We address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) is asymptotically stable. Next, we develop a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations.

Abstract-We investigate collaborative optimization of an objective function expressed as a sum of local convex functions, when the agents make decisions in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, assumed independent and identically distributed. Specifically, we study the performance of the consensus-based multi-agent distributed subgradient method and show how it depends on the probability distribution of the random graph. For the case of a constant stepsize, we first give an upper bound on the difference between the objective function, evaluated at the agents' estimates of the optimal decision vector, and the optimal value. Second, for a particular class of convex functions, we give an upper bound on the distances between the agents' estimates of the optimal decision vector and the minimizer. In addition, we provide the rate of convergence to zero of the time varying component of the aforementioned upper bound. The addressed metrics are evaluated via their expected values. As an application, we show how the distributed optimization algorithm can be used to perform collaborative system identification and provide numerical experiments under the randomized and broadcast gossip protocols.

The authors investigate the ion conduction of molecular beam epitaxy grown CaF2∕BaF2 multilayers perpendicular to the interfaces. Unlike previous measurements along the heterostructure boundaries, the more resistive contributions dominate here; the detailed analysis allows for a complementary insight into the charge carrier distribution. The features of perpendicular conductivites in both semi-infinite and mesoscopic situations can be qualitatively as well as quantitatively explained by the same defect chemical model used for parallel ion conduction. The authors can distinguish three different size regimes. For large interfacial spacings (ℓ>50nm), the conduction is dominated by bulk parts of the CaF2 layers, showing only a slight increase with decreasing layer thickness. For very small spacings, i.e., ℓ<30nm, the conductivity increases steeply and tends toward a saturation value, corresponding to the space charge overlap situation with the overall value that can be attributed to Fi′ accumulated in CaF2. The intermediate range (30nm<ℓ<50nm) is characterized by markedly lower activation energies in which the transition from Fi′ (depleted near the interface) to VF• (enriched near the interface) in BaF2 plays a significant role.