PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
March 2014
271
A Statistical Model Inspired by the
National Map Accuracy Standard
F.J. Ariza-López and J. Rodríguez-Avi
Abstract
This work proposes a statistical model inspired by the Nation-
al Map Accuracy Standard pass/fail philosophy. The model
is formulated as the composition of a statistical Binomial
model on other statistical base models (parametric or non-
parametric). This formulation allows adapting of the pass/
fail philosophy of the
NMAS
to any desired statistical base
model, tolerance, percentage of points in error, and risks. The
main contribution of this proposal is a common framework
for dealing with sampling and risks with independence of
the underlying base model (parametric or nonparametric).
The use of nonparametric base models is explained and
exemplified for the 1
D
case. For 2
D
and 3
D
, the Gaussian
base model has been adopted. The Gaussian models allow
the combining of error components by means of the Chi
Squared and the Gamma distributions. For the 2
D
case,
different situations have been considered in order to ana-
lyze the pass/fail behavior, and producer’s and user’s risks.
Introduction
The positional accuracy of geospatial products has always
been of great importance. This is, together with logical consis-
tency, the quality element of geographic information most ex-
tensively used by the National Mapping Agencies (
NMA
), and
also the more commonly evaluated quality element option
(Jakobsson and Vauglin, 2002). Positional accuracy is a matter
of renewed interest because of the capabilities offered by the
Global Navigation Satellite System (
GNSS
) and the need of a
greater spatial interoperability for supporting the Spatial Data
Infrastructures. Different positional behaviors of geographic
data sets mean the existence of an inter-product positional
distortion and a barrier to interoperation (Church
et al
., 1998).
This barrier exists not only for the positional and geometric
aspects, but also for thematic ones which are greatly affect-
ed by position (Carmel
et al
., 2006). For these reasons many
NMAS
are currently involved in the development of positional
accuracy improvement programs (EuroSDR, 2004).
In a Spatial Data Set (
SDS
) the position of a real world
entity is described with values in an appropriate coordinate
system. Positional accuracy represents the nearness of those
values to the entity’s “true” position in that system. The po-
sitional accuracy requirements for an
SDS
are directly related
to its intended use(s). Positional accuracy is determined by
means of a statistical evaluation of random and systematic
errors (DOD, 1990) and specified by means of the Root Mean
Squared Error (
RMSE
) or by the mean value of errors (
μ
) and
their standard deviation (
σ
). Comparison with an independent
source of greater accuracy is the preferred method for assess-
ing positional accuracy (ANSI, 1998).
Since positional accuracy is essential in geospatial produc-
tion, all
NMAS
have used statistical methods for its control,
which we call here Positional Accuracy Assessment Meth-
odologies (
PAAM
s). Many of these have been established as
national or international standards and can be used for spec-
ifying spatial data products but also the resultant positional
accuracy assessment compliance criteria. Standards should be
taken into account when seeking an economic optimization of
the quality of geographic information (Krek and Frank, 1999):
with a quality standard the producer provides the product
according to the known specification and characteristics, as
defined in the standard. This assures a certain level of reli-
ability and certainty, allowing the acquirer to avoid excessive
measuring of the quality and thus reducing the measuring
cost and shortening the decision-making process.
The International Organization for Standardization (
ISO
)
considers positional accuracy to be one of the quantitative
quality elements of geographic information as stated in its
international standard 19157 (
ISO
2012), which is a general
framework for describing and reporting the quality of geo-
graphic information. This International Standard also propos-
es a general quality evaluation methodology for geographic
information which must be applied to all the quality elements
of geographic information (e.g., position, completeness,
consistence, thematic accuracy, and so on). This standard is a
generic guideline, and there is no specific or preferred method
for positional quality assessment. Because this International
Standard is a general framework, there is a need to clearly
define aspects such as the computation of errors, sample size,
and schema, acceptation/rejection criteria, and so on. We
believe that the future of positional accuracy assessment must
be resolved within
ISO
standards, but prior to this we need to
know about current methods and their improvement possibil-
ities in order to develop appropriate assessment methods for
the positional aspect of geographic information.
This work is about the National Map Accuracy Standard
(
NMAS
) (USBB, 1947), a standard of very simple application
and broadly used in the entire world from its publication
date. We propose a statistical formulation based on well-
known statistical models, and given the current interest in
controlling 3
D
positional accuracy (e.g., Cai and Rasdorf,
2009; Li
et al
. 2009), our proposal incorporates the third
dimension as a logical extension of the 2
D
model. We also de-
velop a 1
D
non-parametric case. The interest of our approach
is twofold: first it can be used to better understand past re-
F.J. Ariza-López is with Universidad de Jaén, Departamento de
Ingeniería Cartográfica, Geodésica y Fotogrametría.
E-23071-Jaén, Spain (
).
J. Rodríguez-Avi is with Universidad de Jaén, Departamento
de Estadística e Investigación Operativa. E-23071-Jaén, Spain).
Photogrammetric Engineering & Remote Sensing
Vol. 80, No. 3, March 2014, pp. 271–281.
0099-1112/14/8003–271
© 2014 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.80.3.271
