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 signal prior to estimating the speech LPCs. It is shown that the improved speech and noise LPCs enable the AKF to minimize the residual noise as well as distortion in the enhanced speech. Experimental results show that the enhanced speech produced by the proposed method exhibits higher quality and intelligibility than the benchmark methods in various noise conditions for a wide-range of SNR levels.