Kalman tracking of linear predictor and harmonic noise models for noisy speech enhancement

This paper presents a speech enhancement method based on the tracking and denoising of the formants of a linear prediction (LP) model of the spectral envelope of speech and the parameters of a harmonic noise model (HNM) of its excitation. The main advantages of tracking and denoising the prominent energy contours of speech are the efficient use of the spectral and temporal structures of successive speech frames and a mitigation of processing artefact known as the ‘musical noise’ or ‘musical tones’.The formant-tracking linear prediction (FTLP) model estimation consists of three stages: (a) speech pre-cleaning based on a spectral amplitude estimation, (b) formant-tracking across successive speech frames using the Viterbi method, and (c) Kalman filtering of the formant trajectories across successive speech frames.The HNM parameters for the excitation signal comprise; voiced/unvoiced decision, the fundamental frequency, the harmonics’ amplitudes and the variance of the noise component of excitation. A frequency-domain pitch extraction method is proposed that searches for the peak signal to noise ratios (SNRs) at the harmonics. For each speech frame several pitch candidates are calculated. An estimate of the pitch trajectory across successive frames is obtained using a Viterbi decoder. The trajectories of the noisy excitation harmonics across successive speech frames are modeled and denoised using Kalman filters.The proposed method is used to deconstruct noisy speech, de-noise its model parameters and then reconstitute speech from its cleaned parts. Experimental evaluations show the performance gains of the formant tracking, pitch extraction and noise reduction stages.