In this paper, we introduce an uplink optical wireless positioning system for indoor applications. This technique uses fingerprints based on the indoor optical wireless channel impulse response for localization. Exploiting the line of sight peak power (LOS), the second power peak (SPP) of the impulse response, and the delay between the LOS and SPP, we present a proof of concept design and theoretical analysis for localization employing a single fixed reference point, i.e., a photodetector (PD) on the ceiling. Adding more PDs leads to more accurate transmitter position estimation. As a benchmark, we present analytical expressions of the Cramer-Rao lower bound (CRLB) for different numbers of PDs and features. We further present closed form analytical approximations for the chosen features of the channel impulse response. Simulation results show a root mean square (RMS) positioning accuracy of 25\,cm and 5\,cm for one and four PDs, respectively, for a typical indoor room at high SNR. Numerical results verify that the derived analytic approximations closely match the simulations.