In this paper, we consider state estimation over a network subject to limited sensorcommunications. A sensor needs to decide when to send its local state estimate to a remoteestimator in order to minimize the average estimation error at the estimator subject to thatthe total communication time is no more than a pre-specified value. We propose a novel sensorschedule that combines conventional time and event-based methods and demonstrate that theestimator performance is improved compared with the optimal time-based schedule and thecomputation complexity is reduced compared with the optimal event-based schedule. Thus theproposed schedule provides a tradeoff between the two classic approaches.