# Robustness and Sensitivity Tuning of the Kalman Filter for Speech Enhancement
###### Abstract  
Inaccurate estimates of the linear prediction coefficient (LPC) and noise variance introduce bias in Kalman filter (KF) gain and degrade speech enhancement performance. The existing methods propose a tuning of the biased Kalman gain, particularly in stationary noise conditions. This paper introduces a tuning of the KF gain for speech enhancement in real-life noise conditions. First, we estimate noise from each noisy speech frame using a speech presence probability (SPP) method to compute the noise variance. Then, we construct a whitening filter (with its coefficients computed from the estimated noise) to pre-whiten each noisy speech frame prior to computing the speech LPC parameters. We then construct the KF with the estimated parameters, where the robustness metric offsets the bias in KF gain during speech absence of noisy speech to that of the sensitivity metric during speech presence to achieve better noise reduction. The noise variance and the speech model parameters are adopted as a speech activity detector. The reduced-biased Kalman gain enables the KF to minimize the noise effect significantly, yielding the enhanced speech. Objective and subjective scores on the NOIZEUS corpus demonstrate that the enhanced speech produced by the proposed method exhibits higher quality and intelligibility than some benchmark methods. speech enhancement; Kalman filter; Kalman filter gain; robustness metric; specificity; LPC; whitening filter; real-life noise +
Footnote †: journal:  
In [13], [PERSON] et al. introduced an augmented KF (AKF) to enhance colored noise-corrupted speech. In this SEA, both the clean speech and noise signal are represented by two AR processes. The speech and noise LPC parameters are incorporated in an augmented matrix form to construct the recursive equations of AKF. In [13], the AKF processes the colored noise-corrupted speech iteratively (usually 3-4 iterations) to eliminate the noise, yielding the enhanced speech. Specifically, the LPC parameters for the current frame are computed from the corresponding filtered speech frame of the previous iteration by AKF. Although the enhanced speech of the AKF demonstrates an improvement in signal-to-noise ratio (SNR), it suffers from musical noise and speech distortion. Therefore, this method [13] does not adequately address the inaccurate LPC parameter estimation issue in practice. In [17], [PERSON] and [PERSON] proposed a modulation-domain KF (MDKF) for speech enhancement. It was claimed that the modulation domain is able to better model the long-term correlation of speech information than that of time domain speech. It was shown that the MDKF exhibits better objective scores than time-domain KF (TDKF), particularly in the oracle case (LPC parameters are computed from clean speech). However, clean speech is unobserved in practice. For practical applications, they incorporated a traditional MMSE-STSA [9] with MDKF for speech enhancement. Specifically, the MMSE-STSA has been used to pre-filter the noisy speech in the acoustic domain. Then, the pre-filtered speech is transformed in the modulation domain prior to computing the LPC parameters. Therefore, they do not adequately address LPC parameter estimation directly from the noisy speech in the modulation domain. Technically, the characteristics of the speech signal in the acoustic domain are entirely different than that of it in modulation domain. Due to this limitation, it is quite difficult to assess the performance of MDKF for speech enhancement in practice. [PERSON] et al. introduced a sub-band (SB) iterative KF (SBIT-KF)-based SEA [18]. This method enhances only the high-frequency sub-bands (SBs) using iterative KF among the 16 decomposed SBs of noisy speech for a given utterance, with the assumption that the impact of noise in low-frequency SBs is negligible. However, the low-frequency SBs can also be affected by noise, typically when operating in real-life noise conditions.