Multiple stochastic integral expansions are applied to the problem of filtering a signal observed in additive noise. It is shown that the optimal mean-square estimate may be represented as a ratio of two multiple integral series. A formula for expanding the product of two multiple integrals is developed and applied to deriving equations for the kernels of best, finite expansion approximations to the optimal filter. These equations are studied in the quadratic case.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation