  We employ the variational formulation and the Euler-Lagrange equations to
study the steady-state error in linear non-causal estimators (smoothers). We
give a complete description of the steady-state error for inputs that are
polynomial in time. We show that the steady-state error regime in a smoother is
similar to that in a filter of double the type. This means that the
steady-state error in the optimal smoother is significantly smaller than that
in the Kalman filter. The results reveal a significant advantage of smoothing
over filtering with respect to robustness to model uncertainty.
