In this work, the issue of obtaining consistent parameter estimators for nonlinear regression models where the regressors are second -order modulus functions is explored. It is shown that consistent instrumental variable estimators can be obtained by estimating first and second -order moments of non -additive environmental disturbances' probability distributions as nuisance parameters in parallel to the sought-after model parameters, conducting experiments with a static excitation offset of sufficient amplitude and forcing the instruments to have zero mean. The proposed method is evaluated in a simulation example with a model of a marine surface vessel. (c) 2024 Elsevier Ltd. All rights reserved.