William Bobillet

Speech Enhancement Combining Optimal Smoothing and Errors-In-Variables Identification of Noisy AR Processes

In the framework of speech enhancement, several parametric approaches based on an a priori model for a speech signal have been proposed. When using an autoregressive (AR) model, three issues must be addressed. (1) How to deal with AR parameter estimation? Indeed, due to additive noise, the standard least squares criterion leads to biased estimates of AR parameters. (2) Can an estimation of the variance of the additive noise for each speech frame be obtained? A voice activity detector is often used for its estimation. (3) Which estimation rules and techniques (filtering, smoothing, etc.) can be considered to retrieve the speech signal? Our contribution in this paper is threefold. First, we propose to view the identification of the noisy AR process as an errors-in-variables problem. This blind method has the advantage of providing accurate estimations of both the AR parameters and the variance of the additive noise. Second, we propose an alternative algorithm to standard Kalman smoothing, based on a constrained minimum variance estimation procedure with a lower computational cost. Third, the combination of these two steps is investigated. It provides better results than some existing speech enhancement approaches in terms of signal-to-noise-ratio (SNR), segmental SNR, and informal subjective tests.

Errors-In-Variables-Based Approach for the Identification of AR Time-Varying Fading Channels

This letter deals with the identification of time-varying Rayleigh fading channels using a training sequence-based approach. When the fading channel is approximated by an autoregressive (AR) process, it can be estimated by means of Kalman filtering, for instance. However, this method requires the estimations of both the AR parameters and the noise variances in the state-space representation of the system. For this purpose, the existing noise compensated approaches could be considered, but they usually require a long observation window and do not necessarily provide reliable estimates when the signal-to-noise ratio is low. Therefore, we propose to view the channel identification as an errors-in-variables (EIV) issue. The method consists in searching the noise variances that enable specific noise compensated autocorrelation matrices of observations to be positive semidefinite. In addition, the AR parameters can be estimated from the null spaces of these matrices. Simulation results confirm the effectiveness of this approach, especially in presence of a high amount of noise.

Multichannel AR parameter estimation from noisy observations as an errors-in-variables issue

In various applications from radar processing to mobile communication systems based on CDMA or OFDM, M-AR multichannel processes are often considered and may be combined with Kalman filtering. However, the estimations of the M-AR parameter matrices and the autocorrelation matrices of the additive noise and the driving process from noisy observations are key problems to be addressed. In this paper, we suggest solving them as an errors-in-variables issue. In that case, the noisy-observation autocorrelation matrix compensated by a specific diagonal block matrix and whose kernel is defined by the M-AR parameter matrices must be positive semi-definite. Hence, the parameter estimation consists in searching every diagonal block matrix that satisfies this property, in reiterating this search for a higher model order and then in extracting the solution that belongs to both sets. A comparative study is then carried out with existing methods including those based on the Extended Kalman Filter (EKF) and the Sigma-Point Kalman Filters (SPKF). It illustrates the relevance and advantages of the proposed approaches.

Noisy speech dereverberation as a SIMO system identification issue

This paper deals with the speech dereverberation issue based on a single input multiple output (SIMO) system, when the reverberations are modeled by finite impulse response (FIR) filters. In most of the existing methods, the authors assume either that the white noises have the same variance or that the noise statistics are available. Here, we investigate the blind speech deconvolution using two microphones, when the white noise variances are not equal. For this purpose, we present a modified version of an identification approach previously developed in the framework of control and based on the properties of the definiteness and the positiveness of the autocorrelation matrices of the reverberated versions of the speech and the observations. This makes it possible to estimate both the variances of the additive noises and the FIR. Then, the speech signal is retrieved in the least square (LS) or minimum variance (MV) sense

Cancelling convolutive and additive coloured noises for speech enhancement

In the framework of speech enhancement, many approaches have been developed when the speech signal is only corrupted by additive noise. However, in an auditorium, when echoes appear, spatial transformations between the sources and the microphones must be considered. For this reason, we propose to deal with speech contaminated by both convolutive and additive coloured noise. The two-microphone based noise canceller we present operates as follows: firstly, a prewhitening step is carried out. Secondly, the blind deconvolution method we use makes it possible to estimate the finite impulse responses (FIR), their orders and the variances of the additive noise, which is a great advantage. Then, the filtered versions of speech, estimated by means of a subspace method, are used to retrieve the original speech.

Identification of Time-Varying Frequency-Flat Rayleigh Fading Channels Based on Errors-In-Variables Approach

This paper deals with the identification of time-varying frequency-flat Rayleigh fading channels disturbed by an additive white Gaussian noise, using a training sequence based approach. When the channel is modeled by an autoregressive (AR) process, it can be estimated by using a Kalman filter. However, this solution requires the preliminary unbiased estimations of the AR parameters and the variances of both the additive noise and the driving process in the state space representation of the system. Instead of using the existing noise compensated approaches which usually require a long observation window and do not necessarily provide reliable estimates when the signal to noise ratio is low, we propose an alternative approach using recent results developed for the errors-in-variables (EIV) issue. This method consists in estimating the kernel of specific autocorrelation matrices and has the advantage of providing both the noise variances and the channel AR parameters. Moreover, the maximum Doppler frequency can be also deduced