1. A feature compensation apparatus for speech recognition in a noisy environment, the feature compensation apparatus comprising a computer readable medium storing computer readable code that implements: a feature extractor configured to extract corrupt speech features from a corrupt speech signal with additive noise that consists of two or more frames; a noise estimator configured to estimate noise features based on the extracted corrupt speech features and compensated speech features; a linear model generator configured to approximate a Gaussian mixture model (GMM) probability distribution, the estimated noise features and the extracted corrupt speech features into a linear model; a probability calculator configured to calculate a correlation between adjacent frames of the corrupt speech signal; and a speech feature compensator configured to generate the compensated speech features by eliminating noise features of the extracted corrupt speech features while taking into consideration the correlation between adjacent frames of the corrupt speech signal and the estimated noise features, and to transmit the generated compensated speech features to the noise estimator, wherein the noise estimator estimates an average and variance of the noise features based on a dynamics model of noise features of the extracted corrupt speech features and a nonlinear observation model of corrupt speech features, and wherein the noise estimator reduces a Kalman gain of the average and variance of noise features that are to be updated in inverse proportion to a ratio of the extracted corrupt speech feature to the noise feature.