PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
October 2017
659
SECTOR
INSIGHT:
.
edu
and dissertation projects as will be discussed in three exam-
ples. The first example relates to the Rational Polynomial
Coefficients (RPC) sensor model that is prolific in the satel-
lite imaging community. The RPC format allows for only two
error modeling terms: one for “bias” and one for “random”.
PhD research has been performed to demonstrate techniques
for full error covariance propagation from “physical sensor
model space” to “RPC space” with generic and efficient rep-
resentation and application by an end user. The second ex-
ample relates to verification of consistency between errors,
compared to ground truth and “predicted accuracy” when us-
ing a sensor model, and photogrammetric applications. While
it is acceptable for a Ph.D. researcher to show that his/her
processes are capable of improving accuracy by some mea-
surable quantity (e.g., change in root mean square errors or
change in the size of an empirically calculated error ellipse),
it is even more helpful if that researcher demonstrates that
the actual error dispersion (e.g., as represented by an em-
pirically calculated error ellipse) is consistent with the error
ellipse computed via rigorous error covariance propagation.
A third example relates to verification of the error propaga-
tion itself, and can be used to identify issues with respect to
the sensitivity (i.e., Jacobian) matrices; e.g., a mistake could
have been made in the analytical computation of the partial
derivatives, or the problem is so non-linear that the standard
linear error propagation techniques are not a good represen-
tation. A popular technique is called “Monte Carlo Analysis,”
and involves writing a computer program that begins with
a model with an “errorless” transformation to which known
errors will be introduced for each input random variable via
a random number generator. Then it evaluates the transfor-
mation thereby computing errors for each output random
variable, and repeats the procedure for multiple trials (e.g., a
thousand times) so that a statistical distribution for the out-
put variables can be empirically computed and compared to
that derived via error covariance propagation.
C
onclusion
Error budgets, sensor models, and uncertainty estimation are
all critical to developing and using geospatial products. They
allow us not only to estimate the accuracy of the products,
guiding us on how they should be used, but also plan mis-
sions, develop processing workflows, and rigorously fuse data.
In industry, it is important for each custodian of geospatial
data along their life cycle to understand and carry-forward
rigorous and reliable uncertainty metadata with the products
for the benefit of subsequent users; therefore, geospatial ed-
ucators have a duty to include these ideas when discussing
all types of measurement systems, to produce graduates with
a firm understanding of them. Here, we described some fun-
damental ideas, but the subject is rich and there are many
resources that go into depth on the subject. Furthermore, the
photogrammetry community is pursuing ongoing research,
and the reader is encouraged to dig deeper.
As a “Call to Action”, we recommend that the interested
reader pursue undergraduate or graduate studies at one of
the many universities with excellent Geomatics programs.
Second, we recommend reading textbooks that specialize in
data adjustment and error propagation; following are few ex-
amples based on the authors’ own experience:
•
Analysis and Adjustment of Survey Measurements
,
by Edward M. Mikhail and Gordon Gracie
•
Observations and Least Squares
, by Edward M.
Mikhail, with contributions by F. Ackermann
•
Adjustment Computations
, by Charles D. Ghilani
•
The Manual of Photogrammetry, 6th Edition
, J.
Chris McGlone (ed.)
•
Elements of Photogrammetry
, Paul Wolf, Bon Dewitt,
Benjamin Wilkinson
•
Introduction to Modern Photogrammetry
, Edward
Mikhail, James Bethel, J. Chris McGlone
Finally, we invite you to read the forthcoming scenario
article that will provide a deeper commentary with use cas-
es and graphics that illustrate the impacts of rigorous error
modeling.
A
uthors
Benjamin E. Wilkinson
is an Assistant Professor at the
University of Florida. There, he teaches the Introductory
and Advanced Photogrammetry courses, Marine Geomatics,
and co-leads UF’s three course certificate in Mapping with
Unmanned Aerial Systems (UAS). His research focuses
on small UAS sensor integration with emphasis on laser
scanning, imagery and lidar data processing and adjustment,
and uncertainty estimation.
Henry J. Theiss
is the Chief Scientist in Photogrammetry
at Integrity Applications Incorporated (IAI) in Chantilly,
Virginia where he is responsible for a large team of scientists
who perform research and analyses in photogrammetry,
error propagation, EO/IR/SAR/LIDAR sensor modeling from
airborne and spaceborne platforms, image formation, close
range applications, registration, and tool validation.
