Investigation of the Attitude Error Vector Reference Frame in the INS EKF

Abstract

The Extended Kalman Filter is used extensively for inertial navigation. If initial attitude errors are small, many authors choose to represent the attitude states as a vector of small angles in the vehicle body frame. Some authors choose to represent this vector in the navigation frame instead, but the corresponding reduction of filter performance in the closed loop filter is not discussed. Performance is regained when switching to an open loop filter, but closed loop filters are widely desired. This paper investigates this performance reduction. To show the effect,Monte Carlo simulation results are shown for several cases with a simplified inertial navigation problem using a closed and open loop filter and attitude states in the body and inertial frames. A qualitative argument is given to explain the effects, which stem from a state propagation model that poorly reflects the true system model for this case. A method is proposed to regain performance by using an estimated inertial frame for the attitude states. This method is only beneficial when the attitude states are measured indirectly via the velocity state equation. Results with this new frame are shown and discussed.