NUMERICAL DIFFERENTIATION AND PARAMETER-ESTIMATION IN HIGHER-ORDER LINEAR STOCHASTIC-SYSTEMS

For a linear time-invariant system of order d greater than or equal to 2 with a white noise disturbance, the input and the output are assume d to be sampled at regular time intervals. Using only these observatio ns, some approximate values of the first d - 1 derivatives are obtaine d by a numerical differentiation scheme, and the unknown system parame ters are estimated by a discretization of the continuous-time least-sq uares formulas, These parameter estimates have an error which does not approach zero as the sampling interval approaches zero, This asymptot ic error is shown to be associated with the inconsistency of the quadr atic variation estimate of the white noise local variance based on the sampled observations. The use of an explicit correction term in the l east-squares estimates or the use of some special numerical differenti ation formulas eliminates the error in the estimates.