Proposals have been presented in literature to estimate line parameters and monitor their changes. Synchrophasor measurements from phasor measurement units (PMUs) have appeared as a possible breakthrough for accurate estimation. However, few methods consider a realistic measurement chain including PMUs and instrument transformers and their systematic and random error contributions. This paper proposes an improved method to simultaneously estimate line parameters and systematic measurement errors on multiple network lines. The algorithm is designed to deal with realistic PMU measurement errors and, in particular, with phase-angle errors caused by common time-base errors on multiple PMU channels. The impact of PMU measurement errors is investigated to achieve a comprehensive view of the performance under realistic conditions. The results obtained on an IEEE test network prove the advantages of the proposed method with respect to other recent methods and its robustness in the presence of mismatches in the error model.