Distributed Parameter Estimation Under Byzantine Nodes in Sensor Networks

In this paper, we study the problem of parameter estimation in a sensor network, where the measurements and updates of some sensors might be arbitrarily manipulated by adversaries. Despite the presence of such misbehaviors, normally behaving sensors make successive observations of an unknown <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula>-dimensional vector parameter and aim to infer its true value by cooperating with their neighbors over a directed communication graph. To this end, by leveraging the so-called dynamic regressor extension and mixing algorithm, we transform the problem of estimating the vector parameter to that of estimating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> scalar ones. For each of the scalar problem, we propose a resilient combine-then-adapt (RCTA) diffusion algorithm, where each normal sensor performs a resilient combination to discard the suspicious estimates in its neighborhood and to fuse the remaining values, alongside an adaptation step to process its streaming observations. With a low computational cost, the proposed estimator guarantees that each normal sensor exponentially estimates the true parameter under some conditions. In particular, they consist of a sharp condition on the network topology and an excitation condition that requires only a subset of normal sensors to be sufficiently excited. It is further demonstrated that the proposed algorithm is robust to time delays and switching interactions.