Introduction: The ECG Bayesian filtering framework has been shown to be a promising method to extract the foetal electrocardiogram (FECG) from abdominal recordings. This framework requires an estimation of the ECG morphology, which is obtained by approximating an average beat with a number of Gaussian kernels. This approximation results in a high dimensional nonlinear optimization problem (finding ideal positions, width and height for these kernels). Methods: Proposed methodologies in the literature initialize the optimization algorithm using fixed positions for the kernel functions. This contribution benchmarks alternative schemes for finding the Gaussian parameters, namely an approach based on the stationary wavelet transform and random search. The goal is minimizing the normalized mean squared error between the average beat and the approximated model, while increasing foetal QRS detection accuracy. Results: The suggested methods are able to produce improved morphology approximations of the averaged beat up 4.05% (depending on the selected method). The proposed method using the stationary wavelet transform improves the goodness of the fit, while reducing the computational load. However, no immediate improvement on the accuracy of FQRS detections was noticed. Such findings render the proposed method a promising tool. However, further research should be directed at transferring the improved fit to an improvement of FQRS detections.