Localization via Taylor series approximation for UWB based human motion tracking

In this paper, we propose and investigate a low-complexity human motion tracking system which is based on ultra-wideband (UWB) radio nodes. The maximum likelihood (ML) solution of the localization problem that arises in such a system has been presented in. However, the ML solution has a computational complexity that prohibits cost-effective real-time human motion tracking. In this paper, an iterative solution of the localization problem, which is based on the first order Taylor series (TS) approximation of the ranges between the anchors and the agents, is presented. The localization algorithm can handle range measurements with unknown offsets which arise due to the asynchronism between the clock of the agents and the anchors. By means of computer simulations, it is shown that the TS based approximate solution performs close to the ML solution within a few number of iterations if it is started with a “good” initial guess of the agents position. With the a priori knowledge of the agents trajectory and position estimates in the previous time-steps, the position in the next time-step can be predicted. It has been shown that using these predicted positions as an initial guess for the TS based approximation scheme greatly improves performance.