It appears the use of vector taylor series approximation in speech has already existed

An analytical approach to environment compensation for speech recognition. Uses the Vector Taylor Series expansion to characterize the effects on speech statistics of unknown noise.

From the abstract:The statistical linear approximation (SLA) method is proposed as a novel way to approximate a nonlinear function by a linearized model. In the proposed method, an optimization criterion for approximation is defined in terms of statistical expectation. The SLA is applied to environment compensation where the speech contamination rule appears as a highly nonlinear function of the relevant variables.