A recent comment (Chang, 2014) theoretically demonstrated that for the linear system with the correlated process and measurement noises, the GASF framework proposed in the paper Wang et al. (2012) was equivalent to the conventional de-coupling filtering framework. In this note, we would further show that such equivalence between the two frameworks can be justified in a more general way, even for the nonlinear system. (C) 2014 Elsevier Ltd. All rights reserved.