Three high-resolution positioning methods based on the FluoroBancroft linear-algebraic method [S. B. Andersson, Opt. Express 16, 18714 (2008)] are proposed for wavelength-shifting fiber (WLSF) neutron detectors. Using a Gaussian or exponential-decay light-response function, the non-linear relation of photon-number profiles vs. x-pixels was linearized and neutron positions were determined. After taking the super-Poissonian photon noise into account, the proposed algorithms give an average of 0.03-0.08 pixel position error much smaller than that (0.29 pixel) from a traditional maximum photon algorithm (MPA). The new algorithms result in better detector uniformity, less position misassignment (ghosting), better spatial resolution, and an equivalent or better instrument resolution in powder diffraction than the MPA. These improvements will facilitate broader applications of WLSF detectors at time-of-flight neutron powder diffraction beamlines, including single-crystal diffraction and texture analysis.