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.