The discovery of slow slip events (SSEs) based on the installation of dense geodetic observation networks has provided important clues to understanding the process of stress release and accumulation in subduction zones. Because short-term SSEs (S-SSEs) do not often result in sufficient displacements that can be visually inspected, refined automated detection methods are required to understand the occurrence of S-SSEs. In this study, we propose a new method based on which S-SSEs can be detected in observations derived by a Global Navigation Satellite System (GNSS) array by using l₁ trend filtering, a variation of sparse estimation, in conjunction with combined -value techniques. The sparse estimation technique and data-driven determination of hyperparameters are utilized in the proposed method to identify candidates of S-SSE onsets. In addition, combined -value techniques are used to provide confidence values for the detections. The results of synthetic tests demonstrated that almost all events can be detected with the new method, with few misdetections, compared with automated detection methods based on Akaike’s information criteria. The proposed method was then applied to daily displacements obtained at 39 GNSS stations in the Nankai subduction zone in western Shikoku, southwest Japan. The results revealed that, in addition to all known events, new events can be detected with the proposed method. Finally, we found the number of low-frequency earthquakes in the target region increased around at the onsets of potential events.