  We consider the problem of self-localization by a resource-constrained mobile
node given perturbed anchor position information and distance estimates from
the anchor nodes. We consider normally-distributed noise in anchor position
information. The distance estimates are based on the log-normal shadowing
path-loss model for the RSSI measurements. The available solutions to this
problem are based on complex and iterative optimization techniques such as
semidefinite programming or second-order cone programming, which are not
suitable for resource-constrained environments. In this paper, we propose a
closed-form weighted least-squares solution. We calculate the weights by taking
into account the statistical properties of the perturbations in both RSSI and
anchor position information. We also estimate the bias of the proposed solution
and subtract it from the proposed solution. We evaluate the performance of the
proposed algorithm considering a set of arbitrary network topologies in
comparison to an existing algorithm that is based on a similar approach but
only accounts for perturbations in the RSSI measurements. We also compare the
results with the corresponding Cramer-Rao lower bound. Our experimental
evaluation shows that the proposed algorithm can substantially improve the
localization performance in terms of both root mean square error and bias.
