Lessons in digital estimation theory
Lessons in digital estimation theory
Subspace algorithms for the stochastic identification problem
Automatica (Journal of IFAC)
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
Subspace-based methods for the identification of linear time-invariant systems
Automatica (Journal of IFAC) - Special issue on trends in system identification
A unifying theorem for three subspace system identification algorithms
Automatica (Journal of IFAC) - Special issue on trends in system identification
Choice of state-space basis in combined deterministic-stochastic subspace identification
Automatica (Journal of IFAC) - Special issue on trends in system identification
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Journal of Computational and Applied Mathematics
Discrete Random Signals and Statistical Signal Processing
Discrete Random Signals and Statistical Signal Processing
Linear Prediction of Speech
Signal Processing - Fractional calculus applications in signals and systems
Fast communication: Fast filtering of noisy autoregressive signals
Signal Processing
Temporally correlated source separation using variational Bayesian learning approach
Digital Signal Processing
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When enhancing a speech signal using a single microphone system, various approaches based on an autoregressive speech model are referenced in the literature. Using a Kalman filter, they operate in two steps: (1) the noise variances and the autoregressive parameters are estimated, (2) the speech signal is retrieved using standard Kalman filtering. However the existing methods are usually iterative and a voice activity detector (VAD) is often required to find the silent frames for the estimation of the variance of the white noise. To avoid these drawbacks, we propose to consider Kalman filter-based speech enhancement as a realisation issue, i.e. as the estimation of the system matrices in the state space representation using the estimation of the correlation function of the observations. For this purpose, we first present various solutions, based on works initially developed in the field of identification by Van Overschee et al. and Verhaegen. Their non-iterative extensions to coloured noise are also addressed and used with car noise. In the second part of the paper we propose an alternative approach based on Mehra et al. and Belanger's approaches dealing with the estimation of the steady Kalman gain and previously derived in the framework of identification. This approach still avoids the use of a VAD.