Identification via Non-linear Filtering

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 state x(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