  In this paper we present new algorithms and analysis for the linear inverse
sensor placement and scheduling problems over multiple time instances with
power and communications constraints. The proposed algorithms, which deal
directly with minimizing the mean squared error (MSE), are based on the convex
relaxation approach to address the binary optimization scheduling problems that
are formulated in sensor network scenarios. We propose to balance the energy
and communications demands of operating a network of sensors over time while we
still guarantee a minimum level of estimation accuracy. We measure this
accuracy by the MSE for which we provide average case and lower bounds analyses
that hold in general, irrespective of the scheduling algorithm used. We show
experimentally how the proposed algorithms perform against state-of-the-art
methods previously described in the literature.
