Mobile Localization in Non-Line-of-Sight Using Constrained Square-Root Unscented Kalman Filter

Localization and tracking of a mobile node (MN) in non-line-of-sight (NLOS) scenarios, based on time-of-arrival (TOA) measurements, is considered in this paper. We develop a constrained form of a square-root unscented Kalman filter (SRUKF), where the sigma points of the unscented transformation are projected onto the feasible region by solving constrained optimization problems. The feasible region is the intersection of several disks formed by the NLOS measurements. We show how we can reduce the size of the optimization problem and formulate it as a convex quadratically constrained quadratic program, which depends on the Cholesky factor of the a posteriori error covariance matrix of the SRUKF. As a result of these modifications, the proposed constrained SRUKF (CSRUKF) is more efficient and has better numerical stability compared to the constrained unscented Kalman filter (UKF). Through simulations, we also show that the CSRUKF achieves a smaller localization error compared to other techniques and that its performance is robust under different NLOS conditions.