On Lower Bounds for the Nonlinear Filtering Problem

The system model dxt =m(xt) dt+σ0dwt and the observation dyt= h (xt) dt + P dvt are considered, and a lower bound on the error for the least-square estimate of a function of xt say z(xt), is derived. This bound is then applied to derive a lower bound on the error in estimating xt in the case where the constant σ 0in the equation for the system dynamics is replaced by σ(xt).