Parameter Estimation

An Enhanced TEA Algorithm for Modal Analysis

Authors:

Gabriella Olmo,
Letizia Lo Presti,
Paolo Severico,

Page (NA) Paper number 1223

Abstract:

Turbo Estimation Algorithms (TEAs) for non random parameters are able to yield high accuracy estimates by means of an iterative process. At each iteration, a noise reduction is performed by means of an External Denoising System (EDS), which exploits the estimation results obtained at the previous step; the enhanced data are then input to the master Estimation Algorithm (EA) for next iteration. Recently, a basic TEA scheme has been proposed in the context of modal analysis, which makes use of the Tufts and Kumaresan (TK) algorithm as the master EA, and of a multiband IIR filter as the EDS. In this paper, two improvements of this basic scheme are proposed; the former implies a different design of the EDS, able to achieve better estimation accuracy while reducing the outlier probability; the latter permits the autodetermination of the number of modes making up the signal.

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An Inverse Problem Approach To Robust Regression

Authors:

Jean-Jacques J. Fuchs,

Page (NA) Paper number 1383

Abstract:

When recording data large errors may occur occasionally. The corresponding abnormal data points, called outliers, can have drastic effects on the estimates. There are several ways to cope with outliers * detect and delete or adjust the erroneous data, * use a modified cost function. We propose a new approach that allows, by introducing additional variables, to model the outliers and detect their presence. In the standard linear regression model this leads to a linear inverse problem that, associated with a criterion that ensures sparseness, is solved by a quadratic programming algorithm. The new approach (model + criterion) allows for extensions that cannot be handled by the usual robust regression methods.

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The Extended Least-Squares and The Joint Maximum-A-Posteriori - Maximum-Likelihood Estimation Criteria

Authors:

Arie Yeredor,
Ehud Weinstein,

Page (NA) Paper number 1387

Abstract:

Approximate model equations often relate given measurements to unknown parameters whose estimate is sought. The Least-Squares (LS) estimation criterion assumes the measured data to be exact, and seeks parameters which minimize the model errors. Existing extensions of LS, such as the Total LS (TLS) and Constrained TLS (CTLS) take the opposite approach, namely assume the model equations to be exact, and attribute all errors to measurement inaccuracies. We introduce the Extended LS (XLS) criterion, which accommodates both error sources. We define 'pseudo-linear' models, with which we provide an iterative algorithm for minimization of the XLS criterion. Under certain statistical assumptions, we show that XLS coincides with a statistical criterion, which we term the 'joint Maximum-A-Posteriori - Maximum-Likelihood' (JMAP-ML) criterion. We identify the differences between the JMAP-ML and ML criteria, and explain the observed superiority of JMAP-ML over ML under non-asymptotic conditions.

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Conditional Maximum Likelihood Timing Recovery

Authors:

Jaume Riba,
Gregori Vázquez,

Page (NA) Paper number 1518

Abstract:

The Conditional Maximum Likelihood (CML) Principle, well known in the context of sensor array processing, is applied to the problem of timing recovery. A new self-noise free CML-based timing error detector is derived. Additionally, a new (Conditional) Cramer-Rao Bound (CRB) for timing estimation is obtained, which is more accurate than the extensively used Modified CRB (MCRB).

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Sequential Extraction of Components of Multicomponent PPS Signals

Authors:

Paulo M Oliveira,
Victor A N Barroso,

Page (NA) Paper number 1894

Abstract:

A procedure for parameter estimation of multicomponent Polynomial Phase Signals is presented. This scheme, while restricted to high SNR's, has the advantage of being extremely simple. It is also insensitive to the equal-coefficient identifiability problem of HAF (High-order Ambiguity Function) based methods. It poses, however, some restrictions on the component amplitudes. Its performance in noise is investigated, and confirmed with several examples.

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An E-M Algorithm for Joint Model Estimation

Authors:

Paul M Baggenstoss,
Tod E Luginbuhl,

Page (NA) Paper number 2001

Abstract:

In the unlabeled data problem, data contains signals from various sources whose identities are not known a priori, yet the parameters of the individual sources must be estimated. To do this optimally, it is necessary to optimize the data PDF, which may be modeled as a mixture density, jointly over the parameters of all the signal models. This can present a problem of enormous complexity if the number of signal classes is large. This paper describes a algorithm for jointly estimating the parameters of the various signal types, each with different parameterizations and associated sufficient statistics. In doing so, it maximizes the likelihood function of all the parameters jointly, but does so without incurring the full dimensionality of the problem. It allows lower-dimensional sufficient statistics to be utilized for each signal model, yet still achieves joint optimality. It uses an extension of the class-specific decomposition of the Bayes minimum error probability classifier.

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Performance Measures for Estimating Vector Systems

Authors:

Arye Nehorai,
Malcolm Hawkes,

Page (NA) Paper number 2152

Abstract:

We propose a framework of performance measures for analyzing estimators of geometrical vectors that have intuitive physical interpretations, are independent of the coordinate frame and parameterization, and have no artificial singularities. We obtain finite-sample and asymptotic lower bounds on them for large classes of estimators and show how they may be used as system design criteria. We determine a simple asymptotic relationship that is applicable to both the measures and their bounds.

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A Reversible Jump Sampler for Polynomial-Phase Signals

Authors:

Céline Theys, I3S,CNRS/UNSA,41 Bd. Napoleon III,06041 Nice, France (France)
Michelle Vieira, I3S,CNRS/UNSA,41 Bd. Napoleon III,06041 Nice, France (France)
Gérard Alengrin, I3S,CNRS/UNSA,41 Bd. Napoleon III,06041 Nice, France (France)

Page (NA) Paper number 1547

Abstract:

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of order and parameters estimation of noisy polynomial-phase signals within a Bayesian framework. As posterior distributions of the parameters are not tractable, MCMC methods are used to simulate them. Efficient model jumping is achieved by proposing model space moves from the conditional density of the polynomial coefficients, estimated with the ``one variable at a time'' Metropolis Hasting algorithm. This algorithm provides simultaneous order and parameters estimation from simulated marginal posterior distributions. Results on simulated data are given and discussed.

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