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Most power spectrum estimation methods such as Pisarenko, Maximum Entropy, and conventional methods, assume that the given correlation functions are uniformly sampled in location. The situation where correlation functions are uniformly sampled but with uncertainty in their sample location has been overlooked by the spectrum estimation community. In this paper, the effects upon spectrum estimates are derived when there is location uncertainty in the correlation functions. To alleviate these effects, a modified approach that takes into account the uncertainty is developed. Simulation examples are given to demonstrate the uncertainty effects and to justify the improvements gained by using the new approach.