beam angle α _rLess than the distance to 3dB beam angle θ _3dB, then do not carry out broadening, L _t=L _r

Step 4: obtain confusion region number N r;

$R_{a\max }=\sqrt{{(R_e+H)}^2-{R_e}^2}---\left(8a\right)$

$R_{a\min }=\sqrt{y^2+{(R_e+H-r)}^2}---\left(8b\right)$

$S_{\min }=-[\frac{2(R_{\min }-R_{a\min })}{c}\·\mathrm{PRF}]---\left(8c\right)$

$S_{\max }=-[\frac{2(R_{\max }-R_{a\max })}{c}\·\mathrm{PRF}]---\left(8d\right)$

Nr＝S _max-S _min (8e)

Wherein, R _AmaxAnd R _AminBe respectively confusion region oblique distance and nearest oblique distance farthest, S _MaxAnd S _MinBe respectively the maximum sequence number in confusion region and smallest sequence number, the maximum integer that is not more than x, R are got in [x] expression _eBe the radius of a ball fifty-fifty, H is orbit altitude, r for mapping band central point B point place distance to little radius of circle, c is the light velocity, PRF is pulse repetition rate, y is with the Y-axis coordinate of central point B for mapping;

Step 5: obtain confusion region energy E a;

(1), upwards evenly chooses Fr position in mapping band distance; Fr is that distance is to the chosen position number;

(2), ask for the oblique distance R that surveys and draws band apart from make progress j position and satellite platform _j

$\mathrm{\Δ\γ}=\frac{\mathrm{SW}\_r}{r\·\mathrm{Fr}}---\left(9b\right)$

$R_j=\sqrt{{(\sin ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})}^2\·r^2+y^2+{((\cos ({\mathrm{\γ}}_B-{\mathrm{\γ}}_1)+j\·\mathrm{\Δ\γ})\·r-(R_e+H))}^2}---\left(9d\right)$

Wherein, Δ γ is circle heart angle Walk distance, SW_r be distance to the mapping bandwidth, r for mapping band central point B point place distance to little radius of circle, Fr be distance to the chosen position number, r for survey and draw be with central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, γ ₁Be the central angle of half mapping bandwidth correspondence in roundlet, γ _BBe the central angle of mapping band central point B point place roundlet, y is the Y-axis coordinate of mapping band central point B;

(3), ask for S _iThe oblique distance of j position and satellite platform in the confusion region With off-axis angle α _Ij

$R_{a_{\mathrm{ij}}}=R_j+\frac{S_i\·c}{2\·\mathrm{PRF}}---\left(10a\right)$

$\cos {\mathrm{\γ}}_{\mathrm{ij}}=\frac{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}{2r\·(R_e+H)}---\left(10b\right)$

$\frac{r}{{\sin a}_{\mathrm{ij}}}=\frac{\sqrt{r^2+{(R_e+H)}^2+y^2-{R_{\mathrm{aij}}}^2}}{\sin {\mathrm{\γ}}_{\mathrm{ij}}}---\left(10c\right)$

Wherein, γ _IjBe corresponding central angle, S _iBe the confusion region sequence number, PRF is pulse repetition rate, and c is the light velocity, R _jBe the upwards oblique distance of j position and satellite platform of mapping band distance, r for mapping be with central point B point place apart to little radius of circle, R _eBe the radius of a ball fifty-fifty, H is orbit altitude, and y is the Y-axis coordinate of mapping band central point B;

(4), ask for S _iThe distance of j position is to antenna radiation pattern Wr in the confusion region _Ij

${\mathrm{Wr}}_{\mathrm{ij}}=\frac{{\sin }^2(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}{{(\mathrm{\π}\·L_t\·(\sin {\mathrm{\α}}_{\mathrm{ij}}-\sin {\mathrm{\α}}_B)/\mathrm{\λ})}^2}---\left(11\right)$

α wherein _IjBe off-axis angle, λ is the radar operation wavelength, L _tFor the distance behind the broadening to sky line width, α _BFor the distance to off-axis angle;

(5), ask for S _iJ energy E that the position is returned in the confusion region _Ij

$\cos (\mathrm{\π}-{{\mathrm{\β}}_{\mathrm{ij}}}^{\text{'}})=\frac{{R_{a_{\mathrm{ij}}}}^2+{R_e}^2-{(R_e+H)}^2}{2R_e\·R_{a_{\mathrm{ij}}}}---\left(12a\right)$

$E_{\mathrm{ij}}=\frac{{{\mathrm{Wr}}_{\mathrm{ij}}}^2\·{\mathrm{\σ}}_0}{\sin {{\mathrm{\β}}_{\mathrm{ij}}}^{\text{'}}\·{R_{\mathrm{aij}}}^3}---\left(12b\right)$

Wherein, β _Ij' be the incident angle sequence, σ ₀Expression ground backscattering coefficient, R _eBe the radius of a ball fifty-fifty, H is orbit altitude,

Represent S _iThe oblique distance of j position and satellite platform in the confusion region;

(6), repeating step (2) is to (5), calculates the energy that all positions are returned;

(7), ask for the gross energy E that returns j position _AlljWith confusion region energy E a _j

$E_{\mathrm{allj}}=\underset{i}{\mathrm{\Σ}}{E}_{\mathrm{ij}}---\left(13a\right)$

${\mathrm{Ea}}_j=E_{\mathrm{allj}}-E_{\left(\right|S_{\min }|+1)j}---\left(13b\right)$

S wherein _MinBe confusion region smallest sequence number, E _IjBe S _iJ energy that the position is returned in the confusion region,

Be i=|s _Min|+1 o'clock S _iJ energy that the position is returned in the confusion region;

Step 6: ask for the distance of j position to blur level RASR _j;

${\mathrm{RASR}}_j=10\·\log 10\left(\frac{{\mathrm{Ea}}_j}{E_{\left(\right|S_{\min }|+1)j}}\right)---\left(14\right)$

Ea wherein _jBe confusion region energy, S _MinBe the confusion region smallest sequence number;

Step 7: draw distance to blur level with the change curve of distance to the position.

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