The parametric estimation of stochastic error signals is a common task in many engineering applications such as inertial sensor calibration. In the latter case the error signals are often of complex nature and very few approaches are available to estimate the parameters of these processes. A frequently used approach for this purpose is the Maximum Likelihood (ML) which is usually implemented through a Kalman filter and found via the EM-algorithm. Although the ML is a statistically sound and efficient estimator, its numerical instability has brought to the use of alternative methods, the main one being the Generalized Method of Wavelet Moments (GMWM). The latter is a straightforward, consistent and computationally efficient approach which nevertheless loses statistical efficiency compared to the ML method. To narrow this gap, in this paper we show that the performance of the GMWM estimator can be enhanced by making use of model moments in addition to those provided by the vector of wavelet variances. The theoretical findings are supported by simulations that highlight how the new estimator not only improves the finite sample performance of the GMWM but also allows it to approach the statistical efficiency of the ML. Finally, a case study with an inertial sensor demonstrates how useful this development is for the purposes of sensor calibration.