This technical note examines the design of constrained input signals for data-centric estimation methods which systematically generate a local function approximation from a database of regressors at a current operating point. The proposed method addresses the optimal distribution of regressor vectors under constraints for a linear time-invariant (LTI) system. The resulting nonconvex optimization problems are solved using semidefinite relaxation methods. Numerical examples illustrate the benefits and usefulness of the proposed input signal design formulations.