Preliminary Design of the Constellation Distribution for a Proposed Mars GNSS

HAN Tingting SHI Xian JIAN Nianchuan FENG Laiw u PING Jinsong

(1 Department of Geographical Science,Hubei Normal University ,Hubei 435002,China)

(2 Shanghai Astronomical Observatory/CAS,Shanghai 200030,China)

1 Introduction

Deep space exploration is the first step for human beings to understand the Earth and beyond,in a long process of studying ,exploring and ultimately settling dow n on other celestial bodies in the solar system.Missions to the Moon and M ars in recent years have been playing some key roles in this discipline.

M ars exploration,especially,has aroused w orldwide interest again since the 1990s.Even in China,after accomplishing a successful Chang' e lunar mission,a joint Chinese-Russian mission(know n as YH-1 & Phobos-Grunt) will be launched later this year to explore the M artian planetary system.To facilitate future exploration of Mars,most space agencies are aw are of the need to set up more reliable communication and navigation systems in the M ars environment.Currently ,we still use ground-based deep space stations to support radio communication and navigation betw een the Earth and M ars,but these facilities have undesirable restrictions in communication bandwidth and navigation accuracy.

The concept of a Mars Global N avigation Satellites System (MGNSS)constellation involves a number of satellites flying around M ars to monitor Mars orbiters and landers,and to carry out relay communication betw een these vehicles and Earth stations.The global navigation satellite systems for the terrestrial planets should be based on an open standard supporting communication and navigation services for a wide variety of spacecraft.Furthermore,Earth stations should be able to carry out communication and navigation operations with all the spacecraft bound for different planets using internet IP addresses as their unique identifications.One of the key objectives for future deep space exploration missions is to establish a constellation for a M artian global navigation satellite system[1-4].

At present,the mature GPS global positioning and navigation system consists of 28 satellites moving in four orbital planes around the Earth.Each plane has six uniformly distributed satellites,with a spare one reserved for standby.The orbital altitude of GPS satellites is 20200 km w hile their inclination is about 56°.T his system supports accurate position and speed acquisition,and also provides high-precision time standards for users located over most(98%)of the Earth surface.Aclient uses at least four satellites to quickly identify his or her location and attitude on earth[5].

It should be pointed out that dynamic measurements performed for most GPS applications are not usually required in the exploration of other planets.T rading betw een costs and features,our proposed MGNSS constellation will only provide limited services such as real-time vehicle navigation for M ars orbiters,landers and rovers,as well as static positioning to support scientific data collection.Hence designers of early constellations may use fewer satellites to provide non-continuous coverage,and employ Doppler tracking techniques to support MGNSS orbits for satellite navigation and positioning.As a result,there will probably be few er satellites in early M GNSS as compared with today' s GPS.

Satellite orbit simulation is very common during space mission preparation,so as to match the scientific and technical goals of the space mission to its intended applications.AUS company AGI has developed a satellite simulation softw are toolkit(STK),w hich is a rare instrument that can be used to quickly analyze complex land,sea and air tasks,provide easy-to-understand charts and texts to determine the best solutions.S TK can also produce position and attitude parameters for remote sensing data analysis[6-7].

In GNSS study ,the Walker constellation[8]has advantages of uniformity and symmetry.It is usually the first choice for navigation satellite constellation designs.There are four key parameters i,T ,P,F in the Walker method,standing respectively for the orbital inclination,the total number of satellites in the satellite constellation,the number of orbital planes,and the phase factor.This article will use the Walker constellation for establishing the optimal satellite distribution of the considered constellation.

Alow circular-orbit constellation is more suitable for global coverage.This article chooses the use of inclined circular orbits to establish the proposed MGNSS.Considering that the smallest number of orbital planes for a large coverage in the constellation design should be used,we find that three or less orbital planes in the MGNSS can satisfy the above requirement.In the following study,based on the distribution pattern of the Walker constellation,we use S TK to analyze various designs of the MGNSS constellation,while assessing and analyzing the system characteristics and global coverage.

2 Performance of MGNSS constellation

In the following part,w e first carry out a preliminary design of the MGNSS constellation.Then we use the S TK to analyze its coverage and navigation/positioning performance,so as to check and test w hether its performances meet the mission requirements,and to assess the best designs of the constellation.

As in the case of the Earth GPS system,we use the following quality factors to evaluate the quality of the MGNSS performance:

1)T he number of visible satellites for different regions of the w orld(that is parameters of coverage resources).

2)The geometric factor DOP (Dilution of Position)[5]for assessing the constellation' s availability ,accuracy and reliability,in order to compare the M GNSS to other in-orbit operations of the GNSS.

How ever,in such circumstances the standard definition of the DOP (see Table1)cannot be directly used because it needs more visible satellites at the same time and the elevation angle must meet a certain limit.So this geometric factor cannot be directly used for the MGNSS because there are few er visible satellites at low elevation.M ost MGNSS users are landers,rovers or slow-moving vehicles.So the cumulative value of DOP,w hich is obtained by a certain amount of accumulated DOP value in a time period,can apply in the positioning accuracy to assess the system.It also considers the user-equivalent range errors.Therefore,this study uses the cumulative value of DOP to assess the constellation.

Table1 DOP Factor and Positioning Accuracy(PA)

3)The concept of navigation precision is similar to that of DOP,but it takes into account onew ay ranging method that is not accurate[2-3,9-10].

3 Distribution configuration of MGNSS constellation

In 1999,the researchers of NASA's JPL proposed a M GNSS concept.This constellation is made up of six circular orbit satellites and the orbital altitude is designed to be 800 kilometers.It uses ranging and Doppler method to provide navigation services for Mars users.The designation considered the balance betw een the needs of communications and navigation,involving the equatorial satellite and the polar-orbiting satellites comprehensively.As ground control points on Mars have not been established,the system provides full service for M ars surface and the Mars probe from the earth[11-12].

1)The Costs Considered in the Constellation Designation

We divide M ars into three regions to consider and to discuss the constellation designation.

First,the polar and the 2nd equator area of M ars,they are the most interesting places in Mars exploration.Secondly,the area of the middle latitude,some Landers are planned to land in the middle latitude regions in future.U sing an equator orbital plane to meet the needs of equatorial region coverage,navigation and positioning.Similarly,considering the corresponding orbital planes to meet the need for polar and the middle latitude region.The design has certain relevance with the purpose of practical application.The constellation parameters are read in Table2 and the simulation results are given in Table3.

There are only 6 satellites in NASA' s design,so the coverage resource is poor.We improve NASA' s design.The coverage performance of the improved NASA' s design is better compared with the original one.In the middle latitude region,the coverage resource is nine,and for the majority of the global region the coverage resource becomes 4.The Design-1 refers to the Phobos orbit w hich is also near to equator.Its coverage performance is similar to the improved NASA' s design.The Design-2' s coverage performance is superior to the other three designs.The Design-2 refers to the Phobos and Deimos' orbit,so it can easily make full use of resources with exploring Phobos and Deimos,see Fig.1.This design considers applying to Mars' satellite orbit about equator.From the coverage performance point,the Design-2 is the best one.

Table2 Parameters of the Constellation Design

Table3.1 Coverage resources

Table3.2 DOP values

Table3.3 Navigation accuracy m

The accumulated value in the NASA' s design of DOP factor is more than 1 000 in an hour.This design in navigation performance needs to be improved.This article only analyzes the other three systems in navigation performance.The improved NASA' s design' s accumulated value of DOP factor in an hour is much w orse than the Design-1 and Design-2.The navigation accuracy for the three designs is not more than 250 meters,w hich is precise enough for the surface of M ars and M ars exploration vehicle navigation requirements in the initial tasks.

The Design 2 is to establish a M ars exploration radio navigation,communication relay and remote sensing system of the outpost based on Phobos and Demios landing detection.Considering the costs and resource utilization,and taking the advantages of the natural satellites of the M ars,the Design-2 for the constellation distributions is the best choice for M GNSS.

2)M ulti-Satellites Constellation Design

It is possible to establish Mars global navigation system by using much more satellites like the Earth GNSS in future.And the system can meet the needs of users to see four or more satellites on the Mars' surface at any time over a certain elevation.So referring to the designation Earth's GNSS,we give another designation by means of F-Design,for Mars constellation of global navigation satellite system without considering the cost[8,10,13-14].

Using Walker constellation design to distribute the satellite,the orbit parameters are given as Table4 and the simulated results are read as Table5.

Table4 F-design parameters

Fig.1 Design-2 constellation

Table5 F-design' s results of the simulation

T he coverage performance of F-design is excellent in all designations,the average coverage resource is 8 and more than 100%region of the M ars can be covered,including the both regions of highlatitude and low latitude.The DOP values of F-design is better in most regions of the M artian surface.And it is less than 10 and about 2 with the excellent positioning accuracy.M ars surface navigation accuracy is less than 50,and most of the region is around 20.From this point of view ,for the F-Design,the constellation design is better and can meet the requirements of navigation and positioning w hich is similar to Earth's global navigation system.It can be used as a choice for the future development of MGNSS constellation designation.

4 Summary

This article discusses the principles of constellation design and various configurations for establishing the MGNSS.The popular ST K tool is used to analyze the constellation coverage,DOP factor and navigation accuracy.We also try to optimize constellation designs in order to obtain the best performance of the constellations.Considering costs and features,one of our proposed designs(Design 2)using Phobos and Demos as platforms can be used as a baseline for designing the MGNSS.This design seems to taking full advantage of all available resources,and may also be able to meet the requirements of coverage as w ell as navigation/positioning accuracy.

In the future,w hen cost is no longer the most important factors,we may consider using more satellites to construct enhanced Mars global navigation systems.These less restricted configurations can be based on the F-design,using the Walker constellation to distribute the satellites.The results presented here may benefit the design of future M GNSS.

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