The authors present an efficient method for positioning of orthogonal frequency division multiplexing (OFDM) signals. The method, called direct position determination (DPD), enables one to determine the emitter position in a single search operation. In formerly published articles on DPD, the signal was assumed to be a narrowband Gaussian source, which was subjected to a rather simple flat-fading channel model. Here, the authors extend the DPD algorithm to handle the OFDM signals that propagate through a frequency-selective channel, and derive the least squares estimator (LSE) for the problem. In addition, the authors present a method for a fine 2D position estimation, which enables one to reduce the DPD computational complexity without compromising on its estimation accuracy.