  In two-way time-of-arrival (TOA) systems, a user device (UD) obtains its
position by round-trip communications to a number of anchor nodes (ANs) at
known locations. The objective function of the maximum likelihood (ML) method
for two-way TOA localization is nonconvex. Thus, the widely-adopted
Gauss-Newton iterative method to solve the ML estimator usually suffers from
the local minima problem. In this paper, we convert the original estimator into
a convex problem by relaxation, and develop a new semidefinite programming
(SDP) based localization method for moving UDs, namely SDP-M. Numerical result
demonstrates that compared with the iterative method, which often fall into
local minima, the SDP-M always converge to the global optimal solution and
significantly reduces the localization error by more than 40%. It also has
stable localization accuracy regardless of the UD movement, and outperforms the
conventional method for stationary UDs, which has larger error with growing UD
velocity.
