  An important preliminary procedure in multi-sensor data fusion is
\textit{sensor registration}, and the key step in this procedure is to estimate
sensor biases from their noisy measurements. There are generally two
difficulties in this bias estimation problem: one is the unknown target states
which serve as the nuisance variables in the estimation problem, and the other
is the highly nonlinear coordinate transformation between the local and global
coordinate systems of the sensors. In this paper, we focus on the 3-dimensional
asynchronous multi-sensor scenario and propose a weighted nonlinear least
squares (NLS) formulation by assuming that there is a target moving with a
nearly constant velocity. We propose two possible choices of the weighting
matrix in the NLS formulation, which correspond to classical and weighted NLS
estimation and maximum likelihood (ML) estimation, respectively. To address the
intrinsic nonlinearity, we propose a block coordinate descent (BCD) algorithm
for solving the formulated problem, which alternately updates different kinds
of bias estimates. Specifically, the proposed BCD algorithm involves solving
linear LS problems and nonconvex quadratically constrained quadratic program
(QCQP) problems with special structures. Instead of adopting the semidefinite
relaxation technique, we develop a much more computationally efficient
algorithm based on the alternating direction method of multipliers (ADMM) to
solve the nonconvex QCQP subproblems. The convergence of the ADMM to the global
solution of the QCQP subproblems is established under mild conditions. The
effectiveness and efficiency of the proposed BCD algorithm are demonstrated via
numerical simulations.
