Estimating the spatial accuracy of coordinates
Owens, T., and D. McConville. 1996. Geospatial application: Estimating the
spatial accuracy of coordinates collected using the Global Positioning System.
National Biological Service, Environmental Management Technical Center,
Onalaska, Wisconsin, April 1996. LTRMP 96-T002. 13 pp. + Appendix.
ABSTRACT
Evaluating the accuracy of spatial data is important to determine appropriate use
of these data. However, a good method has not been documented to measure
locational accuracy. The Global Positioning System (GPS) reduces the
difficulty of measuring the location of objects and enables non-surveyors to
determine their location with relative ease. This study applied a
straight-forward, repeatable, and statistically sound method of estimating the
horizontal accuracy of GPS-derived location data. We concentrated on the
spatial accuracy of points because points represent simple locations and not
cartographic abstractions such as lines or polygons.
When GPS coordinates are taken at surveyed locations, the quantity of interest
is the difference from the surveyed (assumed true) coordinates. This difference
in coordinates is a bivariate quantity and the probability distribution function
(PDF) can be described by an ellipse with the center at and . An ellipse is an
appropriate shape for a PDF; it has two dimensions but is not rectangular
because the joint probability of points occurring in the corners is very small, and
it is generally not circular because X and Y are not necessarily the same. There
are three ellipses of interest: the standard ellipse, the confidence ellipse, and the
tolerance ellipse. The standard ellipse is a descriptive tool used to visualize the
ellipse's shape and orientation. It contains about 40% of the sample, is not
dependent on the sample size, and cannot be used for statistical inference. The
other two ellipses have identical shapes and orientation but different major and
minor axes. The confidence ellipse is an estimate of accuracy; the sample mean
is or is not significantly different from the survey locations at a given à. The
tolerance ellipse is an estimate of precision; a given percentage of the population
sampled is enclosed in the tolerance ellipse at a given à.
Thirty-six locations were measured and compared to surveyed locations. The
average offset was -1.13 m in the northing (Y) direction and 0.18 m in the
easting (X) direction. Hotelling's one- sample test determined that H0 (no
significant departure from the survey locations exists) was rejected at the 0.05
level, which indicates there was a systematic error in the sample in the south and
east directions. Ninety-five percent of the population sampled (at the 0.05
level) was contained in an ellipse that was centered on 0.18, -1.13, and had a
major axis of 7.49 m, and a minor axis of 5.12 m with an angle of 87.74o.
Thus, if an additional point were taken, we are 95% confident that it would fall
within this tolerance ellipse.
KEYWORDS
ellipse, Global Positioning System, locational accuracy, spatial accuracy