A Simple Attitude Unscented Kalman Filter: Theory and Evaluation in a Magnetometer-Only Spacecraft Scenario

A quaternion-based attitude unscented Kalman filter is formulated with quaternion errors parameterized by small angle approximations and is applied to a filter with a state vector consisting of the attitude quaternion and the gyro bias vector. The filter is evaluated using extensive Monte Carlo data in a simulated lost-in-space scenario of a low-Earth orbiting spacecraft processing only three-axis magnetometer and gyro measurements. The filter is found to be robust, accurate, and rapidly convergent in this scenario for small true gyro biases and small initial uncertainties in their values, often converging in only one half of an orbit period to an attitude accuracy of 0.1 degrees. The filter convergence is found to depend significantly on the value of the true gyro biases as well as the initial gyro bias covariances. Monte Carlo results also indicate that this unscented Kalman filter is significantly less robust than an extended Kalman filter with the same attitude approach, but performs slightly better than another unscented Kalman filter with a generalized Rodrigues parameter approach to quaternion errors.