In this paper, a novel sequential noise estimation algorithm is proposed based on the 1st-order vector Taylor series (VTS) approximation to the nonlinear environmental function. The estimation formulas are derived in the sequential expectation-maximum (EM) criterion. Noise parameters, both the mean vectors and the covariance matrices, are estimated frame by frame directly with the aim to maximize the objective function. Experimental results demonstrate the great advantage of the proposed sequential noise estimation algorithm over the alternatives in the 1st-order VTS based feature compensation framework and show that the performance improvement comes partly from the involvement of noise covariance in the 1st-order VTS based noise compensation and partly from the introduction of noise covariance in the sequential noise estimation