Attitude estimation by multiplicative exogenous Kalman filter

This paper presents a novel attitude estimator called the multiplicative exogenous Kalman filter. The estimator inherits the stability properties of a nonlinear observer and the near-optimal steady-state performance of the linearized Kalman filter for estimation in nonlinear systems. The multiplicative exogenous Kalman filter is derived in detail, and its error dynamics is shown to be globally exponentially stable, which provides guarantees on robustness and transient performance. It is shown in simulations and experiments to yield similar steady-state performance as the multiplicative extended Kalman filter, which is the workhorse for attitude estimation today. The filter assumes biased angular rate measurements and two or more time-varying vector measurements, and it estimates the attitude represented by the quaternion and the angular rate sensor bias.