The Crazy Lune

Now here are some simulations for different paths the astronaut takes and how the algorithm estimates the its location. Videos of this simulations can be found in the Simulation section.

The first scenario is when the Astronaut walks on a linear path. This is the worst case, as all tags (and the lander) are lined up and therefore the dilution of precision is maximal. Even in this case, the algorithm did a pretty good job and for a distance of 2 km it achieved an average estimate error under 13m.

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Fig 1: Path taken by astronaut (blue) and estimated by algorithm (red) for linear path. Here, a drift in the z-axis can be observed.

Fig 4: Position estimation error over time for random path

2nd scenario where the astronaut takes a random path away from the lander

Fig 3: Path taken by astronaut (blue) and estimated by algorithm (red) for random path.

Fig 4: Position estimation error over time for random path

The third scenario is some kind of sinusoidal path. Here the position error is very small.

Fig 5: Path taken by astronaut (blue) and estimated by algorithm (red). Both are very close

Fig 6: Position estimation error over time.

As a conclusion, we can say, that our algorithm gives us a 2D position error estimate of under 10m in a distance of 2km, if the astronaut walks on a reasonable (not linear) path.