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This paper presents the formulation and analysis of a novel distributed maximum likelihood algorithm that utilizes a first-order optimization scheme. The proposed approach utilizes a static average consensus algorithm to reach agreement on the initial condition to the iterative optimization scheme and a dynamic average consensus algorithm to reach agreement on the gradient direction. The current distributed algorithm is guaranteed to exponentially recover the performance of the centralized algorithm.

In this presentation, the effects of quantisation on distributed convex optimisation algorithms are explored via the lens of monotone operator theory. Specifically, by representing transmission quantisation via an additive noise model, we demonstrate how quantisation can be viewed as an instance of an inexact Krasnoselskii-Mann scheme. In the case of two distributed solvers, the Alternating Direction Method of Multipliers and the Primal Dual Method of Multipliers, we further demonstrate how an adaptive quantisation scheme can be constructed to reduce transmission costs between nodes.

In this paper, we address the problem of distributed state estimation, where a set of nodes are required to jointly estimate the state of a linear dynamic system based on sequential measurements. In our distributed scenario, all the nodes 1) are interested in the full state of the observed system and 2) pursue a consensus-based state estimate with high accuracy. We exploit the equivalent relation between the maximum-a-posteriori (MAP) estimation and the Kalman filter (KF) in the minimum mean square error (MMSE) sense under the Gaussian assumption.