A note on sampling and parameter estimation in linear stochastic systems

Numerical differentiation formulas that yield consistent least squares parameter estimates from sampled observations of linear, time invariant higher order systems have been introduced previously by Duncan et al. The formulas given by Duncan et al. have the same limiting system of equations as in the continuous time case. The formula presented in this note can be characterized as preserving asymptotically a partial integration rule. It leads to limiting equations for the parameter estimates that are different from the continuous case, but they again imply consistency. The numerical differentiation formulas given here can be used for an arbitrary linear system, which is not the case in the previous paper by Duncan et al.