PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
February 2014
171
An Automatic Parameter Selection Procedure for
Pushbroom Sensor Models on Imaging Satellites
Inseong Jeong and James Bethel
Abstract
For the rigorous, physical modeling of spaceborne, push-
broom imaging sensors, over-parameterization and the
resulting dependencies among sensor model parameters
are a continuing issue causing instability and ambiguity
during parameter estimation. Traditionally, this problem has
been tackled by a fixed subset approach or by using a priori
stochastic constraints, which generally require the user’s in-
tuition or intervention but with no guarantee that an optimal
solution is obtained. An efficient and automated procedure
to find an optimal parameter subset, that is independent and
meets accuracy requirements, has been developed and tested
using six images from six representative sensors. The exper-
imental results show a stable performance of the developed
procedure which results in a quality subset by the evaluation
criteria and tries to minimize the checkpoint misclosure (i.e.,
LOOCV RMSE
) so that the resulting subset can be considered
optimum. Therefore, the proposed procedure can be bene-
ficial to the users and sensor model developers by provid-
ing an optimal and subjective solution to the well known
over-parameterization problem in satellite sensor model.
Introduction
Parameters considered in the physical pushbroom sensor
model generally consist of time-dependent platform posi-
tion and attitude, interior orientation, and offset parameters
between platform and sensor. Since actual imaging mechanics
are considered in the physical sensor model, any parameter-
ization scheme that describes the imaging process tends to
carry redundant parameters, i.e., it is over-parameterized. The
over-parameterization in the physical sensor model manifests
itself as correlation or dependency among the parameters.
The presence of such dependencies has been pointed out
in various works (Gugan, 1987; Konecny
et al
., 1987; Krat-
ky, 1989; Orun and Natarajan, 1994; Radhadevi
et al
., 1998;
Fritsch and Stallmann, 2000; Chen and Teo, 2002; Kim and
Dowman, 2006; Crespi
et al
., 2007).
Since parameter dependency is an inevitable outcome
for linear array spaceborne pushbroom sensors, many solu-
tions have been suggested in sensor model communities.
One approach is to select an independent parameter subset
from the full set. This type of approach has been traditional-
ly employed in some photogrammetric applications such as
block adjustment with self calibration (Ebner, 1976). By this
approach, a parameter or a group of parameters are removed
or fixed to constant. Sometimes position parameters are cho-
sen for the sensor model with attitude parameters fixed (Chen
and Teo, 2002), or vice versa (Konecny
et al
., 1987). Orun
and Natarajan (1994) suggested removal of
~
and
{
param-
eter groups. Similar to Orun and Natarajan’s model, Makki
(1991) tested many possible subsets and then concluded that
the group of position plus yaw parameters is the best subset
among his experiments. Another similar subset model, but
with constant angle parameters, was chosen by Michalis and
Dowman (2008). A completely physical-based model would
explicitly incorporate atmospheric drag, solar radiation pres-
sure, gravity field variability, etc; but these are usually collec-
tively modeled by low order polynomials. Thus finding the
“best” model involves fitting imagery to control points with
the smallest parameter set that gives expected misclosures.
Another popular approach to deal with dependency is to
weight model parameters based on
a priori
stochastic infor-
mation (Salamonowicz, 1986; Westin, 1990; Westin, 1991a;
Westin and Frosgren, 2001; Radhadevi
et al
., 1998; Robertson,
2003; Poli, 2007). In this approach, the amount of adjustment
for each parameter is constrained by a weight matrix which is
derived from
a priori
parameter uncertainty. A related work
was presented by Westin (1991b) regarding time dependent
attitude variability for
SPOT
.
Those two approaches have been adopted in many of wide-
ly used photogrammetric software. ERDAS
LPS
recommends
to use a default parameter subset for
SPOT
, i.e., second order
polynomial for perspective center (X, Y, Z) and
l
, and zero
th
order for
~
and
{
, (ERDAS
LPS
Project Manual, 2011). In the
case of SOCET SET, it is suggested to use a parameter subset
for some sensors like
SPOT5
and QuickBird. It also gives a sen-
sor-specific default weight if
a priori
variance information is
supplied in image support data (SOCET SET Manual, 2011).
At the same time, both software provide flexibility for a user
to choose parameters to be adjusted. However, these strategies
by commercial software are not sufficient for several rea-
sons: (a) for long strips one needs to customize the parameter
selection, (b) adjustment algorithm developers need guidance
on parameter selection, and (c) prior covariance or weight
information can be incorrect or unavailable.
Therefore, a parameter selection “procedure” can be ben-
eficial to resolve the parameter dependency and determine
which ones are to be adjusted without the user’s decision or
intervention. This can be done to minimize the number of ir-
relevant parameters, guarantee independence among the cho-
sen parameters, and ensure that image or object space misclo-
sures are acceptable. However, despite its potential benefits,
very few procedures have been suggested. A recent example
of a selection procedure for sensor model was introduced by
Inseong Jeong is with NOAA/NGS Remote Sensing Division
(DST), 1315 East West Highway, Silver Spring, MD, 20910
(
.
James Bethel is with the Geomatics Area, School of Engi-
neering, School of Civil Engineering, Purdue University, 550
Stadium Mall Drive, West Lafayette, IN, 47907.
Photogrammetric Engineering & Remote Sensing
Vol. 80, No. 2, February 2014, pp. 171–178.
0099-1112/14/8002–171
© 2013 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.80.2.171
