14,848 research outputs found
Structured least squares with bounded data uncertainties
In many signal processing applications the core problem reduces to a linear system of equations. Coefficient matrix uncertainties create a significant challenge in obtaining reliable solutions. In this paper, we present a novel formulation for solving a system of noise contaminated linear equations while preserving the structure of the coefficient matrix. The proposed method has advantages over the known Structured Total Least Squares (STLS) techniques in utilizing additional information about the uncertainties and robustness in ill-posed problems. Numerical comparisons are given to illustrate these advantages in two applications: signal restoration problem with an uncertain model and frequency estimation of multiple sinusoids embedded in white noise. ©2009 IEEE
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An LFT/SDP approach to the uncertainty analysis for state
A state estimator is an algorithm that computes the current state of a time-varying system from on-line measurements. Physical quantities such as measurements and parameters are characterised by uncertainty. Understanding how uncertainty affects the accuracy of state estimates is therefore a pre-requisite to the application of such techniques to real systems. In this paper we develop a method of uncertainty analysis based on linear fractional transformations (LFT) and obtain ellipsoid-of-confidence bounds by recasting the LFT problem into a semidefinite programming problem (SDP). The ideas are illustrated by applying them to a simple water distribution network
Probabilistic Combination of Noisy Points and Planes for RGB-D Odometry
This work proposes a visual odometry method that combines points and plane
primitives, extracted from a noisy depth camera. Depth measurement uncertainty
is modelled and propagated through the extraction of geometric primitives to
the frame-to-frame motion estimation, where pose is optimized by weighting the
residuals of 3D point and planes matches, according to their uncertainties.
Results on an RGB-D dataset show that the combination of points and planes,
through the proposed method, is able to perform well in poorly textured
environments, where point-based odometry is bound to fail.Comment: Accepted to TAROS 201
A unified framework for solving a general class of conditional and robust set-membership estimation problems
In this paper we present a unified framework for solving a general class of
problems arising in the context of set-membership estimation/identification
theory. More precisely, the paper aims at providing an original approach for
the computation of optimal conditional and robust projection estimates in a
nonlinear estimation setting where the operator relating the data and the
parameter to be estimated is assumed to be a generic multivariate polynomial
function and the uncertainties affecting the data are assumed to belong to
semialgebraic sets. By noticing that the computation of both the conditional
and the robust projection optimal estimators requires the solution to min-max
optimization problems that share the same structure, we propose a unified
two-stage approach based on semidefinite-relaxation techniques for solving such
estimation problems. The key idea of the proposed procedure is to recognize
that the optimal functional of the inner optimization problems can be
approximated to any desired precision by a multivariate polynomial function by
suitably exploiting recently proposed results in the field of parametric
optimization. Two simulation examples are reported to show the effectiveness of
the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic
Control (2014
Assessment of uncertainties in hot-wire anemometry and oil-film interferometry measurements for wall-bounded turbulent flows
In this study, the sources of uncertainty of hot-wire anemometry (HWA) and
oil-film interferometry (OFI) measurements are assessed. Both statistical and
classical methods are used for the forward and inverse problems, so that the
contributions to the overall uncertainty of the measured quantities can be
evaluated. The correlations between the parameters are taken into account
through the Bayesian inference with error-in-variable (EiV) model. In the
forward problem, very small differences were found when using Monte Carlo (MC),
Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow
velocity measurements with HWA, the results indicate that the estimated
uncertainty is lower when the correlations among parameters are considered,
than when they are not taken into account. Moreover, global sensitivity
analyses with Sobol indices showed that the HWA measurements are most sensitive
to the wire voltage, and in the case of OFI the most sensitive factor is the
calculation of fringe velocity. The relative errors in wall-shear stress,
friction velocity and viscous length are 0.44%, 0.23% and 0.22%, respectively.
Note that these values are lower than the ones reported in other wall-bounded
turbulence studies. Note that in most studies of wall-bounded turbulence the
correlations among parameters are not considered, and the uncertainties from
the various parameters are directly added when determining the overall
uncertainty of the measured quantity. In the present analysis we account for
these correlations, which may lead to a lower overall uncertainty estimate due
to error cancellation. Furthermore, our results also indicate that the crucial
aspect when obtaining accurate inner-scaled velocity measurements is the
wind-tunnel flow quality, which is more critical than the accuracy in
wall-shear stress measurements
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