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Register a new userDistributed Local Linear Parameter Estimation using Gaussian SPAWN
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Added by
Mei Leng
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. Sensors exchange messages and cooperate with each other to estimate their own local parameters iteratively. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief propagation, but uses fixed size broadcast messages at each sensor instead. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, the gSPAWN algorithm allows sensors to broadcast a message whose size does not depend on the network size or density, making it more suitable for applications in wireless sensor networks. We show that the gSPAWN algorithm converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of the gSPAWN algorithm to a network localization problem in non-line-of-sight environments. Numerical results suggest that gSPAWN converges much faster in general than the diffusion method, and has lower communication costs, with comparable root mean square errors.
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The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces emph{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 $mathcal{NU}$ (with its linear counterpart $mathcal{LU}$) and the $mathcal{NLU}$. Their update rule combines a emph{consensus} step (where each sensor updates the state by weight averaging it with its neighbors states) and an emph{innovation} step (where each sensor processes its local current observation.) This makes the three algorithms of the textit{consensus + innovations} type, very different from traditional consensus. The paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value,) efficiency, and asymptotic unbiasedness. For $mathcal{LU}$ and $mathcal{NU}$, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms $mathcal{LU}$ and $mathcal{NU}$ are analyzed in the framework of stochastic approximation theory; algorithm $mathcal{NLU}$ exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in the paper.
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We study the problem of estimating the parameters (i.e., infection rate and recovery rate) governing the spread of epidemics in networks. Such parameters are typically estimated by measuring various characteristics (such as the number of infected and recovered individuals) of the infected populations over time. However, these measurements also incur certain costs, depending on the population being tested and the times at which the tests are administered. We thus formulate the epidemic parameter estimation problem as an optimization problem, where the goal is to either minimize the total cost spent on collecting measurements, or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general, and then propose approximation algorithms with performance guarantees. We validate our algorithms using numerical examples.
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