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[.Colomina*, M.Giménez*, J.J.Rosales*
REDUNDANT IMUS FOR PRECISE TRAJECTORY DETERMINATION
, M.Wis*, A.Gómez,!, P.Miguelsanz!
* [nstitute of Geomatics -
Generalitat de Catalunya & Universitat Politécnica de Catalunya
Castelldefels, Spain
* StereoCARTO
Madrid, Spain
Working Group 1/5
KEY WORDS: Photogrammetry, Sensor, IMU, Simulation, Modelling, Processing, Acquisition
ABSTRACT:
^ redundant inertial measurement unit (IMU) is an inertial sensing device composed by more than three accelerometers
and three gyroscopes. This paper analyses the performance of redundant IMUs and their potential benefits and applica-
tions in airborne remote sensing and photogrammetry. The theory of redundant IMUs is presented through two different
algorithmic approaches. The first approach is to combine the inertial observations, in the observation space, to generate
a "synthetic" non-redundant IMU. The second approach modifies the INS mechanization equations so that they directly
account for the observational redundancy. The paper ends with an empirical assesment of the concept. For this pur-
pose, redundant IMU data was generated by combining two IMUS in a non-orthogonal configuration and flying them.
Preliminary results of this flight are presented.
1 INTRODUCTION
The use of redundant IMUs for navigation purposes is not
new. From the very early days of the inertial technology,
the inertial navigation community was aware of the need
and benefits of redundant information. However, to the
best knowledge of the authors, the focus of the research
and development efforts was fault detection and isolation
(FDI). In the early days, the idea was to make use of the
redundancy in order to support fault-safe systems. A fault-
safe system detects that a sensor —i.e., an angular rate
sensor or an accelerometer— is not working properly and
shuts the system down. A fault-tolerant system is able
not only to detect a defective sensor, but also to isolate
it. After isolating a defective sensor, the system may keep
working as a fault-tolerant or a fault-safe system depending
on the number of remaining sensors. By means of voting
schemes (Pejsa, 1973), it can be shown that a minimum of
four sensors are needed to devise a fault-safe system and a
minimum of five to devise a fault-isolation one (compare
to the parallel development in photogrammetry (Fórstner,
1985)). Sensor configuration for optimal state estimation
and optimal FDI was, as well, a topic of research in the
early works.
In (Sturza, 1988b) and (Sturza, 1988a) a comprehensive
analysis of the optimal spatial configuration of sensors for
FDI applications is provided together with FDI algorithms.
In addition, the performance for fail-isolation systems in
case a sensor is removed due to failure. is analyzed.
In the literature, usually, two general geometries for re-
dundant sensor configurations are considered. Assume that
there are n sensors. The first geometric configuration dis-
tributes the sensors on a cone of half angle o in a way that
there is a constant solid angle between any two consecutive
sensors. This type of geometry is referred as Class I. In the
second geometric configuration, named Class II, n — 1 sen-
sors are evenly distributed on a cone with half angle « and
the remaining is in the cone axis. For these geometries
there are different values for o that maximize the amount
of information captured by the sensors and hence, allow
for an optimal state estimation. Then, by means of hy-
pothesis testing and maximum likelihood estimation, FDI
is performed. For a detailed derivation of the optimal val-
ues for o as a function of the number of sensors, as well as
for sensor FDI algorithms, the reader is referred to (Sturza,
1988b, Sturza, 1988a). More recent results on the use of re-
dundant inertial sensors for FDI can be found in (Sukkarieh
et al., 2000) and (Lennartsson and Skoogh, 2003). The for-
mer is mainly concerned with the use of skewed redundant
configurations for unmanned air vehicles while the latter
focuses in guidance, navigation and control of underwa-
ter vehicles. The two references are good examples of the
wide range of applications for skewed redundant configu-
rations that are currently under research.
The approach to and applications of redundant inertial sen-
sors proposed in this paper are different. The approach
taken is the geodetic one; i.e., use redundancy as a fun-
damental strategy to asses the quality of the navigation
parameters and, together with an appropriate mission de-
sign, to calibrate the instrument systematic errors. The ap-
plication is focused on the precise, accurate and reliable
INS/GPS trajectory determination for airborne photogtam-
metry and remote sensing (APRS). This includes, among
