tanbul 2004
Iready that
n the geo-
ontributions
discussed:
a. All three
to mobile
ission IMU
ors is very
ie minimum
andard way
k as a filter
ents in the
ications are
ws a more
rest can be
. This is of
rms in the
oling (AR).
sis become
> advantage
orward and
ring this is
smoother is
capacity, a
» be briefly
‘techniques
noise from
st to apply
1sors. They
orientation
in standard
. and of 20
J. In Figure
| applying a
5. The noise
nGal (a) to
as done by
rediction to
mance of a
m walk.
irements
The state vector model typically used to process IMU data is
made up of two sets of parameters. The first set contains the
errors resulting from the Newtonian model, ie. errors in
position, velocity, and orientation. The second set contains the
sensor errors, such as accelerometer and gyro biases. While the
models for the first set of variables are given by the physics of
the problem, the models for the second set are rather arbitrary.
They are usually chosen by looking for a structure that makes
state space modeling simple. Typical models of this type are
random ramp, random walk, or first-order Gauss-Markov
processes. Often a combination of these models is used to fit a
specific error distribution, but in general model identification
techniques are not applied to verify the model itself. Since most
of the terms to be determined are long-wavelength features, an
AR model can be used to determine what type of model
structure would best fit the data. This idea was recently studied
by Nassar et al (2003). Results are quite encouraging, especially
if de-noising is applied first. The data sets studied so far all
show significant second- order effects, and in some cases small
third-order effects. When they are included in the state-space
model, results improve by about 30%. However, if the order of
the model is further increased, results get worse. Thus, it may
be efficient and advisable to determine the optimal model order
for typical classes of IMUs in advance and incorporate them
into the state vector.
Post-mission processing, when compared to real-time filtering,
has the advantage that data of the whole mission can be used to
estimate the trajectory. This is not possible when using filtering
because only part of the data is available at each trajectory
point, except the last. When filtering has been used in a first
step, one of the optimal smoothing methods, such as the Rauch
et al (1965) algorithm can be applied. It uses the filtered results
and their covariances as a first approximation. This
approximation is improved by using the additional data that
were not used in the filtering process. Depending on the type of
data used, the improvement obtained by optimal smoothing can
be considerable. This improvement comes at a price, however.
The price is in terms of storage requirement and computation
time. It is not only necessary to store all estimated state vectors,
but also their complete covariance matrices before and after
updates.
In cases where the IMU is mainly used to bridge GPS-outages,
such as in land-vehicle applications in urban centers, a simple
algorithm can be used very effectively. It calculates the
difference between the IMU position and the GPS position at
the beginning and the end of the outage. The resulting
difference is attributed to a C-error. The choice of this simple
error mode resulted from an analysis of the complete INS error
model for short-time periods up to a few minutes; see Nassar
and Schwarz (2002) for details. This model has been tested in
both airborne and land-vehicle applications and has consistently
modeled between 9094-9594 of the accumulated error (ibid).
Requirements in terms of storage and time are minimal and the
algorithm is very simple. The error graph for a 85 second
outage and its model fit is shown in Figure 8. .
International Archives of the Photogrammetry, Remote Sensing and Spatial [Information Sciences, Vol XXXV, Part B5. Istanbul 2004
2
N
eo
T
T
Coordinate Difference (m)
b 5 2
co eo
Q 17 34 51 68 85
Outage Interval At (sec)
Figure 8: SINS (a navigation-grade - Honeywell LRF-III)
Positioning Errors during DGPS Outage
6. CURRENTLY ACHIEVABLE ACCURACIES AND
ONGOING DEVELOPMENTS
The tables of results shown in the following are not based on a
comprehensive analysis of published results. They are rather
samples of results achieved with specific imaging systems and
have been taken from company brochures and technical
publications. The authors think that they are representative for
the systems that have been discussed previously. The following
will include three examples of post-mission systems, one
airborne, one van based, and one portable, and one airborne
real-time system.
The accuracy specifications for the Applanix family of
POS/AV™ airborne direct georeferencing systems are listed in
Table 2 (Mostafa et al, 2000). The primary difference in system
performance between the POS/AV'" 310 and POS/AV™ 510
systems is the orientation accuracy, which is directly a function
of the IMU gyro drifts and noise characteristics. For example,
the gyro drifts for the POS/AV™ 310 and POS/AV™ 510
systems are 0.5deg/h and 0.ldeg/h, respectively. While the
corresponding gyro noises are 0.15 and 0.02 deg/sqrt(h),
respectively.
ESO Accuracy | possav"" 240 | POS/AV"" 310 | POS/AV"" 410 | POS/AV™ 510
Position (m) 0.05 - 0.30 0.05 - 0.30 0.05 - 0.30 0.05 - 0.30
Velocity (m/s) 0.010 0.010 0.005 0.005
Roll & Pitch (Deg) 0.040 0.013 0.008 0.005
True Heading (Deg) 0.080 0.035 0.015 0.008
Table 2: Post-processed POS/AV ™ navigation parameter
accuracy (Mostafa et al, 2000]
The second example is for land MMS. Accuracies achieved
with many land MMS systems, such as the VISAT system (El-
Sheimy, 1996) are suitable for all but the most demanding
cadastral and engineering applications. Accuracies in this case
mainly depend on availability of GPS and how long the INS
systems can work independently in stand-alone mode. If GPS is
available, the positioning accuracy is uniform at a level of 3-5
cm (rms). If GPS is not available, the positional accuracy
depends on the length of the outage, see Table 3. It lists the
stand-alone accuracy of a strapdown navigation-grade system
