A set of exact nonlinear filters is derived and analyzed. The filters perform recursive state estimation when only coarsely quantized output signals are available. A system with the dynamics given by n integrators, together with a uniform prior on the state vector, form the model assumptions. In the case,vith one integrator, properties of the quantizer allows the construction of an exact recursive algorithm for the updating of the probability density function (pdf), using only the corners of a convex polygon defining the region where the pdf is nonzero. It is also shown how to generalize the algorithm to handle multiple measurements quantized with vector quantizers.