This work deals with the problem of state estimation for a class of discrete time linear systems forced by non-Gaussian noise where the quantization on measured output is modeled, as usual, as additive noise having uniform probability distribution. The best linear estimate, computed through the Kalman filter, in this case may not give good results. To improve the covariance of the estimation error the best estimator with quadratic structure is developed in this paper. The optimal quadratic filter, proposed by Santis et al. (1995), is preliminarily introduced using a geometric approach. Then its application is shown in a case in which the state noise is strongly non-Gaussian to best appreciate the improvement w.r.t. standard linear filtering.