Model compensation approach has been successfully applied to various noise robust speech recognition tasks. In this paper, based on Continuous Time (CT) approximation, the dynamic mismatch function is derived without further approximation. With such mismatch function, a novel approach to deriving the formula for calculating the dynamic statistics is presented. Besides, we also provide an insight on the processing of the pseudo inverse of non-square discrete cosine transform (DCT) matrix during model compensation. Experiments on Aurora 4 showed that the proposed approach obtained 23.2% relative WER reduction over traditional first-order Vector Taylor Series (VTS) approach.