  We present a framework which incorporates three aspects of the estimation
problem, namely, sparse sensor configuration, optimal precision, and robustness
in the presence of model uncertainty. The problem is formulated in the
$\mathcal{H}_{\infty}$ optimal observer design framework. We consider two types
of uncertainties in the system, i.e. structured affine and unstructured
uncertainties. The objective is to design an observer with a given
$\mathcal{H}_{\infty}$ performance index with minimal number of sensors and
minimal precision values, while guaranteeing the performance for all admissible
uncertainties. The problem is posed as a convex optimization problem subject to
linear matrix inequalities. Numerical simulations demonstrate the application
of the theoretical results presented in this work.
