Table 1 Main parameters of MOMS-02rD2 and MOMS-2PrPRIRODA
MOMS-02rD2 MOMS-2PrPRIRODA
Camera carrier Space shuttle
MIR space station Mission duration
10 days at least 18 months
Data storage HDT recorder
onboard mass memory and telemetry to ground stations
w x
Orbital height km 296
400 w x
Orbital inclination 8 28.5
51.6 w x
Ground pixel size nadirrstereo m 4.5r13.5
6.0r18.0 w
x Swath width nadirrstereo km
37r78 50r105
Geometric camera calibration laboratory
laboratory, inflight Orbit information
TDRSS tracking GPS
Attitude information IMU
IMU, star sensor
countries in Europe and North America. Due to several problems, only a few MOMS-2PrPRIRODA
images were acquired between September 1996 and April 1997. Since January 1998 MOMS-2P is operat-
ing again.
The camera geometry including the alignment of the MOMS-2P camera axes has been determined not
only by calibration in the laboratory, but also by Ž
. inflight calibration Kornus and Lehner, 1997 .
A special navigation package MOMSNAV con- sisting of high precision GPS and Inertial Measure-
Ž .
ment Unit IMU ensures precise orbit and attitude data, synchronized with the MOMS-2PrPRIRODA
imagery to 0.1 ms. Based on GPS observations during a time interval of ca. 5 min and a sophisti-
cated short arc modelling, the MIR orbit has been determined with 5 m absolute accuracy. The Astro 1
star sensor, which is mounted on the QUANT mod- ule of the MIR station provides 10
Y
. attitude accu- racy. The alignment, however, between the QUANT
and the PRIRODA module is known only in the order of 200
Y
.
3. Combined bundle adjustment
The photogrammetric point determination is based on the principle of bundle adjustment and comprises
the determination of object points and the reconstruc- tion of the exterior orientation of the three-line im-
ages. It represents a central task within the pho- togrammetric processing chain on which all subse-
quent products are based. The collinearity equations
c
ˆ
u s u x , x t ,u t
1
Ž . Ž .
Ž . ˆ ˆ
Ž .
formulate the relationship between the observed im- Ž
.
T
age coordinates u s u ,u , the unknown object
x y
ˆ ˆ ˆ
T
Ž .
point coordinates x s X,Y, Z of a point P and the
ˆ
unknown parameters of exterior orientation x
c
s
ˆ ˆ
c
ˆ
c
ˆ
c T
ˆ
T
Ž .
Ž .
X ,Y , Z and u s v,w,k , respectively, of the
ˆ ˆ ˆ
image I taken at time t. The orientation angles v, w
j
and k have to be chosen in such a way that singular- ities are avoided. In space photogrammetry the three
Euler angles z , h and u , which are related to the spacecraft motion along the trajectory, are well suited
in conjunction with a geocentric object coordinate system.
3.1. Orientation point approach In general, the mathematical model for the recon-
struction of the exterior orientation should use six unknown parameters for each three-line image I . In
j
practice, however, there is not enough information to determine such a large number of unknowns. In the
orientation point approach, the exterior orientation parameters are estimated only for so-called orienta-
tion points or orientation images I , which are intro-
k
duced at certain time intervals, e.g., once for every 1000th readout cycle. In between, the parameters of
each three-line image I are expressed as polynomial
j
functions of the parameters at the neighboring orien- Ž
. tation points Ebner et al., 1994 . While this ap-
proach reduces the number of unknown exterior orientation parameters to a reasonable amount, its
inherent disadvantage is that the estimated position parameters are not associated with a physical model
of the spacecraft trajectory.
3.2. Orbital constraints approach To overcome this drawback, the bundle adjust-
ment algorithm is supplemented by a rigorous dy- namical modeling of the spacecraft motion to take
orbital constraints into account. The camera position
c
Ž .
parameters x t which have been estimated so far
ˆ
at certain time intervals, are now expressed by the six parameters of the epoch state vector y
and
ˆ
additional force model parameters p:
ˆ
x
c
t s x
c
t , y , p 2
Ž . Ž .
ˆ ˆ
ˆ ˆ
Ž .
The force model parameters p may comprise,
e.g., the drag coefficient. For the epoch state vector observation equations
y s y y
3
Ž .
Ž .
ˆ
are introduced, where the observations y are taken
from the results of the previous orbit determination. Fig. 2 demonstrates the orbital constraints ap-
proach, which exploits the fact that the spacecraft proceeds along an orbit trajectory and all camera
positions lie on this trajectory.
Fig. 2. Orbital constraint approach for the reconstruction of the Ž
. exterior orientation of three-line images Ohlhof et al., 1994 .
Compared to the orientation point approach the orbital constraints approach has essential advantages,
which can be summarized as follows: Ø
Full utilization of the information content of the tracking data in a statistically consistent way.
Ø A reduced number of unknown parameters.
Ø Accuracy improvements for the photogrammetric
results as well as the epoch state vector. Statistically, the resulting estimation procedure is
equivalent to a combined orbit determination and bundle adjustment from tracking data and three-line
image data. Due to the lack of a dynamical model describing
the camera’s attitude behavior during an imaging sequence, it is not possible to introduce attitude
constraints into the bundle adjustment in a similar way as the orbital constraints. To this end, the
concept of orientation points is maintained for the camera’s attitude. The attitude
ˆ ˆ
ˆ
u t s u t ,Q 4
Ž . Ž .
Ž .
of the camera can be represented by the attitude vector Q at selected orientation points. Based on
Ž . Ž . Ž .
Eqs. 1 , 2 and 4 , the image coordinates may finally be written as
c
ˆ ˆ
u s u x , x t ,u t
s u t , x , y , p,Q 5
Ž . Ž .
Ž . ˆ ˆ
ˆ ˆ ˆ
Ž .
Ž .
For the incorporation of preprocessed attitude data corresponding observation equations are formulated.
Systematic errors of the attitude observations are modeled through additional estimation parameters.
By limitation to constant and time-dependent linear terms which describe the main effects, six additional
parameters, namely a bias and a drift parameter for each attitude angle, are used for each orbital arc
Ž
. s imaging sequence .
The observation equations for the attitude parame- ters, which are introduced at selected orientation
points, are given by
ˆ ˆ
Q s Q Q ,b , 6
Ž .
Ž .
ˆ
where b denotes the unknown bias and drift parame- ters.
The mathematical model of the orbital constraints Ž
. approach is described in detail in Ohlhof 1996 and
Ž .
Ohlhof et al. 1994 .
4. Practical results of MOMS-02 r r
