Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication

By Soummya Kar, José M. F. Moura, Kavita Ramanan. 2008

485 citations recorded by the source corpus.

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy intersensor communication. It introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the NU (with its linear counterpart LU) and the NLU. Their update rule combines a consensus step (where each sensor updates the state by weight averaging it with its neighbors' states) and an innovation step (where each sensor processes its local current observation). This makes the three algorithms of the consensus + innovations type, very different from traditional consensus. This paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value), efficiency, and asymptotic unbiasedness. For LU and NU, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms LU and NU are analyzed in the framework of stochastic approximation theory; algorithm NLU exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in this paper.

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Citations in the corpus

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Fast Distributed Gradient Methods (2011, background): “ization, convergence, fast Nesterov gradient, FISTA, consensus. I. INTRODUCTION Cooperative convex optimization over networks has received much attention recently, motivated by applications in sensor [1], multi-robot [2], or cognitive networks [3], [4], as well as in distributed learning [5]. This p”
Fully Distributed State Estimation for Wide-Area Monitoring Systems (2012, background): “In [20], [25], and [26], it is shown that the algorithm - can be extended 1) to yield more general centralized estimates at each control area, for example, the maximum likelihood estimate; 2) to deal with nonlinear observation models; 3) to operate in unpredictable environments with random inter-con”
Distributed Online Optimization in Dynamic Environments Using Mirror Descent (2016, background): “[48]–[50]) though we recall that we did not analyze this update for a system noise vt with a statistical distribution.”
Consensus + Innovations Approach for Distributed Multiagent Coordination in a Microgrid (2015, methodology): “For a discussion on the robustness of the algorithm, the reader is referred to [8].”
Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms (2013, background): “, distributed inference, [1], or distributed source localization, [2], in sensor networks.”
QD-Learning: A Collaborative Distributed Strategy for Multi-Agent Reinforcement Learning Through Consensus + Innovations (2012, background): “Our distributed approach is of the consensus + innovations type [24], in which the agents simultaneously incorporate the information received from their communicating neighbors and the instantaneous locally sensed costs in the same update rule (see also [25], [26], [27], [28] and [29] for related li”
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Adaptation, Learning, and Optimization over Networks (2014, background): “, [18, 26, 32, 46, 84, 87, 128, 138, 139, 175, 176, 186, 199, 205, 209, 215, 225, 242, 243, 266, 268]; (c) diffusion strategies — see, e.”
Distributed Asynchronous Constrained Stochastic Optimization (2011, methodology): “The algorithms for reaching consensus have proven useful in a wide variety of contexts from formation control [3], distributed parameter estimation [12], [13], load balancing [14], to synchronization of Kuramoto oscillators [15].”
Excess-Risk of Distributed Stochastic Learners (2013, background): “Specifically, we will show that the strategies under study achieve a better convergence rate than noncooperative algorithms, and we will also explain why diffusion strategies outperform other distributed solutions such as those relying on consensus constructions or on doublystochastic combination…”
Social learning and distributed hypothesis testing (2014, background): “ns of the observations. Our results show almost sure convergence and concentration of the nodes’ beliefs when the parameter space is discrete and the log-likelihood function is concave. Kar et al. in [33] consider the problem of distributed estimation of an unknown underlying parameter where the nod”
Adaptive Networks (2014, background): “…time scale for performing multiple consensus iterations similar to (54b) over the states of the neighbors, and a second slower time scale for performing gradient vector updates or for updating the estimators by using the result of the consensus iterations (e.g., [81], [87], [89], and [106]–[109]).”
Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures (2007, methodology): “Before deriving Lemmas 4 and 7, we present a result from [ 49 ] on a property of real number sequences to be used later, see proof in [49].”
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