A possible approach to studying the accuracy of optimal nonlinear filtering is to look at the conditional law on an arbitrary neighborhood of the current ( unknown) state as the time goes to infinity. This paper is devoted to a restricted class of systems with a deterministic state equation, and under additional assumptions, results concerning the concentration of the conditional law are shown, as is how estimating the current state could be different from estimating the initial condition. The assumptions on the system could seem quite restrictive; however, they concern only the observability of the system, without any reference to ergodicity a in previous works.