The authors consider the problem of estimating zero sequence parameters of a transmission line using synchrophasor data. When a set of three-phase transmission lines share, partial or complete, right of way, then their zero sequence models exhibit mutual coupling. As such the zero sequence parameters cannot be estimated by linear least squares or total least squares (TLS) technique which are the preferred methods when dealing with the positive sequence line parameter estimation problem. Further, method design has to factor the constraint of a sparse data set when dealing with zero sequence phasors. Therefore, the authors propose orthogonal distance regression approach for solving the zero sequence parameter estimation problem. This generalises the method of TLS to the non-linear parameter estimation problem considering noise in both the voltage and current synchrophasor measurements. Extensive case studies and comparative evaluations are presented to demonstrate the efficacy of the proposed approach.