Recursive estimation in the presence of uniformly distributed measurement noise

This note examines a discrete-time linear dynamic system, absent of disturbance noise, for which all uncertainties are uniformly distributed. With these assumptions, we prove that the posterior probability distribution of the state variable is also uniformly distributed. This result is exploited to construct a simple minimum error variance state estimation algorithm for the one-dimensional problem. Finally, we show how this algorithm relates to both the problem of estimation using a set-theoretic description of uncertainty, and estimation using order statistics.