ROBUST AVIONICS DEAD RECKONING
FILTERING SCHEME VIA LMI
Paolo Castaldi .,1, Massimo Crisci· and Matteo Zanzi·
• Department of Electronics, Computer Science and Systems,
Viale Risorgimento 2, Bologna
Abstract: A new application of a Kalman-Like robust filtering scheme to Avionics
Dead Reckoning is presented. Inertial and air data measurements are used in order to
reconstruct the attitude and the body frame velocity of a general aviation aircraft. The
proposed estimation algorithm is based on an affine representation of the non linear
model of the system, leading to a Kalman filter gain optimizing procedure under a set
of Linear Matrix Inequality constraints. The resulting procedure fulfills the standard
accuracy requirements for large set of flight condition, and exhibits better robustness
characteristics with respect to the model uncertainty than the classic and widely used
Extended Kalman Filter. Copyright©2001 IFAC
Keywords: ADR, AHRS, Kalman-like filtering, LMI, Non-linear systems
1. INTRODUCTION
The aim of this work is the presentation of a
new application of an Linear Matrix Inequality
(LMI) based filtering procedure for a low cost
dead reckoning system. This filtering procedure
will be part of the algorithms implemented in the
on board computer of a general aviation aircraft,
under development in the project of a Differential
GNSS Instrument Approach System at the Forli
airport (Chiarini et al ., 2000).
It is well known that in the field of navigation,
and especially aircraft navigation, the possibility
of simultaneously employing sensors with different
and complementary features is a primary impor-
tance goal (Farrel et al., 1998) . In other words, it
is often necessary to solve data fusion problems in
order to assure both accuracy and continuity to
navigation. In particular, many systems capable
to integrate information especially from inertial
platforms and GPS receivers, are currently em-
ployed (Parkinson et al., 1996). It is worth observ-
ing that an excellent high dynamic response and
1 To whom all correspondence should be address. Corre-
spondence address: pcastaldiOdeis.unibo. it
276 SESSION 4
continuity of functioning is the main feature of the
former, the opposite for the latter . Unfortunately
inertial platforms are very expensive and this
makes unfeasible their use on board the general
aviation aircrafts. In this paper the possibility to
use a low cost inertial system (e .g. an Attitude
and Heading Reference System, AHRS) in place
of an expensive one is investigated (Mortenson,
1994) . The decrease in performances is partially
compensated by means of a fusion between inertial
data and velocity information obtained from an
air-data computer. The overall air-inertial system
can be considered as an Avionics Dead Reckoning
(ADR) package able to provide, by way of inertial
acceleration, angular rate, magnetic measurement
and true airspeed data, a good estimate of ground
and vertical speed. This information can be even-
tually integrated, in a cascade scheme, with that
provided by a GPS (Savage, 1984). Such a system,
for its performance/cost ratio, can be considered a
good candidate to substitute an inertial platform
in a small size aircraft. In fact it will be shown
how "this filtering approach can assure, during
the approach phase (about 150 s), a satisfactory
continuity of accuracy during lacks of GPS signal.