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

Sparse Sensing and Optimal Precision: Robust $\mathcal{H}_{\infty}$ Optimal Observer Design with Model Uncertainty