Assessing the Accuracy of Your Data
Part 2
• RMS – what it is and how it is
computed
• Pathfinder Office precisions
• Confidence levels for stating GPS
accuracy
• Reporting accuracy
• Overall map accuracy
Topics Covered in
this Slide Show
In order to perform a complete
accuracy assessment for your GPS
dataset, you must understand RMS
and how it is computed, what is
taken into account when Pathfinder
Office computes precisions (accuracy
estimates), the various confidence
levels for stating GPS accuracy and
what they really mean, how to report
the accuracy of your dataset and how
to determine the overall accuracy of
your final map.
Differential Correction Summary:
1 file processed. In this file:
396 (100.0%) of 396 selected positions were code
corrected by post-processing against 2 base providers
394 (99.5%) of 396 selected positions were carrier
corrected by post-processing against 2 base providers
Estimated accuracies for 198 corrected positions are
as follows:
Range
Percentage
------------------0-15cm
15-30cm
87.4%
30-50cm
12.1%
0.5-1m
0.5%
1-2m
2-5m
>5m
Differential correction complete.
Pathfinder Office
Differential
Correction Report
Your first indication of accuracy is
given by the Pathfinder Office
differential correction report.
Remember, the information given
here is ESTIMATED accuracy, not true
accuracy.
RMS
• Standard statistical measure for
specifying GPS accuracy
• The square root of the mean of the
squares of the horizontal error
values (assuming you know truth)
Calculating
Estimated
Accuracy
Root Mean Square (RMS) values are
the standard statistical measure for
specifying GPS accuracy.
RMS is a statistical measure of the
magnitude of a varying quantity.The
name comes from the fact that it is
the square root of the mean of the
squares of the values.
(Ehi)2 is the horizontal error for each
GPS position (the distance from the
known position to the GPScalculated position).
With GPS data, because we don’t
know the TRUE position, we use the
MEAN of all the positions in this
equation.
Horizontal Error
The horizontal distance of a GPS
position from the known position
Horizontal error is simply the
horizontal distance of a GPS position
from the true position.
Calculating RMS values
RMS is the square root of the mean of the
squares of the horizontal error values
(assuming you know truth)
1. Take the horizontal error values and
square them
2. Take the sum of the squares and divide
by the number of observations to find
the mean
3. Take the square root of that value
Calculating
Estimated
Accuracy
Back to the equation. Once you have
the horizontal error values, you
follow these steps to compute the
RMS. We will compute the RMS for a
GPS data set in a future class. To give
you an example, your RMS for a
particular point feature might
calculate out to 50 cm.
RMS is a statistical measure of the
magnitude of a varying quantity. The
name comes from the fact that it is
the square root of the mean of the
squares of the values.
(Ehi)2 = horizontal error for each GPS
position
• HRMS = horizontal distance from truth
within which at least 63% of the recorded
positions fall
• Smaller HRMS = more accurate data
Horizontal RMS
(HRMS)
HRMS is the horizontal distance from
truth within which at least 63% of
the recorded positions fall.
In this example, two ProXRS receivers
were set up side by side for 50 hours,
one logging autonomous data, and
one using WAAS corrections. The
WAAS-corrected file was then
postprocessed (using local Trimble
base station about 30 km away).
Postprocessing achieves better accuracy because
of the ability to use data (multiple base
observations) collected both before and after the
position time. With real-time DGPS, the corrections
are predictions based on broadcast corrections
from a few seconds earlier. The latency produces
lower accuracy. Post-processing software is also
more powerful and uses more sophisticated
algorithms in calculating errors and corrections.
In the autonomous dataset, 68% of
the positions were within 2.08 m. In
the WAAS corrected dataset, 68% of
the positions fell within 0.51 m. After
the WAAS file was postprocessed,
68% of the positions were within
0.33 m.
Commonly used reference values for accuracy
• CEP: 50%
• RMS: 63-68% (percentage for the RMS
depends on the shape of the distribution)
• 2dRMS: 95-98%
Distribution of
Horizontal Error
The data in the first diagram was
generated from repeated tests by
Trimble:
- 7 hours of positions at 5-sec logging
rate
- ProXL receiver at base and rover
The vertical axis of the histogram
shows the number of positions that
fall into each bin of horizontal error.
At every site where you make GPS
measurements, there is a distribution
of horizontal error similar to the one
shown in this graph.
The percentage for the RMS depends
on the shape of the distribution. In a
number of simulated random data
sets, Trimble observed the RMS to
range from 63 to 68%. Similarly, they
observed the 2dRMS fell in the range
95-98%. The CEP had a relatively
constant percentage.
Using the RMS (with the example dataset below)
means that we have 63-68% confidence that our
position measurement is accurate to plus or
minus 69 centimeters
Confidence Levels
How confident are you that your
position measurement has the error
that you think it does?
Using the CEP as an indication of
horizontal error for a particular
position measurement means that
we have 50% confidence that our
position measurement is accurate to
plus or minus 56 cm. Similarly, using
the RMS means that we have 63-68%
confidence that our position
measurement is accurate to plus or
minus 69 centimeters. And, if we use
the 2dRMS to represent our
uncertainty, we can say, with 95-98%
confidence, that our position
measurement is accurate to plus or
minus 138 centimeters.
To have greater confidence in your
accuracy statements, you must be
willing to accept a larger uncertainty.
Precisions are calculated in relation to
the MEAN of the observations (PFO has
no knowledge of the true location)
•
•
•
•
DOP values
# Satellites
Receiver type
Other factors …
Pathfinder Office
Precisions
Precisions are calculated using a complex
algorithm that takes into account DOP
values, number of satellites, receiver type
and other factors (see the complete list
below). Precisions circles can be displayed
to visually show calculated precisions for
features and positions. The precisions
calculation is based on the RMS formula
(with the additional information listed
above taken into account)
Because PFO has no knowledge of the true
location of a feature, precisions are
calculated in relation to the MEAN of the
observations, not the true location, using
the RMS formula. This additional
information is taken into account:
- Receiver type
- DOP values
- # Satellites
- SNRs
- Receiver noise estimates
- Satellite elevation angle
- Correction type
- Carrier lock time / initialization
- Base station distance (if using estimates of
post-processedaccuracy)
• 68% (1s)
• 95% (2s)
• 99% (3s)
RMS
63-68%
• Inverse relationship
• Higher probability: less precise
• Lower probability: more precise
• Example
• For a single GPS position, you might
have a 99% probability that the
position is within 2 meters of truth.
• For the same position, you could have
a 68% probability that the position is
within 0.6 meters of truth.
1s, 2s and 3s refer to
the number of
standard deviations
away from the mean
2dRMS
95-98%
Confidence Level
The Differential Correction utility
outputs a confidence level for each
GPS position. The statistical level of
confidence generated for each
position can be 68% (1s), 95% (2s), or
99% (3s). This is configured under the
Options > Units dialog.
The confidence level, or probability,
and the actual precision estimate have
an inverse relationship. That is, for a
given position, the larger the
probability the smaller the estimate
and vice versa. For example, for a
single GPS position, you might have a
99% probability that the position is
within 2 meters of truth. However, for
the same position, you could have a
68% probability that the position is
within 0.6 meters of truth.
In other words, is you want to have
99% confidence in your estimate, you
have to state a lower accuracy than if
you want to have 68% confidence in
your estimate.
• Accuracy of the original data used
to compile the map
• How accurately these source data
have been transferred to the map
• Resolution at which the map is
printed or displayed
• When presenting a map with
many different layers, accuracy of
the map is determined from the
least accurate layer
Map Accuracy
Correctly reporting the overall
accuracy of your map is important.
Map accuracy depends on the factors
listed here. And, accuracy is
intimately linked to scale  the
locational accuracy of a geographic
file depends on the scale of the
original source map or data
collection method.
•
•
•
•
Differential correction report
• Overall accuracy for the entire
dataset
PFO precisions
• Accuracy of individual features and
positions
Exported precisions
• Shapefile attribute table
• Accuracy of individual features
Accuracy specs for additional
equipment used (external antenna,
rangefinder)
Reporting
Accuracy
The next few slides will show each of
the first three items individually.
Remember to take into account
further effects on accuracy due to
additional equipment used (external
antenna, rangefinder, etc.)
Reporting
Accuracy
Your first estimates of accuracy come
from the differential correction log
file.
Table 1. Estimated accuracy (68% confidence level)
for the project using the MTSU CORS station 5 km
from the mapping site.
Range
Percentage
0 - 15 cm
15 - 30 cm
30 - 50 cm
0.5 - 1 m
1-2m
46.2%
2-5m
36.9%
>5 m
16.9%
Preliminary Data
Quality Report
Use the info from the differential
correction log file to fill out the first
table in your data quality form. Give
the table a descriptive title, including
the confidence level used, the name
of the base station, and the distance
between rover and base.
Generated
Attributes
When you export your
data from PFO, you
will export generated
attributes that contain
precisions info.
Summary
Statistics
Table 2. Summary statistics for estimated accuracy of each
project layer after differential correction.
Feature /
Layer
Maximum
PDOP
Maximum
PDOP
In ArcMap, you will create summary
statistics for each project layer for
this table in your data quality form.
Horizontal
Precision
(68% confidence)
Horizontal
Precision
(68% confidence)
m
m
Average
Range
Average
Range
Trail
5.9
5.9 – 5.9
3.1
3.1 – 3.1
Obstruction
3.4
2.6 – 4.2
1.967
1.7 – 2.2
Pond
6.9
6.5 – 7.3
3.25
3.1 – 3.4
Map Accuracy
Table 3. Estimated horizontal accuracy of data layers in the Oho Trail
Mapping Project.
GIS Layer
Description
Bozeman.tif
2004 Color infrared aerial
photo of Bozeman area
Roads.shp
Paved roads in the
Bozeman area
Trail.shp
Trails in the National
Forest near Bozeman
Obstruction.sh Obstructions along the
p
Forest Service trails
Pond.shp
Ponds within 10 meters of
the Forest Service trails
Estimated Horizontal
Accuracy (m)
1.0
2.0 – 5.0
3.1
1.7 – 2.2
3.1 – 3.4
Finally, the overall map accuracy
table will be filled out.
Maps can be created in may different
ways, including scanning, digitizing,
remote sensng, taking GPS
measurements, and even handdrawing or heads-up digitizing. The
methods used to create a map will
affect its accuracy.
Map accuracy depends on the
accuracy of the original data used to
compile the map, how accurately
these source data have been
transferred to the map, and
resolution at which the map is
printed or displayed.
Reporting map accuracy correctly is
important (this info should always be
part of metadata), and accuracy is
intimately linked to scale  the
locational accuracy of a geographic
file depends on the scale of the
original source map and/or data
collection method.
4 Things to Take Away Today
1.
2.
3.
4.
Accuracy info should always be reported with a dataset
Accuracy data are an important component of your metadata
Know how/where to obtain accuracy data for your project
Evaluate whether your accuracy requirements were met and
explain the impact on your project of the accuracy you
achieved