NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2010 Mar 4, 14:56 +0100
George said:
Somehow, I doubt whether that plot from Andres, which
appears to have been
of observations taken at intervals of half-an-hour
over a period of 4 or 5
hours, was what Frank had in mind when he made that
proposal. It would be
interesting if Andres would repeat that exercise,
showing the group of LOPs
that results if Frank's proposal is followed, of ten
sights over half an
hour, around 1500 hours. Frank doesn't provide all
necessary details, but we
could just choose representative values such as 0
degrees dec, and 45
degrees latitude.
I wonder if the algorithm would look quite so robust
then, in providing a "fix".
Here is the simulation for a Sun rapid-fire fix:
True position 45ºN 3º30’W
|
|
|
GHA |
Dec |
Ho |
20/03/2010 |
15:00:00 |
Sol |
43.134676 |
-0.041704 |
32.959592 |
20/03/2010 |
15:03:00 |
Sol |
43.88483 |
-0.040881 |
32.538172 |
20/03/2010 |
15:06:00 |
Sol |
44.634984 |
-0.040057 |
32.112365 |
20/03/2010 |
15:09:00 |
Sol |
45.385138 |
-0.039234 |
31.682288 |
20/03/2010 |
15:12:00 |
Sol |
46.135291 |
-0.03841 |
31.248054 |
20/03/2010 |
15:15:00 |
Sol |
46.885445 |
-0.037587 |
30.809777 |
20/03/2010 |
15:18:00 |
Sol |
47.635599 |
-0.036763 |
30.367566 |
20/03/2010 |
15:21:00 |
Sol |
48.385753 |
-0.03594 |
29.921531 |
20/03/2010 |
15:24:00 |
Sol |
49.135906 |
-0.035116 |
29.471779 |
20/03/2010 |
15:27:00 |
Sol |
49.88606 |
-0.034292 |
29.018412 |
DeWit/USNO Nautical Almanac/Compac Data, Least squares
algorithm for n LOPs
GHA |
DEC |
HO |
BO |
LO |
LHA |
HC |
Z |
p |
43.1347 |
-0.0417 |
32.9596 |
44.9986 |
-3.4983 |
39.6364 |
32.9596 |
229.4885 |
0.0000 |
43.8848 |
-0.0409 |
32.5382 |
45.0104 |
-3.4816 |
40.4032 |
32.5381 |
230.2503 |
0.0001 |
44.6350 |
-0.0401 |
32.1124 |
45.0222 |
-3.4650 |
41.1700 |
32.1123 |
231.0050 |
0.0001 |
45.3851 |
-0.0392 |
31.6823 |
45.0340 |
-3.4483 |
41.9369 |
31.6822 |
231.7529 |
0.0001 |
46.1353 |
-0.0384 |
31.2481 |
45.0458 |
-3.4316 |
42.7037 |
31.2479 |
232.4939 |
0.0001 |
46.8854 |
-0.0376 |
30.8098 |
45.0576 |
-3.4150 |
43.4705 |
30.8097 |
233.2283 |
0.0001 |
47.6356 |
-0.0368 |
30.3676 |
45.0693 |
-3.3983 |
44.2373 |
30.3674 |
233.9561 |
0.0001 |
48.3858 |
-0.0359 |
29.9215 |
45.0811 |
-3.3816 |
45.0041 |
29.9214 |
234.6774 |
0.0001 |
49.1359 |
-0.0351 |
29.4718 |
45.0929 |
-3.3650 |
45.7710 |
29.4716 |
235.3924 |
0.0002 |
49.8861 |
-0.0343 |
29.0184 |
45.1047 |
-3.3483 |
46.5378 |
29.0183 |
236.1013 |
0.0002 |
Estimate position at time of fix:
Befix [deg] = 44.9986
Lefix [deg] = -3.4983
Least Squares information:
nObservations = 10
AA = 3.6532
BB = 4.8011
CC = 6.3468
DD = -0.0007
EE = -0.0009
FF = 0.0000
G = 0.1354
Error:
S = 0.0000
sigma = 0.0006 nm
sigmaB = 0.0029
sigmaL = 0.0038
Ellipse:
Prob = 0.9500
k = 2.4477
theta = -37.1653
a = 0.0117
b = 0.0004
Improved position at time of fix:
dB [deg] = 0.0008
dL [deg] = -0.0011
DO [deg] = 0.0656 nm
BI [deg] = 44.9994
LI [deg] = -3.4993
iteraciones = 2
The input file, SunRapidFire.obs,
for my program CelestialFix.exe is attached.
See also: [NavList 10065] Re: Time of meridian passage accuracy
http://fer3.com/arc/m2.aspx?i=110065
regards,
---
Andrés Ruiz
Navigational Algorithms
https://sites.google.com/site/navigationalalgorithms/