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This paper describes an adaptive method in continuous time for the estimationof external fields by a team of $N$ agents. The agents $i$ each exploresubdomains $\Omega^i$ of a bounded subset of interest $\Omega\subset X :=\mathbb{R}^d$. Ideal adaptive estimates $\hat{g}^i_t$ are derived for eachagent from a distributed parameter system (DPS) that takes values in thescalar-valued reproducing kernel Hilbert space $H_X$ of functions over $X$.Approximations of the evolution of the ideal local estimate $\hat{g}^i_t$ ofagent $i$ is constructed solely using observations made by agent $i$ on a finetime scale. Since the local estimates on the fine time scale are constructedindependently 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 fusedvia the expression $\hat{g}_t:=\sum_{i=1}^N\Psi^i \hat{g}^i_t$ that uses apartition of unity $\{\Psi^i\}_{1\leq i\leq N}$ subordinate to the cover$\{\Omega^i\}_{i=1,\ldots,N}$ of $\Omega$. Realizable algorithms are obtainedby constructing finite dimensional approximations of the DPS in terms ofscattered bases defined by each agent from samples along their trajectories.Rates of convergence of the error in the finite dimensional approximations arederived in terms of the fill distance of the samples that define the scatteredcenters in each subdomain. The qualitative performance of the convergence ratesfor the decentralized estimation method is illustrated via numericalsimulations.

Strictly Decentralized Adaptive Estimation of External Fields using Reproducing Kernels