Estimator for Dynamic System Using Operating Records

Abstract

An instrumental variable estimation of the parameters of an unknown system is augmented with several additional computations and compared with a least squares estimation. Good results follow from the addition of the following. 1. The mean of the additive uncorrelated noise is a variable included in the list of unknown coefficients to be estimated. 2. Convergence is in the domain of poles and residues, not coefficients of polynomial representation of Laplace or sampled-data transforms or differential or difference equations. 3. The estimation is at least three more than the expected system order. 4. The estimated system model is constrained to be stable and is used to generate the instrumental variables. 5. The initial state (initial conditions) is estimated and used in the model. 6. Iterative sequential recursive estimations are necessary. Bootstrapping is used to obtain the noise vector. 7. When the equation error (residual) is relatively small, the residual is noise, not estimated model error, and the instrumental variable method minimizes the cross-correlation between the noisy residual and the noise-free state variables (instrumental variables) derived from the noise-free model. The residual is not minimized by least squares, which would create a large bias in the estimates.