Marginal Density Averaging for Distributed Node Localization from Local Edge Measurements

Parth Paritosh, Nikolay Atanasov, Sonia Martínez

Abstract: The cooperative localization problem consists of a group of networked agents aiming to find the true probability density function(pdf) of their states. Unlike existing algorithms such as Distributed Kalman filters or non-Bayesian social learning, our algorithm restricts each agent's estimates to a local pdf on its own and its neighbors' state variables. The agents update these pdfs via local observations of their neighbors and their shared messages. This partial state estimation problem is formulated as a distributed constrained optimization in the space of probability density functions. Consistent estimates across the agents are enforced with a constraint requiring equal estimated densities over common states in every communicating agent pair. Stochastic mirror descent steps are then computed to develop a novel cooperative estimation algorithm with geometric averaging over the common marginals to enforce the constraint. We specialize this algorithm to update rules with Gaussian observation models and density estimates. The Gaussian relative position observations are simulated and accuracy is compared to Belief propagation and full state consensus algorithms in varying graph topology.