  We study the design of scheduling policies to minimize monitoring error for a
collection of correlated sources, where only one source can be observed at any
given time. We model correlated sources as a discrete-time Wiener process,
where the increments are multivariate normal random variables, with a general
covariance matrix that captures the correlation structure between the sources.
Under a Kalman filter-based optimal estimation framework, we show that the
performance of all scheduling policies oblivious to instantaneous error, can be
lower and upper bounded by the weighted sum of Age of Information (AoI) across
the sources for appropriately chosen weights. We use this insight to design
scheduling policies that are only a constant factor away from optimality, and
make the rather surprising observation that AoI-based scheduling that ignores
correlation is sufficient to obtain performance guarantees. We also derive
scaling results that show that the optimal error scales roughly as the square
of the dimensionality of the system, even in the presence of correlation.
Finally, we provide simulation results to verify our claims.
