NavList:

Heres a link which compares random vs. systematic errors.

http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html

Greg Rudzinski

Re: The Darn Old Cocked Hat - the sequel 1
From: Richard B. Langley
Date: Mar 15, 15:38 -0300
The two distributions may not have the same standard deviation and are not necessarily independent; there may be some correlation between them. It might be worth having a look at Appendix Q of Bowditch (Navigational Errors). Not sure which editions Appendix Q appeared in -- it is at least in the 1977 edition. The following two paragraphs are particularly germane:

"The value of the most probable position determined as suggested above depends
on the degree to which the various errors are in fact normal, and the accuracy with
the likely error of each is established. From a practical standpoint, the second
is largely a matter of judgment based upon experience. It might seem that inter-
pretation of results and establishment of most probable position is a matter of judgment
anyway, and that the procedure outlined above is not needed. If a person will follow
this procedure while gaining experience, and evaluate his results, the judgment he
develops should be more reliable than if developed without benefit of a knowledge of
the principles involved. The important point to remember is that the relative effects
of normal random errors in any one direction are proportional to their squares.

"Systematic errors are treated differently. Generally, an attempt is made to discover
the errors and eliminate them or compensate for them. In the case of a position deter-
mined by three or more lines of position resulting from readings with constant error,
the error might be eliminated by finding and applying that correction (including sign)
which will bring all lines through a common point."

The following item, although specific to GPS, might also be of general interest:
http://gauss.gge.unb.ca/gpsworld/EarlyInnovationColumns/Innov.1991.07-08.pdf

-- Richard Langley

On 2013-03-15, at 10:17 AM, John Karl wrote:

Hanno, et al.,

We don't need numerical simulation to see that the probability around a ship's location, which is determined by two independent normal distributions of lat(x) & lon(y), is another normal distribution in the distance from the ship, r:

Prob = exp(x/s)*2 exp(y/s)*2 = exp[(x/s)*2 + (y/s)*2] = exp(r/s)*2

which, of course, is maximum at r = 0. Plot is attached with ship at 15,15.

JK

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