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In this work we present a maximum likelihood (ML) approach to high-resolution estimation of the shifts of a spectral signal. This spectral signal arises in application of optically-based resonant biosensors, where high-resolution in the estimation of signal shift is synonymous with high-sensitivity to biological interactions. The underlying signal is nonuniformly sampled and exhibits Poisson noise statistics. Shift estimation accuracies orders of magnitude finer than the sample spacing are sought. The ML-based formulation leads to a solution approach different from typical resonance shift estimation methods based on polynomial fitting and peak (or ) estimation and tracking.