# Robustness and Sensitivity Tuning of the Kalman Filter for Speech Enhancement
###### Abstract
As demonstrated in [13], the SBIT-KF [18] also suffers from speech distortion due to the iterative processing of noisy speech by KF. In [19], [PERSON] et al. propose a robustness metric and a sensitivity metric for tuning the biased KF gain for instrument engineering applications. Later on, [PERSON] et al. applied the tuning of KF gain for speech enhancement in the WGN condition [20,21]. Specifically, the enhanced speech (for each sample within a noisy speech frame) is given by recursively averaging the observed noisy speech and the predicted speech weighted by a scalar KF gain [20]. However, the inaccurate estimates of LPC parameters introduce bias in the KF gain, resulting in leaking a significant residual noise in the enhanced speech. In [20], a robustness metric is used to offset the bias in KF gain for speech enhancement. However, [PERSON] et al. further showed that the robustness metric strongly suppresses the KF gain in speech regions, resulting in distorted speech [21]. In [21], a sensitivity metric was used to offset the bias in KF gain, which produced less distorted speech. In [22], [PERSON] et al. propose a robustness metric-based tuning of the AKF (AKF-RMBT) for enhancing colored noise-corrupted speech. As in [20], the adjusted AKF gain is underestimated in speech regions, resulting in distorted speech. The existing KF methods [20,21] address tuning of biased Kalman gain in the WGN condition with the prior assumption that the impact of WGN on LPCs is negligible. Though the AKF method [22] performs tuning of biased gain in colored noise conditions, it still produced distorted speech. In this paper, we address the tuning of KF gain for speech enhancement in real-life noise conditions. For this purpose, we estimate noise from each noisy speech frame using an SPP-based method to compute the noise variance. To minimize bias in the LPC parameters, we compute them from pre-whitened speech. Then, KF is constructed with the estimated parameters. To achieve better noise reduction, the robustness metric is applied to offset the bias in Kalman gain when there is speech absent to that of the sensitivity metric during speech presence of the noisy speech. We also adopt the noise variance and the AR model parameters as a speech activity detector. The reduced-biased KF gain exhibits better suppression of noise in the enhanced speech. The performance of the proposed SEA is compared against some benchmark methods using objective and subjective testing. The structure of this paper is as follows: Section 2 describes the KF for speech enhancement, including the paradigm shift of the KF recursive equations, the impact of biased KF gain on KF-based speech enhancement in WGN and real-life noise conditions. In Section 3, we describe the proposed SEA, which includes the proposed parameter estimation and the proposed Kalman gain tuning algorithm. Following this, Section 4 describes the experimental setup in terms of speech corpus, objective and subjective evaluation metrics, and specifications of competitive SEAs. The experimental results are then presented in Section 5. Finally, Section 6 gives some concluding remarks.