NavList:

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/