UWB Ranging and IMU Data Fusion: Overview and Nonlinear Stochastic Filter for Inertial Navigation

This paper proposes a nonlinear stochastic complementary filter design for inertial navigation that takes advantage of a fusion of Ultra-wideband (UWB) and Inertial Measurement Unit (IMU) technology ensuring semi-global uniform ultimate boundedness (SGUUB) of the closed loop error signals in mean square. The proposed filter estimates the vehicle's orientation, position, linear velocity, and noise covariance. The filter is designed to mimic the nonlinear navigation motion kinematics and is posed on a matrix Lie Group, the extended form of the Special Euclidean Group $\mathbb{SE}_{2}\left(3\right)$. The Lie Group based structure of the proposed filter provides unique and global representation avoiding singularity (a common shortcoming of Euler angles) as well as non-uniqueness (a common limitation of unit-quaternion). Unlike Kalman-type filters, the proposed filter successfully addresses IMU measurement noise considering unknown upper-bounded covariance. Although the navigation estimator is proposed in a continuous form, the discrete version is also presented. Moreover, the unit-quaternion implementation has been provided in the Appendix. Experimental validation performed using a publicly available real-world six-degrees-of-freedom (6 DoF) flight dataset obtained from an unmanned Micro Aerial Vehicle (MAV) illustrating the robustness of the proposed navigation technique. Keywords: Sensor-fusion, Inertial navigation, Ultra-wideband ranging, Inertial measurement unit, Stochastic differential equation, Stability, Localization, Observer design.