CN108039980A - The more base SAR Topology Structure Design methods of GEO stars-machine - Google Patents

The more base SAR Topology Structure Design methods of GEO stars-machine Download PDF

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CN108039980A
CN108039980A CN201810120389.1A CN201810120389A CN108039980A CN 108039980 A CN108039980 A CN 108039980A CN 201810120389 A CN201810120389 A CN 201810120389A CN 108039980 A CN108039980 A CN 108039980A
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msub
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CN108039980B (en
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武俊杰
安洪阳
王雯璟
胡春宇
杨海光
黄钰林
杨建宇
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a kind of more base SAR Topology Structure Design methods of GEO stars machine.It includes the spatial resolution model for establishing the more base SAR of GEO star machines, construct Topology Structure Design model, it is Model for Multi-Objective Optimization by Topology Structure Design model conversion, solution is iterated using Multipurpose Optimal Method, non-dominated ranking is carried out to obtained disaggregation, selects optimal solution as optimal topological structure.Spatial resolution model of the invention by establishing the more base SAR of GEO star machines, construct Topology Structure Design model, be converted to Model for Multi-Objective Optimization, solution is iterated using Multipurpose Optimal Method again, so as to obtain optimal more base topological structures, it can be optimal the spatial resolution after more bases fusions, significantly improve the spatial resolution of remote sensing images.

Description

The more base SAR Topology Structure Design methods of GEO stars-machine
Technical field
The invention belongs to Radar Technology field, more particularly to a kind of more base SAR Topology Structure Design methods of GEO stars-machine.
Background technology
Synthetic aperture radar (SAR) is a kind of round-the-clock, round-the-clock high-resolution imaging system, by launching big time width Long-pending linear FM signal, when reception, matched filtering obtained pulse compression signal, to obtain distance to high-resolution, utilized conjunction The high-resolution of orientation is realized into aperture technique.Image quality influences from weather condition (cloud layer, illumination) etc., has to remote The characteristics of distance objective is detected and positions.The typical application fields of SAR include disaster monitoring, resource exploration, geological mapping, Military surveillance etc..
The scattered information of the same target area of multiple receiving platforms reception of more base SAR can increase the information content of acquisition, because This, can bring advantage to advanced remote sensing application, such as, scene classification, chromatography SAR, high-resolution large scene are imaged and divide Resolution strengthens.
The more base SAR of GEO stars-machine are made of GEO irradiation sources and multiple airborne receiving stations.Each of which receiving station and GEO Irradiation source forms a double-base SAR system.Since transmitting-receiving separates, airborne receiving platform only includes reception and sychronisation, because This, reception system has the characteristics that miniaturization and low cost.Meanwhile compared to low rail SAR irradiation sources, GEO SAR satellites can be with Realize to target area for a long time, the irradiation that height revisits.Therefore, the more base SAR of GEO stars-machine have using spirit in remote sensing application Living, convenient advantage.
A considerable advantage of more base SAR is that the imaging results obtained by multiple receiving platforms can be merged to improve Resolution ratio.But the spatial resolution after fusion depends critically upon the topological structure of more bases.If employ inappropriate more bases Topological structure, the spatial resolution after fusion, which cannot be greatly improved, even to be deteriorated.Most optimal sorting can be realized in order to obtain More base topological structures of resolution, the prior art analyze the influence of the p- 3dB resolution cells area of more base topologys and propose one kind Optimal sensing station collocation method, but this method only accounts for configuration and this method vacation at fixed reception station or cell site Determine transmit-receive platform and be respectively positioned on ground level.
The content of the invention
The present invention goal of the invention be：In order to solve problem above existing in the prior art, the present invention proposes one kind The more base SAR Topology Structure Design methods of GEO stars-machine.
The technical scheme is that：A kind of more base SAR Topology Structure Design methods of GEO stars-machine, comprise the following steps：
A, the spatial resolution model of the more base SAR of GEO stars-machine is established；
B, resolution cell area and the unbalanced factor of resolution ratio are obtained according to spatial resolution model in step A, construction is opened up Flutter structure design model；
C, it is Model for Multi-Objective Optimization by Topology Structure Design model conversion in step B；
D, solution is iterated to Model for Multi-Objective Optimization in step C using Multipurpose Optimal Method, to obtained disaggregation Non-dominated ranking is carried out, selects optimal solution as optimal topological structure.
Further, the spatial resolution model of the more base SAR of GEO stars-machine is embodied as in the step A：
Wherein, χmul(r) more base SAR generalized fuzzy functions are represented, | | represent modulus, []TRepresent transposition, p () and mA() represents that the output of the matched wave filter of distance signal and normalization receive the inverse Fourier transform of signal amplitude respectively, N is receiving station's number, and r represents the distance between arbitrary point of target point and approaching target point, and c represents the light velocity, and λ represents wavelength, mARepresent that the output of the matched wave filter of bearing signal and normalization receive the inverse Fourier transform of signal amplitude, uTAWith Represent respectively by cell site and receiving station nthIt is directed toward the unit vector of target point, ωTAWithCell site and reception are represented respectively Stand nthAngular speed.
Further, Topology Structure Design model is embodied as in the step B：
Wherein, F1(x) the first aim function of topology design, S are representedcell(x) resolution cell area, γ (x) tables are represented Show the unbalanced factor of resolution ratio, ρmaxAnd ρminWorst and optimal resolution is represented respectively.
Further, Topology Structure Design model conversion is embodied as by the step C for Model for Multi-Objective Optimization：
Wherein, F2(x) the first aim function of topology design is represented.
Further, the step D is iterated Model for Multi-Objective Optimization in step C using Multipurpose Optimal Method and asks Solution, non-dominated ranking is carried out to obtained disaggregation, selects optimal solution as optimal topological structure, specifically include it is following step by step：
D1, the parameter for initializing Multipurpose Optimal Method, the parameter include Population Size M, maximum iteration Gmax, crossover probability Pc, mutation probability Pm, contest scale T, intersect factor Ic, mutagenic factor Im；
D2, set genetic algebra as 1, generates multiple individual composition initial populations at random in decision space, calculates population In each individual fitness value, obtain target function value；
D3, judge whether genetic algebra is more than the maximum genetic algebra of setting；If so, non-branch then is carried out to obtained disaggregation With sequence, optimal solution is selected as optimal topological structure；If it is not, then carry out next step；
D4, obtain two female generation individuals using contest selection opertor, then using the crossover operator generation filial generation of simulation binary system Individual, forms progeny population；
D5, using multinomial mutation operator in progeny population individual carry out mutation operation；
D6, the target function value for calculating each individual in progeny population after making a variation, mother is merged for population with progeny population New population is formed, by new population dividing is multiple and different non-dominant disaggregation according to decomposition strategy；
D7, using selection opertor select multiple optimal solutions from new population, obtains population of future generation, to genetic algebra plus 1 is updated, return to step D3.
The beneficial effects of the invention are as follows：Spatial resolution model of the invention by establishing the more base SAR of GEO stars-machine, construction Topology Structure Design model, is converted to Model for Multi-Objective Optimization, then is iterated solution using Multipurpose Optimal Method, so that To optimal more base topological structures, it can be optimal the spatial resolution after more bases fusions, significantly improve the sky of remote sensing images Between resolution ratio.
Brief description of the drawings
Fig. 1 is the flow diagram of the more base SAR Topology Structure Design methods of GEO stars-machine of the present invention.
Fig. 2 is the geometry schematic diagram of the more base SAR of GEO stars-machine of the present invention.
Fig. 3 is 1 schematic diagram of Bistatic SAR image before being merged in the embodiment of the present invention.
Fig. 4 is 2 schematic diagram of Bistatic SAR image before being merged in the embodiment of the present invention.
Fig. 5 is Bistatic SAR image schematic diagram after being merged in the embodiment of the present invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, it is right The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only to explain the present invention, not For limiting the present invention.
In order to facilitate description present disclosure, following term is explained first：
Term 1：Bistatic SAR (synthetic aperture radar, synthetic aperture radar)
Bistatic SAR refers to the SAR system that system cell site and receiving station are placed in different platform, wherein at least one Platform is motion platform, conceptually belongs to bistatic radar.
Term 2：GEO SAR (Geosynchronous SAR, geostationary orbit synthetic aperture radar)
GEO SAR are geostationary orbit Synthetic Aperture Radar satellite, operate in the Geo-synchronous rail with certain inclination angle On road, the cycle of operation is identical with earth rotation period.
As shown in Figure 1, the flow diagram of the more base SAR Topology Structure Design methods of GEO stars-machine for the present invention.It is a kind of The more base SAR Topology Structure Design methods of GEO stars-machine, comprise the following steps：
A, the spatial resolution model of the more base SAR of GEO stars-machine is established；
B, resolution cell area and the unbalanced factor of resolution ratio are obtained according to spatial resolution model in step A, construction is opened up Flutter structure design model；
C, it is Model for Multi-Objective Optimization by Topology Structure Design model conversion in step B；
D, solution is iterated to Model for Multi-Objective Optimization in step C using Multipurpose Optimal Method, to obtained disaggregation Non-dominated ranking is carried out, selects optimal solution as optimal topological structure.
In an alternate embodiment of the present invention where, as shown in Fig. 2, the geometry of the more base SAR of GEO stars-machine for the present invention Structure diagram.The bidimensional resolution capability of double-base SAR system on the ground can be by generalized fuzzy function table in above-mentioned steps A Show, the more base generalized fuzzy function representations for using non-coherent addition to obtain to N number of biradical ambiguity function, so as to establish GEO stars-machine The spatial resolution model of more base SAR, is embodied as：
Wherein, χ mul (r) represent more base SAR generalized fuzzy functions, | | represent modulus, []TRepresent transposition, p () And mA() represents that the output of the matched wave filter of distance signal and normalization receive the inverse Fourier change of signal amplitude respectively Change, N is receiving station's number, and r represents the distance between arbitrary point of target point and approaching target point, and c represents the light velocity, and λ represents ripple It is long, mARepresent that the output of the matched wave filter of bearing signal and normalization receive the inverse Fourier transform of signal amplitude, uTAWithRepresent respectively by cell site and receiving station nthIt is directed toward the unit vector of target point, ωTAWithCell site is represented respectively and is connect Receive station nthAngular speed, nth represent n-th th receiving station,WithSubscript n represent corresponding receiving station, be expressed as
Wherein, RTWithCell site and the position of receiving station nth are represented respectively；
Wherein,For the height of receiving station nth,For the incidence angle of receiving station nth,For the orientation of receiving station nth Angle；
ω TA andCell site and the angular speed of receiving station nth are represented respectively, are expressed as
Wherein, I is unit matrix, vTFor GEO cell sites velocity,For receiving station nthVelocity is simultaneously expressed as：
Wherein,For receiving station nthThe size of speed,For receiving station nthVelocity angle；
- 3dB the sections of the spatial resolution model of the more base SAR of GEO stars-machine are the resolution cell of more base SAR systems.Dividing Distinguish the resolution ratio ρ on unit any direction φφObtained by following formula
Wherein, rφ=ρφ·[cosφ,sinφ,0]T。
Work as ρφWhen meeting above formula, the resolution ratio on φ directions is ρφ。
Except systematic parameter, the resolution ratio of the more base SAR of GEO stars-machine is closely related with the topology of more base SAR.Due to track Limitation, under conditions of image scene and orbit time are selected, what the position of GEO cell sites and speed were to determine.Therefore, The generalized fuzzy function of the more base SAR of GEO stars-machine and the position of N number of receiving station and velocity correlation.Consider for simplicity, receive The speed stoodAnd heightSize assume to fix, therefore the incidence angle of given receiving stationAzimuthVelocity angleThe resolution ellipse of the more base SAR of GEO stars-machine determines that.
Differentiating elliptical feature can be by ρmaxWith ρminRepresent and be expressed as
Wherein ρmaxRepresent elliptical major axis and represent worst resolution ratio, ρminRepresent elliptical short axle and represent most Excellent resolution ratio,WithIt is illustrated respectively in the maximum and minimum value for differentiating the resolution ratio on ellipse.Meanwhile they with More base SAR'sIt is related.The cartographic represenation of area of resolution cell is
WhereinRepresent corresponding more base topological structures.
In an alternate embodiment of the present invention where, in above-mentioned steps B the more base SAR of GEO stars-machine spatial resolution characteristic Characterized by resolution cell area, in order to find the more base SAR topological structures that can realize optimal resolution cell area, by topology design First aim function representation be
minF1(x)=Scell(x)
In addition, in practical applications, the directive spatial resolution of institute should be as far as possible identical, so as to obtain in all directions Equal target information, this is conducive to the target identification in later stage.Therefore, it is used to weigh using the unbalanced factor gamma (x) of resolution ratio Measure ρmaxWith ρminBetween lack of uniformity, be expressed as
So as to construct Topology Structure Design model, it is embodied as：
Wherein, F1(x) the first aim function of topology design, S are representedcell(x) resolution cell area, γ (x) tables are represented Show the unbalanced factor of resolution ratio, ρmaxAnd ρminWorst and optimal resolution is represented respectively.
In an alternate embodiment of the present invention where, above-mentioned steps C sets the more base topologys for obtaining optimal spatial resolution ratio Meter problem is converted to the multi-objective optimization question being made of two object functions, i.e., is more mesh by Topology Structure Design model conversion Mark Optimized model is embodied as：
Wherein, F2(x) the first aim function of topology design is represented.
In an alternate embodiment of the present invention where, above-mentioned steps D is right using Multipurpose Optimal Method (NGSA-II algorithms) Model for Multi-Objective Optimization is iterated solution in step C, specifically include it is following step by step：
D1, the parameter for initializing Multipurpose Optimal Method, the parameter include Population Size M, maximum iteration Gmax, crossover probability Pc, mutation probability Pm, contest scale T, intersect factor Ic, mutagenic factor Im；
D2, set genetic algebra as 1, generates multiple individual composition initial populations at random in decision space, calculates population In each individual fitness value, obtain target function value；
In an alternate embodiment of the present invention where, above-mentioned steps D2 initializes population P first1Even genetic algebra G= 1, random M individual composition initial population P of generation in decision space D1.Make xi,g=(x1,i,g,x2,i,g,x3,i,g,…, xDim,i,g) represent that G represents decision space dimension for i-th of individual in population, Dim, that is, in multi-objective optimization question Independent variable number.Therefore, random initializtion procedural representation is
xj,i,1=xj,min+randij[0,1]×(xj,max-xj,min)
Wherein, xj,i,1Represent the value of j-th of variable of i-th of individual in first generation population, xj,minAnd xj,maxRespectively determine The minimum value and maximum for j-th of independent variable that plan space D is limited.randij[0,1] it is equally distributed random between being 0 to 1 Number.Therefore above-mentioned initialization procedure is according to being uniformly distributed random one value tax of generation between independent variable maximum and minimum value To corresponding individual.
In M individual of initialization and obtain initial population P1Afterwards, the fitness value of each individual in population is calculated, that is, Target function value.
D3, judge whether genetic algebra is more than the maximum genetic algebra of setting；If so, non-branch then is carried out to obtained disaggregation With sequence, optimal solution is selected as optimal topological structure；If it is not, then carry out next step；
In an alternate embodiment of the present invention where, if above-mentioned steps D3 genetic algebras are more than the maximum hereditary generation of setting Number, then illustrate that iterative process terminates, obtained last generation population PG, to PGIn all individuals carry out non-dominated rankings, and select Go out in the first non-dominant disaggregation F1In solution as optimal solution set.Using non-dominated ranking principle, according to the constraints of environment, Therefrom select more bases topology that optimal solution is solved.
D4, obtain two female generation individuals using contest selection opertor, then using the crossover operator generation filial generation of simulation binary system Individual, forms progeny population；
In an alternate embodiment of the present invention where, above-mentioned steps D4 obtains two female generations using contest selection opertor first Individual.Q individual is randomly choosed from current population, compares the quality of its target function value, selection target functional value is optimal Individual is as a female generation individual；Another female generation individual obtains in the same way.After two female generation individuals are obtained, use Simulate binary system crossover operator generation offspring individual.
If generate number p at random between [0,1]1, meet p1＜ Pc, then it is female to above-mentioned two for individual x1,gAnd x2,gCarry out Following operation.To i-th of decision variable, number u is generated at random between [0,1]i, calculate dispersion factor βqi。
Wherein, βiRepresent the dispersion factor of i-th of decision variable,ηcRepresent to intersect the factor, uiRepresent to i decision variable Random number between [0,1] of generation；
Then i-th of variable of offspring individual is obtained by following formula
xI, 1, G+1=0.5 [(1+ βqi)xI, 1, G+(1-βqi)xI, 2, G]
xI, 2, G+1=0.5 [(1- βqi)xI, 1, G+(1+βqi)xI, 2, G]
To x1, gAnd x2, gEach variable carry out aforesaid operations i.e. can obtain two offspring individual x1, g+1And x2, g+1。
If p1≥Pc, then mother is directly passed into offspring individual for individual.
M offspring individual and composition progeny population O are generated in the manner described aboveg。
D5, using multinomial mutation operator in progeny population individual carry out mutation operation；
In an alternate embodiment of the present invention where, above-mentioned steps D5 is in generation progeny population OgAfterwards, become using multinomial Exclusive-OR operator carries out mutation operation to individual in population.
For progeny population OgIn each individual, generation random number p2∈ [0,1], if p2＜ Pm, then to the every of the individual One variable carries out mutation operation.Offspring individual after variation produces in the following way：
yI, j, g+1=xI, j, g+1+o(xI, max-xI, min)
Wherein, yI, j, g+1Represent the result after each variable variations of i of j-th of individual in G+1 generations.δ is given by, ri For the random number between [0,1]：
Wherein, δ1And δ2It is given by：
To OgIn it is each carry out mutation operation after, the progeny population produced after variation is denoted as OG。
D6, the target function value for calculating each individual in progeny population after making a variation, mother is merged for population with progeny population New population is formed, by new population dividing is multiple and different non-dominant disaggregation according to decomposition strategy；
In an alternate embodiment of the present invention where, above-mentioned steps D6 calculates progeny population O after variationGIn each individual Target function value.Mother is merged to the population to form that scale is 2M for population with progeny population：UG=XG∪OG, | UG|=2M, wherein |UG| it is UGIn number, to the population U after mergingGIn 2M individual carry out quick non-dominated ranking.
For UGIn each individual xi,gCalculate two parameter niAnd Si；Wherein niExpression dominates current individual in population xi,gIndividual amount, SiRepresent by individual xi,gThe group of individuals of domination.
First, all n in population are foundiThey are stored in the first non-dominant grade F by=0 individual1In, ni=0 represents In UGIn without dominate xi,gSolution.
Then, for current non-dominant disaggregation F1In each individual j investigate its individual collections S dominatedj.Will set SjIn each individual k nk1 is subtracted, if nk- 1=0, then be stored in the second non-dominant disaggregation F by individual k2。nk- 1=0 is represented Removing has been dispensed into F1In solution, in UGIn interior remaining solution, which is in non-dominant status, therefore puts it into second Non-dominant disaggregation F2In.
Continue above-mentioned hierarchical policy until all solutions are all completed to divide, at this time by UGIn solution be divided into F1,F2,F3,... Etc. multiple and different non-dominant disaggregation, the non-dominated ranking for the solution that more forward grade solution is concentrated is higher, namely their target Functional value is better, therefore bigger into follow-on possibility in selection opertor.
D7, using selection opertor select multiple optimal solutions from new population, obtains population of future generation, to genetic algebra plus 1 is updated, return to step D3.
In an alternate embodiment of the present invention where, above-mentioned steps D7 is by UGIn solution be divided into different non-dominant disaggregation Afterwards, selection opertor will be from UGIn select the classic solutions of L and enter evolutionary process of future generation.
Selection strategy is as follows：
From the first non-dominant disaggregation F1Start to select, if F1In solution more than M, then to F1In solution carry out crowding Sequence.F is calculated first1In the crowding that each solves, be then ranked up according to their crowding.
Crowding computational methods are as follows：
First, to F1In solution according to each object function size order carry out sequence from big to small.Then will The minimum and maximum individual crowding distance of target function value is all set to ∞.The crowding distance of i-th of individual is set as i+1 With the normalized summation of the i-th -1 individual all object function value difference, which is：
Wherein, dis (i) represents the crowding distance of i-th of individual, Fl(i) the 1st object function of i-th of individual is represented Value, L is object function number.max(Fl) represent the 1st object function F in current populationlMaximum.
Obtaining F1In after all individual crowding distances, according to the descending arrangement of their crowding distance, selection The maximum preceding M solution of crowding distance enters population P of future generationg+1, selection completion.
If F1In solution less than M, then F1In solution all including into population P of future generationg+1, it is remaining solution continue exist Non-domination solution below, which is concentrated, to be obtained.If F1And F2In solution sum exceeded M, then in F2It is middle to be sorted simultaneously using crowding distance The solution for selecting part crowding distance maximum enters Pg+1M solution of composition.If F1And F2In solution still inadequate M, then continue in F3 Middle searching, until filling up Pg+1。
After selection opertor is completed, population P of future generation has just been obtainedg+1.At this time, update genetic algebra G=G+1 and return Return step D3.
As shown in figure 3, it is 1 schematic diagram of Bistatic SAR image before fusion in the embodiment of the present invention.As shown in figure 4, it is the present invention 2 schematic diagram of Bistatic SAR image before being merged in embodiment.As shown in figure 5, it is Bistatic SAR image after fusion in the embodiment of the present invention Schematic diagram.It can be seen from the figure that the present invention can be optimal the spatial resolution after more bases fusions, remote sensing is significantly improved The spatial resolution of image.
Those of ordinary skill in the art will understand that the embodiments described herein, which is to help reader, understands this hair Bright principle, it should be understood that protection scope of the present invention is not limited to such special statement and embodiment.This area Those of ordinary skill these disclosed technical inspirations can make according to the present invention and various not depart from the other each of essence of the invention The specific deformation of kind and combination, these deform and combine still within the scope of the present invention.

Claims (5)

  1. A kind of 1. more base SAR Topology Structure Design methods of GEO stars-machine, it is characterised in that comprise the following steps：
    A, the spatial resolution model of the more base SAR of GEO stars-machine is established；
    B, resolution cell area and the unbalanced factor of resolution ratio are obtained according to spatial resolution model in step A, constructs topology knot Structure designs a model；
    C, it is Model for Multi-Objective Optimization by Topology Structure Design model conversion in step B；
    D, solution is iterated to Model for Multi-Objective Optimization in step C using Multipurpose Optimal Method, obtained disaggregation is carried out Non-dominated ranking, selects optimal solution as optimal topological structure.
  2. 2. the more base SAR Topology Structure Design methods of GEO stars-machine as claimed in claim 1, it is characterised in that in the step A The spatial resolution model of the more base SAR of GEO stars-machine is embodied as：
    <mrow> <mo>|</mo> <msub> <mi>&amp;chi;</mi> <mrow> <mi>m</mi> <mi>u</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;ap;</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>p</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>u</mi> <mrow> <mi>T</mi> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>u</mi> <mrow> <msub> <mi>RA</mi> <mi>n</mi> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>&amp;CenterDot;</mo> <mi>r</mi> </mrow> <mi>c</mi> </mfrac> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mi>A</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;omega;</mi> <mrow> <mi>T</mi> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mrow> <msub> <mi>RA</mi> <mi>n</mi> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>&amp;CenterDot;</mo> <mi>r</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mo>)</mo> </mrow> </mrow>
    Wherein, χmul(r) more base SAR generalized fuzzy functions are represented, | | represent modulus, []TRepresent transposition, p () and mA () represents that the output of the matched wave filter of distance signal and normalization receive the inverse Fourier transform of signal amplitude, N respectively For receiving station's number, r represents the distance between arbitrary point of target point and approaching target point, and c represents the light velocity, and λ represents wavelength, mA Represent that the output of the matched wave filter of bearing signal and normalization receive the inverse Fourier transform of signal amplitude, uTAWithPoint Do not represent by cell site and receiving station nthIt is directed toward the unit vector of target point, ωTAWithCell site and receiving station are represented respectively nthAngular speed.
  3. 3. the more base SAR Topology Structure Design methods of GEO stars-machine as claimed in claim 2, it is characterised in that in the step B Topology Structure Design model is embodied as：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>min</mi> <mi> </mi> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> </mrow> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>&amp;gamma;</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;rho;</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&amp;rho;</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced>
    Wherein, F1(x) the first aim function of topology design, S are representedcell(x) resolution cell area is represented, γ (x) represents to divide The unbalanced factor of resolution, ρmaxAnd ρminWorst and optimal resolution is represented respectively.
  4. 4. the more base SAR Topology Structure Design methods of GEO stars-machine as claimed in claim 3, it is characterised in that the step C will Topology Structure Design model conversion is embodied as Model for Multi-Objective Optimization：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>min</mi> <mi> </mi> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mi>c</mi> <mi>e</mi> <mi>l</mi> <mi>l</mi> </mrow> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>min</mi> <mi> </mi> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>&amp;gamma;</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>
    Wherein, F2(x) the first aim function of topology design is represented.
  5. 5. the more base SAR Topology Structure Design methods of GEO stars-machine as claimed in claim 4, it is characterised in that the step D is adopted Solution is iterated to Model for Multi-Objective Optimization in step C with Multipurpose Optimal Method, non-dominant row is carried out to obtained disaggregation Sequence, selects optimal solution as optimal topological structure, specifically include it is following step by step：
    D1, the parameter for initializing Multipurpose Optimal Method, the parameter include Population Size M, maximum iteration Gmax, hand over Pitch probability Pc, mutation probability Pm, contest scale T, intersect factor Ic, mutagenic factor Im；
    D2, set genetic algebra as 1, generates multiple individual composition initial populations at random in decision space, calculates every in population Individual fitness value, obtains target function value；
    D3, judge whether genetic algebra is more than the maximum genetic algebra of setting；If so, non-dominant row then is carried out to obtained disaggregation Sequence, selects optimal solution as optimal topological structure；If it is not, then carry out next step；
    D4, obtain two female generation individuals using contest selection opertor, then uses simulation binary system crossover operator generation offspring individual, Form progeny population；
    D5, using multinomial mutation operator in progeny population individual carry out mutation operation；
    D6, the target function value for calculating each individual in progeny population after making a variation, mother is merged for population with progeny population to be formed New population, by new population dividing is multiple and different non-dominant disaggregation according to decomposition strategy；
    D7, using selection opertor select multiple optimal solutions from new population, obtains population of future generation, to genetic algebra plus 1 into Row renewal, return to step D3.
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