In this paper, we present the Gauss-Newton method as a unified approach to estimating noise parameters of the prevalent nonlinear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, we demonstrate that such approaches are variants of the Gauss-Newton method. Furthermore, we propose a novel noise variance estimation algorithm that is consistent with the Gauss-Newton principle. The formulation of the Gauss-Newton method reduces the noise estimation problem to determining the Jacobians of the corrupted speech parameters. For sampling-based compensations, we present two methods, sample Jacobian average (SJA) and cross-covariance (XCOV), to evaluate these Jacobians. The proposed noise estimation algorithm is evaluated for various compensation models on two tasks. The first is to fit a Gaussian mixture model (GMM) model to artificially corrupted samples, and the second is to perform speech recognition on the Aurora 2 database. The significant performance improvements confirm the efficacy of the Gauss-Newton method to estimating the noise parameters of the nonlinear compensation models.