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Applications of synchrophasors to parameter estimation (and state estimation) in power systems are investigated. Joint state-and-parameter estimation in parameter estimation is reformulated as two loosely-coupled linear subproblems of state tracking and parameter tracking. This paper focuses on the state tracking, which can be used to determine bus voltages in parameter estimation or to track the system state in (dynamic) state estimation. Dynamic behavior of bus voltages under possible abrupt changes is studied, using a novel and accurate prediction model. The measurement model is also improved. An adaptive filter based on optimal tracking with correlated prediction-measurement errors, including the module for abrupt-change detection and estimation, is developed. With the above settings, accurate solutions are obtained. They provide a reliable support for the parameter tracking presented in a companion paper. Simulation results reveal that the proposed approach yields improved state estimation accuracy. It also has a desired convergence property.