A Message Passing Based Iterative Algorithm for Robust TOA Positioning in Impulsive Noise

In this contribution, we explore further possibilities for statistical robustification of the traditional
$\ell _{2}$
-space based time-of-arrival location estimator under impulsive noise conditions. We replace the non-robust
$\ell _{2}$
loss by the
$\ell _{p}$
counterpart with
$1 \leq p < 2$
, and devise an iteratively reweighted least squares (IRLS) type approach to tackle the
$\ell _{p}$
-minimization formulation in
$\mathcal {O}(N_{\text{IRLS}}L)$
time. Here, the iteration number
$N_{\text{IRLS}}$
is a constant typically of several tens and
$L$
represents the number of sensors. The key enabler for the rapid but reliable update of location estimate at each iteration, is the sum-product message passing implemented in an acyclic factor graph derived from the corresponding subproblem. Numerical results demonstrate the superiority of our algorithm over several existing statistical robustification methods in terms of computational simplicity and positioning accuracy in the presence of impulsive noise.