calculated. The attitude
; height abouve ground
ing a wide-angle aerial
.] are necessary for the
in the following. For
iracies have to be at the
vel of five milli-degrees
cations at the scale of
e mapping applications
he level of one metre or
degree for attitude are
rated GPS/INS systems
the exterior orientation
tly determined exterior
steps. First, the in-flight
integrated GPS/INS is
rameters independently
yy using a large number
ne position and attitude
measurements. Second,
ts on the ground are
models whose exterior
rated GPS/INS system.
ATION
le performance, the INS
ntial measurements in a
igure 1). The GPS filter
yut is used to update the
udorange, carrier phase
surement vector in the
city) is taken as a set of
a 1996
pseudo-measurements which are used to update the INS master
filter. The noise in these 'pseudo-measurements' is determined by the
GPS filter covariance matrix. Updated error states in the INS master
filter are fed back to correct INS raw measurements. The output of
the strapdown mechanization therefore contains GPS/INS integrated
position, velocity and attitude information. This information is used
to check the validity of GPS measurements and to help resolve the
carrier phase ambiguities in the event of cycle slips or serious loss of
. lock in the GPS measurements. The INS error model has 15 states
including navigation errors (attitude, position, velocity) and
correlated sensor noise terms (gyro drift, accelerometer biases). The
timevarying nature of gyro drifts and accelerometer biases is
modelled by Gauss-Markov processes. The GPS error state model
includes position and velocity errors. In addition, the state is
augmented by double difference ambiguity parameters. The detailed
equation describing the 15 state error model as well as strapdown
INS mechanization in the earth-fixed frame can be found in Schwarz
and Wei (1994).
Since the GPS antenna and the INS system are physically displaced
from the perspective centre of the imaging sensor, a constant
displacement vector dr — (dx, dy, dz)! has to be added to the
GPS/INS integrated position to obtain the position of the camera
perspective centre in the GPS reference frame. The components of
the translation vector are measured by using conventional surveying
techniques before the flight mission.
Similarly, a constant misorientation dR} = f(8 ,8 , 8 ) exists
between INS and the imaging sensor and has to be taken into
account to obtain correct orientation parameters of the camera
perspective centre. Determining the misorientation matrix dR} is
more complicated since the sensor axes in either device cannot be
physically observed. However, a solution can be obtained by
implementing an in-flight calibration. This is possible for either
frame cameras (Skaloud et al, 1994) or push-broom scanner
imagery (Cosandier et al., 1994). A key assumption for in-flight
calibration is that no changes in relative position and orientation
between the imaging device, INS and GPS antenna will occur. This
can be achieved by hard-mounting the GPS antenna and INS on a
rigid platform in the aircraft and by locking the imaging device, e.g.
the aerial camera, down to the same platform.
The measurements of the integrated system have to be interpolated
at the exposure times of the imaging sensor. This can be done using
the high rate navigation output of 64 Hz. Combining the GPS/IN S
derived position (X 9, Yo, Zo )T and attitude with the spatial
displacement dr=(dx, dy, dz)! and the misorientation matrix dR
between the INS and the imaging sensor, Equation 1 takes the form
2 5) «RE | +» BR” dR, vs c
7 Z dz 7
P/ m 0/m 5 of) p
Thus, after supplying GPS/INS derived position and attitude together
with sensor calibration, all terms on the right hand side of the
Equation 2 are known and reduced image points coordinates Xp: Vo
can be represented in object space by this simple transformation.
3. TEST FLIGHT SCENARIO AND REFERENCE
TRAJECTORY ACCURACY
A well-defined photogrammetric test field close to Cologne,
Germany was used to asses the accuracy of an actual airborne data
collection system. The geodetic receivers selected for the test are
pairs of dual frequency receivers Trimble 4000 SSE and Ashtech
712. Two of them were used at the base stations located close to the
network origin in the middle of the block (Ashtech Z12) and at the
airport (Trimble 4000 SSE) about 30 km away from the test field.
The inertial navigation system to be tested is a Litton LTN-90
strapdown system with gyro drift rates of about 0.03 deg/hour. The
photogrammetric camera installed in the twin-engine Partenavia
P68C aircraft is a Zeiss RMK A aerial camera with a precise shutter
pulse output being recorded by the receiver (Trimble 4000 SSE) in
GPS time. The time synchronisation with other on-board sensors is
realized via a data collection computer receiving raw INS output and
GPS data (Ashtech Z12) together with a receiver provided precise 1
pulse per second (PPS) signal.
51.02
Flight Trejectory, 07.07.95
51.00
50.98
50.96
50.94
50.92
North [deg]
50.90
50.88
50.86
East [deg]
Figure 2: Test Flight Scenario
The test area has an extension of about 4 x 2 km and is normally
used to determine the ground movement of the overburden dump
"Sophienhóhe" in the open pit mining area. Therefore, about 160
points are marked permanently on the ground and their coordinates
are measured in regular time intervals using GPS supported aerial
triangulation. For this test flight a subset configuration of 47 ground
control points in the flight test area has been chosen in such a way
that camera orientation parameters can be derived with highest
possible accuracy by inverse photogrammetry. The 3-D coordinates
of 16 control points were determined by adjusting a network of GPS
static baselines with a relative positioning accuracy of 1 part per
million. Additionally, 31 vertical control points were established and
their ellipsoidal heights were determined by levelling and
computation of geoid undulation.
Nine photogrammetric strips, three of them repetitive, were flown
over the test area in early July 1995 (Figure 2). The length of the
strips differs from approximately 1 to 4 km. From the total number
of 168 photographs a subset of 77 centre located images was chosen.
Together, they form a photogrammetric block with 80% forward and
60% side overlap. The average flying height of about 900 m and the
15 cm camera focal length resulted in a photo scale of 1:6000.
127
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
