NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Rejecting outliers
From: George Huxtable
Date: 2011 Jan 8, 14:10 -0000
From: George Huxtable
Date: 2011 Jan 8, 14:10 -0000
In his computer analysis of the data set that had been provided by Peter Fogg, I had questioned the freedom that Peter Hakel allowed for its slope to be determined from the data, when it was already predetermined from known information ---------------------------------------------------------------------------------------- and Peter Hakel responded- "In some cases yes, but perhaps not all. Answering your question would require me to simply repeat what I had written earlier about bad weather, position tracking vs. position determining, getting a good quality data set later in better conditions, etc. I also said that I have no problem with precomputing the slope; I was simply interested in developing a useful tool that deals with the problem of sight averaging from a slightly different starting point. I cannot think of adding anything else that would explain my motivation better. Given enough time, navigators can process their data by several methods and decide in the end with what result they feel most comfortable with. Having a choice in that regard is not a bad thing." Yes, I agree with Peter about all of that... ============ "It seems to me, however, that your well-known skepticism is applied inconsistently in this case. On the one hand you object to rejecting data points that don't seem to belong (by common-sense visual inspection, like Peter Fogg does), while on the other you are OK with constraining data set to a predetermined trend (slope) by trusting the DR (common sense in SOME cases). I thought your skepticism would lead you to join me in asking: "What if, in this case, the DR is not quite reliable? What useful processing can we do with this data then?" It appears that I was wrong on that account." My "well-known skepticism" remains undimmed, I hope. I was most sceptical about the use, in Peter's computer analysis, of a slope of 24' (over 5 minutes of time) deduced from a short sequence of highly-scattered data. Indeed, there was so much scatter in it that a slope of 32' was, statistically speaking, perfectly compatible with that set, if a somewhat worse fit than the 24', deduced and employed in Peter Hakel's analysis. Is Peter prepared to defend his value against the other? I pointed to the details of the observation that was made, because it tells us (unless there was some major error as yet undisclosed, which is always conceivable) that indeed 32' was the known, correct, slope, and the slope of 24' which Peter Hakel derived from that data and used in his analysis was simply way-out from that truth. Peter Fogg's data provides a good example of a case where precalculating slope can be useful. Under other conditions, a different situation might well arise, in which a very uncertain DR generates greater uncertainties in precalculating a slope than does the observed trend of altitudes, and perhaps Peter Hakel and I might agree that one should choose the most appropriate method depending on the circumstances. The logical flaw in any procedure that uses a predetermined slope as an important factor in a data analysis is that it first has to ASSUME an observer's position, when the end-result of the operation is to DETERMINE the observer's position. The get-out, from this catch, is that usually the geometry is such that even a very uncertain DR does not greatly perturb the slope, though this isn't always the case. A second get-out is that the problem can, if necessary, be treated as an iteration, though that may be taking such matters over-seriously. A simpler alternative is just to work with simple mean-values, of time and altitude, which together give a result independent of any slope. George.