Photoactivated localization microscopy (PALM) produces an array of localization coordinates by means of photoactivatable fluorescent proteins. However, observations are subject to fluorophore multiple blinking and each protein is included in the dataset an unknown number of times at different positions, due to localization error. This causes artificial clustering to be observed in the data. We present a 'model-based correction' (MBC) workflow using calibration-free estimation of blinking dynamics and model-based clustering to produce a corrected set of localization coordinates representing the true underlying fluorophore locations with enhanced localization precision, outperforming the state of the art. The corrected data can be reliably tested for spatial randomness or analyzed by other clustering approaches, and descriptors such as the absolute number of fluorophores per cluster are now quantifiable, which we validate with simulated data and experimental data with known ground truth. Using MBC, we confirm that the adapter protein, the linker for activation of T cells, is clustered at the T cell immunological synapse.