In this paper, we present a novel, low-cost approach to indoor localization that is capable of performing localization processes in real indoor environments and does not require calibration or recalibration procedures. To this end, we propose a single-anchor architecture and design based on an electronically steerable parasitic array radiator (ESPAR) antenna and Nordic Semiconductor nRF52840 utilizing Bluetooth Low Energy (BLE) protocol. The proposed algorithm relies on received signal strength (RSS) values measured by the receiver equipped with the ESPAR antenna for every considered antenna radiation pattern. The calibration-free concept is achieved by using inexpensive BLE nodes installed in known positions on the walls of the test room and acting as reference nodes for the positioning algorithm. Measurements performed in the indoor environment show that the proposed approach can successfully provide positioning results better than those previously reported for single-anchor ESPAR antenna localization systems employing the classical fingerprinting method and relying on time-consuming calibration procedures.