E
1 i 1 1 L 1 1 1 +
O
3
20 arcseconds and is due to aircraft vibration and wind
gusts. If the vibrational effects above the aircraft
dynamics of 10 Hz are eliminated, the noise drops to 11
arcseconds in pitch and roll, see Fig. 2d. Adding error
components due to the interaction of synchronization
errors and aircraft dynamics, the pitch and roll noise to
be expected under dynamic conditions will be about 15 -
20 arcseconds.
To achieve this noise level, systematic errors due to
Schuler-type oscillations in attitude have to be completely
eliminated by 1HZ GPS position and velocity updates.
Figure 3 shows again a lab experiment where such
updates have been used for the roll component.
0.015 : -
0.01 | E .
0.005 | +
T
= o
* j
„0.005 - | =
-0.01} 1
-0.015 L i
oO 60 100 150
time (s)
Figure 3: Roll error, static case, lab, GPS velocity
updates (G = 12")
The residual error of 12" seems to indicate that Schuler-
type oscillations can indeed be eliminated. However, a
closer analysis reveals that this is not the case for all
three attitude components. To show this, consider the
relationship between INS acceleration errors à v,
misalignment errors e, accelerometer biases b, and
specific force components f. They are of the form
dv. = fz. rth
dv E x f es + f eo + b.
Bu, = ÉstnaSs- fs anb (4)
n e ew u
where the subscripts n, e, u denote north, east, and
upward. The upward component of specific force
contains the effect of gravity and is thus always
considerably larger than the north and east components.
In a photogrammetric flight, constant velocity along a
straight line is the preferred operational environment.
Thus, f, and fe are rarely larger than 0.1 m/s?, while f, is
always about 10 m/s?.
Rewriting the second equation with respect to eu and en
results in
f ar dv +b,
E =
=
fe +5v +b (S)
gn =
f
Assuming a flight to the north, these equations show the
heading and roll errors as functions of specific force,
misalignment, acceleration error, and accelerometer
bias. Assuming the same magnitude of errors in both
cases and introducing typical error sizes, the following
conclusions can be drawn. Due to the size of the specific
force component in the denominator, the determination of
roll (and pitch) will be more accurate than the
determination of heading. Actually, the better the
constant velocity condition is maintained, the better pitch
and roll will be determined and the poorer the estimation
of heading will be. Only when the aircraft manoeuvres in
such a way that major horizontal accelerations are
introduced, will the heading accuracy be improved. It can
therefore be concluded that GPS updates are sufficient to
eliminate pitch and roll oscillations to the level of INS
attitude noise, but that similar results cannot be achieved
in heading without a regular pattern of large horizontal
aircraft accelerations. For a more detailed discussion of
these interrelationships, see Schwarz and Wei (1994)
and Zhang (1995).
Besides Schuler-type oscillations which are caused by
the interaction of small initial errors with the natural
frequency of the INS, additional errors can be expected
which are due to the interaction of small systematic
sensor errors and aircraft dynamics. These errors are
difficult to isolate in a controlled experiment. Their order
of magnitude can be assessed, however, by conducting
airborne tests where the attitude parameters determined
by the onboard GPS/INS are compared to attitude
parameters independently determined from accurate
ground control by photogrammetric methods. Targeted
control points in the photographs are used to estimate
camera attitude at flying height by a bundle adjustment.
Two such tests will be briefly discussed.
In both cases the system consists of an LTN 90/100, a
navigation-grade INS, which was integrated with two
Ashtech Z12 receivers, one on the airplane and one at
the master station. A Zeiss LMK aerial camera was used
to obtain a block of photographs of a test field with dense
GPS control. The attitude estimated from this control was
compared to the attitude obtained from the integrated
INS/GPS. For details of this test, see Skaloud (1995).
The attitude accuracy determined from the ground
control is typically at the level of 4-5 arcseconds in each
component, about twice as accurate as expected from
the INS under the best circumstances. The comparison
with the INS-derived attitude indicates that the
differences are between 15 and 35 arcseconds, which
was expected in this case because no vibration filtering
has been applied. Thus, the differences represent largely
the INS noise under operational conditions plus some
additional errors due to residual Schuler oscillations and
aircraft dynamics. However, due to constraints in this
specific test, the time period shown is only two minutes.
A large effect of errors due to residual Schuler-type
oscillations and aircraft dynamics could therefore not be
expected. Thus for time intervals of a few minutes an
attitude noise level of 20 - 30 arcseconds can be
maintained.
To investigate whether this is also true for time periods
typically encountered in production flights, a small test
field with accurate GPS ground control was overflown
nine times from different directions, accumulating a total
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B6. Vienna 1996
