A new nonlinear filtering formula non-Gaussian discrete time measurements

An exact formula for computing the conditional mean of a random variable is derived for discrete time observations with non-Gaussian measurement noise. This formula is analogous to the well-known result of Fujisaki-Kallianpur-Kunita for continuous time observations, and it is a generalization of the discrete time formula recently derived by Takeuchi and Akashi. The derivation of the new formula is extremely elementary, and it is based on the judicious choice of a certain homotopy function.