Positioning for NLOS Propagation: Algorithm Derivations and Cramer–Rao Bounds

Mobile positioning has drawn significant attention in recent years. Nonline-of-sight (NLOS) propagation error is the dominant error source in mobile positioning. Most previous research in this area has focused on NLOS identification and mitigation. In this paper, we investigate new positioning algorithms to take advantage of the NLOS propagation paths rather than canceling them. Based on a prior information about the NLOS path, a geometrical approach is proposed to estimate mobile location by using two NLOS paths. On top of this, the least-squares (LS)-based position estimation algorithm is developed to take multiple NLOS paths into account, and its performance in terms of root mean-square error (RMSE) is analyzed. A general LS algorithm considering both LOS and NLOS paths is also derived, and the maximum likelihood-based algorithm is presented to jointly estimate the mobile's and scatterers' positions. The Cramer-Rao lower bound on the RMSE is derived for the benchmark of the performance comparison. The performance of the proposed algorithms is evaluated analytically and is done via computer simulations. Numerical results demonstrate that the derived analytical results closely match the simulated results.