Limitations of the unscented Kalman filter for the attitude determination on an inertial navigation system

One of the main challenges of the inertial navigation algorithms is the initial attitude determination (ie heading, roll and pitch). Indeed, as long as the attitude is not known precisely enough, the propagation of navigation parameters is highly nonlinear, and the Kalman filter used for the navigation cannot be applied. As an alternative to the traditional Kalman filter, the Unscented Kalman Filter (UKF) has received a lot of attention in the last few years since it allows releasing the non linear constraint of traditional Kalman Filter or Extended Kalman Filter (EKF). The idea behind the UKF is to represent the probability distribution of the states defining the system with a set of samples, called sigma-points, instead of the covariance matrix. This paper demonstrates why such algorithm cannot be used to determine the attitude, in order to prepare the development of a new algorithm that will extend the capabilities of the UKF in highly non linear cases.