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Dynamic mode decomposition (DMD) provides a practical means of extractinginsightful dynamical information from fluids datasets. Like any data processingtechnique, DMD's usefulness is limited by its ability to extract real andaccurate dynamical features from noise-corrupted data. Here we showanalytically that DMD is biased to sensor noise, and quantify how this biasdepends on the size and noise level of the data. We present three modificationsto DMD that can be used to remove this bias: (i) a direct correction of theidentified bias using known noise properties, (ii) combining the results ofperforming DMD forwards and backwards in time, and (iii) a totalleast-squares-inspired algorithm. We discuss the relative merits of eachalgorithm, and demonstrate the performance of these modifications on a range ofsynthetic, numerical, and experimental datasets. We further compare ourmodified DMD algorithms with other variants proposed in recent literature.

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition