An Embedded Quaternion-Based Extended Kalman Filter Pose Estimation for Six Degrees of Freedom Systems

Abstract

This paper proposes a formulation of quaternion-based Extended Kalman Filter pose estimation for six degrees of freedom systems embedded in an FPGA with commercial processors. Our approach uses the fusion of a camera and an inertial measurement unit to estimate simultaneously the position and the orientation of the system of interest. In addition, a Stewart platform is used to validate and evaluate the estimated pose. Although this work considers the use of common low-cost sensors and the use of markers with simple geometry, the results show excellent performance of the developed filter, being able to estimate the pose and orientation with an error below 8.14 mm and 0.63 o ¯, respectively. Furthermore, the effectiveness of the approach has also been evaluated, showing that the filter is able to converge quickly when the markers are retrieved after a loss of camera data for a short period of time.

Simultaneous Localization and Mapping (SLAM) and Data Fusion in Unmanned Aerial Vehicles: Recent Advances and Challenges

“…Monocular Camera: The monocular camera is simple, cost-effective, and easy to operate. The camera projects a 3D environment in a 2D form due to its 6 degrees of freedom (DoF) movement [77,89,108]. However, accuracy of the obtained map is based on the uncertainty associated with 6-DoF rigid body transformations [109].…”

“…As error is accumulated, the UAV's estimate of the position variance increases the uncertainty about its location. For a UAV in space, its position is described by the x, y, z coordinates and an angle, i.e., q n = [q x , q y , q z , θ] T n , where q x , q y , q z are positions on three axes and θ is the angle [108]. As shown in Equation ( 2), the change in position and angle between two timestamps is ∆q n = [∆q x , ∆q y , ∆q z , ∆θ] T n .…”

Three-Dimensional Dead-Reckoning Based on Lie Theory for Overcoming Approximation Errors

“…However, Euler angles can lead to gimbal lock, where a particular rotation axis becomes aligned with another axis [10,11]. Euler angles indeed encounter difficulties in accurately representing all attitudes, particularly when the pitch axis nears ±90 degrees, thereby complicating processing and representation tasks [12,13]. However, when it comes to DR, the challenges are more nuanced and stem from the limitations of Euler angles in expressing and operating rotations.…”

A chattering-free discrete sliding mode filter

“…In this regard, some researchers have studied a lot of nonlinear filter algorithms. For example, Kalman filters [4][5], median filters [6][7], sliding window filters [8][9]. The sliding mode variable structure control theory has received widespread attention from scholars due to its strong robustness and simple implementation [10][11][12].…”