Fast Self-Triggering and Segment-Fitting of Cosmic Muons with a small-Diameter Monitored Drift Tube Detector

We present a fast self-triggering and segment-fitting algorithm that identifies cosmic muons and reconstructs their directions using a small-diameter Monitored Drift Tube (sMDT) chamber without an external trigger detector. The muon arrival time is determined using a Legendre-based algorithm combined with coarse- and fine-grid searches. We implement the algorithm in FPGA firmware on an ATLAS MDT miniDAQ board and evaluate its efficiency, resolution, and latency. The results demonstrate standalone sMDT triggering and trigger-level reconstruction of muon directions, providing a solution for chamber commissioning and potentially MDT-based triggers for charged massive stable particle searches at the High Luminosity-LHC.