  In this paper, we address the problem of controlling a network of mobile
sensors so that a set of hidden states are estimated up to a user-specified
accuracy. The sensors take measurements and fuse them online using an
Information Consensus Filter (ICF). At the same time, the local estimates guide
the sensors to their next best configuration. This leads to an LMI-constrained
optimization problem that we solve by means of a new distributed random
approximate projections method. The new method is robust to the state
disagreement errors that exist among the robots as the ICF fuses the collected
measurements. Assuming that the noise corrupting the measurements is zero-mean
and Gaussian and that the robots are self localized in the environment, the
integrated system converges to the next best positions from where new
observations will be taken. This process is repeated with the robots taking a
sequence of observations until the hidden states are estimated up to the
desired user-specified accuracy. We present simulations of sparse landmark
localization, where the robotic team achieves the desired estimation tolerances
while exhibiting interesting emergent behavior.
