  The solution $\vartheta =(\vartheta_{t})_{t\geq 0}$ of a class of linear
stochastic partial differential equations is approximated using Clark's robust
representation approach (\cite{c}, \cite{cc}). The ensuing approximations are
shown to coincide with the time marginals of solutions of a certain
McKean-Vlasov type equation. We prove existence and uniqueness of the solution
of the McKean-Vlasov equation. The result leads to a representation of
$\vartheta $as a limit of empirical distributions of systems of equally
weighted particles. In particular, the solution of the Zakai equation and that
of the Kushner-Stratonovitch equation (the two main equations of nonlinear
filtering) are shown to be approximated the empirical distribution of systems
of particles that have equal weights (unlike those presented in \cite{kj1} and
\cite{kj2}) and do not require additional correction procedures (such as those
introduced in \cite{dan3}, \cite{dan4}, \cite{dmm}, etc).
