  Two related numerical schemes for the realization of the Mortensen observer
or minimum energy estimator for the state reconstruction of non-linear
dynamical systems subject to deterministic disturbances are proposed and
compared. Both approaches rely on a polynomial approximation of the value
function associated with the energy of the disturbances of the system. Such an
approximation is obtained via interpolation considering not only the values but
also first and second order derivatives of the value function in a set of
sampling points. The scheme is applied to four examples and the results are
compared with the well known extended Kalman filter.
