Autonomous Navigation for Mars Landing Spacecraft
Using a Proposed Martian
Satellite Network
The Navigation for all spacecraft landing on the Martian surface is currently performed using NASA’s Deep Space Network (DSN). This system uses twoway radio communication to locate and guide a spacecraft on its journey to Mars. The DSN provides excellent navigational capabilities, however, these capabilities are restricted by the speed of light. As a spacecraft travels further from Earth, the communication lag time associated with the finite speed of light grows. This lag time becomes a critical issue as a spacecraft enters the final phase of its approach to Mars. At a certain point during the approach, the time until the craft enters the Martian atmosphere will be less than the time required for the DSN to contact the spacecraft. From this point on, no navigational corrections can be sent to the spacecraft and it must continue its descent along the last trajectory update received from the DSN. Given the critical nature of this final approach, it is desirable to extend the active navigation of the spacecraft up to atmospheric entry. This paper considers the use of JPL’s proposed Mars satellite network to autonomously navigate a Mars landing spacecraft beyond the final DSN communication contact. The Mars network concept is based on a satellite constellation with GPS and interplanetary communication capabilities. JPL’s goals for the satellite network are centered on extending communication with and navigation of Martian surface missions and orbiting satellites once they have arrived at Mars. This paper describes how the satellite network’s navigational capabilities can be extended to assist a spacecraft as it approaches Mars for a surface landing. An incoming spacecraft would utilize the GPS transmitters on the Mars network satellites to determine its real time position within the network’s reference frame. This information would be used by the spacecraft to analyze its trajectory and autonomously correct for any detected errors, thus improving the accuracy of its landing.
Introduction:
NASA, ESA and several other space agencies have extensive plans for the investigation of Mars, with a total of at least 18 distinct exploration elements slated for possible deployment between 2003 and 2010.[i] The significant increase in the number of missions on the Martian surface and orbiting Mars will place a considerable strain on NASA’s current deep space communication and navigation system (DSN). In addition, the demands for higher quality and quantity of science data, such as streaming video and highresolution multicolour mapping will stretch the DSN to its limits.[ii] When the potential for a manned mission to Mars in the near future is considered, the need for additional Martian communication and navigational infrastructure becomes obvious.
With these considerations in mind JPL proposed “the implementation of a Martian satellite constellation of microsatellites with the task of providing navigation and communication services to the Mars insitu users. This constellation would extend the existing capabilities of NASA’s Deep Space Network.”[iii] The proposed “constellation would consist of six satellites based on the common micromission bus being designed for piggyback launch on the Ariane 5. Each microsat would be equipped with a UHF transceiver that would provide data communication relay and navigational services to user platforms in the vicinity of Mars.”[iv]
Most studies of JPL’s Mars network concept have centered on the increased data communication capabilities and/or the use of the microsat constellation as a Martian GPS for the navigation of orbiting satellites or surface users, such as rover and planes. This paper will focus on how the navigational capabilities of the Mars network can be extended to serve the navigation needs of incoming Mars spacecraft. Specifically this paper will address the use of the Mars network’s GPS capabilities to assist in the autonomous navigation of incoming spacecraft that will deliver missions to the Martian surface.
Background:
JPL’s Mars Network:
The Mars network concept balances the cost of building and launching each microsat with increased communication and navigational capabilities of the constellation as additional microsats are added. Ely et al^{iii} proposed that a constellation consisting of six microsats would meet the desired communication and navigational capabilities at an acceptable level of cost. The six microsat Mars network, has been designed to evolve into the full constellation through a series of launches. The first launch is proposed for 2003, sending a single microsat into Martian orbit. This microsat is considered a prototype and will not be used as a component in the final constellation. Subsequent missions are designed to launch two microsats at each Earth to Mars opportunity (~ 26 months). The Ely et al^{iii} design aims for dual launch missions in March 2005, September 2007 and October 2009, with a fully operable constellation of six microsats in place by January 2011.
The microsat design is centered on maintaining the cost effectiveness of the Mars network. The microsats would utilize a microspacecraft bus being developed by the Mars Surveyor Program (MSP) for a series of small, inexpensive science micromissions. To reduce development cost, MSP is designing the bus to be primarily “singlestring”, with a proposed design life of five years. Launch costs are addressed by designing the microsat as an auxiliary payload for the ESA Ariane 5. The auxiliary payload space on the Ariane 5 defines the dimensions for the microsat to be approximately 250cm by 60cm by 80cm in a “banana shaped”
configuration shown in figure 1^{i}. Figure 2[v], below, gives an illustration of the Ariane 5 booster.
The total mass of the microsat including fuel would be roughly 220kg with 140kg as fuel mass. This fuel mass would require the microsat to perform an Earthlunar gravity assist and^{ }Martian aerobraking to arrive in its final orbit with enough remaining fuel to maintain attitude control during operation.^{i}
In order to fulfill the desired communication and navigation capabilities each microsat would be equipped with two separate antenna systems. For communication with the DSN the microsat would use a pointed high gain antenna operating in the Xband (8.4 GHz). As more microsats are added to the network it would be possible to upgrade to Kaband antennas. For the insitu communication and navigation link to Mars exploration elements the microsats would utilize a UHF transceiver and omnidirectional antenna.^{iii}
Ely et al’s investigation of possible orbit configurations for the six microsats focused on balancing the communication and surface navigation capabilities of the constellation and achieving the following primary performance goals; providing global coverage over a selected time span, providing large volume communication support of the equatorial regions and minimizing the coverage variability due to longterm orbit perturbations, which in turn minimizes the orbital maintenance of the constellation in terms of operations time and cost versus expended delta V.^{iii}
Using these and several other performance goals as the design drivers, Ely et al determined that a retrograde hybrid constellation with two subconstellations at differing inclinations optimized the capabilities of the Mars network. This configuration, called 4retro111 is outlined in table 1, which gives altitude (h), inclination (i), longitude of the ascending node (Ω) and mean anomaly (M) for each of the six microsats.
Table 1: Proposed Microsat Constellation^{iii} 
4retro111: (h, I, Ω, M) (km, deg, deg, deg) 
Microsat 1: (800, 172, 0, 0) 
Microsat 2: (800, 172, 180, 0) 
Microsat 3: (800, 111, 0, 0) 
Microsat 4: (800, 111, 90,
90)

Microsat 5: (800, 111, 180, 180) 
Microsat 6: (800, 111, 270, 270) 
The 4retro111 constellation consists of two subconstellations. The first of which contains two microsats, situated near the Martian equator at 172° inclination, their orbit planes spaced 180° apart in ascending node. The second subconstellation contains four microsats at 111° inclination, with the orbit planes equally spaced 90° apart in ascending node.
Deep Space Network:
The DSN consists of three separate Deep Space Communication Complexes (DSCC), which are evenly dispersed around the globe and networked to a central operations center in Pasadena, CA. The DSCC are located at Goldstone, CA, another near Madrid, Spain and one near Canberra, Australia. Each complex consists of several parabolic reflector antennas, each equipped with highpower radio transmitters and an ultrasensitive radio receiver system. The diameters of the dishes at each sight are given in table 2. Figure 3[vi] gives a picture of one of the 70meter deep space antennas.
Table 2: DSCC dish diameters 
70meter 
34meter 
26meter 
11meter 
To compensate for the Earth’s daily rotation the DSCC are located 120° apart in longitude. This insures continuous communication with interplanetary missions.^{vi} The DSCC antennas are design to transmit and receive simultaneously. This twoway communication is facilitated by a ten percent upward shift in the frequency of the “downlink” signals transmitted by a spacecraft in relation to a DSCC antenna’s “uplink” Xband frequency.[vii]
The DSCC antennas are capable performing two types of navigation measurements on a spacecraft, range (position) and rangerate (radial velocity). Rangerate is obtained by using the Doppler shift in frequency of the twoway communications from the DSN antenna to a spacecraft. The uplink signal transmitted from Earth is received by a spacecraft, which replicates the incoming frequency, shifts it up by ten percent, and retransmits the signal. The relative velocity of a spacecraft away from Earth during the reception and transmission of the radio signal introduces a “Doppler” downshift in the frequency of the signal. The difference between the original frequency sent by the DSN antenna and Doppler shifted frequency received by the antenna (adjusted for the ten percent shift) is used to calculate the craft’s radial velocity,^{vii}
(1)
where F_{T} gives the frequency transmitted by the DSCC antenna, F_{R} gives the Doppler shifted frequency received and c is the speed of light. In practice the received frequency is compared to the frequency currently being transmitted by the antenna. The error introduced by this method is negligible due to the stability of the transmitted frequency (better than one part in 10^{13}).^{vii} The range measurement is calculated by determining the roundtrip time for the radio signal to reach the spacecraft and return to the antenna. While the Doppler system continually tracks the rangerate of a spacecraft ranging measurements are taken at discrete times.^{vii}
Accumulated range and rangerate data are used to determine the RMS error in the spacecraft’s position with respect to a precalculated model for a spacecraft’s orbit. The orbital model is calculated before the launch of the spacecraft and attempts to account for all possible forces that will affect a spacecraft’s trajectory, such as solar radiation pressure, gravitational effects of the planets or atmospheric drag. The RMS error between the DSN position measurements and the calculated trajectory is used to refine the model for the spacecraft’s orbit and determine if corrective maneuvers are needed to keep the craft on track. The orbit determination process requires the accumulation of a significant amount of range and rangerate data. It can take days of observation to determine if the orbital model for a spacecraft needs to be modified and to decide if any trajectory corrections are warranted. With DSN tracking and orbit corrections calculated on Earth and uplinked to the spacecraft, past Mars missions have achieved position uncertainties of 15km at 125km above Mars and 75km on the Martian surface.^{i}
Mars Surface Landing Missions:
A minimum energy Hohmann transfer is assumed as the model for the Earth to Mars orbit. This model is a good approximation for the interplanetary transfer orbit used for most Mars missions. In addition it is assumed that the spacecraft performs a direct insertion into the Martian atmosphere, no orbital maneuvering is treated. This assumption matches with the insertion technique used on the Mar’s Pathfinder mission and the techniques planned for use on the two upcoming Mars rover missions. The calculations for the Hohmann transfer use twobody dynamics and assume that Earth and Mars are in circular coplanar orbits.
Figure 4 illustrates the elliptic Hohmann transfer orbit as well as the positions of Earth and Mars at beginning and end of the transfer. The launch of the mission from Earth coincides with perihelion for the transfer orbit, while arrival of the spacecraft at Mars coincides with the transfer orbit aphelion. Initiation of the transfer requires the proper phase angle between Earth and Mars, such that the travel time of Mars and the spacecraft to the aphelion arrival point are identical. The calculations needed to determine the appropriate phase angle (θ_{phase}) are given below,
(2) (3)
(4) (5)
(6) (7)
Figure 4:
Earth to Mars Hohmann Transfer[viii]
where a_{Earth}, a_{Mars} and a_{trans} give the semi major axes of Earth, Mars and the Transfer orbit, respectively. μ_{Sun} gives the gravitational parameter of the sun. ω_{Earth} and ω_{Mars} represent the mean motion of Earth and Mars, τ_{trans} gives the travel time for the Earth to Mars transfer and α_{L} gives the Earth to Mars lead angle. See Vallado page 346 [ix] for a full description of circular coplanar transfers.
These equations clearly demonstrate the dependence of the phase angle on angular velocity of Mars and the time needed to complete the transfer orbit. To initiate an Earth to Mars Hohmann transfer the phase angle must be equal to approximately –44.34°. By comparing the mean motions of Earth and Mars^{ix} it can be determined that the Hohmann transfer phase angle repeats every 2.135 years; this gives the wait time between possible Mars mission launches.
The circular coplanar Hohmann transfer requires that the velocity vectors of the spacecraft and Mars (with respect to the sun) be parallel at the aphelion arrival of the spacecraft. In addition twobody dynamics is assumed, which ignores the gravitational effects of Mars on the spacecraft. These conditions allow the velocity of the spacecraft with respect to Mars (the approach velocity (v_{sc/Mars})) to be calculated by simply subtracting the velocity of Mars with respect to the sun (v_{Mars/Sun}) from the aphelion transfer velocity of the spacecraft (v_{SC/Sun}). The equations for the approach velocity of the spacecraft, the velocity of Mars with respect to the sun, and the aphelion transfer velocity of the spacecraft are given below.
(8)
(9) (10)
Note that radius of aphelion for the spacecraft is equal the orbital radius of Mars. Using the above equations the velocity of Mars (with respect to the Sun) equals 24.13km/s, while spacecraft aphelion transfer velocity equals 21.48km/s, which gives an approach velocity of 2.649km/s.
Martian GPS:
^{ }
Equipping a spacecraft with a GPS receiver allows the spacecraft to determine its range and rangerate with respect to a GPS satellite. The ranging technique discussed here is based on the pseudorandom code sequence continuously transmitted by a GPS satellite^{x}. The transceiver on each GPS satellite produces its own unique sequences of code. A spacecraft equipped with a compatible GPS receiver knows the code sequence associated with each GPS satellite. Upon receiving a GPS signal, the spacecraft’s receiver replicates the appropriate sequence of code for the transmitting satellite. Due to the finite travel time of the GPS transmission, the received code sequence will be offset with respect to the sequence generated on the spacecraft. The shift needed to align the two sequences gives a measurement of the signal’s travel time. Both a satellite’s transceiver and spacecraft’s receiver are equipped with clocks that control the generation of the pseudorandom code. Ideally these clocks are synchronized with an exact “GPS time”, allowing the two sequences to be directly compared. This would permit the range between the two craft to be calculated by multiplying the measured signal travel time by the speed of light. However, in reality an offset exists between each craft’s clock and GPS time, which prevents direct measurement of the signal travel time. Cruickshank[x] details how the clock bias can be accounted for, allowing a spacecraft to calculate an accurate pseudorange (P) to a GPS satellite,
(11)
where ρ is the ideal range with no clock offset, c is the speed of light and dT is the bias of the spacecraft’s clock with respect to ideal GPS time.
The relative motion between a spacecraft and GPS satellite generates a Doppler shift in the frequency of the signal received by the spacecraft. Rangerate measurements are obtained by a spacecraft using the Doppler shift in the received GPS signal. The spacecraft’s GPS receiver contains an oscillator that outputs the original transmission frequency of the GPS satellite. The oscillator output is combined with the Doppler shifted signal received by the spacecraft to generate a beat frequency that can be used to calculate the rangerate of the spacecraft with respect to the GPS satellite,
(12)
where c is the speed of light, f_{o} is the proper frequency transmitted by the GPS satellite and f_{D} is beat frequency generated onboard the spacecraft. Equation 6 assumes that clock offset has been adjusted for. See Cruickshank^{x} for the full derivation of equations 5 and 6. Combining range and rangerate measurements from four or more GPS satellites allows a spacecraft to unambiguously estimate its real time 3D position and clock offset with respect to the GPS constellation^{iii}.
The microsat constellation proposed by Hastrup et al^{iv} is designed to function as a GPSlike constellation. Each microsat is equipped with a UHF transceiver and an omnidirectional antenna allowing it to continually broadcast a GPSlike beacon. This permits any spacecraft with a compatible receiver to obtain range and rangerate measurements with respect to the individual microsats. If four or more microsats are within view of a spacecraft, it can determine a real time approximation of its 3D position and clock offset with respect to the microsat constellation reference frame. The constellation is designed to maintain a stable spatial and temporal Martian reference frame with minimal dependence on Earthbased assets. To achieve this goal each microsat transceiver is equipped with an ultrastable oscillator, which allows autonomous Mars frame ties to Earth using sparse oneway links. In addition the network is designed to crosslink between the individual microsats allowing the network to constantly check the range and rangerate measurements between microsats^{iv}. The refined model for the Martian gravity field assists in maintaining the stability of the constellations reference frame. Ely et al^{iii} calculated that the microsat orbital errors associated with uncertainties in the gravity field are on the order of 2m radial (σ_{R}), 7m along track (σ_{T}) and 7m cross track (σ_{R}). The stability of the constellation with respect to Mars will allow a spacecraft to approximate its location with respect to Mars based on the real time position measurements received from the microsat constellation.
Extension:
Autonomous Navigation of a Mars Landing Spacecraft:
For the assumed circular coplanar Hohmann transfer orbit, a spacecraft will be approximately 238 million kilometers from the Earth as it approaches Mars for its final decent. At this range the DSN to spacecraft communication lag time is approximately 13.25 minutes for a oneway signal. This means that when the spacecraft has less than 13.25 minutes of travel time left to reach Mars it can no longer receive trajectory corrections from the DSN. A spacecraft would be on the planet before any signal sent after this time could reach it. This final communication time corresponds to a relative spacecraft to Mars distance of approximately 2100km. This is close enough to the microsat network that a spacecraft can begin tracking its position with respect to the constellation.
The method by which a spacecraft autonomously navigates during its final decent is similar to the method used by the DSN to navigate a spacecraft during its journey to Mars. A spacecraft’s orbital model, determined from initial calculations and inflight observations, is uploaded onto the spacecraft as it approaches the final DSN communication point; this model is treated as the desired or ideal trajectory for the spacecraft. When a spacecraft is within the transmission range of the UHF transceivers onboard the microsats, it begins to measure and record its position with respect to the microsat constellation. The error between the measured position and the position predicted by the model is calculated and recorded. As a spacecraft builds up a bank of error measurements (residuals) it determines the RMS error in its position. The uploaded trajectory model is not considered to be perfect. The significant number variables and unknown conditions associated with interplanetary flight result in modeling errors. Thus, correction criterion determining the magnitude or gradient in the RMS error that trigger an autonomous correction are preloaded onto the spacecraft or could be uplinked from the DSN during flight. These criterion allow a spacecraft to distinguish short period errors that cancel out over the remaining flight time from secular and long period errors that significantly affect the trajectory of the craft. If the criterion are met a spacecraft could then calculate the delta V required to return to the modeled trajectory. This decision needs to account for the remaining fuel onboard the spacecraft; a corrective maneuver must conserve some fuel in case any further corrections are required.
In order for the spacecraft to autonomously navigate it must be able to determine its real time position with respect to the constellation’s reference frame and thus its position with respect to Mars. To achieve this goal at least four microsats must be in view of a spacecraft during the 13.25 minute descent. In analyzing whether or not the proposed microsat constellation meets these visibility criterion, it has been assumed that an incoming spacecraft has a near equatorial approach angle during its final decent; this is plausible considering that most proposed Mars surface missions plan to operate near the Martian equator. In addition atmospheric entry is assumed as the cutoff point for corrections of a spacecraft’s trajectory; the cruise phase of a spacecraft is usually jettisoned before entry and the craft’s supersonic entry generates a shockwave and burn around the spacecraft. It is also assumed that the twophase transmission of the microsat GPS beacon is sufficient to correct for any signal delays associated with the Martian ionosphere.
To determine if the four or more microsat visibility criterion are met by Ely et al’s^{iii} proposed microsat constellation the orbital elements from table 1 where used to model the constellation with Satellite Tool Kit. Unfortunately, analysis of this constellation revealed several fatal flaws in its design. Microsats 1 and 3 have identical altitudes, ascending nodes and initial mean anomalies, which results in these two microsats passing through the exact same location at the same time, thus destroying both satellites. Microsat 5 is at the same altitude with the ascending node and initial mean anomaly both rotated by 180°, this orbit intersects with microsats 1 and 3 such that microsat 5 is also destroyed in the collision. The orbits of microsats 4 and 6 cross at the equator such that they also destroy each other in a collision. With these observed results the design of the constellation was augmented to prevent any collisions. The original JPL constellation was designed to balance the communication and navigational needs of surface based and orbiting Mars missions, unfortunately the effects of the redesign on these capabilities could not be determined. In light of this, the redesign of the constellation focuses on eliminating the collisions and keeping at least four microsats in view of an incoming spacecraft. To minimize effects on the original JPL design, and thus hopefully maintain its surface and orbit mission capabilities, the redesign uses a small number of changes. The orbital elements for the augmented microsat constellation are given in table 3 below.
Table 3: Redesigned Microsat Constellation^{iii} 
(h, I, Ω, M) (km, deg, deg, deg) 
Microsat 1: (800, 172, 0, 0) 
Microsat 2: (800, 172, 180, 0) 
Microsat 3: (800, 69, 180, 90) 
Microsat 4: (800, 69, 270, 0)

Microsat 5: (800, 111, 180, 270) 
Microsat 6: (800, 111, 270, 180) 
In effect the redesigned constellation can be thought of as three pairs of satellites, (1 and 2, 3 and 5, 4 and 6). Each pair has an offset of 180° between the microsat’s ascending nodes. Microsats 1 and 2 form a “nearequatorial” pair, whose orbits keep them on opposite sides of planet. Microsats 3 and 5 form one of the high inclination pairs, their orbits cross at the equator and are phased such that the microsats are also on opposite sides of the planet at all times. The final pair, microsats 4 and 6, also have orbits that cross at the equator and keep the satellites on opposite sides of Mars. This configuration eliminates any collisions and satisfies the four or more visibility criterion. In addition it is achieved with minimal alterations to the original JPL configuration. The 800km altitude is unchanged for all six microsats and the orbital planes as well as the angular spacing between them also remain unaltered. For microsats 1 and 2 none of the orbital elements are altered. For the high inclination microsats some changes are needed to prevent collisions and increase visibility. For microsats 5 and 6 only the initial mean anomalies are altered, a 180° increase in mean anomaly eliminates collisions with the near equatorial microsats. To eliminate collisions of the high inclination pairs at their equatorial crossings the orbits of microsats 3 and 4 are essential flipped to reverse the direction of their motion. Rotating the ascending node of each microsat by 180° and then subtracting 42° from each microsat’s inclination achieves this. This maintains the same orbital planes and plane spacing for the constellation.
To analyze the visibility performance of the redesigned constellation the orbital elements from table 3 were used to model the constellations behavior in Satellite Tool Kit. All six microsats have the same altitude. Thus, assuming circular orbits, the period for every microsat is identical and equal to approximately 2 hours and 17 minutes (137 minutes). This means that the orbital configuration of the entire constellation repeats every 137 minutes. An incoming spacecraft will be dependant on the microsats to determine its position for approximately 13.25 minutes. Since this time is significantly shorter than the orbital period of the constellation, microsat visibility is analyzed for a single period. Figures 5 through 8, given below, show a near equatorial view of the behavior of the constellation over a time of 120 minutes.
These figures give a good representation of the microsat visibility over one full period. The redesigned constellation gives excellent visibility for an incoming spacecraft, with at least four (Figures 5, 6, 8) and sometimes five satellites (Figure 7) visible at all times. Figure 8 demonstrates the worstcase scenario for microsat visibility, with microsat 5 coming into view just before microsat 6 is eclipsed. The constellation also displays a good spatial distribution of the microsats. The greater the overall spread between the individual microsats, the faster and more accurately a spacecraft is able to determine its real time position. Once again, figure 8 gives the worstcase scenario observed for this configuration. The figures above only treat a nearequatorial approach with a slight offset from one of the fourway orbit intersections. However, the equal spacing of the microsat orbit planes yields a highly symmetric configuration for the constellation. The near symmetry of the constellation with respect to the rotational axis of Mars basically negates any difference in visibility base on the direction of approach. Thus the approach angle (inclination) of a spacecraft is the major factor affecting microsat visibility. Several approach angles, ranging from equatorial to polar, were analyzed using Satellite Tool Kit. From the observed results it can be safely assumed that this constellation provides the minimum fourmicrosat visibility required for GPS real time positioning and autonomous navigation for any approach angle. Extending the active navigation of a landing spacecraft up to atmospheric entry would decrease the uncertainty in its final landing position, thus improving the safety and quality of the mission.
Conclusion:
The need for increased accuracy in Martian navigational capabilities is paramount for the continued exploration of Mars. The high cost and risk associated with missions to Mars demands a reliable return of high quality scientific data. Boosting the navigational resources available to rovers, landers and satellites on and around Mars will greatly assist in reducing the cost and risk of these missions as well increasing the ease of operation and ability to deliver precise measurements. This paper has outlined a method by which a proposed Mars network of costeffective microsatellites could be used to extend the navigational capabilities of spacecraft landing on Mars. The GPSlike capabilities of the Mars network allow for autonomous navigation of a spacecraft during the final phase of its landing. Unfortunately, the original design proposed for the constellation had several fatal flaws; requiring a redesign to prevent collisions between the orbiting microsats. While the effects of the redesign on surface navigation could not be determined the redesigned microsat constellation displayed excellent navigational capabilities for a spacecraft on approach to Mars. The minimum fourmicrosat visibility condition required for real time positioning and autonomous navigation is met and in some cases exceeded by the redesigned constellation. In addition the constellation provides an excellent distribution of visible microsats, increasing the speed and accuracy with which an inbound spacecraft can determine its position. This paper has centered on missions performing direct landings on Mars, however, the navigational capabilities of this constellation could easily be extended to approaching spacecraft that will perform more complex maneuvers to land on Mars or enter orbits about the planet. Additional research is warranted into the effects of the redesign on the surface navigation and communication capabilities. In order to justify the cost of the network it must also yield a satisfactory performance in these areas. In addition the feasibility of algorithms necessary for autonomous control of a spacecraft during time critical events should be investigated.
[ii] Asker, James R. ,“Will Phoning Home Yield a Busy Signal?” , Aviation Week, December, 11, 2000
[iii] Todd A. Ely, Rodney Anderson, Yoaz E. BarSever, David Bell, Joseph Guinn, Moriba Jah, Pieter Kallemeyn, Eirk Levene, Larry Romans, SienChiong Wu, “Mars Network Constellation Design Driver and Strategies”, AAS 99301
[iv] R.C. Hastrup, R.J. Cesarone, J.M. Srinivasan, D.D. Morabito, “Mars Comm/NaV MircroSat Network”, SSC99 – VII – 5
[vii] Navigation: Land, Sea, Air, and Space Kayton, Myron, IEEE Press New York, NY 1990
[ix] Fundamentals of Astrodynamics and Application: 2^{nd} Edition Vallado, David, Microcosm Press, El Segundo, CA 2001
[x] D.R. Cruickshank, “Algorithms for Autonomous Satellite Navigation Using GPS” , Masters Thesis, University of Colorado Boulder, 1994