Multi-objective parameter estimation via minimal correlation criterion

The paper deals with the problem of parameter estimation using two different sources of information, namely a time series with dynamic data and steady-state data. The new estimator is based on a two-step procedure: first a multi-objective optimization is performed, leading to a set of Pareto-optimal vectors of parameter estimates and, second, a single model is chosen based on the free-run simulation error which is required to be minimally correlated with the model output. The procedure is general in nature and can be applied to any model representation, but for the sake of simplicity, the new procedure is illustrated using NARX polynomial models for which closed formulae for generating the Pareto-set are readily available. Monte Carlo simulation studies suggest that the new estimator, which does not assume any particular noise model, is fairly unbiased even when the conventional least-squares estimator is biased.