Biological olfactory neurons are deployed as a population, most responding to a large variety of chemical compounds, that is, they possess unspecific receptive fields. The question of whether this unspecificity results from some physical constraint placed upon chemical transduction, or on the other hand, is beneficial to system performance is unclear. In this paper we employ the notion of Fisher information to address this question by quantifying how both the distribution and the tunings of the receptive fields within olfactory receptor populations affect the optimal estimation performance of the system. Our results show that overlapping sensory neuron tunings that respond to common chemical compounds have better estimation performance than perfectly specific tunings. Our results suggest two phenomena that might represent general principles of organization within biological sensory systems responding to multiple stimuli: maximization of the diversity of tunings and homogeneity in the distribution of these different receptive fields across the stimulus space (independent of the statistics of the input stimuli). Our model predicts that a local randomized mechanism controlling receptor specificities generates optimal multidimensional stimulus estimation, for which there is some experimental evidence from the biology.