We address the problem of power system state estimation based on information coming from ubiquitous power demand time series and a limited number of PMUs. The presence of time synchronization error in the PMU measurements is explicitly considered. It is shown how incorrect modeling of synchronization errors easily lead to incorrect results, ruining the estimation performance of standard approaches. Resorting to a novel linear approximation for the power flow equations, we propose a Kalman based algorithm for the simultaneous estimation of system state and synchronization error parameters. Compelling numerical simulations, based on the IEEE C37.118.1 standard on PMUs, validate the proposed approach.