PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
October 2017
657
SECTOR
INSIGHT:
.
edu
E
ducation
and
P
rofessional
D
evelopment
in
the
G
eospatial
I
nformation
S
cience
and
T
echnology
C
ommunity
By Benjamin E. Wilkinson and Henry J. Theiss
Educational Needs for Rigorous Sensor Modeling and Error Budgeting
G
eomatics professionals are in a business of error
analysis, or at least they should be. Acknowledging
there is error (i.e., variation in observation from a
“true value”) is the first step towards quantifying
and minimizing it. Many can mark the locations of features
or measure distances in digital photographs or other geospa-
tial products, but those measurements are made immensely
more valuable when we understand the processes that led
up to making them. This includes how geospatial data are
collected and the metadata that comes along with them.
Specifically, estimates of uncertainty, or ranges of expected
magnitudes and directions of errors, are crucial to countless
geospatial applications. Our understanding of the uncertain-
ty in geospatial measurements is what sets us apart. For ex-
ample, some would say a key difference between the photo-
grammetric and computer vision fields is photogrammetry’s
emphasis on geometric accuracy, uncertainty estimation, and
preference for model rigor over computer vision’s preoccupa-
tion with speed and simplicity. The concepts and practical
applications of rigorous sensor modeling and error budgeting
(i.e., how much unexplainable variation we are willing to ac-
cept from the “true value”) are crucial to the professional and
educational realms of the geospatial world.
An error budget can simply be a list of errors that accumu-
late along the collection and processing pipeline and induce
error in the final product, or, more valuably, be represent-
ed in a mathematical model of the collection and processing
algorithms and their accompanying errors. Central to this
mathematical model is the
sensor model. A sensor model is
defined as the relationship linking object space coordinates
and sensor space measurements. Many refer to a rigorous
sensor model, meaning the model attempts to closely capture
the physical phenomena occurring during acquisition, while
maintaining a level of complexity that makes the model use-
able. This brings to mind the statistician George Box’s quote:
“Since all models are wrong the scientist cannot obtain
a “correct” one by excessive elaboration. On the contrary
following William of Occam he should seek an economical
description of natural phenomena. Just as the ability to
devise simple but evocative models is the signature of the
great scientist so overelaboration and overparameteriza-
tion is often the mark of mediocrity.”
The existence and quality of sensor models and error bud-
geting are critical to generating accuracy reports, planning
collection and processing, and data adjustment and inte-
gration. They also inform developers how to target needs in
terms of hardware and software improvements. Arguably the
simplest method for reporting uncertainty is the inclusion of
standard deviations. There is, however, considerable value in
using full error covariance matrices:
Considerforexampletwostates(
i
and
j
),witheachstatehaving
two parameters (
x
and
y
). These states could be associated with,
for example, observations of
x
and
y
made at different times or
locations. While it is much simpler to represent the uncertainty
of each parameter independently from one another in terms
of standard deviations, ignoring the “intra-state” covariances
between
x
and
y
and the “inter-state” covariances between these
parameters at two states
i
and
j
can have a profound effect on
estimated uncertainties in many ways.
Covariance matrices enable the generation of error ellipses
for locations at given confidence levels, accurate estimation
of uncertainty in the calculation of distances, areas, and vol-
umes, and also allow for rigorous adjustment and fusion of
geospatial products. We will explore these concepts in more
detail in a forthcoming article.
H
ow
are
sensor modeling
and
error
budgeting
addressed
in
academia
?
Educators are obliged to ensure graduates have a solid con-
ceptual and practical foundation of error budgeting and sen-
sor modeling. Furthermore, understanding, quantifying, and
applying spatial uncertainty in photogrammetric and remote
sensing products require an understanding of the hardware
and algorithms used to collect and process the data in ad-
dition to their associated errors. Thus, learning these topics
synergistically illuminates measurement error concepts, the
Photogrammetric Engineering & Remote Sensing
Vol. 83, No. 10, October 2017, pp. 657–659.
0099-1112/17/657–659
© 2017 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.83.10.657
