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Peter Händel, Tampere University of Technology (Finland)
Anders Høst-Madsen, K-JIST (Korea)
A mathematical treatment of particle size and velocity estimation from two channel laser anemometry measurements is considered. Cramer-Rao bounds for the general case are derived, and the corresponding maximum likelihood estimator is analyzed through computer simulations. Low complexity correlation based estimators are derived and their performance is characterized. The results predicted by theory are illustrated by some numerical examples.
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Ercan E. Kuruoglu, University of Cambridge (U.K.)
William J. Fitzgerald, University of Cambridge (U.K.)
Peter J.W. Rayner, University of Cambridge (U.K.)
In this paper, for the estimation of the model coefficients of a polynomial autoregressive process with non-Gaussian innovations least l_p-norm estimation (LLPN) is suggested. Simulations showed that LLPN estimation leads to better estimates than the least squares estimation in terms of the mean and the standard deviations of the estimates. The algorithm is also employed in modeling audio data in non-Gaussian noise with the objective of separating signal from noise and superior results have been obtained when compared to the linear autoregressive modeling. Directions of future research is also addressed.
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Christophe Couvreur, FPMs (Belgium)
Yoram Bresler, UIUC (U.S.A.)
We address the problem of estimating the motion of a wide-band source from single passive sensor measurements, for example, estimation of the speed and position of a car moving on a road from the recording of its acoustic signature at a microphone located next to the road. We present a new computationally efficient method based on a time-varying ARMA model for Doppler-shifted random processes. Unlike previously proposed approaches which rely on a ``local'' periodicity hypothesis for the signal source, or a cyclostationary assumption, our method assumes only that the source is stationary and admits a rational (ARMA) model. The method is tested on synthetic and real acoustic data.
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2112_a.wav Simulation of Doppler shift for moving random source TOPAnanthram Swami, ARL (U.S.A.)
Current algorithms for estimating the parameters of a symmetric alpha-stable ARMA process are either highly non-linear, or assume small MA orders (q < 4), or invoke the minimum-phase assumption. We use results from the statistics literature to show that the normalized correlation is well-defined; we show that the normalized cumulants are also well-behaved. We propose to use the correlation to estimate the spectrally-equivalent minimum-phase parameters, and then to use the cumulants to resolve the phase of the model. We also show that correlation-based techniques (such as ESPRIT) work well for estimating the parameters of harmonics observed in alpha-stable noise. Correlation-based algorithms are shown to work well despite the infinite variance of the alpha-stable process.
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Marc Fayolle, LSS-CNRS (France)
Jérôme Idier, LSS-CNRS (France)
We design a model meant to be the equivalent of Blake's weak string but in the probabilistic framework. Independent line sites delimit piecewise stationary Gaussian autoregressives AR(1) corrupted with Gaussian white noise. Thanks to the Bayesian interpretation, we define the joint probability which in turn yields the likelihood. We demonstrate how to make its computation possible in cubic time. This calculation allows the set of parameters to be tested but not estimated due to the complex form of the criterion. Yet the computations done so far provide the materials for an iterative maximization. Indeed, the Expectation Maximization algorithm happens to match the features of this model and is also easily calculable. When the likelihood is known, the cost of one step of the latter algorithm is negligible in comparison with the previous calculations.
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Shawn M. Verbout, MIT (U.S.A.)
James M. Ooi, MIT (U.S.A.)
Jeffrey T. Ludwig, MIT (U.S.A.)
Alan V. Oppenheim, MIT (U.S.A.)
The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (pdf). Because the likelihood function for this problem is typically unbounded in the vicinity of undesirable, degenerate parameter estimates, a global maximum likelihood approach is not appropriate. Hence, an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought. This approach, which is termed the quasi-maximum likelihood (QML) approach, is used to obtain estimates of the AR parameters as well as the means, variances, and weighting coefficients that define the Gaussian-mixture pdf. A technique for generating solutions to the QML problem is derived using a generalized version of the expectation-maximization principle.
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Céline Theys, I3S UNSA/CNRS (France)
Michelle Vieira, I3S UNSA/CNRS (France)
André Ferrari, I3S UNSA/CNRS (France)
The aim of this paper is the Bayesian estimation of the parameters of a polynomial phase signal. This problem, encountered in radar systems for example, is usually solved using a time-frequency analysis or phase-only algorithms. A Bayesian approach using Markov chain Monte Carlo (MCMC) methods for estimating a posteriori densities of the polynomial parameters is proposed. This approach gives at least three main advantages : it requires only the a priori density form of the process allowing others noise probability densities than the gaussian one, it works directly on the noisy samples, contrary to phase-only algorithms and it gives a whole estimation of the polyno- mial coefficients.
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Edward R. Beadle, State University of New York at Stony Brook (U.S.A.)
Petar M. Djuric, State University of New York at Stony Brook (U.S.A.)
It is proposed to jointly estimate the parameters of non-Gaussian autoregressive (AR) processes in a Bayesian context using the Gibbs sampler. Using the Markov chains produced by the sampler, an approximation to the vector MAP estimator is implemented. The results reported here used AR(4) models driven by noise sequences where each sample is iid as a two component Gaussian sum mixture. The results indicate that using the Gibbs sampler to approximate the vector MAP estimator provides estimates with precision that compares favorably with the CRLBs. Also briefly discussed are issues regarding the implementation of the Gibbs sampler for AR mixture models.
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Ali H. Sayed, UCLA (U.S.A.)
Andrea Garulli, Universita' di Siena (Italy)
S. Chandrasekaran, UCSB (U.S.A.)
This paper deals with the important problem of parameter estimation in the presence of bounded data uncertainties. Its recent closed-form solution in [1] leads to more meaningful results than alternative methods (e.g., total least-squares and robust estimation), when a priori bounds about the uncertainties are available. The derivation in [1] requires the computation of the SVD of the data matrix and the determination of the unique positive root of a nonlinear equation. This paper establishes the existence of a fundamental contraction mapping and uses this observation to propose an approximate recursive algorithm that avoids the need for explicit SVDs and for the solution of the nonlinear equation. Simulation results are included to demonstrate the good performance of the recursive scheme.
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Christian Riou, ENSTB, S.C. Dpt. (France)
Thierry Chonavel, ENSTB, S.C. Dpt. (France)
A new adaptive subspace estimation algorithm is presented, based onthe maximisation of the likelihood functional. It requires littlecomputational cost and the particular structure of the algorithmensures the orthonormality of the estimated basis ofeigenvectors. Application to moving sources localization shows thevery good behavior of the algorithm when applied to problems ofpractical interest.
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Mark C.M. Hsieh, Cambridge University (U.K.)
Peter J.W. Rayner, Cambridge University (U.K.)
A set of approximations have been applied to allow the inclusion of Gaussian distributed priors for the linear parameters of the General Linear Model in order that the parameters may be integrated out alongside the Gaussian error noise variance, to give the model evidence and posterior distributions in analytic form. The extended model achieves greater accuracy in parameter estimation and evidence approximation when applied in a Bayesian inference framework, with no increase in computational load.
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Ergang Liu, Auburn University (U.S.A.)
Jitendra K. Tugnait, Auburn University (U.S.A.)
Given a linear stationary non-Gaussian signal, suppose that we fit a linear model using higher-order statistics and one of several existing methods. The model is fitted under certain assumptions on the data and the underlying (true) model. Having obtained a model, how do we know if the fitted model is ``good?'' This paper is devoted to the problem of model diagnostics and validation. We propose some simple frequency-domain tests that are applicable to both third-order and fourth-order statistics-based model fitting unlike existing tests. A computer simulation example is presented to illustrate the proposed tests.
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