1. A feature-vector compensating apparatus for compensating a feature vector of speech used in speech processing under a background noise environment, comprising: a first storing unit that stores therein a compensation vector for compensating the feature vector of the speech for each of a plurality of noise environments; a second storing unit that stores therein a noise-environment hidden Markov model that maintains each of the noise environments as a state and is obtained by modeling parameters of a Gaussian mixture model that is a probability model of the feature vector in each of the noise environments and a state transition probability between states; a feature extracting unit that extracts the feature vector of the speech in each of a plurality of frames of input speech; an estimating unit that estimates a noise-environment series based on the noise-environment hidden Markov model, a feature-vector series including a plurality of extracted feature vectors for the frames and a degree of similarity that indicates a certainty that a respective feature vector is generated under the noise environment in each current frame and at least one of an immediately previous frame and an immediately subsequent frame of the current frame, the noise-environment series being a series of noise environments which generates each of the plurality of extracted feature vectors in the feature-vector series; a calculating unit that obtains a compensation vector corresponding to each noise environment in the estimated noise-environment series based on the compensation vectors present in the first storing unit, wherein the calculating unit obtains a first compensation vector from the compensation vector present in the first storing unit, and calculates a second compensation vector by performing a weighting addition of the obtained first compensation vector with an occupation probability of each state obtained from the noise-environment hidden Markov model as a weighting coefficient; and a compensating unit that compensates the extracted feature vectors of the speech based on the obtained second compensation vectors.