# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Resolution of systematic error
From: Peter Fogg
Date: 2007 Mar 1, 10:45 +1100

There is a method for the resolution of systematic error that I understand was first proposed by the German geodesist Lehmann.

In the example below, the lines represent portions of position lines (aka LOPs). The arrows point towards the sub-stellar point or, to put that another way, indicate the direction of the azimuth.

The arrows should, of course, form a right angle with the position line. This drafting inaccuracy is not important for our purposes; the arrows just indicate direction. The small circle indicates (again; roughly) the fix position.

If all arrows point in the same direction (all pointing out or all pointing in) it means the azimuths used cover an arc of less than 180 degrees. This is less than ideal, and one reason is that if there is any systematic error the actual position will lie outside the triangle.

Lehmann (as have others since) proposed a simple method for establishing a position that has a higher probability of being correct.

Shadow (dotted) lines are drawn towards the direction indicated, parallel to and at the same distance from the position lines.

Then lines are drawn that pass through the intersecting position lines and the intersecting shadow position lines.

These blue lines meet at a common point: the centre of a circle whose radius, touching the original position lines, indicates the extent of the systematic error.

Note that the distance of the shadow lines from the position lines is not relevant, although this distance must be consistent and the shadow lines must be parallel with the lines they are derived from (again, this freehand diagram is a little crude  try drawing it as accurately as possible on graph paper to check whether it works).

The point of intersection of the blue lines is the improved fix position. With systematic error and azimuths that cover less than 180 degrees the actual position will ALWAYS lie outside the triangle.

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