Polytopic Robust Distributed Kalman Consensus Filter for Sensor Networks

Abstract

Distributed estimation is a fundamental task performed by sensor networks, often achieved through the Kalman consensus filter. However, it requires exact models, which is seldom possible in practice since parametric uncertainties are usually unavoidable. We address in this paper the robust distributed filtering problem regarding linear discrete-time systems subject to polytopic uncertainties. We consider uncertainties in all parameter matrices of the target system and sensing models. First, we introduce a centralized filter, obtained as the solution to a min-max optimization problem whose cost function collectively weights all the underlying polytope vertices. Then, we derive a fully distributed version of this filter by applying the hybrid consensus on measurements and information approach. The estimators are recursive and do not rely on numerical solvers, appealing features for real-time applications. We validate our approach and assess its performance with a numerical example, comparing it with other robust distributed strategies.