Discriminatively trained HMMs are investigated in both clean and noisy environments in this study. First, a recognition error is defined at different levels including string, word, phone and acoustics. A high resolution error measure in terms of minimum divergence (MD) is specifically proposed and investigated along with other error measures. Using two speaker-independent continuous digit databases, Aurora2(English) and CNDigits (Mandarin Chinese), the recognition performance of recognizers, which are trained in terms of different error measures and using different training modes, is evaluated under different noise and SNR conditions. Experimental results show that discriminatively trained models performed better than the maximum likelihood baseline systems. Specifically, for MD trained systems, relative error reductions of 17.62% and 18.52% were obtained applying multi-training on Aurora2 and CNDigits, respectively.