Pre-Phase A Report - Lisa - Nasa

142 Chapter 6 Mission Analysis
For purposes of determining the arm lengths, a short analysis was performed assuming
ground tracking of each spacecraft for 8 hours every other day, and combined with
phase measurements from the laser system sampled once every 30 minutes. The phase
measurements were assumed to have an accuracy of 5×10−4 m/ √ Hz at the frequency
corresponding the round-trip light time. A phase bias needs to be estimated for each
arm along with the spacecraft positions and velocities. Uncertainties in the positions of
the planets, especially the Earth, have been taken into acocunt, as have uncertainties in
station locations and Earth media calibrations. The analysis was performed for a configuration
when the LISA constellation was at 0◦ declination as viewed from the Earth,
which is when the poorest orbit determination is expected.
Table 6.2 shows the achievable orbit determination accuracy using combinations of ground
tracking and measurements from the laser system. After 16 days of ground and laser
tracking, the arm lengths can be determined to about the required 200 m accuracy. The
system performance might end up being somewhat better since the assumptions on the
laser-system measurements were very conservative.
Table 6.2 Achievable orbit determination accuracy (1-σ).
Case Accuracy (σrms)
Position Arm 1 Arm 2 Arm 3
Radio tracking only 5.94 km 3.75 km 1.49 km 5.56 km
over 16 days
Radio and laser tracking 1.79 km 0.19 km 0.07 km 0.14 km
over 16 days
If the laser systems include some means of directly measuring the arm lengths, such as
incorporation of a ranging signal in addition to the laser carrier phase, then the arm
lengths would not need to be inferred from the ground tracking measurements and laser
phase measurements. Further studies will need to refine the navigation analysis and
determine the optimal means of determining the arm lengths.
3-3-1999 9:33 Corrected version 2.08