Linear and Nonlinear Regression with Application to Unbalance Estimation

This paper considers estimation of parameters that enters nonlinearly in a regression model. The problem formulation is closely connected to unbalance estimation of rotating machinery. The parameter estimation problem can after approximation be formulated as a linear estimation procedure, while neglecting the effects of the disturbing term. Two such estimators are derived. In addition, a third approach that handles the uncertainty in a statistically sound way is presented. The three methods are compared and analyzed with respect to their statistical accuracy. Using the example of unbalance estimation of a separator, the nonlinear approach is shown to outperform the other two.