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Many methods have been developed for spectral analysis of irregularly sampled data. Currently, popular methods such as Lomb-Scargle and resampling tend to be biased at higher frequencies. Slotting methods fail to consistently produce a spectrum that is positive for all frequencies. In this paper, a new estimator is introduced that applies the Burg algorithm for autoregressive spectral estimation to unevenly spaced data. The new estimator can be perceived as searching for sequences of data that are almost equidistant, and then analyzing those sequences using the Burg algorithm for segments. The estimated spectrum is guaranteed to be positive. If a sufficiently large data set is available, results can be accurate up to relatively high frequencies.