We demonstrate a computational phase correction algorithm that is able to correct for phase and timing fluctuations of arbitrary dual comb spectra. By augmenting a Kalman filter with a global search and decoupling the interferogram estimation, we show that dual comb signals having a wide range of structures can be predicted and corrected. Furthermore, we derive an upper bound for the accuracy of any self-correction technique and show that the augmented filter is capable of reaching this bound when the phase and frequency noise are bandlimited. Finally, we show how expectation maximization can be used to learn the statistical parameters of a system without any free parameters. This approach is hands-off, robust, and accurate for a wide range of dual comb systems. Demonstration code is provided.
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4 June 2019: A typographical correction was made to Fig. 2 and the abstract.
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