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... distributed implementations of both the MGSR and LPR algorithms using single-bit [34] or multi-bit [35] messages broadcasted between the sensors, or transmitted via local (single-hop) communications =-=[36]-=-, to account for limitations on the sensors’ communication range and bandwidth. APPENDIX A PROOF OF COROLLARY 1 Proof: Consider the geometry of Fig. 13. The current position, pi(k), of sensor-i is den...

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...dden Markov random field models in [21] and by a graph-based method in [22]. For constrained optimization problems, a recently developed technique is to construct a consensus optimization formulation =-=[23]-=-, [24]. Each sensor holds its own local estimates of all the unknowns, and the estimates of neighboring sensors are forced to consent asymptotically. A powerful implementation tool to solve the constr...

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...ngle-shot distributed estimation algorithms utilizing a snapshot of data, and (ii) distributed model-based Kalman filtering and smoothing. For related works on estimation using ad hoc WSNs, see e.g., =-=[1]-=- and references therein. Here we deal with online estimation/tracking of (non-) stationary signals, incorporating new sensor data in real-time. Most importantly, we account for the fact that in many a...

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...elf-organized systems. Notably, for those systems designed to provide a valuable alternative to classical centralized solutions (e.g., robotic swarms [3, 16, 17, 20, 22, 23], wireless sensor networks =-=[19, 27, 28]-=-, virtual agents operating in high-dimensional spaces [6, 7, 11, 12]). Artificial selforganized systems achieve high degrees of scalability, flexibility, and robustness by relying on limited perceptio...

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... side result a convergence proof of the stochastic coordinate descent versions of the proximal gradient algorithm, since this algorithm can be seen as the application of a 1/2-averaged operator [8]. More importantly in the context of this paper, this idea leads to provably convergent asynchronous distributed versions of ADMM+. 3) Putting together both ingredients above, we apply our findings to asynchronous distributed optimization. First, the optimization problem (1) is rewritten in a form 2 where the operator M encodes the connections between the agents within a graph in a manner similar to [9]. Then, a distributed optimization algorithm for solving Problem (2) is obtained by applying ADMM+. Using the idea of coordinate descent on the top of the algorithm, we then obtain a fully asynchronous distributed optimization algorithm that we refer to as Distributed Asynchronous Primal Dual algorithm (DAPD). At each iteration, an independent an identically distributed random subset of agents wake up, apply essentially the proximity operator on their local functions, send some estimates to their neighbors and go idle. An algorithm that has some formal resemblance with ADMM+ was proposed in [1...

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...e with stationary statistical properties and do not address the issue of outliers that results from unmodeled perturbations. Among the few existing works addressing the issue of outliers are [13] and =-=[14]-=-, which use a primal-dual formulation to extend consensus to strictly convex functions and to a class of maximum likelihood problems, respectively. However, the derivation in [13] is not correct, as w...