Sensor Fusion for Underwater Vehicle Navigation Compensating Misalignment Using Lie Theory - Da Bin Jeong; Nak Yong Ko (Sensors, 2024)
This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group (<semantics>SE(3)</semantics>) and 3-sphere space (<semantics>S3</semantics>) are used to express the pose (position and attitude) and misalignment, respectively. <semantics>SE(3)</semantics> contains position and attitude transformation matrices, and <semantics>S3</semantics> comprises unit quaternions. The increments in pose and misalignment are represented in the Lie algebra, which is a linear space. The use of Lie algebra facilitates the application of an extended Kalman filter (EKF). The previous EKF approach without Lie theory is based on the assumption that a non-differentiable space can be approximated as a differentiable space when the increments are sufficiently small. On the contrary, the proposed Lie theory approach enables exact differentiation in a differentiable space, thus enhances the accuracy of the navigation. Furthermore, the convergence and stability of the internal parameters, such as the Kalman gain and measurement innovation, are improved.