Analysis of waypoint range uncertainty
The effect on waypoint projection of pose uncertainty is approximately time
invariant:
- Earlier estimates are more accurate
in an absolute sense, but later poses have drifted farther from the absolute
reference frame, nulling this advantage.
- Later estimates contain less uncertainty due to the travel from the
estimate point to the projected waypoint, but that projection depends on the
projection of the waypoint ray into our current FOV. This is a function of
the larger relative uncertainty of the estimate point w.r.t. the waypoint base.
However, the overall projection quality improves significantly as we approach
the waypoint:
- Stereo range uncertainty decreases as the square of distance, so closer
ranges are much more accurate than longer ones.
- The only reason that flat earth assumption is at all reasonable is that
remaining segment of the terrain increasingly resembles a plane as we approach
the waypoint.
Note that strictly speaking, the quality improves as we close on the waypoint,
which is not necessarily the same as improving as time passes. We might be
moving away from the waypoint due collision avoidance, etc. It nevertheless
seems reasonable to approximate this effect by doing a running average
that gives more weight to recent
projections (e.g. a low-pass filter.)
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