PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
April 2016
245
The following Table is a sample on calculating the differences or the residuals in the elevation fit:
Point ID
Northing
Easting
Surveyed H
Lidar H
Difference (ft)
Difference (cm)
PT-1
248625.003
2099927.620
1101.788
1101.319
-0.47
-14.30
PT-2
106224.367
2111913.255
1189.472
1189.538
0.07
2.01
PT-3
196036.487
2168118.736
1216.597
1216.350
-0.25
-7.53
PT-4
207652.511
2117099.375
1182.528
1182.496
-0.03
-0.98
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“Users of the new ASPRS Positional Accuracy
Standards for Digital Geospatial Data ar
e encouraged
to start defining the accuracy of the final
deliverables in terms of RMSE (i.e. x-cm) and to
stay away from expressing the product accuracy in
terms of map scale and contour interval”
2. Compute the RMSE
z
using the following formula:
1
Where,
Z
i
(
map
)
is the elevation of the
i
th
checkpoint in the
data set,
Z
i
(
surveyed
)
is the elevation of the
i
th
checkpoint in the
independent source of higher accuracy,
n
is the number of checkpoints tested,
i
is an integer ranging from 1 to
n.
3. Compute the NVA using the following formula:
Vertical Accuracy at 95% Confidence Level = 1.96 x
(
RMSE
Z
)
Computing VVA
:
a. Consolidate the 30 checkpoints located in the “Low
Vegetation” area, the 20 checkpoints located in the
“Medium Vegetation” area and the 20 checkpoints
located in the “High Vegetation” area into one table to
represent the VVA.
b. Recalculate the statistics for the differences in the 70
checkpoints located in the vegetated areas as illustrated
in the following table:
VVA
(ft)
(centimeter)
Count
70
70
Mean
-0.109
-3.33
Median
-0.082
-2.48
Minimum
-0.985
-30.02
Maximum
0.426
12.98
STD DEV
0.314
9.58
RMSEz
0.331
10.08
VVA 95th Percentile
0.348
10.61
Or simply,
VVA
(centimeter)
Count
70
Mean
-3.33
STD DEV
9.58
RMSEz
10.08
VVA 95th Percentile
10.61
Due to the combined effects of the questionable quality and
inconsistency in the surveying practices under and between
trees, especially if the survey relies on GPS techniques and
the reliability of the lidar filtering process around vegetated
areas, RMSE
z
cannot be used to estimate VVA. RMSE
z
only
should be used to estimate the accuracy of a data sample
if the error is normally distributed. Unfortunately, errors
estimated around vegetated areas may be skewed due to the
two reasons mentioned earlier concerning the reliability of
the survey and the lidar data filtering process. That was the
reason behind the use of “95% percentile” to represent the
VVA in the new standard. To compute the VVA follow the
following instructions:
1. Compute the differences between the surveyed elevation
and the lidar-derived elevation for all the checkpoints
located in vegetated areas as we did for the NVA
computations.
2. Compute the VVA using the 95
th
percentile for the 70
elevation differences of the checkpoints located within
the vegetated areas. The easiest way to do this is by
using the following formula from Microsoft Excel:
The 95
th
percentile
=PERCENTILE(G
i
:G
i+70
,0.95)
Reporting NVA and VVA according to the ASPRS
Positional Accuracy Standards for Digital Geospatial
Data
:
The new standard provided clear guidelines and statements
to report products accuracy. According to such guidelines,
the reported accuracy for Vicotr’s product can be expressed
as follow:
“This data set was tested to meet ASPRS Positional Ac-
curacy Standards for Digital Geospatial Data (2014)
for a 20-cm RMSE
z
Vertical Accuracy Class (the derived
VVA limit is 60 cm). Actual NVA accuracy was found
continued on page 248
