Error-Covariance Reset in the Multiplicative Extended Kalman Filter for Attitude Estimation

Abstract

This paper presents a study of the reset step in the multiplicative extended Kalman filter (MEKF). This filter is widely used for spacecraft attitude estimation, which typically involves estimating the attitude and gyro drift in real time using external sensors such as star trackers. The basic idea of the MEKF is to use the quaternion or direction-cosine matrix as the “global” attitude parameterization and a three-component state vector for the “local” parameterization of attitude errors. The true attitude is expressed as the product of the error attitude and the estimate rather than as the sum of the error and the estimate. The reset operation moves the local error to the global variable. This reset does not add new information, but it changes the reference frame for the attitude error covariance. This results in an error-covariance reset that is very different from the measurement update of the error covariance in the MEKF. The effects of using an error-covariance reset in the MEKF are analyzed in this work. The results from this work can be applied to any application involving attitude estimation as part of its process, such as inertial navigation.