NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: The Darn Old Cocked Hat - the sequel 1
From: Marcel Tschudin
Date: 2013 Mar 15, 23:04 +0200
From: Marcel Tschudin
Date: 2013 Mar 15, 23:04 +0200
As a lurker of this thread I would finally also like to add something from my back seat. I did not read all contributions but from some of them I gained the impression that there are misunderstandings arising from mixing up two cases which in my opinion require to be regarded differently.
Case 1 Estimation:
In the "real" situation the navigator does not know his true location; he tries to estimate it using e.g. three (independent) observations resulting in 3 LOPs. Each of his three lines is actually a "mountain range", each of them having a different bell shaped cross section (Gaussian or skew) representing the probability distribution of the LOP's position. The navigator's best estimate would be the point with the highest combined probability. This is a point in the "land scape" resulting from the intersection of the three "mountain ranges" (similar to Greg's drawing). If the navigator would have determined before from a lot of tests the probability distributions of his LOP measurements he could feed them in a computer together with the LOPs and calculate this point with the highest combined probability and show this final result as his best estimate.
Case 2 Verification:
In this "theoretical" situation the true location is known. With the help of it one tries to evaluate the accuracy of the "measuring system" (navigator using a certain sextant) by comparing estimated versus true location. Here it is of interest how the navigator's final estimations scatter around the known target. By systematically performing and analysing such measurements the navigator could derive the probability distribution for his LOPs which he then could use in a "real" case 1 situation for finding the most probable point in the LOP pattern.
Please excuse if such thoughts should already have been mentioned before.
Marcel
Case 1 Estimation:
In the "real" situation the navigator does not know his true location; he tries to estimate it using e.g. three (independent) observations resulting in 3 LOPs. Each of his three lines is actually a "mountain range", each of them having a different bell shaped cross section (Gaussian or skew) representing the probability distribution of the LOP's position. The navigator's best estimate would be the point with the highest combined probability. This is a point in the "land scape" resulting from the intersection of the three "mountain ranges" (similar to Greg's drawing). If the navigator would have determined before from a lot of tests the probability distributions of his LOP measurements he could feed them in a computer together with the LOPs and calculate this point with the highest combined probability and show this final result as his best estimate.
Case 2 Verification:
In this "theoretical" situation the true location is known. With the help of it one tries to evaluate the accuracy of the "measuring system" (navigator using a certain sextant) by comparing estimated versus true location. Here it is of interest how the navigator's final estimations scatter around the known target. By systematically performing and analysing such measurements the navigator could derive the probability distribution for his LOPs which he then could use in a "real" case 1 situation for finding the most probable point in the LOP pattern.
Please excuse if such thoughts should already have been mentioned before.
Marcel
