The auto-regressive (AR) model is an effective method to describe the correlation of time series. The classic AR coefficient estimation method utilizes a simple assumption about residual signal. It is a challenge to accurately estimate the auto-regressive coefficients in a complex environment such as noise or interference. Even though Deep Neural Networks (DNN) based AR (DNN-AR) coefficient estimation method can estimate the AR coefficients in a complex environment

the DNN-AR method is easily affected by the numerical stability of Levinson-Durbin recursion (LDR) approach during the training stage. The main target is to improve the stability and overall performance of the DNN-AR based method. In this paper

the precision transform method is utilized to improve computational efficiency while keeping system stability

and the generalized analysis-by-synthesis combing DNN (GABS-DNN) model is proposed for improving the accuracy of AR coefficient estimation and stability of the DNN training in the noisy environment. The GABS-DNN model consists of three main parts: Spectrum enhancement network in the modifier

DNN preprocessing and LDR parameter estimation at the encoder

and the conversion from autoregressive coefficient to power spectrum at the decoder. In the process of optimizing the objective function

the error between the enhanced spectrum and the observed spectrum is added for reducing the influence of the gradient of the LDR on the enhanced network during back-propagation

which results in a stable estimation of the AR coefficients of noisy speech.