Re: Statistics on prediction accuracies

From: Frank@reednavigation.com
Date: Sat Apr 09 2011 - 00:59:29 UTC

  • Next message: Ted Molczan: "TJM obs of 2011 Apr 09 UTC"

    Thanks for the replies, everyone. I'll elaborate on what I'm up to.
    
    I'm trying to develop a "semi-practical" navigation backup by visual satellite observation. Really I'm thinking about two systems: one more automated, the other purely visual and as much paper-driven as possible. The latter is the one I'm trying to field first. I'm aware that such systems were proposed and tested to a limited extent decades ago, but of course cheap computation has completely changed the game. 
    
    The principle is simple: if I see a particular satellite pass, let's say, a tenth of a degree from a particular identifiable star at some instant of time, I can determine my position on Earth within fairly narrow limits. A visual observer equipped with low-power binoculars and a decent watch could certainly estimate a satellite's position to a tenth of a degree, occasionally quite a bit better, and timing to the nearest second is do-able especially if you have a partner that you can call out to. A tenth of a degree accuracy in apparent position corresponds to a position fix accuracy on the ground of 1 kilometer for a satellite near the zenith 573 kilometers high: 1/573 is a tenth of a degree. That's better than normal expectations for ordinary celestial navigation which some folks still look to as a backup navigation system (and which I teach!), but it requires no sextant, very little training, and almost no computation after the "charts" as prepared. Also, at the right time!
     s of the year, it's available all night, and at stratospheric altitudes (this more for the automated system), it's also available in daylight.
    
    A basic principle of navigation is that one is never actually lost. You always know where you are at some level of estimation. I can safely assume that anyone trying this out would know their position to the nearest degree or several of latitude and longitude. So I make up some charts plotting trajectories of a few bright satellites showing where they would be for various integral degrees of latitude and longitude on the night in question. Then the visual observer sees the actual position of the satellite among the stars and visually interpolates for position on the ground. For example, there is a popular sailing race from Marion, Massachusetts to Bermuda that will occur this year in June. Teams can declare that they will not use GPS or other electronic navigation for a handicap advantage. Times for the trip are three to five days. If the weather's clear, that would make visual satellite observing a viable, realistic navigation system during the nights. I should add that I h!
     ave tried this, and it has worked beautifully in tests. I'm just trying to standardize it now, and I'm not sure how much I have benefited from good luck in my trials.
    
    So back to my original question, I am trying to think of ways of selecting satellites that are low enough to give good position discrimination but high enough so that variable drag and other prediction uncertainty are not a big concern over a period of up to a couple of weeks. Also I'm trying to select satellites that do not maneuver. Note that some uncertainty in mean orbital longitude of the satellites is not a huge concern. The track of a polar orbit satellite nicely determines longitude even if it's five or ten seonds late or if the timing information is not as accurate, and a non-polar orbit satellite in low orbit (obviously harder to come by) will determine latitude very nicely. In the language of navigation, you get "lines of position" from each satellite and cross them for a fix.
    
    Although the ISS is obviously a great choice just by virtue of being so bright, its high-drag orbit and frequent orbital adjustments seem to rule it out as an option. I'm currently thinking that 500-1000km are the ideal heights for this application.
    
    -FER
    
    
    
    
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