P
roduct
A
ccuracy
C
omputation
Currently, users of geospatial data express product accuracy
based on the agreement or disagreement of the tested prod-
uct per the surveyed checkpoints, ignoring checkpoint errors
that have resulted from inaccurate surveying techniques.
In other words, users consider the surveyed checkpoints to
be free of error. The following section details how errors are
propagated into the mapping product when we are trying to
determine the location of a ground point “A”. Let us intro-
duce the following terms:
ACC
SurveyDatum
equals the accuracy in determining the
survey datum, generated when realizing the intended or
true datum through surveying techniques. In other words, it
represents the errors in the surveyed checkpoints. Due to this
inaccuracy, the point will be located at location A
..
(Figure 3).
ACC
MappingDatum
equals the accuracy of determining the
mapping datum, or the errors introduced during the map-
ping process, in reference to the already inaccurate survey
datum represented by the surveyed checkpoints. In other
words, it is the fit of the aerial triangulation (for imagery) or
the boresight/calibration (for lidar) to the surveyed ground
control points represented as the survey datum. This accu-
racy is measured using the surveyed checkpoints during the
product accuracy verification process. Due to this inaccuracy,
the point will be located at location A
...
(Figure 3).
ACC
TrueDatum
equals the accuracy of the mapping product
in reference to the true datum, as in NAD83(2011). The point
location A
.
(Figure 3) is considered the most accurate location
determined in reference to the true datum.
Using the above definitions, the correct product accuracy
should be modeled using error prorogation principles accord-
ing to the following formula:
ACC
TrueDatum =
1
However, according to our current practices, product accura-
cy is computed according to the following formula, ignoring
errors in the surveying techniques:
ACC
TrueDatum
= ACC
MappingDatum
2
Practical Method of Computing Accuracy
Components
As we are dealing with three-dimensional error components,
we would need to employ vector algebra to accurately com-
pute the cumulative error.
Computing Horizontal Accuracy
To compute the horizontal accuracy for a two-dimensional
map, as with orthorectified imagery, we will ignore the error
component of the height survey. In other words, we will use
the error component from easting and northing only. We will
also assume that the accuracy of determining the X coordi-
nates (or easting) is equal to the accuracy of determining the
Y coordinates (or northing). Using error propagation princi-
ples and Euclidean vector in Figures 3 and 4, we can derive
the following values for product horizontal accuracy:
AccXTrueDatum =
3
AccYTrueDatum =
4
AccXYTrueDatum =
5
As an example, when modeling horizontal product accuracy
according to the above formulas, let us assume the following:
a) We are evaluating the horizontal accuracy for ortho-
imagery using independent checkpoints.
b) The control survey report states that the survey for
the checkpoints, which was conducted using RTK
techniques, resulted in accuracy of RMSE
XorY
equal
to 2cm.
c) When the checkpoints were used to verify the hor-
izontal accuracy of the orthoimagery, it resulted in
an accuracy of RMSE
XorY
equal to 3cm.
400
July 2020
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
Figure 3: Influence of error propagation on point location
accuracy.
