A note on the application of Dvoretzky´s theorem to nonlinear filtering

Abstract-Let [X I , X2, - - ) be the states of a nonlinear dynamical system. Given noisy observations of the states, a sequence x.,, xz, - - - ) of estimates is desired such that X, converges to X n as n increases. Pearson [l] suggested a sequence of estimates and proved mean-square convergence. Convergence with probability 1 is proved using an approach which hopefully will lead to further results.