Rendezvous under noisy measurements

We describe a distributed algorithm for solving the rendezvous problem based on consensus protocols. We extend our previous work by considering the case when the evolution of the system is affected by measurement noise. The consensus formulation allows us to derive conditions for convergence of the system towards a ball with a finite radius. We derive an upper bound on the radius of the ball and show how it depends on the magnitude of the noise. We also present examples showing that the bound is tight and can be in fact achieved, but that typically the convergence is much better than the bound suggests.