This plot shows the x, y, and z components of position error for the LL_{2} halo orbiter from the simulation mentioned in the previous slide. The lines plotted in black show the error in the position estimate computed onboard the spacecraft. The dashed red lines indicate the ±2σ limits from the estimation error covariance. There is a lot of noise in the error until about day 3 of the simulation, when the EKF converges. The "true" halo orbit used to generate the observations was propagated using a variable step 78th order Runge Kutta integrator, a 20x20 portion of the lunar gravity field LP100K, a solar radiation pressure (SRP) model, and the pointmass gravitational acceleration of the Earth, Moon, Sun, Venus, Mars, Jupiter, and Saturn. The positions of the planets were computed using the JPL DE405 planetary ephemeris. Observations were generated every 60 seconds during nine 1hour tracking periods each day. The orbit propagator in the EKF used a gravity field generated by taking a statistical sample of the LP100K gravity field using its covariance. The EKF SRP model was forced to generate SRP acceleration errors of about 1x10^{9} m/s^{2}. Using the onboard orbit estimates, the halo orbiter computed and executed station keeping maneuvers four times per halo orbit (once every ~3.5 days). The station keeping maneuvers had a 5% execution error, which was also estimated by the EKF. The resulting 1σ position error RSS was 77.78 meters, and the halo orbit station keeping budget for one year was less than 1 m/s.
