  Simultaneous localization and tracking (SLAT) in sensor networks aims to
determine the positions of sensor nodes and a moving target in a network, given
incomplete and inaccurate range measurements between the target and each of the
sensors. One of the established methods for achieving this is to iteratively
maximize a likelihood function (ML), which requires initialization with an
approximate solution to avoid convergence towards local extrema. This paper
develops methods for handling both Gaussian and Laplacian noise, the latter
modeling the presence of outliers in some practical ranging systems that
adversely affect the performance of localization algorithms designed for
Gaussian noise. A modified Euclidean Distance Matrix (EDM) completion problem
is solved for a block of target range measurements to approximately set up
initial sensor/target positions, and the likelihood function is then
iteratively refined through Majorization-Minimization (MM). To avoid the
computational burden of repeatedly solving increasingly large EDM problems in
time-recursive operation an incremental scheme is exploited whereby a new
target/node position is estimated from previously available node/target
locations to set up the iterative ML initial point for the full spatial
configuration. The above methods are first derived under Gaussian noise
assumptions, and modifications for Laplacian noise are then considered.
Analytically, the main challenges to be overcome in the Laplacian case stem
from the non-differentiability of $\ell_1$ norms that arise in the various cost
functions. Simulation results confirm that the proposed algorithms
significantly outperform existing methods for SLAT in the presence of outliers,
while offering comparable performance for Gaussian noise.
