A RECONFIGURABLE MARS CONSTELLATION FOR RADIO OCCULTATION MEASUREMENTS AND NAVIGATION

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1 A RECONFIGURABLE MARS CONSTELLATION FOR RADIO OCCULTATION MEASUREMENTS AND NAVIGATION Iabelle Nann, Dario Izzo, Roger Walker ESA Advanced Concept Team, ESTEC (DG-X) Keplerlaan 1, 2201 AZ Noordwijk ZH, The Netherland ABSTRACT A Martian contellation compriing everal micro pacecraft can be exploited to perform radio occultation meaurement between contellation atellite through the limb of the Martian atmophere. Thi would allow the Martian atmophere and climate cycle to be characterized with unprecedented patio-temporal preciion, leading to a ignificant increae in atmopheric knowledge and hence rik reduction for atmopheric entry probe. Additionally, thi contellation could be reconfigured at relatively low cot uing electric propulion to provide navigation ervice to ubequent Mar miion. Thu, with the ame radio payload, the contellation ha the potential to ubtantially increae the accuracy of orbit inertion, aero-capture and poible landing of thee miion. However, an aement on the feaibility and potential benefit of uch a concept ha to be carried out. Thi paper decribe the optimization of the orbital geometry of two contellation (compriing 4 and 8 atellite), which ha been performed in order to obtain the maximum number of globally ditributed radio occultation event between atellite in the contellation. The reulting contellation geometrie have been explored from a navigation performance perpective, Auming that the navigation aid to incoming pacecraft ha to be given only every 26 month, i.e. when a minimum energy launch window occur between the Earth and Mar, and ome intereting contellation of 4 and 8 atellite are preented in the paper. Some reconfiguration trategie have then been propoed and aeed and the feaibility of the concept ha been proven. INTRODUCTION With the current agencie pace policie on the exploration of the olar ytem Mar appear to be the ultimate goal for many near-future pace miion. More and more miion are planned to fly to Mar a orbiter or lander; however, at preent there i no exiting and effective ytem that either totally decribe the Martian atmophere in pace and time, or that would provide an efficient and precie aid for a pacecraft during final approach to the red planet. Evidence on the poibility to perform ueful meaurement of ome planet atmopheric propertie by mean of inter-atellite link wa firt given in 1995 when a LEO-GNSS occultation meaurement campaign wa performed and ued to improve the exiting numerical model of the Earth atmophere. The European Space Agency founded, in the lat decade, a number of pre-phae A tudie (e.g. the Atmophere and Climate Explorer Plu), but none of them wa applied to Mar. On the other hand, the pacecraft going to Mar at preent largely rely on the Deep Space Network,

2 which provide ufficient navigation aid a long a the targeting doe not require high preciion: thi would be the cae during, for example, an aero-capture or targeted landing. Moreover, the DSN appear to render the pacecraft uncontrollable for the lat 13 minute before arrival at the periapi due to the control ignal time-of-flight to Mar. Thu, thi paper aee the feaibility of a miion to Mar that ha to perform two different tak, i.e. it earche for optimal orbital configuration of contellation of 4 and 8 micro atellite taked with alternately performing radio occultation meaurement and navigation for incoming pacecraft. In thi paper, the radio-occultation technique i briefly reviewed and an objective function i derived. The enitivity to the J 2 gravity harmonic for a choen contellation i then analyzed, and the figure of merit that have to be evaluated to ae navigation performance are introduced. Finally, the numerical method ued to approach the problem are preented, together with the reult. RADIO OCCULTATION PERFORMANCE Atmopheric meaurement The principle of the radio occultation technique (hown in Figure 1) i baed on precie dualfrequency phae meaurement of a atellite receiver in orbit tracking a etting or riing atellite in the ame contellation through the limb of the Martian atmophere. Thee meaurement are combined with the Doppler hift due to the atmophere, and the atellite tate vector information can be ued to obtain the atmopheric bending angle and furthermore vertical profile of the atmophere refractive index. Thi lead to the characteriation of the atmophere (preure, temperature, water vapour, Figure 1: Radio Occultation Technique wind, etc) with high vertical reolution and accuracy in clear or cloudy condition [Walker et al., 2004]. One of the greatet difficultie in obtaining an optimal configuration i the extremely complicated relation between the contellation geometry, i.e. the number of atellite and the et of their oculating parameter, and the poition, length and number of occultation event per Martian day (ol). The aim in thi paper wa to maximie both the number and uniform patial ditribution of occultation event per couple of ol. One occultation i called an occultation event if it lat more than 50 econd and atifie the contraint given by the following formula: ( OP0) ( O1O 2), P0 [ O1O 2] and 0 < altitude( P0) < 300km. In order to define ome index decribing the patial ditribution of the occultation event, the Martian urface wa divided into N=40 ector compried between two latitude λ by taking care that: in λi + 1 in λi 1 = 2in λi 2 in order that the area of each ector i equal, i.e. S= km. For a given geometry the number of occultation event occurring in each ector wa counted and the tandard deviation σ wa introduced a a meaure of the ditribution between ector. Each geometrical configuration wa therefore judged on the bai of both the total number of occultation event and of the value of thi

3 tandard deviation. Though thi problem hould ideally be tackled with a multi-objective approach, it wa decided to olve the problem with a unique formula combining the two objective function in a uitably weighted fahion, hence yielding a calar objective function. The choen objective function ha the form: n J ( n, σ ) = p σ with p =3 or 2 for repectively a 4 or 8-atellite contellation and n the total number of occultation event for two Martian day. Thi wa found to be a very good compromie between a high number of occultation event and the patial ditribution. Mar-oblatene effect The effect of Mar oblatene were tudied in order to define how the above objective function evolve with them, and whether they would neceitate tation-keeping maneuver. To allow u to concentrate on oblatene effect, the altitude of the atellite were contrained above 300 km, uch that drag effect are negligible. Two oblatene effect are ditinguihed, the firt one being a regreion of the node. The econd perturbation effect i an advance of the argument of periapi: thi i however not treated here ince the orbital eccentricity of contellation member wa contrained to be cloe to zero. It wa hown that the occultation performance i inenitive to the J 2 parameter and that therefore no tation-keeping maneuver i neceary. NAVIGATION PERFORMANCE The performance of a navigation ytem i generally evaluated by the three following parameter: availability, accuracy and reliability. Only the firt two are aeed in thi paper. The availability ha been defined a the number of atellite in view of the incoming pacecraft at each obervation tep, i.e. every three minute. In order to compute the poition of the incoming pacecraft, it i neceary to have at leat four atellite in view. The accuracy of a navigation ytem i uually repreented by two quantitie: the Uer Equivalent Range Error (UERE) and the Geometric Dilution of Preciion (GDOP). The UERE i found by mapping all of the ytem and uer error into a ingle error in one uer meaured range. It i mapped into the computed poition by a geometrical factor called DOP. The GDOP i given in meter; the lower it value the tronger the geometry of the obervation model, i.e. the pacecraft pread out in angle with repect to the uer. The GDOP value i only available if at leat four atellite are in view: thu it can alo be ued a a meaure of the availability of the ytem. The DOP by itelf can repreent the accuracy of the ytem if it i aumed that all the meaurement have the ame UERE, which will be the cae in thi paper. The DOP value were derived for an incoming pacecraft on an approaching hyperbola with a perigee altitude target of 150 km (repreentative aero-capture trajectory) from four day before arrival at the periapi to the periapi paage. Thi wa repeated for orbit inclination tarting from 1 6 to 150 degree. The GDOP i defined by the covariance matrix of error ( H T H ) a follow: T GDOP = tr( H H ) 1 1 x, where 2x H =... mx 1y 2 y... my 1z z... mz

4 H i called the enitivity matrix, r i i a unit vector expreed in the Mar Inertial Reference Frame and pointing from the incoming pacecraft toward the i th navigation atellite in the contellation and m i the number of viible atellite from the incoming pacecraft perpective. The um of the number of time that the GDOP i not defined wa ued a the performance index for the Monte Carlo imulation for a 4-day pacecraft approach at an inclination of 6 and 90 degree. A mentioned earlier, no reliability performance evaluation (through evaluating robutne in the face of lo of one or more contellation member) wa performed. NUMERICAL METHODS The following method were applied for contellation of 4, 6 and 8 atellite but the reult will only be preented for 4 and 8 atellite, a thee are the mot intereting cae. Radio occultation event The problem wa firt tackled with a Monte Carlo approach of 50,000 iteration. At each iteration the contellation geometry, i.e. the keplerian element of each atellite, wa initialized randomly, with ome contraint on the emi-major axi and the eccentricity ( 1.2* r _ mar < a < 10* r _ mar and e < ). The objective function wa evaluated and according to the reult the geometry information wa either tored in a file repreenting a population of promiing candidate geometrie, or wa dicarded. Once the population of candidate geometrie wa ufficiently large, thee contellation geometrie were locally optimized with a local gradient decent (uing the ame objective function) and the bet one wa elected to go further in the proce. The Monte Carlo imulation and the local optimization were performed over a period of 2 ol. The elected contellation were then evaluated for navigation ervice (uing the availability and accuracy indice decribed above). However the contellation geometrie optimized for occultation yielded poor performance, leading to the neceary definition of a reconfiguration trategy. Reconfiguration trategy The apparent incompatibility between occultation and navigation geometrie neceitate contellation reconfiguration for navigation event. The ue of electric propulion for the deployment, orbital acquiition and control of the contellation atellite would efficiently upport the feaibility of the concept, by providing ufficient maneuver delta-v for everal reconfiguration of the contellation over the miion lifetime. Known figure on electric propulion [Well et al, 2004, Walker et al, 2004] how that a 120 kg micro atellite arriving at low Mar orbit ha between 6 and 8 kg of Xenon left auming a 30 kg total propellant ma and Ip of 4500 ec. Thi lead to the main reconfiguration contraint, which i the cot of propellant thi ha been et to 1.6 kg per atellite. Auming that the miion length i 4 to 6 year, thi enable the contellation to be reconfigured at leat four time (uppoing that the primary geometry i for radio occultation meaurement and navigation event correpond to minimum energy launch window from Earth i.e. once every 26 month). A the different eccentricitie in the primary geometry are low and a change in inclination i too expenive, thee parameter were fixed along with the argument of perigee. Since the deired time of perigee and right acenion of acending node can be eaily targeted uing differential J 2 drift by chooing the right time when to apply the maneuver, the trategy wa focued on the emi-major axi change, for which the maneuver cot i given by the following approximate formula for a low-thrut orbit-raiing piral: µ 1 1 M fuel = M c(1 exp( ( ))) g I a 0 p 2 a1

5 where i the ma of the pacecraft before the maneuver, M c Ip g0 µ i the gravitational contant of 2 Mar, i the pecific impule, =9.81 /, and a are repectively the initial and target emi-major axi (km). m a1 2 Navigation ervice In order to find the bet contellation, a Monte Carlo imulation of 100,000 iteration wa performed. Only the time of perigee and the right acenion of the acending node were randomly initialized. The emi-major axi wa contrained to an interval defined by the maximum allowed cot for the maneuver. The other keplerian element were kept contant. The population of poible geometrie wa elected with repect to the objective function. Then a finer election wa performed by analyzing both the total number of time that the GDOP i not defined for the following inclination: 6, 10, 20,, 120 and 150 degree (availability) and the value of the GDOP (accuracy). RESULTS The ame cheme will be followed for the preentation of the reult derived for each type of contellation geometry. The bet orbit for radio occultation meaurement (contellation R0) will firt be depicted followed by the patial ditribution of the radio occultation event where the mehing of the planet i alo ditinguihable. The time period for the firt two figure i 10 ol. The detail of the orbit parameter and the reult of the proce will be preented in the two table underneath. Then the reconfigured geometry (contellation R0*) for navigation ervice correponding to the above contellation will be repreented in the next figure along with trajectorie of incoming pacecraft on a hyperbola leg targeting a periapi of 150 km and at 8 different inclination. Each trajectory on the figure top at the periapi. Next will be hown the GDOP value for all the trajectorie repreented in the previou figure. The time pan i 30 minute before arrival of the pacecraft at the periapi. When the GDOP fall below zero, it mean that there are le than four atellite in view. The reult in term of cot and length of the maneuver, availability and accuracy of the navigation contellation for each atellite are preented in the lat two table. 4-atellite contellation Figure 2: Contellation R0 of 4 atellite for radio occultation meaurement Figure 3: Spatial ditribution of the radio occultation event (10 ol)

6 Contellation R0 a (km) e i (deg) Ω (deg) ω (deg) τ (ec) 1 t atellite nd atellite rd atellite th atellite Table 1: Keplerian element of the 4 orbit for radio-occultation meaurement Objective function # occultation event Mean value per lice Standard deviation Table 2: Reult for the radio occultation meaurement for 4 atellite and 2 ol The number of occultation event i very reaonable and all the latitude are covered. ***** Figure 4: Contellation R0* of 4 atellite for navigation ervice Figure 5: GDOP value from 30 minute before the periapi to the periapi arrival Contellation R0* Semi-major axi change (km) Cot (kg) Time of maneuver (day) 1 t atellite nd atellite rd atellite th atellite Table 3: Reconfiguration maneuver detail for 4 atellite Time of non availability ummed through all the inclination for 4 day DOP value through all the inclination in the lat 30 minute R0 Never defined Never defined R0* 291 minute <350 if eclipe taken into account <14 if no eclipe Table 4: Comparion of the Navigation ervice performance for R0 and R0* for 4 atellite The reconfiguration maneuver improve coniderably the navigation ervice, which could not be upported by the initial configuration, R0. The maximum reconfiguration maneuver cot per atellite i kg of Xenon, which i within the contraint and take le than 50 day to be performed. The GDOP i till too high and the availability too weak in order that thi contellation could be conidered for only navigation ervice. It could provide however a very good navigation aid for the incoming pacecraft.

7 8-atellite contellation Figure 6: Contellation R0 of 8 atellite for radio occultation meaurement Figure 7: Spatial ditribution of the radio occultation event (10 ol) Contellation R0 a (km) e i (deg) Ω (deg) ω (deg) τ (ec) 1 t atellite nd atellite rd atellite th atellite th atellite th atellite th atellite th atellite Table 5: Keplerian element of the 4 orbit for radio-occultation meaurement Objective function # occultation event Mean value per lice Standard deviation Table 6: Reult for the radio occultation meaurement for 8 atellite and 2 ol The number of occultation event for 2 ol i very high and the patial ditribution i well balanced except from the pole due to the fact that there i no polar orbit. ***** Figure 8: Contellation R0* of 8 atellite for navigation ervice Figure 9: GDOP value from 30 minute before the periapi to the periapi arrival

8 Semi-major axi change (km) Cot (kg) Time of maneuver (day) 1 t atellite nd atellite rd atellite th atellite th atellite th atellite th atellite th atellite Table 7: Reconfiguration maneuver detail for 8 atellite R0 R0* Time of non availability ummed through all the inclination DOP value through all the inclination for 4 day in the lat 30 minute 8589 minute=5.96 combined hour <5 (but only 2 inclination are defined) 33 minute <2.67 Table 8: Navigation ervice performance for 8 atellite The reconfiguration maneuver enable the formation of a contellation R0* that ha very good navigation figure of merit. The maximum reconfiguration maneuver cot per atellite i kg of Xenon, which i within the contraint and take le than 50 day to be performed. The local DOP i cloe to the Galileo contellation one and at ome inclination it i defined at all time. CONCLUSION In thi article it ha been found that for a contellation of 8 atellite, a ingle multi-micro pacecraft miion can achieve very effective incoming navigation ervice and highly valuable atmopheric cience return. On the other hand, even if the reult were quite promiing with 4 atellite, uch a contellation would fail to perform valuable navigation ervice by itelf but would till be a good aid for orbit inertion. For both contellation and over a 6-7 year period, 4 maneuver can be effected in order to alternate between 3 occultation configuration and 2 navigation configuration. At a ytem level and according to the reult hown in Table 3 and 7, it could be enviaged to grant one pacecraft with more fuel than the other for which the maneuver cot i lower in order to prolong the lifetime of the whole miion. Further work to thi paper will be to analyze the enitivity of the navigation performance to the J 2 oblatene and alo tudy the tandard deviation accuracy of the orbit inertion defined by the B-plane emi-major axi. REFERENCES [1] Abbondanza S., Zwolka F., Alcatel Space Indutrie, Deign of MEO contellation for Galileo: Toward a deign to cot approach, Acta Atronautica V0l 49, No. 12, pp , 2001 [2] Ely et al, Mar Network Contellation Deign Driver and Strategie, AAS [3] Hatrup R. et al, Mar network for enabling low-cot miion, Acta Atronautica 52 (2003) [4] O Keefe Kyle, Availability and Reliability Advantage of GPS/Galileo Integration, Department of Geomatic Engineering The Univerity of Calgary [5] O Keefe K., Lachapelle G., Skone S., GPS goe Martian, GPS World, June 2004, pp24-28 [6] Well N., Walker R., Green S., Ball A., SIMONE: Interplanetrary microatellite for NEO rendezvou miion, Proceeding of 5 th IAA International conference on Low-cot Planetary miion, 2004, pp [7] Walker et al, Concept for a low-cot Mar micro miion, Proceeding of 5 th IAA International conference on Low-cot Planetary miion, 2004, pp