System identification using a linear combination of cumulant slices

In this paper we develop a new linear approach to identify the parameters of a moving average (MA) model from the statistics of the output. First, we show that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. Then, this result is used to obtain a new well-conditioned linear method to estimate the MA parameters of a non-Gaussian process. The proposed method presents several important differences with existing linear approaches. The linear combination of slices used to compute the MA parameters can be constructed from dif- ferent sets of cumulants of different orders, providing a general framework where all the statistics can be combined. Further- more, it is not necessary to use second-order statistics (the autocorrelation slice), and therefore the proposed algorithm still provides consistent estimates in the presence of colored Gaussian noise. Another advantage of the method is that while most linear methods developed so far give totally erroneous estimates if the order is overestimated, the proposed approach does not require a previous estimation of the filter order. The simulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to existing methods.Peer Reviewe

Fir system identification using a linear combination of cumulants

A general linear approach to identifying the parameters of a moving average (MA) model from the statistics of the output is developed. It is shown that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. This result is then used to obtain a new well-conditioned linear method to estimate the MA parameters of a nonGaussian process. The proposed approach does not require a previous estimation of the filter order. Simulation results show improvement in performance with respect to existing methods.Peer ReviewedPostprint (published version

Analytic performance evaluation of cumulant-based arma system identification methods

The authors perform an analytic study of some cumulant-based methods for estimating the AR parameters of ARMA processes. The analysis includes new AR identifiability results for pure AR process and the analytic performance evaluation of system identification methods based on cumulants. The authors present examples of pure AR processes that are not identifiable via the normal equations based on the diagonal third-order cumulant slice. The results of the performance evaluation are illustrated graphically with plots of the variance of the estimates as a function of the parameters of the process.Peer ReviewedPostprint (published version

New hos-based parameter estimation methods for speech recognition in noisy environments

The problem of recognition in noisy environments is addressed. Often, a recognition system is used in a noisy environment and there is no possibility of training it with noisy samples. Classical speech analysis techniques are based on second-order statistics and their performance dramatically decreases when noise is present in the signal under analysis. New methods based on higher order statistics (HOS) are applied in a recognition system and compared against the autocorrelation method. Cumulant-based methods show better performance than autocorrelation-based methods for low SNRPeer ReviewedPostprint (published version

Adaptive blind equalization using weighted cumulant slices

Many linear methods have been proposed in the literature to blindly estimate the ARMA parameters of a time series using HOS. Nevertheless, they are mainly off-line and not much has been done in the adaptive case. The method proposed in this contribution is the adaptive version of the w-slice method. The recursion is based on the inversion lemma when attempting the solution of an undetermined matrix equation. The system impulse response can be recovered regardless of the ARMA or MA character of the system. The number of operations depends on the square of the system order and it is considerably reduced with respect to previous approaches. Application to channel deconvolution is shown.Peer ReviewedPostprint (published version

Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Image restoration using HOS and the Radon transform

The authors propose the use of higher-order statistics (HOS) to study the problem of image restoration. They consider images degraded by linear or zero phase blurring point spread functions (PSF) and additive Gaussian noise. The complexity associated with the combination of two-dimensional signal processing and higher-order statistics is reduced by means of the Radon transform. The projection at each angle is an one-dimensional signal that can be processed by any existing 1-D higher-order statistics-based method. They apply two methods that have proven to attain good one-dimensional signal reconstruction, especially in the presence of noise. After the ideal projections have been estimated, the inverse Radon transform gives the restored image. Simulation results are provided.Peer ReviewedPostprint (published version

Impulse response recovery of linear systems through weighted cumulant slice

Identifiability of the so-called ω-slice algorithm is proven for ARMA linear systems. Although proofs were developed in the past for the simpler cases of MA and AR models, they were not extendible to general exponential linear systems. The results presented in this paper demonstrate a unique feature of the ω-slice method, which is unbiasedness and consistency when order is overdetermined, regardless of the IIR or FIR nature of the underlying system, and numerical robustness.Peer Reviewe