On lower bounds for the nonlinear filtering problem (Corresp.)

The system modeldx_{t}=m(x_{t})dt+sigma_{o}dw_{t}and the observationdy_{t}=h(x_{t})dt+rho dv_{t}are considered, and a lower bound on the error for the least-square estimate of a function ofx_{t}, sayz(x_{t}), is derived. This bound is then applied to derive a lower bound on the error in estimatingx_{t}in the case where the constantsigma_{o}in the equation for the system dynamics is replaced bysigma (x_{t}).