Quaternion attitude estimation for miniature air vehicles using a multiplicative extended Kalman filter

Utilizing the Euler-Rodrigues symmetric parameters (attitude quaternion) to describe vehicle orientation, we develop a multiplicative, nonlinear variation of the Kalman filter to fuse data from low-cost sensors. The sensor suite is comprised of gyroscopes, accelerometers, and a GPS receiver. Our filter states consist of the three components of an Euler attitude error vector. In parallel with the state time update, we utilize the gyroscope measurements for the time propagation of the attitude quaternion. The accelerometer and the GPS sensors are used independently for the measurement update portion of the filter. For both sensors, a vector arithmetic approach is used to determine the Euler attitude error vector. Following each measurement update, a multiplicative reset operation moves the attitude error information from the state into the attitude estimate. This reset operation utilizes quaternion algebra to implicitly maintain the unity-norm constraint. We demonstrate the effectiveness of our attitude estimation algorithm through flight simulations of aggressive maneuvers such as loops and small-radius circles.