Geometric Stochastic Filter with Guaranteed Performance for Autonomous Navigation based on IMU and Feature Sensor Fusion

Abstract

This paper concerns the estimation problem of attitude, position, and linear velocity of a rigid-body autonomously navigating with six degrees of freedom (6 DoF). The navigation dynamics are highly nonlinear and are modeled on the matrix Lie group of the extended Special Euclidean Group $\mathbb{SE}_{2}(3)$. A computationally cheap geometric nonlinear stochastic navigation filter is proposed on $\mathbb{SE}_{2}(3)$ with guaranteed transient and steady-state performance. The proposed filter operates based on a fusion of sensor measurements collected by a low-cost inertial measurement unit (IMU) and features (obtained by a vision unit). The closed loop error signals are guaranteed to be almost semi-globally uniformly ultimately bounded in the mean square from almost any initial condition. The equivalent quaternion representation is included in the Appendix. The filter is proposed in continuous form, and its discrete form is tested on a real-world dataset of measurements collected by a quadrotor navigating in three dimensional (3D) space. Keywords: Localization, navigation, position and orientation estimation, stochastic systems, GPS-denied navigation observer, navigation estimator, vision-aided inertial navigation systems (VA-INSs), stochastic differential equation, Gaussian noise, sensor fusion.