STAR*NET V6 - Circe

Chapter 8 Analysis of Adjustment Output
8.16 Error Ellipse Interpretation
The error ellipse represents the area of uncertainty around a given point. For example,
assume that a survey network point is computed from the intersection of three lines from
known points, each line being of a measured distance and bearing. The measured
distances and bearings all contain some uncertainty, which were expressed as standard
errors in the input data.
The resulting computed point then has standard deviations in Northing and Easting (or in
X and Y), which are computed and listed by STAR*NET. The total effect of all the
random measurement errors results in an error ellipse of a specific size, shape, and
orientation. The ellipse itself is computed by STAR*NET from the standard errors in
Northing and Easting and the correlation between those standard errors.
The size of the ellipse is a measure of the reliability of the computed point position. In a
particular survey, a smaller ellipse means the point has greater reliability than one with a
larger ellipse. Values of the semi-major and semi-minor parameters, as printed in the
listing and on the screen, are the actual ground dimensions across half the ellipse, in the
long and short directions respectively. The lengths of the axes depend on the standard
errors and correlations of the computed coordinates. If N and E are of equal precision,
then the ellipse will be a circle.
The ellipse azimuth is the azimuth of the semi-major axis, and gives the orientation of
the ellipse with respect to the ground coordinate system. The azimuth depends on the
correlation between the adjusted coordinates of the point. If they are uncorrelated, the
ellipse axes will be parallel to the control axes.
STAR*NET allows you to define your own confidence level. A commonly used
confidence level is 95% which produces a 95% error ellipse. That means that there is a
95% probability that the actual point position lies somewhere within the extents of the
reported dimensions of the ellipse.
The plotted error ellipses provide a means of analyzing the strength of the survey
network, and the reliability of the computed points. At a first glance, the absolute
dimensions of the ellipses provide a measurement of positional accuracy. The relative
sizes of the ellipses indicate which points are weaker than others within a given network.
The shapes and orientations of the ellipses indicate how the network can be
strengthened. An elongated ellipse shows that there is a larger uncertainty in one of the
coordinates, and that perhaps an additional distance or angle measurement is required to
that station. A large but circular ellipse means that the point is balanced in Northing and
Easting (or X and Y), but that more accurate measurement techniques are required, or
additional measurements from several other stations are required. If many ellipses are
elongated and point in the same direction, then the network is unbalanced along that
direction. Typically, there may be an azimuth deficiency, and one side of the network has
little resistance to rotation. An additional control point or observed azimuth will help to
stabilize the survey.
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