Page 145 - Green - Maritime Archaeology: A Technical Handbook. 2nd ed

124 Maritime Archaeology: A Technical Handbook, Second Edition
should be almost circular. This shows that there is equal knowledge of the accuracy of the point in all directions. A long, thin ellipse shows that the position of the point is poor in one direction, the direction in which the ellipse is biggest. Error ellipse dimensions are expressed as two values: the semi-major and semi-minor axes. The semi-major axis is half the largest distance across the ellipse, the semi-minor axis is half the smallest distance across the ellipse, and these values are equal for a circle. The measurement errors shown by the error ellipses increase for the points farther away from the control points.
The measurements to each point always possess a measurement error, and this error states how accurately the measurement was made with the tool used. The overall effect of the built-in measurement error in our dis- tance measurements is to give each point a position error, or an uncertainty in the point’s actual position. To this error we can add problems caused by the shape or geometry of the network. Where points being positioned are farthest from the control points, the angle between the two baseline mea- surements is small. The angle between the two baseline measurements can be used as a measure, and this angle is sometimes known as the “angle of cut.” Where the angle of cut is too small or too large the position error ellipses will be long and thin, therefore, the position errors for the points will be large. Ideally the angle of cut should be no smaller than 45° and no larger than 135° for a good network shape. It is important to note that this effect is not obvious unless position errors are computed for the points. If only the residuals for the distance measurements are used as a quality figure the increase in position error would not be noticed; the residuals are zero for all four points yet the actual position error gets worse as you go away from the control network.
4. Position Reference Points
Because of the way the adjustment works, three primary control points must be selected as reference points for the whole survey. The control network would be free to move in all directions if it were not fixed by these three reference points. The position of a point is given in three dimensions: the X direction is usually shown across a typical site chart, the Y direction is drawn up and down the chart, and the Z direction is not shown as it lies perpendicular to the page. The first reference point is fixed in all three dimensions (XYZ) and is not allowed to move at all during the adjustment. The second reference point is fixed in either the X or Y and the Z direc- tion. During the adjustment it can only move toward or away from the first reference point. The third reference point is only fixed in the Z-dimension so it can move horizontally but not vertically. For our survey design it is