The existing augmented Kalman filter (AKF) suffers from poor LPC estimates in real-world noise conditions, which degrades the speech enhancement performance. In this paper, a deep learning technique exploits the LPC estimates for the AKF to enhance speech in various noise conditions. Specifically, a deep residual network is used to estimate the noise PSD for computing noise LPCs. A whitening filter is also implemented with the noise LPCs to pre-whiten the noisy speech prior to estimating the speech LPCs. It is shown that the improved speech and noise LPCs enable the AKF to minimize the \textit{residual} noise as well as \textit{distortion} in the enhanced speech. Experimental results show that the proposed method exhibits higher quality and intelligibility in the enhanced speech than benchmark methods in various noise conditions for a wide-range of SNR levels.