The state-of-the-art robustness metric-based tuning of the augmented Kalman filter (AKF) gives an under-estimated Kalman gain, resulting distortion in the enhanced speech during colored noise suppression. This paper introduces a sensitivity metric-based tuning of the AKF for enhancing speech corrupted with different noises. Specifically, we observe that the sensitivity metric-based tuning of the AKF overcomes the under-estimation issues of Kalman gain in the existing method. It is shown that the reduced-biased Kalman gain enables the AKF to restrict the residual noise passed to the enhanced speech. It also minimizes the distortion in the enhanced speech. Objective and subjective testing on NOIZEUS corpus reveal that the enhanced speech produced by the proposed method exhibits higher quality as well as intelligibility than the benchmark methods in colored and non-stationary noise conditions for a wide range of SNR levels.