In this paper, we present a novel method for estimating short-term linear predictive parameters of speech and noise in the codebook-driven Wiener filtering speech enhancement method. We only use pretrained spectral shape codebook of speech to model the a priori information about linear predictive coefficients of speech, and the spectral shape of noise is estimated online directly instead of using noise codebook to solve the problem of noise classification. Differing from the existing codebook-driven methods that the linear predictive gains of speech and noise are estimated by maximum-likelihood method, in the proposed method we exploit a multiplicative update rule to estimate the linear predictive gains more accurately. The estimated gains can help to reserve more speech components in the enhanced speech. Meanwhile, the Bayesian parameter-estimator without the noise codebook is also developed. Moreover, we develop an improved codebook-driven Wiener filter combined with the speech-presence probability, so that the proposed method achieves the goal of removing the residual noise between the harmonics of noisy speech.