This paper considers the problem of unbalance estimation of rotating machinery. It is formulated as a parameter estimation problem, where the unknowns enter nonlinearly in a regression model. By use of a certain method, the problem can be reformulated as a linear estimation procedure with a closed form solution. This procedure is sometimes known as the influence coefficient method. In its derivation, no special treatment is devoted to disturbing terms and imperfections in the model. Therefore, a novel method is derived which takes disturbances into account, leading to a nonlinear estimator. The two procedures 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 give superior performance. (C) 2010 Elsevier Ltd. All rights reserved.