Milliarcsecond localisation of the repeating FRB 20201124A

Very long baseline interferometric (VLBI) localisations of repeating fast radio bursts (FRBs) have demonstrated a diversity of local environments: from nearby star-forming regions to globular clusters. Here we report the VLBI localisation of FRB 20201124A using an ad-hoc array of dishes that also participate in the European VLBI Network (EVN). In our campaign, we detected 18 total bursts from FRB 20201124A at two separate epochs. By combining the visibilities from both observing epochs, we were able to localise FRB 20201124A with a 1-$σ$ error of 4.5 milliarcseconds (mas). We use the relatively large burst sample to investigate astrometric accuracy, and find that for $\gtrsim20$ baselines ($\gtrsim7$ dishes) that we can robustly reach milliarcsecond precision even using single-burst data sets. Sub-arcsecond precision is still possible for single bursts, even when only $\sim$ six baselines (four dishes) are available. We explore two methods for determining the individual burst positions: the peaks of the dirty maps and a Gaussian fit to the cross fringe pattern on the dirty maps. We found the latter to be more reliable due to the lower mean and standard deviation in the offsets from the FRB position. Our VLBI work places FRB 20201124A 705$\pm$26 mas (1-$σ$ errors) from the optical centre of the host galaxy, and consistent with originating from within the recently-discovered extended radio structure associated with star-formation in the host galaxy. Future high-resolution optical observations, e.g. with Hubble Space Telescope, can determine the proximity of our FRB 20201124A VLBI position to nearby knots of star formation.