Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities
CoRR(2023)
摘要
In this paper, we aim to design and analyze distributed Bayesian estimation
algorithms for sensor networks. The challenges we address are to (i) derive a
distributed provably-correct algorithm in the functional space of probability
distributions over continuous variables, and (ii) leverage these results to
obtain new distributed estimators restricted to subsets of variables observed
by individual agents. This relates to applications such as cooperative
localization and federated learning, where the data collected at any agent
depends on a subset of all variables of interest. We present Bayesian density
estimation algorithms using data from non-linear likelihoods at agents in
centralized, distributed, and marginal distributed settings. After setting up a
distributed estimation objective, we prove almost-sure convergence to the
optimal set of pdfs at each agent. Then, we prove the same for a storage-aware
algorithm estimating densities only over relevant variables at each agent.
Finally, we present a Gaussian version of these algorithms and implement it in
a mapping problem using variational inference to handle non-linear likelihood
models associated with LiDAR sensing.
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