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Register a new userStrictly Decentralized Adaptive Estimation of External Fields using Reproducing Kernels
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This paper describes an adaptive method in continuous time for the estimation of external fields by a team of $N$ agents. The agents $i$ each explore subdomains $Omega^i$ of a bounded subset of interest $Omegasubset X := mathbb{R}^d$. Ideal adaptive estimates $hat{g}^i_t$ are derived for each agent from a distributed parameter system (DPS) that takes values in the scalar-valued reproducing kernel Hilbert space $H_X$ of functions over $X$. Approximations of the evolution of the ideal local estimate $hat{g}^i_t$ of agent $i$ is constructed solely using observations made by agent $i$ on a fine time scale. Since the local estimates on the fine time scale are constructed independently for each agent, we say that the method is strictly decentralized. On a coarse time scale, the individual local estimates $hat{g}^i_t$ are fused via the expression $hat{g}_t:=sum_{i=1}^NPsi^i hat{g}^i_t$ that uses a partition of unity ${Psi^i}_{1leq ileq N}$ subordinate to the cover ${Omega^i}_{i=1,ldots,N}$ of $Omega$. Realizable algorithms are obtained by constructing finite dimensional approximations of the DPS in terms of scattered bases defined by each agent from samples along their trajectories. Rates of convergence of the error in the finite dimensional approximations are derived in terms of the fill distance of the samples that define the scattered centers in each subdomain. The qualitative performance of the convergence rates for the decentralized estimation method is illustrated via numerical simulations.
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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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