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This paper presents novel power system transmission-line fault-location algorithms without requiring transmission-line parameters. The voltages and currents from both ends of a line are taken as inputs and no synchronization is required. Both prefault and fault data may be utilized. The proposed methods are based on a distributed parameter line model and, hence, fully consider the impacts of shunt capacitance of the line. Positive-sequence line parameters may also be estimated as a byproduct. No assumption on the source impedance and fault resistance is made. Evaluation studies based on Electromagnetic Transients Program (EMTP) simulation data demonstrate that the new methods are able to achieve quite accurate estimates.