Identification via Non-linear Filtering

Abstract

ABSTRACT 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<∞. The plant parameter, a, is assumed to have the prior probability density PA .(a). The solution, is obtained by giving the conditional probability density functional p(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. This approach is a variation on the eigenfunction expansion schemes used in the stochastic signals in noise-detection problems by Helstrom and others. This appr...