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    Satellite sights with binoculars and gyros
    From: Peter Monta
    Date: 2013 Nov 9, 16:54 -0800
    Given the recent discussion about optical navigation with satellites, I've been getting in a little practice with binoculars.  Prediction tools like heavens-above.com or stellarium or gpredict make this very easy.  There are just hundreds of easy binocular objects, so many that there are often several in prime observing positions simultaneously (and this is with severely light-polluted skies, with eye/binoculars reaching only to mag 7.2 or so, with mag 6 moving objects being "comfortable").

    Recording position and time of the satellite in the conventional way, though, is rather awkward and gives only a few observations per pass.  The method of marking when the satellite crosses the line between two stars has the problem (for me anyway) of "what were those two stars?".

    So I wonder if the following scheme would work well:

    - securely attach a mobile phone (or other platform containing three MEMS gyros) to a pair of binoculars
    - provide for an illuminated crosshair in the binoculars field
    - record continuously the microphone audio and the gyro data
    - track the moving object with the binoculars, calling out when the object is centered
    - before and after the pass (and perhaps during as well), sight bright stars and call those out too

    At the end of this process, one has a set of observations of the form (object, time, theta_x, theta_y, theta_z).  The bright stars are used to estimate the gyro constants of integration, thus tying the gyro frame to the stellar inertial frame, and then the satellite observations are translated to (time, ra, dec) to drop into the navigation pipeline.

    Gyro bias can also be estimated from the star fixes.  Also, as an alternative to an illuminated crosshair, perhaps the object could be observed multiple times at the very edge of the field of view, say at three or four points on the boundary.  This may not be quite as good as something near the center of the field, but it requires no extra hardware mounted on the binoculars.

    All this is very similar to the "sky scout" class of augmented-reality planetarium apps, of course, but I haven't seen any that do proper global calibration against stars.  (The cameras in mobile phones will not come anywhere near binoculars in sensitivity.)

    If it takes, say, 5 seconds to go from satellite fix to star fix, the gyro will add a noise term of about 3 arcminutes rms assuming a typical consumer-MEMS-gyro angle random walk of 1 degree per root hour.  Repeated observations spread over the session will add strength to the overall solution.

    One can imagine a very user-friendly app that would drive the phone's display with where to point next.  After initial alignment with two or three stars (as with a goto telescope), the app would calculate the best satellite in view and provide a bullseye on the display to guide the user's rough pointing.  Rinse and repeat, alternating with stars.


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