Constrained Extended Kalman Filter for Ultra-Wideband Radio based Individual Navigation

Ultra-wideband radio based individual navigation has recently received much research attention due to its wide applications in health-care, security sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications. In this paper the problem of constrained Extended Kalman Filter for ultra-wideband radio based individual navigation is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional Extended Kalman Filter. The analytical expression of Extended Kalman Filter with linear constraint to exploit additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to linear case. An individual navigation example is presented to illustrate the effectiveness of constrained Extended Kalman Filter, which gets better filtering performance than the traditional Extended Kalman Filter provides. Simulation results between the first-order and second-order nonlinear constrained filters also show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution.