A multi-index assessment method for evaluating coverage effectiveness of remote sensing satellite

Hongliang LI,Dong LI,Yunhua LI

aSchool of Automation Science and Electrical Engineering,Beihang University,Beijing 100083,China

bSchool of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

cBeijing Aeronautical Science and Technology,Research Institute of COMAC,Beijing 102211,China

KEYWORDS Analytic hierarchy process;Coverage ability;Effectiveness evaluation;Entropy weight method;Remote sensing satellite

Abstract This paper deals with the multi-index assessment method for evaluating coverage effectiveness of remote sensing satellite.Because a series of satellite activities such as imaging,moving target observation,and environment investigation need to know the coverage characteristics,the coverage capability of the remote sensing satellite is the most important index.Thus,it is very important to establish the method of effectiveness evaluation of coverage characteristics.This paper focuses on the assessment of coverage effectiveness of remote sensing satellite,and proposes and designs a multi-index evaluation method based on index weight using entropy weight method and analytic hierarchy process.With a simulation case,the effectiveness evaluation results of single satellite coverage and multi-satellite coverage performance are given for the proposed assessment.The experimental results show that the established coverage characteristic model and the proposed assessment method are effective and right.

1.Introduction

Space technology is developing rapidly,and it has become the technological frontier of the twenty- first century.As the main platform of space sensors,the remote sensing satellite has wide applications in the land and sea observation,weather forecast,disaster prediction,national defense and other fields.The coverage performance of the remote sensing satellite has been one of the hotspots.Coverage characteristics refer to the observed performance of airborne sensors in a designated area.The grid method is usually used to analyze the coverage of the satellite.1Because the grid method has high precision,and can be applied to any satellite orbit and any shape of load field of view,it has become one of the important methods to solve the coverage problem.2,3In order to study the coverage analysis and effectiveness evaluation,and improve the utilization of satellite resources,the establishment of a coverage performance simulation system is of the great significance.

Here,we refer to the system as the evaluation system of the performance of an object,a scheme,or a simulation system for short.According to the main factors of the system and the statistical information,the effectiveness evaluation is to determine the system target and establish measure algorithm which reflects the system ability.Effectiveness evaluation can be divided into the following steps:to build the index system,to calculate the value of efficiency index,and to obtain the value of comprehensive evaluation results.

The research of the effectiveness evaluation can be roughly divided into four categories:

(1)The analytical method uses the analytical formula to calculate and analyze the system.4,5The advantage is clear and easy,but it is difficult to cover more factors,and is suitable for the macro model.

(2)The statistical method uses a large amount of statistical data for evaluation.6The advantage is that it can show the indexes affecting of the performance clearly,but the premise is that the established model can clearly reflect the random characteristics of statistical data.

(3)The computer simulation method calculates the performance evaluation results according to the results of computer simulation experiment.7In the establishment of the simulation model of remote sensing satellite system,the de-noising of the image segment must be conducted.8For remote sensing satellite system composed of multiple satellites,the mismatch issue is also to be solved.Wan and Zhang put forward a novel mismatching detection method called P2L method.9The advantage of the computer simulation method is that the details of the whole system can be represented,and its disadvantage is that it is very complicated to establish the system simulation model.

(4)Multi-index comprehensive evaluation method includes entropy weight method,Analytic Hierarchy Process(AHP)method,10,11clustering analysis method,11Fuzzy Comprehensive Evaluation(FCE)method,10,11multiobjective genetic algorithm for multi-sensor satellite imagery12and so on.13–17For complex systems,if the interactions among the various indicators have no specific function,this type of multi-index comprehensive evaluation method is more reasonable.The advantage of this method is that it is applicable to a wide range of application and is very simple.But the indexes are influenced by subjective factors.The entropy weight method and multi-expert comprehensive weighted method can be used to eliminate the subjective effects.

Both multi-objective evaluation method and computer simulation based evaluation method involve a lot of numerical calculation of performance indicators.To accelerate the computation speed and improve the real-time performance of coverage capability,heterogeneous computing model which is composed of Graphics Processing Unit(GPU)and Central Processing Unit(CPU)based on Compute Unified Device Architecture(CUDA)can be used to accelerate numerical computation.In this computation model,GPU is responsible for large-scale floating-point computing,while CPU is responsible for the logic processing of the program,and a magnitude of acceleration ratio can generally be obtained.Poli et al.discussed the framework of computation model of GPU+CPU.18Senthilnath et al.studied GPU-based normalized cuts for road extraction using satellite imagery.19

Remote sensing satellite coverage is a complex multi-index system.According to the characteristic index system of remote sensing satellite constellation,we empathically use entropy weight method and AHP method to construct the index weight in this paper.The single satellite coverage evaluation and multi-satellite coverage evaluation results are given using linear weighted method and fuzzy comprehensive evaluation.

The rest of the paper is arranged as follows.Section 2 is a problem formulation.In Section 3,the grid method is used to carry out the remote sensing modeling,index design and the computation of time visible set.Section 4 studies weight design method of assessment system for coverage of satellite system.Section 5 introduces the utilization of the proposed coverage evaluation method based on GPU and CPU computing model.Finally,the main conclusions of the paper are drawn.

2.Problem formulation

The study of the satellite coverage usually focuses on the analysis of the characteristics of the region or the target,or the optimization method of coverage problem.20–22The coverage scene of the satellite is shown in Fig.1.Currently,the research on the effectiveness evaluation of the whole coverage scene is less.To evaluate the coverage capability of remote sensing satellites on a specific location or region on the earth surface,the most common coverage performance indicators are the coverage times,the percentage of time coverage,the area coverage percentage,the revisit time,and so on.Among these indexes,the revisit time of satellite earth observation process is a very important index.If the revisit period is shorter,the satellite will be at a higher time resolution on the ground covered area sampling.

Fig.1 Coverage scene of satellite.

The above indicators can be calculated using the grid point analysis method.According to the calculation results of a single grid point,and then the statistical average,maximum and minimum values of all grid points can be obtained for the specific location and area coverage performance index.

The coverage of satellite system is usually described from two dimensions of space and time.The spatial coverage of the satellite system can be used to characterize the spatial observation ability of a satellite system in a given period of time,and the time coverage of the satellite system can be used to characterize the time domain capability of the satellite system in a given period of time.Here,six indexes in space coverage efficiency and time coverage efficiency are chosen to describe the coverage characteristics that we choose.The space coverage efficiency(percentage of coverage,Ground Sample Distance(GSD)).The time coverage efficiency(time coverage percentage,average coverage gap,maximum revisit time,and average response time).The evaluation index system of coverage effectiveness of remote sensing satellite system is constituted by the above indexes.

3.Grid method

Based on the simulation of satellite orbit,the satellite position and load range can be obtained.The grid point coverage method is used to obtain the statistical data of the satellite coverage on the ground.The grid point analysis flowchart is illustrated in Fig.2.With the increase in the number of grid points,memory and time consumption will rise sharply.In the simulation,it is found that the time consuming is mainly reflected in the visibility of the satellite and the grid.

3.1.Remote sensing load modeling

To carry out the remote sensing load modeling,the mathematical model of observation on earth needs to be built first.The fundamentals to build the model are the location and kinematics analysis of spacecraft.23We use the perturbation of J2,which has good accuracy in the study of the coverage quality of the constellation.The geometric positioning method is applied to the load modeling,which is based on the field of view.In Fig.3,O is the centre of the earth,OPNis the north direction,OG is the direction of the vernal equinox,S is the remote sensing satellite,P and P′are respectively the remote sensing point and the farther sensing point on the ground,and PBis sub-satellite point.

From Fig.3,the vector triangle under the geocentric inertial system can be established as follows:

The equation of the Earth ellipse is

Fig.2 Grid point analysis.

Fig.3 Remote sensing geometry location.

where （Px，Py，Pz）denotes the coordinates of the point P,and aeand beare the long half axis and short half axis of the Earth ellipse respectively.

Substituting Eq.(1)into Eq.(2)yields the following equations:

According to Eq.(1),we can obtain the coordinates of P as follows:

Apply the coordinate transformation,and the coordinates of P in Earth fixed coordinate system can be obtained as

where G（t）is Greenwich sidereal time angle,Pe（X，Y，Z）is the coordinates of P in Earth fixed coordinate system.

By using the coordinates(X,Y,Z)of Pein Eq.(6),the relationship of the longitude L,latitude B and height H of the ground projection point in geodetic coordinate system can be obtained as

where e is the eccentricity of the Earth;N is the curvature radius of unitary ring of the point P,and the expression of N is defined as

Obviously,Eqs.(7)and(8)formulate the nonlinear implicit equation group to determine L,B and H,and using iteration method can solve this nonlinear equation group.

According to the field of satellite load angle,we can establish the model of satellite load using the geometric positioning method.This is the model basis of grid point analysis.

3.2.Index design based on grid point analysis

To calculate the constellation coverage performance on a region,the grid point method is used generally.This method firstly divides the area into many grids,and then calculates the constellation coverage performance of each grid point,which will eventually derive statistical results in a certain range of ground(average value,maximum value,and minimum value).

Fig.4 illustrates the grid point partition, λminand λmaxdenote the minimum and maximum longitudes,φminand φmaxdenote the minimum and maximum latitudes.Firstly,the boundary of the specified region is determined,and then the maximum and minimum longitude and latitude of the boundary are obtained.The grid points in the region boundary are selected by the radial line method.There are two kinds of grid division methods:the equal latitude and longitude method and the equal area method.Because the grid point method usually uses the number of grids to represent the area of coverage,the grid division usually uses the latter.

Fig.4 Grid point partition.

Fig.5 Principle of radial line method.

Fig.5 shows the principle of the radial line method.In Fig.5,a radial line is made from a point P to right.If P is in a polygon,the number of intersections is odd;in the outside,the number of intersections is even(including 0).In the special cases,if the radial line passes through the polygon vertex,and if the intersection point is located on both sides of the radial line,add 1,otherwise add 2.As an algorithm to judge whether a point is in a polygon region,this method is applicable to any polygon.

Given a region D,after the grid points are divided,we can obtain the grid point set V（G）= ｛G1，G2，G3，...｝.Suppose the longitude λiand latitude φiof Giis ｛λi，φi｝,and the coverage scope of the satellite field of view is R.In a simulation step,the radial line method can be used to determine whether Giis in R,and if so,the grid point can be seen;if not,it is not visible.After a specific time period simulation,the time set for each grid point visibility is finally obtained,and the coverage of the grid points is analyzed based on the visible set of grid points.

3.3.Visible time set

The visible time set is illustrated in Fig.6.It is supposed that the number of satellites is T,and the time set of the satellite k on the grid points iswhere ndenotes the numkber of visible time segment of the satellite k on the grid point.The coverage function of the satellite k is as follows:

Fig.6 Visible time set.

Simulation step is set as tstep,and after two simulation steps,the integrated time set isThe integrated procedure is shown in Fig.6.In Fig.6,the first time axis indicates the visible time set of Satellite 1,the second time axis is the visible time set of Satellite 2,and the third time axis denotes the combined set of visibility of two satellites.

The coverage function of a total of T satellites is as follows:

The visible time set of a total of the grid point Gican be expressed as

where n denotes the number of the visible time segment set;i represents the i-th visible time set;in and out are the time to enter and exit the grid point,respectively.

We can derive coverage characteristics based on visibility time set design,such as the coverage percentage,the maximum revisit time,the average coverage gap,and a series of other indicators.The calculation formulas of each coverage index are as follows:

The maximum revisit time:

The average revisit time:

The maximum coverage time:

The average response time:

The average time gap:

The average coverage gap:

The percentage of time covered:

where tbegin,tendand NGapare the begin time and end time of the simulation,and the number of non-visible time sets,respectively.

4.Weight design method of assessment system for coverage of satellite system

4.1.Analytic hierarchy process

Analytic Hierarchy Process(AHP)24is a solution which is proposed by Saaty to establish the mathematical model of hierarchical relationship for multi-level complex system.It combines quantitative and qualitative analysis,performs the quantification processing according to relative importance of each index,and finally obtains the weight of each index by solving the eigenvector of the comparison matrix of the current layer factors to upper layer factors.This method is generally divided into constructing hierarchical model,formulating judgment matrix,calculating weight vector,and consistency test.

Step 1.Constructing hierarchical model

Based on the indexes to evaluate multi-satellite coverage,the constructed index system is shown in Fig.7.

Step 2.Establishing judgment matrix

Refering Refs.10,11,and using nine-level scaling method proposed by Satty,weight judgment matrix is constructed as

where aij＞ 0，aji=1/aij,aijindicates the important degree of index airelative to index aj.The nine-level scaling method divides the important degree of index airelative to index ajas 9(extremely important),7(very important),5(important),3(slightly important),and 1(identical),respectively.The four level scaling method divides the important degree of index index airelative to index ajas 4(extremely important),3(very important),2(important),and 1(identical),respectively.

Step 3.Computing weight vector

Solve the characteristic equation AW=λmaxW,and calculate the maximum eigenvalue λmaxwith its corresponding eigenvector W= ［w1，w2，...，wn］.

Step 4.Conducting consistency test

After the maximum eigenvalue λmaxis obtained,it is necessary to carry out the consistency test.If it do not meet the consistency rule,the weight result can not reflect the important degree of the reaction index,and the judgment matrix needs to be reconstructed.

Fig.7 Index system.

Consistency checking formulas are as follows:

where CI is consistency test index,n denotes the order of judgment matrix,and RI is the average random consistency index.

When CR＜0.1,it is considered that the judgment matrix satisfies the consistency,otherwise,it does not satisfy the consistency.

4.2.Entropy weight method

The entropy weight method is an objective multi-index evaluation method.After each index of the object is determined,the relative intensity of each index can be calculated.The result is the difference of the information of each index.

Set n to be the number of evaluated object which has m item index.The evaluation matrix is

The standardized method of positive index and reverse index is as follows:

Through the standardization based on Eqs.(23)and(24),the standardized matrix R= ［rij］m×ncan be obtained.Further,according to the definition of Shannon information entropy,we can define entropy Hjof the j-th index as

where 0≤ωj≤1,andThe entropy-weight method can sufficiently analyze the information of the objective data,but it cannot easily reflect the expert suggestion and the relative important degree of the index.If AHP method and entropy weight method are combined,the comprehensive advantages of subjective and objective evaluation will be brought into play.

4.3.Fuzzy comprehensive evaluation

Fig.8 Membership function.

Fuzzy Comprehensive Evaluation(FCE)is an important method to evaluate the effectiveness of the system.According to the fuzzy mathematics theory,the evaluation of multi-index system is transformed into quantitative analysis.We can generally use the fuzzy classification method.The system satisfaction set V is divided into V={Poor,Pass,Medium,Good,Excellent}={E,D,C,B,A},and the membership functions of V are shown in Fig.8.Firstly,the membership parameters of each index are given according to the satisfaction degree,and then the fuzzy vectors of each index are obtained according to the membership degree.Finally,by fuzzy reasoning through all fuzzy vectors and weight vector,the system synthesis results can be obtained.

The membership functions are selected and the membership parameters are set as m1,m2,m3,m4,and m5,x is the input variable of the universe.The selected relationships of the membership functions are as follows:

The fuzzy line vector RFi= ［S1（xi），S2（xi），S3（xi），S4（xi），S5（xi）］（i=1，2，...，n） of each index is calculated according to the above formula.Suppose the index weight W= ［w1，w2，...，wn］ and membership matrix RF= ［RF1，RF2，...，RFn］T,and then fuzzy synthesis results BFcan be obtained as

5.Experiments of satellite coverage characteristic

In this section,we made the experiments of satellite coverage characteristic.Using the developed algorithm program calculated the basic indexes and verified the validity through the comparison with Satellite Tool Kit(STK).STK is a common tool for satellite coverage analysis,but its scalability is not good,it is suitable for calculating the basic performance indexes.Many basic indices of the programs we developed are compared with STK to verify the effectiveness of the program.STK does not have a performance evaluation algorithm,so we focus on this aspect of work.On the basis of AHP-FCE,we added an objective evaluation of entropy weight method,which effectively avoided subjective error.Meantime,in order to solve the issues of computing time long and complexity high of the algorithm,the acceleration method of the grid point analysis was also studied.Then,the experiments of satellite coverage characteristic were made and the results analysis was conducted.

5.1.Acceleration method of grid point analysis

In order to conduct the evaluation analysis,we need to build a general and efficient coverage simulation algorithm based on the grid point analysis method.However,this method is slow,and the time and space complexity is high.Therefore,in this paper,we propose a parallel acceleration method based on CPU+GPU for calculating coverage characteristics of remote sensing satellite system.Because the algorithm principle using by CPU or CPU+GPU is the same,in the program only the dual cycle is given to GPU to accelerate the simulation results.The GPU results are also returned to the CPU,so the results of CPU and CPU+GPU are the same in two different ways.

Fig.9 illustrates the comparison of time spent of the grid point analysis using CPU and CPU+GPU.The CPU+GPU heterogeneous model makes full use of the high storage bandwidth and computing power of GPU,which has many advantages and has been widely used in many fields.The core idea of GPU+CPU computing is to design kernel function.The visibility of the grid point is judged by GPU in order to avoid the excessive multiple cycle design in CPU programming.In general,the calculation speed can be increased by nearly an order of magnitude.The difficulty of software design lies in the design of the mapping relation between the load field of view and the grid point in the multithreading.The parallel algorithm runs as follows:

Step 1.Open up data space of the grid points and the load field of view boundary in CPU and GPU.

Step 2.Call kernel function in GPU to calculate the grid point visibility,and update the visible time set.

Step 3.Visibility results return CPU to update coverage index.

Set up a number of satellite coverage scenarios using the serial model and GPU+CPU heterogeneous parallel model simulation for 24 h respectively.The running time of simulation is statistically shown in Fig.9.

Fig.9 Time spent of grid point analysis using CPU and CPU+GPU.

Fig.10 Comparison of simulation results.

To build the satellite simulation experiment scene and to calculate the area coverage percentage with the established model in Section 3 in this paper,the simulation result is shown in Fig.10.In Fig.10,we choose J2perturbation orbit,0.1°latitudinal step,and equal-area division method,and obtain the coverage percentage in some zone through simulation.Fig.10 also provides the computation result.In order to study the validity and correctness of the model and algorithm,the results of the calculation are compared with the results of the famous STK developed by Analytical Graphics Corporation of the United States.By comparing the computation result of the established model with the result of STK,the maximum error is less than 2%,and the consistency between them is very satisfactory,which means that the established model and the design algorithm are valid.

5.2.Performance evaluation

The satellite remote sensing system is composed of three satellites,the shown areas in Fig.11 are as the target,and then the simulation was carried out for 48 h.The simulation orbit and load parameters of the satellites are set as Table 1.The calculated coverage results of constellation and each satellite are listed in Table 2.Here,GSD denotes ground sample distance.

The six orbital elements of three satellites are listed in Table 1,where a,e,i,Ω,ω,and M are semimajor axis,eccentricity,inclination,longitude of the ascending node,argument of periapsis,and mean anomaly,respectively.The Field Of Vision(FOV)and Ground Sampling Distance(GSD)of the loads are also given in Table 1.

Fig.11 Grid point analysis.

Table 1 Satellite parameters.

Table 2 Results of regional coverage.

In this paper,we discuss the coverage characteristics of grid points in the latitude of China.Because the satellite orbit is the solar synchronous orbit,the coverage characteristics of the grid points on the longitude are very close,and they are not put in the paper.Counting the coverage characteristic result of multi-satellite on the grid point in 41°latitudinal zone yields Fig.12.Fig.12 shows that the grid point analysis method can easily get regional coverage results of the single satellite or constellation,but also can get coverage characteristics of different longitude or latitude grid point.The simulation data can provide the data supports for the next performance evaluation.

The verification of the coverage characteristic of multisatellite on the specific point of latitude 41°and longitude 116°is conducted,and the comparison result between the model in this paper and STK is listed in Table 3.We can see that there is good agreement between two reults.

Fig.12 Coverage characteristic result of multi-satellite on grid point in 41°latitudinal zone.

Table 3 Verification of three indexes of coverage characteristic.

The implementation procedure of the proposed coverage evaluation method is as follows.Firstly,the simulation results in Table 2 are normalized to facilitate the subsequent evaluation,and the results of the normalized coverage index are listed in Table 4.Then,based on AHP method and entropy weight method,the weight vector is determined,respectively.In Table 4,the space efficiency index include 2 indexes,i.e.,area coverage percentage and GSD,and the time efficiency index covers 4 indexes,i.e.,average coverage gap,maximum revisiting time,average response time,and time coverage percentage.

5.2.1.Solution of index weight vector

(1)Analytic hierarchy process

The judgment matrix of space efficiency and time efficiency are as follows:

where A1and A2are the judgment matrix of space efficiency and time efficiency.

To solve their largest eigenvalue λ1max=2,λ2max=4.0310.

Consistency check, CI1=0, CI2=0.0103, and CR1=0＜0.1,CR2=0.011＜0.1,which means the consistency verification to be passed.

To calculate the greatest eigenvalue related eigenvector of each judgment matrix,we can obtain three weight vectors as follows:

Space efficiency index weight:

Time efficiency index weight:

The judgment matrix of the second layer index relative to the first layer efficiency index of the satellite is chosen as

Similarly,we can obtain the index weight W3of the second layer index relative to the first layer index as

After synthesis,all index weights are given as follows:

(2)Entropy weight method

From entropy weight method,building coverage system index matrix,and then normalizing it,yield the standardized matrix R as

Using Eq.(25)calculates the entropy value based on the entropy weight method as follows:

Using Eq.(26)calculates the entropy weight line vector as follows:

5.2.2.Multi-index synthesis method

Hierarchy analysis method considers the expert experience and the preference of decision makers,and is reasonable in general,but cannot overcome the effect of subjective factors.The entropy weight method fully analyzes the objective data objectively,but cannot reflect the relative importance of expert experience,and sometimes cannot reflect the actual index.A comprehensive method combining AHP and entropy weight method for multi-satellite coverage efficiency evaluation is necessary.

When the weight of the entropy weight method and AHP are the same as the index order,as a result,the weight obtained by entropy weight method can effectively eliminate the influence of subjective factors.When the weight of the two kinds of methods is different according to the order of importance,the weight obtained by AHP is the final result.When it is in the middle,a compromise can be used.This method combines the entropy weight method and AHP advantages,and makes the evaluation result more reasonable.

According to the calculation results,the following formula can be used.

where α is the synthesis factor.In this paper,choose α =0.5,and the final index weights are

Table 4 Results of normalized coverage index.

5.2.3.Coverage effectiveness evaluation of each satellite

To evaluate the coverage effectiveness of a region,we should not only know the constellation comprehensive results,but also quantitatively analyze the coverage ability of each satellite.In this part,we use a simple linear weighting method to give the coverage effectiveness of a single satellite to the region.

Fig.13 shows the coverage performance result of each satellite in time and space.

Define the coverage effectiveness of a single satellite as

where dikis normalized value of the index,ωikis the weight of index i,m is the number of indicators,and k represents satellite k.

Based on the data of Table 4,using Eq.(33)can calculate the coverage effectiveness of a single satellite as follows:Satellite A:C1=0.351883347,Satellite B:C2=0.174093062,and Satellite C:C3=0.214809823.Fig.14 shows the coverage effectiveness of each satellite.As seen from Fig.14,the coverage effectiveness of Satellite A is the best,and Satellite B is the worst.

5.2.4.Comprehensive coverage effectiveness evaluation of constellation

In this part,we use fuzzy comprehensive evaluation to evaluate the constellation coverage efficiency.The parameters of the membership functions in Fig.8 can be set as{0,0.25,0.50,0.75,1.00}.

Fig.13 Coverage result of each satellite.

Fig.14 Coverage effectiveness of each satellite.

Substituting the normalized coverage index of satelite constellation in line 4 of Table 4 into Eqs.(27)–(29)yields fuzzy membership matrix as follows:

Then,using Eq.(30),the fuzzy comprehensive evaluation vector BFcan be calculated as follows:

The maximum membership degree of the result is 0.3541.According to the maximum membership degree rule of fuzzy evaluation,the performance of the constellation coverage on the region is ‘‘Medium”,which means that the synthesis performance of the constellation coverage on the region is better.

5.2.5.Brief summary

At the end of Section 5,we provide a brief summary for this section.Firstly,according to the time-space coverage characteristic of the remote sensing satellite,the represented coverage characteristic indexes are chosen and calculated,as shown in Table 4;then,using AHP and entropy-weight methods,an assessment system of coverage characteristic of the satellite is built.In this section,Fig.13 presents the comparison of the coverage characteristic of each satellite,and it can compare the good and bad of a single index,but it is difficult to compare the good and bad of the comprehensive ability.Fig.14 provides the result of comprehensive coverage ability of each satellite,the conclusion is that the comprehensive coverage effectiveness of Satellite A is the best,and this method is used to distinguish the good and bad of the comprehensive coverage ability of the different satellites for some zones.Using the fuzzy synthesis method,Section 5.2.4 makes the comprehensive evaluation on the constellation made up of three satellites:Satellite A,Satellite B and Satellite C,and the evaluation result is ‘‘Medium”;this method is suitable for evaluating the good and bad of the comprehensive coverage effectiveness of the constellation made up of many satellites.

6.Conclusions

In this paper,focused on the requirement to evaluate the satellite coverage characteristic of the remote sensing satellite from the view point of multi-index system,the AHP and entropy weight method are used to design the weight value,and the weight of each index can be determined scientifically and objectively.The main conclusions are as follows:

(1)The proposed method not only avoids the arbitrariness of weight determination,but also considers the fuzziness of human thinking judgment.It is of clear logicality and strong operability.

(2)The proposed linearity weighting method and fuzzy comprehensive evaluation method can be respectively used to the single satellite coverage evaluation and the constellation coverage efficiency evaluation.Using the proposed multi-index evaluation method for the coverage efficiency evaluation model,more in-depth study on the simulation of coverage characteristics can be made.

(3)The computation model based on GPU and CPU can obviously decrease computing time for the calculation of index of multi-satellite.

(4)The simulation results based on the established mathematical model and computation method of coverage characteristic of remote sensing satellite and one of STK software are very consistent.

Acknowledgements

This study was co-supported by the National Key Basic Research Program of China(No.2014CB046403)and the research project of Beijing Institute of Spacecraft System Engineering.Moreover,the authors would like to thank the supports from senior engineer Qian Wang.