A Linear Approach for Parameters Estimation of Multivariable Models in a Parameter Matrix Form

Abstract

Abstract When a model output is a linear function of the model parameters, the estimation process is significantly simplified, since the optimal estimates can be determined without the usage of a numerical optimization method. Moreover, some types of nonlinear models w.r.t. their parameters can be interpreted as linear (obviously introducing a discrepancy). This is the main premise behind the linear approach for parameter estimation, where the Least Squares (LS) method is used for parameters estimation. As this assumption contradicts with the non-linear parameterized model structure, the estimation process becomes iterative. In spite of this, the linear approach is frequently preferable due to the reduced number of computations, compared with the non-linear approach, where the model is correctly considered as non-linear. Moreover, some issues with the starting point selection, stuck at a local minima, etc., natural for the non-linear approach, are avoided. In this paper estimators are presented, based on the linear approach, for both MIMO linear and non-linear parameterized models in a parameter matrix form. The representatives of the first group are LS and Weighted LS (WLS). For non-linear models, this approach is presented in terms of Extended LS (ELS). The topic regarding the efficient realizations of the estimators is also discussed