Distributed Mean-Field Density Estimation for Large-Scale Systems

This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by recent swarm control technique that uses approximations represent collective effect swarm, wherein (especially its gradient) is usually used feedback design. In first part, we formulate estimation problem as filtering associated partial differential equation (PDE), for which employ kernel (KDE) construct noisy observations and use theory PDE design an optimal (centralized) filter. It turns out covariance operator observation noise depends on unknown density. Hence, obtain suboptimal filter, prove both estimates their gradient convergent remain close one using notion input-to-state stability (ISS). second continue study decentralize filter such each agent can based only own position local information exchange with neighbors. We also remains centralized sense ISS. Simulation results suggest able generate estimates, converge