Photogrammetric Astronavigation is just a fancy way of saying "using information from pictures of the sky to figure out where the heck you are." It could also be called "Astrometric Navigation". The XO comes with a built-in camera, why not use it to augment short-range, highly accurate position determination techniques like Acoustic Tape Measure with a broad-scale solution.
Using pictures or video of the stars and moon from a stationary location over time, one can calculate one's geographical location. This could be as simple as setting the XO down at night with the camera pointed up and letting it record for a couple of minutes. Then, the activity would automagically process the image data to identify observed star systems, correct for laptop vibration, measure the relative movement of the moon and stars, correct for expected atmospheric interference, and return a range of coordinates.
Obviously, these calculations might become complex, but we can greatly simply the process using existing astronomical datasets, software, or approximation-charts. Furthermore, one of the greatest challenges of ancient celestial navigation, accurate timekeeping, is already solved by virtue of the XO's internal timekeeping.
We can also augment some of the image-processing tasks through increased student participation (playful education, anyone?). For example, the camera input could be fed back to the display, where children could use overlaid shapes, text instructions/information, and filters to identify currently-visible sky objects. An easy sample of this process would be to have a circle that children could center around the moon. A more complex example would be to have them "erase"/filter-out non-sky objects in obstructing the camera's view of the heavens.
 Input Data
 System Knowns
(data we start with)
- Accurate Absolute Time
- Possibly checked through wireless-mediated confirmation sources.
- Camera/lens characteristics
- Localization information
- i.e. "where this computer is supposed to be"
- Expected positions and motions of the stars and moon
 Image/Video Observables
- The Moon
- Moon size
- Moon motion
- Moon features (for determination of libration, camera orientation)
- Star positions (only for bright stars, most likely)
- Star motion (rather unlikely)
(data that would be helpful, but are not immediately apparent)
- Angle of camera relative to the horizon
- Real-time cloud cover/atmospheric variation
- Absolute camera orientation
- Given the limitations of the human eye and the XO's camera, the expected maximum resolution would be within an approximately 100 km radius. Not exactly precise, but "in the ballpark"
- This is not intended to be a continuous-use solution, since weather and the rotation of the Earth mean that geolocation is only possible at certain times.
- This activity could easily be replaced with the addition of a cheap GPS unit.
- The accuracy of the activity could be dramatically improved with even a moderate-magnification camera peripheral.
- Star-pattern recognition for motion calibration might become processing-intensive without the implementation of high-efficiency algorithms (some of which are available in the scientific theory literature, but not broadly distributed/accessible).
 Companion Ideas
- Combine this activity with a general open-source stargazer activity for constellation identification, astronomical education, etc.
- Combine this activity with other time-lapse photography activities for artistic exploration.
- Use this activity as another anti-theft tool by asking users to "check in" with a run of this activity every couple of months to confirm that the XO is still in the right country.
 More Informations/Links
- A Short Guide to Celestial Navigation - An easy-to-understand primer.
- Alternatives to GPS Pappalardi et al examine several astronavigation applications.
- Astrometry.net, a web service that does this, to some extent, plus a (large) open-source codebase that might be trimmed down to fit and run in the XO.