  This paper studies a nonlinear filtering problem over an infinite time
interval. The signal to be estimated is driven by a stochastic partial
differential equation involves unknown parameters. Based on discrete
observation, strongly consistent estimators of the parameters are derived at
first. With the optimal filter given by Bayes formula, the uniqueness of
invariant measure for the signal-filter pair has been verified. The paper then
establishes approximation to the optimal filter, showing that the pathwise
average distance, per unit time, of the computed approximating filter from the
optimal filter converges to zero in probability. Simulation results are
presented at last.
