Roberto Diversi

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.

A New Criterion in EIV Identification and Filtering Applications

Abstract One of the advantages of errors-in-variables (EIV) models consists in the symmetrical description of all variables. These models, on the other hand, are characterized by more complex identification schemes that require, when applied to real data, the definition of suitable criteria. This paper introduces a new efficient and robust criterion based on covariance-matching properties and tests its performance by means of a Monte Carlo simulation concerning also the application of the identified models in EIV filtering.

Brief paper: Maximum likelihood identification of noisy input-output models

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cramer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations.

Brief Optimal errors-in-variables filtering

This paper deals with optimal (minimal variance) filtering in an errors-in-variables framework. Differently from many other contexts, errors-in-variables models treat all variables in a symmetric way (no partition of the variables into inputs and outputs is required) and assume additive noise on all the variables. The filtering technique described in this paper can be easily implemented in a recursive way and does not require the use of a Riccati equation at every update. The results of Monte Carlo simulations have shown the effectiveness and consistency of the approach.

Identification of ARX and ARARX Models in the Presence of Input and Output Noises

ARX (AutoRegressive models with eXogenous variables) are the simplest models within the equation error family but are endowed with many practical advantages concerning both their estimation and their predictive use since their optimal predictors are always stable. Similar considerations can be repeated for ARARX models where the equation error is described by an AR process instead of a white noise. The ARX and ARARX schemes can be enhanced by introducing the assumption of the presence of additive white noise on the input and output observations. These schemes, that will be denoted as “ARX + noise” and “ARARX + noise”, can be seen as errors-in-variables models where both measurement errors and process disturbances are taken into account. This paper analyzes the problem of identifying ARX + noise and ARARX + noise models. The proposed identification algorithms are derived on the basis of the procedures developed for the solution of the dynamic Frisch scheme. The paper reports also Monte Carlo simulations that confirm the effectiveness of the proposed procedures.

Kalman filtering in extended noise environments

This note introduces an extended environment for Kalman filtering that considers also the presence of additive noise on input observations in order to solve the problem of optimal (minimal variance) estimation of noise-corrupted input and output sequences. This environment includes as subcases both errors-in-variables filtering (optimal estimate of inputs and outputs from noisy observations) and traditional Kalman filtering (optimal estimate of state and output in presence of state and output noise). A Monte Carlo simulation shows that the performance of this extended filtering technique leads to the expected minimal variance estimates.

A Bias-Compensated Identification Approach for Noisy FIR Models

A new bias-compensated least-squares method for identifying finite impulse response (FIR) models whose input and output are affected by additive white noise is proposed. By exploiting the statistical properties of the equation error of the noisy FIR system, an estimate of the input noise variance is obtained and the noise-induced bias is removed. The results obtained by means of Monte Carlo simulations show that the proposed algorithm outperforms other bias-compensated approaches and allows to obtain an estimation accuracy comparable to that of total least-squares without requiring the a priori knowledge of the input-output noise variance ratio.

Algorithms for optimal errors-in-variables filtering

This paper introduces a new algorithm for optimal filtering of data generated by errors-in-variables processes and compares its efficiency with that of two previous algorithms (Optimal errors-in-variables filtering, to appear in Automatica). It is shown that the new approach proposed here, based on the Cholesky decomposition of a matrix, is characterized by a high level of efficiency, superior to the efficiency of all other algorithms. An expression of the expected performance of the filtering algorithms is also developed; a Monte Carlo simulation confirms its accuracy.

Comparison of three Frisch methods for errors-in-variables identification

Abstract The errors–in–variables framework concerns static or dynamic systems whose input and output variables are affected by additive noise. Several estimation methods have been proposed for identifying dynamic errors–in–variables models. One of the more promising approaches is the so–called Frisch scheme. This paper decribes three different estimation criteria within the Frisch context and compares their estimation accuracy on the basis of the asymptotic covariance matrices of the estimates. Some numerical examples support well the theoretical results.

A NEW ESTIMATION APPROACH FOR AR MODELS IN PRESENCE OF NOISE

Abstract This paper considers the problem of estimating the parameters of an autoregressive (AR) process in presence of additive white noise and proposes a new identification method, based on theoretical results originally developed in errors-in-variables contexts. This approach allows to estimate the AR parameters, the driving noise variance and the variance of the additive noise in a congruent way in that these estimates assure the positive definiteness of the autocorrelation matrix. The performance of the proposed algorithm is compared with that of bias-compensated least-squares methods by means fo Monte Carlo simulations. The results show the effectivenesss of the new method also in presence of high amounts of noise.