  A two-way time-of-arrival (TOA system is composed of anchor nodes (ANs and
user devices (UDs . Two-way TOA measurements between AN-UD pairs are obtained
via round-trip communications to achieve localization and synchronization (LAS
for a UD. Existing LAS method for a moving UD with clock drift adopts an
iterative algorithm, which requires accurate initialization and has high
computational complexity. In this paper, we propose a new closed-form two-way
TOA LAS approach, namely CFTWLAS, which does not require initialization, has
low complexity and empirically achieves optimal LAS accuracy. We first
linearize the LAS problem by squaring and differencing the two-way TOA
equations. We employ two auxiliary variables to simplify the problem to finding
the analytical solution of quadratic equations. Due to the measurement noise,
we can only obtain a raw LAS estimation from the solution of the auxiliary
variables. Then, a weighted least squares step is applied to further refine the
raw estimation. We analyze the theoretical error of the new CFTWLAS and show
that it empirically reaches the Cramer-Rao lower bound (CRLB with sufficient
ANs under the condition with proper geometry and small noise. Numerical results
in a 3D scenario verify the theoretical analysis that the estimation accuracy
of the new CFTWLAS method reaches CRLB in the presented experiments when the
number of the ANs is large, the geometry is appropriate, and the noise is
small. Unlike the iterative method whose complexity increases with the
iteration count, the new CFTWLAS has constant low complexity.
