Error Modeling and Management for Data
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where:
and
C is a constant that determines the probability levels of the error ellipses
Once the error ellipses for arbitrary points along the straight line segment are
defined, the area that these ellipses encompass creates the confidence region around
the line. This region is used to represent the uncertainty of a line segment. Fig. 5
illustrates this concept for an arbitrary line segment.
A very interesting property of this modeling procedure is that it can be easily
extended to determine the uncertainty of a curve. If the curve function, y = f(x), is
known, for example in the case of a road design, the only modification that occurs in
the method is that the distance from two points on the curve should be computed by the
following equation:
and
are the diagonal elements of the covariance matrix of U,
is the correlation factor,