Integrated Sensing and Communications (ISAC) has emerged as a promising paradigm for Sixth Generation (6G) and Wi-Fi 7 networks, with the communication-centric approach being particularly attractive due to its compatibility with current standards. Typical communication signals comprise both deterministic known pilot signals and random unknown data payloads. Most existing approaches either rely solely on pilots for positioning, thereby ignoring the radar information present in the received data symbols that constitute the majority of each frame, or rely on data decisions, which bounds positioning performance to that of the communication system. To overcome these limitations, we propose a novel method that extracts positioning information from data payloads without decoding them. We consider an opportunistic scenario in which communication signals from a user are captured by an opportunistic radar equipped with a Uniform Linear Arrays of antennas. We show that, in this setting, the estimation can be efficiently implemented using Fast Fourier Transforms. Finally, we demonstrate superior localization performance compared to existing methods in the literature through numerical simulations.