Pi-Invariant Unscented Kalman Filter for sensor fusion

Abstract

A novel approach based on Unscented Kalman Filter (UKF) is proposed for nonlinear state estimation. The Invariant UKF, named π-IUKF, is a recently introduced algorithm dedicated to nonlinear systems possessing symmetries as illustrated by the quaternion-based mini Remotely Piloted Aircraft System (RPAS) kinematics modeling considered in this paper. Within an invariant framework, this algorithm suggests a systematic approach to determine all the symmetrypreserving terms which correct accordingly the nonlinear statespace representation used for prediction, without requiring any linearization. Thus, based on both invariant filters, for which Lie groups have been identified and UKF theoretical principles, the developed π-IUKF has been previously and successfully applied to the mini-RPAS attitude estimation problem, highlighting remarkable invariant properties. We propose in this paper to extend the theoretical background and the applicability of our proposed π-IUKF observer to the case of a mini-RPAS equipped with an aided Inertial Navigation System (INS) which leads to augment the nonlinear state space representation with both velocity and position differential equations. All the measurements are provided on board by a set of lowcost and low-performance sensors (accelerometers, gyrometers, magnetometers, barometer and even Global Positioning System (GPS)). Our designed π-IUKF estimation algorithm is described in this paper and its performances are evaluated by exploiting successfully real flight test data. Indeed, the whole approach has been implemented onboard using a data logger based on the well-known Paparazzi system. The results show promising perspectives and demonstrate that nonlinear state estimation converges on a much bigger set of trajectories than for more traditional approaches. 53rd IEEE Conference on Decision and Control

Unscented Kalman filtering on Lie groups

“…Another line of research uses the unscented transform on Lie groups and Lie exponential coordinates to derive uncertainty ellipsoids that are proved to contain with certainty the state, when faced with bounded sensor errors, see [14,15]. [16,17] also introduced an Invariant UKF, as an UKF capable of taking into account the symmetries of the system's equations, for state spaces that are generally not Lie groups.…”

Guidance algorithm for smooth trajectory tracking of a fixed wing UAV flying in wind flows

“…In such a case the UAV does not experience any acceleration in its lateral body axes. This is desirable since many of the attitude estimation algorithms employed in projects like Paparazzi, such as [16], [17], are based on the observation of gravity. We also consider that in a trimmed flight, the pitch angle θ remains constant and usually is close to zero.…”

Invariant unscented Kalman filter with application to attitude estimation

“…Nevertheless, the IEKF, and more generally invariant observers, are characterized by a larger convergence domain, due to the exploitation of systems' symmetries within the estimation algorithm (i.e., within filter equations and gains computation), and present very good performances in practice. In order to derive more tractable nonlinear invariant state estimation algorithms, motivated by the practical problems encountered by the authors with miniUAVs flight control and guidance, civil Aircraft modeling and identification and dynamic system fault detection, isolation and recovery, an hybridization of the Unscented KF (UKF) principles [20], [16], [19] with invariant observers theory has been recently proposed in [10], [11]. Among other things, it has been proved in these bibliographical references that an Invariant UKF-like estimator (named IUKF) could be simply designed by introducing both notions of invariant state estimation and invariant output errors within any UKF algorithm formulation, whatever this latter corresponds to the standard version of the algorithm or to some square-root/UD factorized ones.…”

“…Inspired by the theory of continuous-time symmetry preserving observer [7] a novel and original UKF-based approach has been developed in [12] to address the approximation issue of the invariant EKF without requiring any linearization of the dynamical systems equations or compatibility condition such as proposed in the π-IUKF algorithm [10], [11]. The IUKF relies on the basic theoretical principles developed by Julier and Uhlmann at the beginning of 2000s (see [16]) which have been since widely applied to various nonlinear state estimation problems (cf.…”

“…Although dynamical systems possessing symmetries have been studied in control theory, few results taking benefit of system invariances for observers design exist today. Invariant nonlinear estimation theory appears so as a young research area in which the first main contributions can be dated from the beginning of 2000s ( [1], [3], [2], [5], [4], [6], [8], [9], [15], [10], [11], [17], [18] This optimality must be considered here w.r.t. an invariant state estimation error which will be defined precisely further.…”