This paper presents a method for the input trajectory design of dynamical systems with the aim of enhancing state estimation accuracy. The method is based on the optimization of a modified version of an index derived from a set-theoretic approach to observability. The presented technique is applied to a model representing a fed-batch bioreactor and the results are compared to a traditional method. Applying the input trajectory obtained from the devised design method results in a significantly better state estimation performance than the one found when applying the control actions obtained by the traditional design approach.