  The distributed filtering problem sequentially estimates a global state
variable using observations from a network of local sensors with different
measurement models. In this work, we introduce a novel methodology for
distributed nonlinear filtering by combining techniques from transportation of
measures, dimensionality reduction, and consensus algorithms. We illustrate our
methodology on a satellite pose estimation problem from a network of direct and
indirect observers. The numerical results serve as a proof of concept, offering
new venues for theoretical and applied research in the domain of distributed
filtering.
