THE DERIVATION OF A DESIGN MATRIX FOR A FOOT-MOUNTED INERTIAL PEDESTRIAN NAVIGATION USING INVARIANT OBSERVER APPROACH

Abstract

This paper describes a derivation of a design matrix for a foot-mounted inertial pedestrian navigation. The design matrix sometimes known as state space propagation matrix, or transition matrix, that propagate the modelled states over time. An inertial sensor is assumed to be strapped tightly on the foot of a pedestrian, and therefore the measurements obtained are assumed to be highly correlated with the movement of a foot. This permit the use of velocity update whenever the foot is on the ground. The design matrix is then derived using the Invariant Extended Kalman Filter (IEKF) framework. The navigation state is represented as an element of the matrix Lie group of double direct isometries, which is a mathematical description of the space in which the pedestrian moves, including position, velocity, and attitude. The model also incorporates accelerometers and rate-gyros biases, which are common in inertial sensors. A comparison with the design matrix derived from the standard Extended Kalman Filter (EKF) are made, and will be shown unvarying with attitude estimates, which is an improvement over the standard EKF.