  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
work. To this end, we develop a constrained form of 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 discs 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 (QCQP), which depends on the Cholesky factor of the \textit{a
posteriori} error covariance matrix of SRUKF. As a result of these
modifications, the proposed constrained SRUKF (CSRUKF) is more efficient and
has better numerical stability compared to the constrained 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.
