  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 $\Omega\subset X :=
\mathbb{R}^d$. 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 $\hat{g}_t:=\sum_{i=1}^N\Psi^i \hat{g}^i_t$ that uses a
partition of unity $\{\Psi^i\}_{1\leq i\leq N}$ 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.
