For meaningful distribution system analysis, correct information of the feeder parameter is necessary. However, in many cases (especially in the developing countries), these parameters are not known accurately. To address this issue, a methodology for estimating the feeder parameters from the measured values of power flow and node voltages is proposed in this paper. It is shown that the resulting system of equations is extremely ill-conditioned in nature and to solve this ill-conditioned system of equations, an optimization-based procedure is developed. The feasibility of the proposed methodology has been validated on the IEEE 123-bus three-phase unbalanced radial distribution system.