Analysis of Difficulty in Estimating Physically-Meaningful Model Parameters based on Normalized Parameter Sensitivity Plot

In this paper, a new approach for analyzing the degree of the difficulty in estimating parameters is proposed. The approach targets at linear continuous-time models with physically-meaningful parameters and is based on the newly introduced normalized parameter sensitivity plot. The plot illustrates how the identification inputs contribute to the estimation accuracy in frequency domain and visualize the relative relationship between the model sensitivities for the parameters. In the paper, it is proven that there is a practically important accuracy limitation derived from the relative relationship. And the proposed plot enables to evaluate the limitation in a visual way. To show the applicability of the theoretical discussion in practical situations, a numerical experiment based on a mechanical system model is presented. And, a model of a rechargeable battery for electric vehicles is analyzed by the proposed approach to illustrate the effectiveness of the approach in devising strategies for estimating model parameters and selecting model structures.