APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
Accuracy vs. Precision. The following definitions are from Appendix 1-A,
Glossary of Terms, of FGDC-STD-007.1-1998, Geospatial Positioning Accuracy
Standards. "Accuracy - closeness of an estimated (e.g., measured or computed)
value to a standard or accepted [true] value of a particular quantity. NOTE:
Because the true value is not known, but only estimated, the accuracy of the
measured quantity is also unknown. Therefore, accuracy of coordinate
information can only be estimated … Precision - in statistics, a measure of the
tendency of a set of random numbers to cluster about a number determined by
the set. NOTE: If appropriate steps are taken to eliminate or correct for biases in
positional data, precision measures may also be a useful means of representing
accuracy."
Precision essentially defines the consistency of multiple measurements as those
measured values cluster about a number determined by those same
measurements. But when these multiple measurements include systematic
errors or biases, highly precise measurements may nonetheless yield highly
inaccurate results. For example, suppose benchmark A (see *) has a published
value of 100.00 ft in elevation, and the difference in elevation between
benchmark A and new benchmark B is measured 10 times by differential
leveling. If all 10 measurements indicate that benchmark B is between 0.99 ft and
1.01 ft higher than benchmark A, it is logical to conclude that benchmark B has
an elevation of 101.00 ft (and some people would say 101.00 ft ±0.01 ft).
Although "±0.01 ft" may be a measure of precision in this example, it may be very
misleading if erroneously understood to represent accuracy, especially if it is later
determined that the elevation of benchmark A is really 98.26 ft, for example,
instead of 100.00 ft. When correcting for the systematic error or bias of 1.74 ft,
then the true elevation of benchmark B would be 99.26 ft instead of 101.00 ft,
assuming there were no other systematic errors in the measurements.
*
Note, a benchmark is a relatively permanent, natural or artificial, material
object bearing a marked point whose elevation above or below an adopted
vertical datum is known; a benchmark surveyed with differential leveling
normally does not have surveyed geographic coordinates, latitude and
longitude, as has a survey monument surveyed with GPS. A survey
monument may either be a 2-D monument (latitude and longitude only) or
a 3-D monument (latitude, longitude, and elevation).
Relative and Absolute Accuracy. As defined by the American Society for
Photogrammetry and Remote Sensing (ASPRS) in "Digital Elevation Model
Technologies and Applications: The DEM Users Manual," page 471, Relative
accuracy is a "measure that accounts for random errors in a data set. Relative
accuracy may also be referred to as point-to-point accuracy. The general
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APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
measure of relative accuracy is an evaluation of the random errors … in
determining the positional orientation (e.g., distance, azimuth) of one point or
feature with respect to another." In construction surveying for example, it is
important for construction stakes to have good accuracy relative to the boundary
markers used to define the corners of the lot on which the construction is to
occur, but it may be immaterial whether or not the corner boundary markers are
accurately surveyed relative to the geodetic datum so long as the boundary
markers are authoritative and define legal ownership rights. Similarly, ASPRS
defines absolute accuracy as "a measure that accounts for all systematic and
random errors in a data set. Absolute accuracy is stated with respect to a
defined datum or reference system." When the "reference system" is the
National Spatial Reference System (NSRS), the "defined datum" is the North
American Vertical Datum of 1988 (NAVD 88) for elevation surveys and the North
American Datum of 1983 (NAD 83) for horizontal surveys. Both NAVD 88 and
NAD 83 are geodetic datums used to control the surveying and mapping of North
America. NAD 83 is based on the Geodetic Reference System of 1980 (GRS 80)
ellipsoid which is nearly identical to the World Geodetic System of 1984 (WGS
84) ellipsoid used internationally in conjunction with the Global Positioning
System (GPS) which is based on the WGS 84 ellipsoid and datum.
All ECs are surveyed with relative accuracy — relative to a survey monument or
benchmark from which elevations are derived.
Local and Network Accuracy. Closely related to relative accuracy, the local
accuracy of a control point, as defined in FGDC-STD-007.1-1998, is "a value that
represents the uncertainty in the coordinates of the control point relative to the
coordinates of other directly connected, adjacent control points at the 95-percent
confidence level. The reported local accuracy is an approximate average of the
individual local accuracy values between this control point and other observed
control points used to establish the coordinates of the control point." Closely
related to absolute accuracy, network accuracy, as defined by FGDC-STD-007.11998,
"is a value that represents the uncertainty in the coordinates of the control
point with respect to the geodetic datum at the 95-percent confidence level. For
NSRS network accuracy classification, the datum is considered to be best
expressed by the geodetic values at the Continuously Operating Reference
Stations (CORS) supported by NGS. By this definition, the local and network
accuracy values at CORS sites are considered to be infinitesimal, i.e., to
approach zero."
Before the satellite era, geodesists were unable to establish a geocentric (center
of earth) ellipsoid and datum, but current geodetic datums are geocentric
because the center of the earth can be defined as that point about which
satellites orbit, and GPS surveys can be referenced to the center of the earth as
well as to multiple CORS stations on the earth's surface, surveyed so accurately
that they are assumed to have absolute positioning errors of zero.
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APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
When using differential GPS survey procedures with survey-grade receivers,
GPS surveys are normally tied directly or indirectly to CORS stations, providing
both local accuracy and network accuracy of a few centimeters at the 95%
confidence level. However, when using single, inexpensive mapping-grade GPS
receivers, GPS surveys are not relative to any local survey monument or
benchmark, and the network accuracy is on the order of 10-meters horizontally
and 20-meters vertically at the 95% confidence level.
Land Surveying Standards. Traditional land surveying procedures yield relative
accuracy, expressed in terms or orders and classes of surveys. Table B.1 shows
how the various orders and classes of conventional vertical surveys have relative
accuracies expressed in terms of the distance between two points, i.e., the
reference benchmark and the newly surveyed point.
Table B.1 — Relative Accuracy Standards for Conventional Vertical Surveys
Vertical
Survey Order
Vertical
Survey Class
Relative Accuracy between directly
connected points
1st I Standard Error = 0.5 mm vK
1st II Standard Error = 0.7 mm vK
2nd I Standard Error = 1.0 mm vK
2nd II Standard Error = 1.3 mm vK
3rd N/A Standard Error = 2.0 mm vK
where vK is the square root of the distance K in kilometers between the two
points
Table B.2 shows a similar distance-based relative accuracy standard for a survey
method called trilateration which measures the distances of lines for horizontal
positioning.
Table B.2 — Relative Accuracy Standards for Conventional Horizontal Surveys
Horizontal
Survey Order
Horizontal
Survey Class
Relative Accuracy between directly
connected points
1st N/A Standard Error = 1 part in 1,000,000
2nd I Standard Error = 1 part in 750,000
2nd II Standard Error = 1 part in 450,000
3rd I Standard Error = 1 part in 250,000
3rd II Standard Error = 1 part in 150,000
Table B.3 shows a different distance-based relative accuracy standard for
differential GPS surveys that measure distances to multiple satellites to compute
baselines between a GPS base station and "rover," for both horizontal and
vertical positioning.
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APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
Table B.3 — Relative Accuracy for GPS Horizontal Surveys
GPS Class Local Accuracy at 95% Confidence Level
AA 0.3 cm + 1 part per 100,000,000
A 0.5 cm + 1 part per 10,000,000
B 0.8 cm + 1 part per 1,000,000
First 1.0 cm + 1 part per 100,000
When GPS surveys correctly use CORS or selected NSRS monuments as the
GPS base stations for the differential surveys, then the network accuracies of the
newly surveyed points can be estimated and centimeter-level accuracies can be
achieved. But when only a single GPS receiver is used, errors are typically on
the order of 10 meters horizontally and 20 meters vertically at the 95%
confidence level.
National Map Accuracy Standards (NMAS). Whereas surveying standards have
traditionally referenced relative accuracy, mapping standards have traditionally
referenced absolute accuracy. The NMAS, in use since 1947, defines absolute
accuracy at the 90% confidence level. Horizontally, for large-scale maps, 90% of
clearly defined checkpoints must be accurate within 1/30th of an inch at the
publication scale of the map; there is no real limit on the 10% of errors that may
be larger than 1/30th of an inch. Vertically, 90% of checkpoints used to validate
the accuracy of contour lines should be accurate within ½ the contour interval
with no errors larger than the full contour interval; and 90% of checkpoints used
to validate the accuracy of spot heights should be accurate within ¼ the contour
interval with no spot height errors larger than ½ the contour interval. Apparent
vertical errors can be offset by permissible horizontal errors; this makes it difficult
to perform vertical accuracy checks.
National Standard for Spatial Data Accuracy (NSSDA). Implemented in 1998 to
replace the NMAS for all digital mapping products, the NSSDA defines absolute
accuracy at the 95% confidence level, compared with the NMAS' 90% standard.
This equates to the FGDC's definition of network accuracy. The FGDC has
specified: "Federal agencies collecting or producing geospatial data, either
directly or indirectly (e.g., through grants, partnerships, or contracts with other
entities), shall ensure, prior to obligating funds for such activities, that data will be
collected in a manner that meets all relevant standards adopted through the
FGDC process" and specifically mandates that the "accuracy of new or revised
spatial data will be reported according to the NSSDA."
According to FGDC-STD-007.1-1998, "The reporting standard in the horizontal
component is the radius of a circle of uncertainty, such that the true or theoretical
location of the point falls within that circle 95-percent of the time. The reporting
standard in the vertical component is a linear uncertainty value, such that the true
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APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
or theoretical location of the point falls within ± of that linear uncertainty value 95percent
of the time."
The NSSDA provides root-mean-square error (RMSE) criteria for computing
accuracy values at the 95% confidence level, but only when errors are known to
follow a normal error distribution. However, the National Digital Elevation
Program (NDEP) has determined that many forms of elevation errors do not
follow a normal error distribution (bell curve) and specifies that an alternative 95th
percentile method be used to establish accuracy at the 95% confidence level.
The ASPRS "DEM Users Manual" defines percentile as follows: "As used in this
manual, a percentile is any of the values in a dataset of errors dividing the
distribution of the individual errors in the dataset into one hundred groups of
equal frequency. Any of these groups can specify a specific percentile, e.g., the
95th percentile. The 95th percentile indicates that 95% of the errors will be of
equal or lesser value and 5 percent of the errors will be of larger value."
In testing the accuracy of a dataset at the 95% confidence level, the NSSDA
states: "A minimum of 20 check points shall be tested, distributed to reflect the
geographic area of interest and the distribution of error in the dataset. When 20
points are tested, the 95% confidence level allows one point to fail the threshold
given in product specifications."
Table B.4 compares NMAS and NSSDA vertical accuracy standards for checking
contours or digital terrain models or individual points based on their equivalent
contour interval. The NMAS and NSSDA standards for spot heights are half the
values shown in this Table. For example, for 2 ft equivalent contours, 95% of
spot heights should be accurate within 0.6 ft.
Table B.4 — Comparison of NMAS/NSSDA Standards
NMAS
Equivalent
Contour Interval
NMAS Vertical
Accuracy Standard
90% Confidence Level
NSSDA
RMSEz
NSSDA Vertical
Accuracy at 95%
Confidence Level
1 ft 0.5 ft 0.3 ft 0.6 ft
2 ft 1.0 ft 0.6 ft 1.2 ft
5 ft 2.5 ft 1.5 ft 3.0 ft
10 ft 5 ft 3.0 ft 6.0 ft
20 ft 10 ft 6.1 ft 11.9 ft
NOAA Technical Memorandum NOS NGS-58. Normally referred to as "NGS58,"
the correct title of this document is NOAA Technical Memorandum NOS
NGS-58, "Guidelines for Establishing GPS-Derived Ellipsoid Heights (Standards:
2 cm and 5 cm)," November, 1997. This is the "bible" for GPS elevation surveys,
and NOAA contracted with Dewberry in 2002 to perform research necessary to
validate the various operational procedures necessary to ensure that 2 cm local
accuracy , 5 cm local accuracy, or 5 cm network accuracy are achieved with
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APPENDIX B — GEOSPATIAL ACCURACY STANDARDS
specified baseline lengths, observation times, satellite configurations that control
vertical accuracy, and other variables. Survey procedures consistent with NGS58
were followed for all check surveys to establish "ground truth" for this study
and the evaluation of various remote sensing technologies.
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