NavList:

   

Reply

George H wrote previously:
"Now, I don't know how that program operates, internally, and I doubt whether
Jeremy or Frank know either. It seems worthwhile, then, to ask some probing
questions about the value of such an exercise, before building on to such an
insecure foundation, as Frank has done."

Insecure foundation? You're way off, George. 

As for the supposed "black box", most of these software packages do exactly 
the same thing: they use the least squares solution for multiple sights 
provided in many sources, including every copy of the Nautical Almanac for 
some twenty-odd years. 

The calculational details are not the point of all this. The POINT is that you 
can get a good fix with a series of sights over a fairly brief period of 
time. This is not widely known among celestial navigation 
enthusiasts/practitioners.

In a (typical) rapid-fire fix, the error ellipse will be aligned with its long 
axis perpendicular to the mean azimuth of the sights (quite comparable to 
lat/lon at noon, by the way). The error in this direction is given 
approximately by (3/2)*S/(sqrt(N)*A) where S is the standard deviation of the 
observations themselves, N is the number of sights, and A is the range of 
azimuth in the sights (azimuth expressed as a pure number, "in radians"). So 
take Jeremy's moon sights in his "Exercise #14". First, we need the standard 
deviation of observations. Jeremy has posted quite a few cases, and he gets 
pretty good sights, with s.d. around 0.5 minutes of arc. In this particular 
set, N is 11, A is 0.1 (5.5 degrees is a tenth of a radian). So the standard 
deviation "cross-range" would be 2.3 nautical miles. Pretty good. 

In the direction towards the object, the error ellipse "down-range" has a 
width of about S/sqrt(N). We're not generally worried about the error in this 
direction, but it's worth mentioning that you would bump up againt systematic 
error fairly quickly. So if the equation says your error is 0.05 nautical 
miles in that direction, don't take it seriously.

-FER
PS: The factor (3/2) above may be wrong. I got that twice, but a third time I 
found (4/5). Whatever that constant is, it is "of order unity"




--~--~---------~--~----~------------~-------~--~----~
Navigation List archive: www.fer3.com/arc
To post, email NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply