Statistical properties of the 'Hopfield estimator' of dynamical systems.

This paper analyses the statistical properties of a method for estimating the parameters of systems defined by ordinary differential equa- tions. Previously, this estimator was defined as an adapted version of Hop- field neural networks, and its convergence and robustness with respect to signal disturbances were proved, even when parameters are time-varying. This contribution aims at analysing the estimation error by performing a set of simulations where a random noise with known probability distribu- tion is added to signals. It is shown that, asymptotically, the estimator is unbiased and its variance vanishes. Further theoretical work is being undertaken in order to rigourously support these empirical findings.