Approximate Maximum Likelihood Estimation (AMLE) is an algorithm for estimating the states and parameters of models described by stochastic differential equations (SDEs). In previous work (Varziri et al., Ind. Eng. Chem. Res., 47(2), 380-393, (2008); Varziri et al., Comp. Chem. Eng., in press), AMLE was developed for SIDE systems in which process-disturbance intensities and measurement-noise variances were assumed to be known. In the current article, a new formulation of the AMLE objective function is proposed for the case in which measurement-noise variance is available but the process-disturbance intensity is not known a priori. The revised formulation provides estimates of the model parameters and disturbance intensities, as demonstrated using a nonlinear CSTR simulation study. Parameter confidence intervals are computed using theoretic al linearization-based expressions. The proposed method compares favourably with a Kalman-filter-based maximum likelihood method. The resulting parameter estimates and information about model mismatch will be useful to chemical engineers who use fundamental models for process monitoring and control.