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This paper presents a new approach for synchronized phasor measurement-based state estimation, which starts from the buses with synchronized phasor data and enables highly accurate estimation of portions of the power system with connectivity to these phasor data buses. Observability analysis is used to assemble the buses for this Phasor State Estimator (PSE). The state estimation is formulated as an iterative least-squares problem, with bus voltage and line current magnitudes and phases as the estimated variables. An important aspect of this formulation is its ability to correct for constant or random phase biases that may exist in some phasor measurement equipment. Beside being a standalone state estimator, the PSE can enhance the reliability of a conventional state estimator. The PSE methodology is demonstrated for a power transfer path in the New York power system.