Tonic sympathetic arousal is often inferred from spontaneous fluctuations in skin conductance, and this relies on assumptions about the shape of these fluctuations and how they are generated. We have previously furnished a psychophysiological model for this relation, and an efficient and reliable inversion method to estimate tonic arousal from given data in the framework of dynamic causal modeling (DCM). Here, we provide a fast alternative inversion method in the form of a matching pursuit (MP) algorithm. Analyzing simulated data, this algorithm approximates the true underlying arousal up to about 10 spontaneous fluctuations per minute of data. For empirical data, we assess predictive validity as the ability to differentiate two known psychological arousal states. Predictive validity is comparable between the methods for three datasets, and also comparable to visual peak scoring. Computation time of the MP algorithm is 2-3 orders of magnitude faster for the MP than the DCM algorithm. In summary, the new MP algorithm provides a fast and reliable alternative to DCM inversion for SF data, in particular when the expected number of fluctuations is lower than 10 per minute, as in typical experimental situations.