This paper presents a novel indoor positioning approach that leverages antenna radiation pattern characteristics through Received Signal Strength Indication (RSSI) measurements in a single-antenna system. By rotating the antenna or reconfiguring its radiation pattern, we derive a maximum likelihood estimation (MLE) algorithm that achieves near-optimal positioning accuracy approaching the Cramer-Rao lower bound (CRLB). Through theoretical analysis, we establish three fundamental theorems characterizing the estimation accuracy bounds and demonstrating how performance improves with increased signal-to-noise ratio, antenna rotation count, and radiation pattern variations. Additionally, we propose a two-position measurement strategy that eliminates dependence on receiving antenna patterns. Simulation results validate that our approach provides an effective solution for indoor robot tracking applications where both accuracy and system simplicity are essential considerations.