Chair: Dan Fuhrmann, Washington University (USA)
Christophe Couvreur, University of Illinois at Urbana-Champaign (USA)
Yoram Bresler, University of Illinois at Urbana-Champaign (USA)
We consider the problem of detecting and classifying an unknown number of multiple simultaneous Gaussian autoregressive (AR) signals with unknown variances given a finite length observation of their sum and a dictionary of candidate AR models. We show that the problem reduces to the maximum likelihood (ML) estimation of the variances of the AR components for every subset from the dictionary. The ``best'' subset of AR components is then found by applying the minimum description length (MDL) principle. The ML estimates of the variances are obtained by combining the EM algorithm with the Rauch-Tung-Striebel optimal smoother. The performance of the algorithm is illustrated by numerical simulations. Possible improvements of the method are discussed.
T. Gouraud, Universite de Nantes
F. Auger, LRTI
M. Guglielmi, Universite de Nantes (FRANCE)
Most methods estimating noisy sinusoidal signals assume the noise to be white, and fail when they are used on real signals with colored noise. In this paper, we propose two new recursive algorithms, deduced from a recent work of Kay and Nagesha, for the estimation of sinusoidal signals embedded in an AR noise. The first one is a RLS, whereas the second one uses Kalman Filtering. Their convergence speed, computational burden and statistical characteristics are compared and the advantages brought by these estimators for real signals are shown.
Mounir Ghogho, ENSEEIHT/GAPSE (FRANCE)
Parameter estimation for multiplicative noisy data is a pertinent signal processing problem encountered in a wide range of signalling and data-processing applications, including radar, sonar, radio astronomy, seismology and vibroacoustics. The assumption of additive noise is, in these contexts, insufficient for adequate signal modeling. The model considered here incorporates the gaussian amplitude-modulated sinusoids. New algoithms are developed for frequency estimation. The corresponding probability density, prediction, innovation process and ergodicity property are presented. Higher order statistics are used, especially when the process is also contaminated by an additive noise.
Maria Hansson, Lund University (SWEDEN)
Tomas Gansler, Lund University (SWEDEN)
Goran Salomonsson, Lund University (SWEDEN)
This paper proposes a new multiple window method for estimating a peaked spectrum. The multiple windows are adapted to the signal, giving a less biased estimate for estimation of peaks than does the Thomson Multiple Window method. Still the result from estimation of a flat spectrum shows comparable results in variance reduction. The method is based on solution of an eigenvalue problem where the eigenvectors of a special correlation matrix are used as multiple windows. The correlation matrix corresponds to a low frequency dominant spectrum with limited bandwidth. The design results in windows that are further improved by a penalty function to reduce leakage from nearby frequencies. This gives a better estimate when the process contains of large spectrum dynamics.
William B. Bishop, SUNY at Stony Brook (USA)
Petar M. Djuri, SUNY at Stony Brook (USA)
In this paper, we investigate the problem of model order selection of damped sinusoids from a Bayesian perspective. We derive a maximum a posteriori (MAP) criterion through a combination of Bayesian inference and predictive densities. The MAP criterion is more appropriate for damped sinusoidal models (and transient models in general) than are the SVD based information theoretic criteria in [1]. Simulation results are provided that display the breakdown of the AIC and MDL when the data record length is not properly coupled with the information bearing portion of the data model. This deterioration in performance is related to both the underlying asymptotics upon which the AIC and MDL rules were originally based and to their invalid penalty terms. Conversely, the MAP criterion is not based on asymptotics, and proves to be more reliable and consistent when the observation length is varied.
A. Sano, Keio University (JAPAN)
Y. Ashida, Keio University (JAPAN)
K. Ohnishi, Keio University (JAPAN)
This paper proposes a method for estimating the mixed spectrum which is composed of line and continuous spectra, the latter of which is characterized by an AR or ARMA noise model. Line spectrum is represented by multiple sinusoids. In order to avoid simultaneous minimization of a prediction error criterion with respect to all unknown parameters, we give an efficient iterative algorithm for estimating the frequencies of the sinusoids and other parameters separately. By adopting the genetic algorithm in choice of initial values of the AR or ARMA parameters in the iterative estimation, we can attain a globally optimal estimate of unknown parameters. The frequency estimate is given by a modified Toeplitz approximation method using a shifted correlation matrix of observed signals. The effectiveness of the proposed algorithm is validated in numerical simulations.
Thomas Frederick, Sensormatic Electronics
Nurgun Erdol, Florida Atlantic University (USA)
This paper considers the use of filter banks for estimating the spectral correlation density function (SCD). Past techniques have used FFT techniques to lower the computational complexity of SCD estimation. We study an alternative approach of using FIR filter banks. The time resolution, bi-frequency resolution, and complexity of the two techniques will be compared. Examples from communication theory are considered.
Ying-Chang Liang, Tsinghua University (PEOPLES REPUBLIC OF CHINA)
Xian-Da Zhang, Tsinghua University (PEOPLES REPUBLIC OF CHINA)
Yan-Da Li, Tsinghua University (PEOPLES REPUBLIC OF CHINA)
This paper addresses the harmonic retrieval problem in colored noise. As contrasted to the reported studies in which Gaussian noise was assumed, this paper focuses on additive non-Gaussian ARMA noise. We propose an unified prefiltering-based approach to this problem. Our approach is hybrid in the sense that 3rd-order cumulants are first used to identify the AR part of the non-Gaussian noise process, and then correlation-based high resolution methods may be used for the filtered output process to estimate the parameters of harmonics. Simulation examples are presented to demonstrate the high resolution of this approach.
Wei Lin, Dialogic Corporation (USA)
Chris Hamilton, Dialogic Corporation (USA)
Prabhakar Chitrapu, Dialogic Corporation (USA)
Based on physical considerations, Kaiser recently proposed a new energy function for discrete time signals, known as Teager-Kaiser Energy Function (TKEF). An interesting property of the TKEF is that if the input signal consists of two closely-spaced tones (amplitude modulated signal), the TKEF produces the difference frequency tone (envelope signal). However, a drawback is that the TKEF is highly sensitive to additive noise. In this paper, we propose a Generalized TKEF (GTKEF) to reduce the noise sensitivity. Fortunately, it turns out that the generalization can be used to enhance the sum frequency tone as well. This enables us to apply the GTKEF to resolve two closely-spaced tones. The result can be viewed as an interesting nonlinear preprocessing scheme to transform a signal consisting of two closeby frequencies at f1 and f2 into a signal consisting of frequencies at (f1-f2) and (f1+f2). Clearly, it is much easier to resolve the latter frequencies, whichever spectral analysis method is used.
Roman Ugrinovsky, Russian Academy of Sciences (RUSSIA)
A novel rigorous approach to the spectral density estimation problem based on the trigonometric moment problem technique is considered. Using the trigonometric moment problem results, all possible extrapolations of the autocorrelation function, which are in agreement with a set of known values are found. A wide set of spectral estimators is described in terms of polynomials orthogonal with respect to the given autocorrelation sequence. The parametric representation for this set is given. The performance of the proposed spectral estimator with arbitrary parametrization function is established.