Consensus analysis of random sub-graphs for distributed filtering with link failures

In this paper we carry out a stability analysis of a distributed consensus algorithm in presence of link failures. The algorithm combines a new broadcast version of a Push-Sum algorithm, specifically designed for handling link failures, with a new recursive consensus filter. The analysis is based on the properties of random Laplacian matrices and random sub-graphs and it may also be relevant for other distributed estimation problems. We characterize the convergence speed, the minimum number of consensus steps needed and the impact of link failures and for both the broadcast Push-Sum and the recursive consensus algorithms. Numerical simulations validate the theoretical analysis.