Nature has evolved many molecular machines such as kinesin, myosin, and the rotary flagellar motor powered by an ion current from the mitochondria. Direct observation of the step-like motion of these machines with time series from novel experimental assays has recently become possible. These time series are corrupted by molecular and experimental noise that requires removal, but classical signal processing is of limited use for recovering such step-like dynamics. This paper reports simple, novel Bayesian filters that are robust to step-like dynamics in noise, and introduce an L1-regularized, global filter whose sparse solution can be rapidly obtained by standard convex optimization methods. We show these techniques outperforming classical filters on simulated time series in terms of their ability to accurately recover the underlying step dynamics. To show the techniques in action, we extract step-like speed transitions from Rhodobacter sphaeroides flagellar motor time series. Code implementing these algorithms available from http://www.eng.ox.ac.uk/samp/members/max/software/
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