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.     

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.