A unity-norm preserving quaternion extended Kalman filter

Abstract

Preserving the quaternion unity norm has significant importance when combined with the extended Kalman filter (EKF) for state estimation of nonlinear systems perturbed by noise using noisy measurements. Although this unity challenge is solved numerically on the estimated quaternion, it is normalized out of the EKF algorithm. Projecting this constraint on the derivation of the EKF algorithm to preserve the quaternion unity norm is the purpose of this paper. The quaternion unity norm constraint is derived in two forms and projected on the EKF gain derivation. Then this gain is used to update the quaternion vector keeping its unity norm. The results show that the unity norm is preserved using the proposed constrained quaternion EKF (CQEKF) even though sudden changes occur.