The problem of estimating the state of a discrete-time linear system can be addressed by minimizing an estimation cost function dependent on a batch of recent measure and input vectors. This problem has been solved by introducing a receding-horizon objective function that includes also a weighted penalty term related to the prediction of the state. For such an estimator, convergence results and unbiasedness properties have been proved. The issues concerning the design of this filter have been discussed in terms of the choice of the free parameters in the cost function. The performance of the proposed receding-horizon filter has been evaluated and compared with other techniques by means of a numerical example.