This section explains the designs trades that led to the choice of a position determination method.
10.2.1.1 Active versus Passive Position Determination
Position determination may be performed with or without input from the user. The first case is referred to as ‘active position determination’ and the second ‘passive position determination’.
Passive position determination may be performed using the same systems used in target tracking, for example, IR (infrared) and radar systems. The advantage of passive position determination is that it does not require communication with the user. The primary disadvantage of passive systems is the increase in the computational burden.IR detection uses the heat emitted by objects to detect them. Successful detection therefore requires a temperature difference between the object being detected and the ambient. Since dust storms can raise the ambient temperature by 10°C, detection in storms may be difficult.
Accurate position determination requires precise attitude control of the satellite, and the strictness of this requirement increases with altitude. Once an IR image has been collected, it has to be processed in order to identify the target. This implies that there will be a high computational requirement per position determination solution.Radar position determination involves bouncing an RF signal off the target and using the time delay from transmission to reception to determine the target range. Unfortunately, the surrounding ground also reflects the radar signal. Unwanted ground return is called ground clutter. If the target is moving, its Doppler frequency may be used to distinguish it from the ground clutter. Stationary targets may be detected using high resolution SAR or similar systems to map the ground and target. Since the entire search area has to be mapped in order to identify the target, this results in a very high computational load per position determination solution.
Since the communication requirement means that there will be a communication link between the satellites and the rovers, and given the above disadvantages of passive systems, we decided to use active position determination.
10.2.1.2 One-way versus Two-way Position Determination
In the presence of a communication link between the satellites and the MSEs, range or Doppler shift measurements provide useful positioning information and are not computationally demanding.
Active positioning methods can use either a one-way or a two-way communication link.
Systems that require only a one-way link, like the Global Positioning System (GPS), present the advantage of being available to any number of simultaneous users. On the other hand, measuring a one-way time delay adds the satellite/user clock offset as a new unknown, unless their clocks are perfectly synchronized. Similarly, measuring one-way Doppler shift adds the satellite/user frequency offset as a new unknown, unless they both have precise frequency references. Such an unknown offset is time varying. Solving for it
therefore requires simultaneous redundant measurements, which means increasing the number of satellites.
Since the number of Mars surface elements (MSEs) is limited and since they will all establish a two-way communication link with the MINERVA system, we decided to use a two-way positioning method.
Table 10.8: Characteristics of Different Positioning Methods
Positioning One-Way Two-Way Ranging Infra Red methods Ranging
(GPS type)
Range Range & Doppler
Doppler
Advantages Clock problems Limited number of users Never used
‘GPS receivers’ Users require transponders Limited by attitude control
Disadvantages Proven method Proven method (Transit) No ambiguity
No clock problem 2D at once
2D Solution Triple coverage 3 1 (2) 1 (2) 1
3D Solution Quadruple 2 2 (3) 2 (3) 2
coverage
Altitude High High Medium Low Low
The advantages and disadvantages of the different possible positioning methods are summarized in Table 10.8. Numbers in italics indicate the number of satellites necessary to resolve the ambiguity in real time. With inclined orbits, ambiguities can also be resolved by waiting long enough for the planet's rotation to break the symmetry around the satellite ground track.
10.2.1.3 2D versus 3D Position Determination
Determining an MSE position involves solving for three unknown coordinates, which a-priori requires at least three independent measurements. Prior to any measurement, we know that MSEs are located near the Mars surface. Operators of Mars surface missions require their spacecraft’s position with respect to a Martian surface grid of reference. This means that only two-dimensional positioning is required, provided the Martian topology can be estimated to the required accuracy.
We decided to capitalize on the data currently being collected by the Mars Orbiter Laser Altimeter (MOLA) on board the Mars Global Surveyor (MGS) spacecraft. This experiment has already determined the Martian topology with an accuracy of 13 m on a 0.25° x 0.25° surface grid [Smith, 1999]. This means that the altitude of the Martian surface is known at points placed every 15 km over the whole planet. The accuracy of an interpolation between these reference points is limited by the surface topology variability.
Slopes of up to 4 km elevations over 300 to 1300 km are observed in the transition phase between the smooth Northern hemisphere and the rough Southern hemisphere of Mars [Aharonson, 1998]. This corresponds to 200 m elevation over 15 km.
We decided to perform two-dimensional position determination assuming knowledge of the Martian altitude at any point with an accuracy of 200 m. Knowledge of the Martian topology is still being improved by the MOLA experiment and can be expected to give better estimates by the time the MINERVA mission is operational.
10.2.1.4 Instantaneous versus Long-term Position Determination
Instantaneous two-dimensional positioning requires taking two independent simultaneous measurements. This can be done by measuring both two-way range and two-way Doppler shift between one satellite and the MSE. This is easily done with typical communication hardware [Levanon, 1998], which already exists on the MINERVA satellites to meet the communication requirements. Simply adding a stable frequency reference improves the measurement accuracy.
However, this method leads to ambiguous solutions and singularities that can be resolved only by the use of a second satellite. Continuous double coverage would therefore be required to provide instantaneous position determination with 100 m accuracy.
Since most Mars surface elements are very slow moving, instantaneous positioning is not required. Determining an MSE's position with 100 m accuracy makes sense if the MSE has traveled less than 50 m during the measurement period. The requirement is therefore to gather sufficient positioning information in less than three hours (three hours positioning update rate).
This time period enables the MINERVA system to gather enough positioning information without the need for either double or continuous coverage.
We therefore decided to provide positioning by measuring two-way range and two-way Doppler shift between an MSE and one satellite at a time.
10.2.1.5 Communication Signal versus Positioning Signal
Communication between a MINERVA satellite and an MSE during the time in view is continuous and performed at a relatively high data rate. Positioning measurements on the other hand can be performed at discrete instants during a satellite pass and can use a very low data rate.
In order to simplify the concurrent handling of these two functions, MINERVA allocates a dedicated frequency channel to the positioning message.
Code division multiplexing is used on this channel. A separate spread spectrum code will be allocated to each MSE. This code will enable MINERVA to isolate signals from different MSEs within the same satellite footprint. CDMA provides a convenient method for measuring range, as used by GPS.
Range measurement accuracy is inversely proportional to the frequency used for coding.
This frequency must however be at least an order of magnitude smaller than the carrier frequency, namely 400 MHz. MINERVA will use pseudo-random codes at about 4 MHz.
Overlap of satellite footprints can occur in the existing MINERVA constellation and is expected to increase as the mission expands. Therefore, satellites must isolate their positioning signals from those originating from different satellites. This is achieved by assigning each satellite a low frequency code, which is superimposed on the MSE code.