Non-linear filtering problems are being recognized more arid more as significant. Generally, an exact solution is not available but must be approximated. However, this paper gives the exact non-linear filter associated with identifying a scalar stochastic dynamical system,dx(t)/dt=ax(t)+ξ(t), disturbed by gaussian white noise ξ(t) when the system statex(t) is observed in an additive gaussian white noise environment, i.e.z(t)=x(t)+η(t) is observed over the interval of time 0≤t≤T<∞. The plant parameter,a, is assumed to have the prior probability densityPA.(a). The solution, is obtained by giving the conditional probability density functionalp(a\z(t), 0≤t≤T<∞). The minimum mean-square-error estimate, that is, the Bayes estimate or conditional expectation, is given along with the minimum-mean-square-error. Limiting cases are described.