  The discrete-time approximation for nonlinear filtering problems is related
to both of strong and weak approximations of stochastic differential equations.
In this paper, we propose a new method of proof for the convergence of
approximate nonlinear filter analyzed by Jean Picard (1984), and show a more
general result than the original one. For the proof, we develop an analysis of
Hilbert space valued functionals on Wiener space.
