Euler Angle Estimation of an UAV using Extended Kalman Filter

Abstract

The problem description of this assignment is provided by Kongsberg de- fence systems. They have developed an unmanned aerial vehicle (UAV) that is rolling, but the roll angle is unknown. KDS want to estimate the orienta- tion of the UAV to navigate with a higher precession. This assignment has two main sections; 6-DOF UAV modelling and Euler angle estimation. Vector and matrix operations is the most essential mathe- matical theory used to solve this thesis and is therefore reviewed first. To simulate the dynamics of the UAV a mathematical model is derived and implemented in Matlab using the general differential equations for an air- plane. Equations expressing the forces and torques acting on the airframe are also included. These equations depends on a set of aerodynamic param- eters that are given by KDS. To stabilize the orientation of the UAV a total of three PID-controllers are used in the roll, pitch and yaw loops with angular feedback from the UAV model. The main objective in this assignment is to estimate the roll angle, but also the pitch- and yaw-angle. This is achieved by using an Extended Kalman filter (EKF) which is an extension of the ordinary linear Kalman filter de- signed for non-linear processes. The states to be estimated are quaternions representing the orientation of the UAV, and the gyroscope bias. The EKF is based on measurements from a three axes gyroscope and a three axes mag- netometer. These measurements are generated by using the output from the UAV simulator and adding noise. In the estimation process several scenarios are simulated to demonstrate how the flight direction has an influence on performance of the estimator. The estimates of the inclination angles roll and pitch are not satisfactory in all flight directions wile using measurements from gyroscope and magnetometer only. On the other hand, the yaw angle estimate is pretty good while flying approximately horizontal. Better results is achieved by adding an accelerometer to the Kalman filter. The results clearly indicates improvements in the attitude estimate by adding measurements from a accelerometer, especially the roll and pitch angles. Further on, I would recommend to follow up this project where the estimator should be tested on a simulator that also includes a navigation loop to verify if there is any improvements of the navigation precision. If results show improvement, the EKF should be applied into the actual UAV.