NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Andrés Ruiz
Date: 2010 Mar 22, 12:27 +0100
There must be something wrong!
I have played with “rapid fire fix” few
times, on the beach and aboard, and also with simulated data. And the method is
good enough. Of course it would be preferable some nearly simultaneous shoots
with good distribution in azimuth.
This method is suitable to use with a star-tracker.
See the following study. And see in [NavList]:
http://www.fer3.com/arc/m2.aspx?i=112143&y=201003
http://www.fer3.com/arc/m2.aspx?i=112169&y=201003
Using calculated
altitude:
Input file: 20100317NavList.hc.obs
DeWit/USNO Nautical Almanac/Compac Data, Least
squares algorithm for n LOPs
GHA DEC HO BO LO LHA HC Z p
50.2093 -1.2202 35.1810 41.9600 -87.6350 322.5743 35.1810 131.9796 -0.0000
50.8553 -1.2195 35.5369 41.9600 -87.6350 323.2203 35.5369 132.6404 -0.0000
51.3387 -1.2190 35.8007 41.9600 -87.6350 323.7037 35.8007 133.1389 -0.0000
51.8722 -1.2184 36.0893 41.9600 -87.6350 324.2372 36.0893 133.6929 -0.0000
52.4140 -1.2178 36.3797 41.9600 -87.6350 324.7790 36.3797 134.2597 0.0000
52.8724 -1.2173 36.6233 41.9600 -87.6350 325.2374 36.6233 134.7427 -0.0000
53.3933 -1.2167 36.8976 41.9600 -87.6350 325.7583 36.8976 135.2953 0.0000
53.7559 -1.2163 37.0870 41.9600 -87.6350 326.1209 37.0870 135.6823 0.0000
54.3727 -1.2156 37.4061 41.9600 -87.6350 326.7377 37.4061 136.3452 -0.0000
54.8061 -1.2151 37.6280 41.9600 -87.6350 327.1711 37.6280 136.8144 -0.0000
Estimate position at time of
fix:
Befix [deg] = 41.9600
Lefix [deg] = -87.6350
Least Squares information:
nObservations = 10
AA = 4.9057
BB = -4.9920
CC = 5.0943
DD = 0.0000
EE = -0.0000
FF = 0.0000
G = 0.0706
Error:
S = 0.0000
sigma = 0.0000 nm
sigmaB = 0.0002
sigmaL = 0.0002
Ellipse:
Prob = 0.9500
k = 2.4477
theta = 44.4592
a = 0.0006
b = 0.0000
Improved position at time of
fix:
dB [deg] = -0.0000
dL [deg] = -0.0000
DO [deg] = 0.0002 nm
BI [deg] = 41.9600
LI [deg] = -87.6350
iteraciones = 1
Applying a normal
noise to HC
Input file: 20100317NavList.hcdistor.obs
DeWit/USNO Nautical Almanac/Compac Data, Least
squares algorithm for n LOPs
GHA DEC HO BO LO LHA HC Z p
50.2093 -1.2202 35.2090 42.0059 -87.5694 322.6399 35.1865 132.0705 0.0225
50.8553 -1.2195 35.5363 42.0059 -87.5694 323.2859 35.5416 132.7320 -0.0053
51.3387 -1.2190 35.8036 42.0059 -87.5694 323.7693 35.8048 133.2310 -0.0012
51.8722 -1.2184 36.0728 42.0059 -87.5694 324.3027 36.0928 133.7854 -0.0200
52.4140 -1.2178 36.3736 42.0059 -87.5694 324.8445 36.3826 134.3528 -0.0090
52.8724 -1.2173 36.6385 42.0059 -87.5694 325.3029 36.6255 134.8363 0.0130
53.3933 -1.2167 36.8969 42.0059 -87.5694 325.8239 36.8992 135.3894 -0.0023
53.7559 -1.2163 37.0741 42.0059 -87.5694 326.1864 37.0881 135.7768 -0.0140
54.3727 -1.2156 37.3974 42.0059 -87.5694 326.8032 37.4064 136.4402 -0.0091
54.8061 -1.2151 37.6533 42.0059 -87.5694 327.2367 37.6278 136.9099 0.0255
Estimate position at time of
fix:
Befix [deg] = 42.0059
Lefix [deg] = -87.5694
Least Squares information:
nObservations = 10
AA = 4.9220
BB = -4.9923
CC = 5.0780
DD = 0.0000
EE = -0.0000
FF = 0.0021
G = 0.0707
Error:
S = 0.0021
sigma = 0.9765 nm
sigmaB = 8.1451
sigmaL = 8.2732
Ellipse:
Prob = 0.9500
k = 2.4477
theta = 44.5525
a = 28.4080
b = 0.7561
Improved position at time of
fix:
dB [deg] = -0.0000
dL [deg] = -0.0000
DO [deg] = 0.0000 nm
BI [deg] = 42.0059
LI [deg] = -87.5694
iteraciones = 3
Notice how are the two axes of the ellipse (a,b) in
both cases.
Doing reverse
calculations for obtaining Hs from Hc:
|
17/03/2010 |
15:29:10 |
|
35.181044 |
|
35º 10.9' |
|
34.999127 |
|
34º 59.9' |
|
35 |
0 |
35 |
|
35º .0' |
|
35.181918 |
|
35º 10.9' |
|
17/03/2010 |
15:31:45 |
|
35.536859 |
|
35º 32.2' |
|
35.354647 |
|
35º 21.3' |
|
35 |
23 |
35.3833333 |
|
35º 23.0' |
|
35.565569 |
|
35º 33.9' |
|
17/03/2010 |
15:33:41 |
|
35.800686 |
|
35º 48.0' |
|
35.618259 |
|
35º 37.1' |
|
35 |
38 |
35.6333333 |
|
35º 38.0' |
|
35.815773 |
|
35º 48.9' |
|
17/03/2010 |
15:35:49 |
|
36.089316 |
|
36º 5.4' |
|
35.906657 |
|
35º 54.4' |
|
35 |
52 |
35.8666667 |
|
35º 52.0' |
|
36.049294 |
|
36º 3.0' |
|
17/03/2010 |
15:37:59 |
|
36.379736 |
|
36º 22.8' |
|
36.196846 |
|
36º 11.8' |
|
36 |
12 |
36.2 |
|
36º 12.0' |
|
36.382892 |
|
36º 23.0' |
|
17/03/2010 |
15:39:49 |
|
36.623298 |
|
36º 37.4' |
|
36.440218 |
|
36º 26.4' |
|
36 |
27 |
36.45 |
|
36º 27.0' |
|
36.633088 |
|
36º 38.0' |
|
17/03/2010 |
15:41:54 |
|
36.89761 |
|
36º 53.9' |
|
36.714318 |
|
36º 42.9' |
|
36 |
44 |
36.7333333 |
|
36º 44.0' |
|
36.91664 |
|
36º 55.0' |
|
17/03/2010 |
15:43:21 |
|
37.086962 |
|
37º 5.2' |
|
36.903525 |
|
36º 54.2' |
|
36 |
58 |
36.9666667 |
|
36º 58.0' |
|
37.150151 |
|
37º 9.0' |
|
17/03/2010 |
15:45:49 |
|
37.40607 |
|
37º 24.4' |
|
37.222393 |
|
37º 13.3' |
|
37 |
13 |
37.2166667 |
|
37º 13.0' |
|
37.40034 |
|
37º 24.0' |
|
17/03/2010 |
15:47:33 |
|
37.628008 |
|
37º 37.7' |
|
37.444165 |
|
37º 26.6' |
|
37 |
29 |
37.4833333 |
|
37º 29.0' |
|
37.667205 |
|
37º 40.0' |
|
|
|
|
|
|
Hc |
|
|
|
Hc2Hs |
|
|
|
|
|
Hs |
|
|
|
Ho |
And the absolute
and relative error in minutes is:
|
|
e
Abs |
e
rel |
|
15:29:10 |
0.052 |
0.150 |
|
15:31:45 |
1.721 |
4.868 |
|
15:33:41 |
0.904 |
2.539 |
|
15:35:49 |
2.399 |
6.682 |
|
15:37:59 |
0.189 |
0.523 |
|
15:39:49 |
0.587 |
1.611 |
|
15:41:54 |
1.141 |
3.108 |
|
15:43:21 |
3.789 |
10.266 |
|
15:45:49 |
0.344 |
0.923 |
|
15:47:33 |
2.350 |
6.276 |
Knowing the skills of Frank, I suppose the problem
would be in the octant…
Regards,
--
Andrés Ruiz
Navigational Algorithms
http://sites.google.com/site/navigationalalgorithms/
