A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2010 Oct 25, 11:27 -0700
But section 11.10 supports your position of dropping a perpendicular from the DR to the LOP but also takes into consideration their relative uncertainties.
The formula in the manual for doing this is, of course, an approximation, a "rule of thumb", but is, never the less, useful. The scale of the approximation makes sense for flight navigation where the available accuracy and the required accuracy are less than for marine navigation so would have to be modified for marine practice, perhaps you could propose a better formula for marine navigators to use.
Looking at your method, I think the problem is that, even though EP1 is the best estimate of the position at the time of LOP1, using it later to determine EP2 ignores possible large (though unlikely) errors in DR1 that determined EP1. Let's to a simplified analysis, reductio ad absurdum. Let's shorten the time between LOP1 and LOP2 to zero, the traditional "fix." Your method would use the information from DR1 to establish EP1 along LOP1 and then immediately run a perpendicular from there to LOP2 to establish EP2 completely ignoring the intersection of the LOPs, the "fix!" This seems to be a bizarre outcome since fixes are given much more weight than DRs and, in this situation, the difference between the DR and the fix is (and probably rightly so) attributed to unexpected error in the DR. Although your determination of DR1, and though it EP1, incorporated your best estimate of DR uncertainty, at that time, the fix proves that your estimate was wrong. The same problem persists with your method for determining EP2 after an additional dead reckoned leg.
On 10/25/2010 9:55 AM, John Karl wrote:
Yes Garry, in the article I'm considering the long-run fix, where the accuracy of the LOP far exceeds the accuracy of the EP, such as after a long DR run (many hours, or even days) followed by an LOP of 1-2 mile uncertainty (could be a celestial LOP, or others). An example of the opposite case, the short-run fix, is in the classic round of stars in a slow moving vessel where the relative position among the LOPs would have superior accuracy compared to the location of the individual LOPs. This is where the traditional running fix, TRF, is valid, as discussed in the AF manuals.
I argue that it's completely wrong to use the TRF in a long-run situation, where we're really making an estimate because of the large uncertainty in the EP. And in logically making estimates, we want to use all the information available, make no unnecessary assumptions, and make no contradictions.
The TRF completely ignores information about the location of the ship along LOP1. But in actual reality, we always have some idea of where our ship is. So the TRF fails to use all available information.
Furthermore, as can be seen from Figure 3 in the article, the traditional running fix assumes the component of estimated track perpendicular to LOP1 is exact, while in contrast, it assumes that the component of the estimated track along LOP1 is capable of unlimited error. Thus it nonsensically allows the orientation of LOP1 to decree the directions of exact information and of arbitrarily large error, when it's obvious that whatever the direction and magnitude of dead-reckoning errors, they're independent of LOP1's orientation. So that's a contradiction piled upon unjustified assumptions, all while disregarding available information. Is there a worse approach to estimation logic?
(The concept of relative uncertainty and most probable position is a completely different topic: It's treated rather naively by AFPAM 11-216 with an equation that's dimensionally incorrect; it's too complex to be of interest to Ocean Voyager; and to most NavList members, including me. Nonetheless, a trivial example of a known directionally-dependent uncertainty is attached, showing how the DR uncertainty is reduced by the recent LOP.)
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