186 research outputs found
Minimum mean square distance estimation of a subspace
We consider the problem of subspace estimation in a Bayesian setting. Since
we are operating in the Grassmann manifold, the usual approach which consists
of minimizing the mean square error (MSE) between the true subspace and its
estimate may not be adequate as the MSE is not the natural metric in
the Grassmann manifold. As an alternative, we propose to carry out subspace
estimation by minimizing the mean square distance (MSD) between and its
estimate, where the considered distance is a natural metric in the Grassmann
manifold, viz. the distance between the projection matrices. We show that the
resulting estimator is no longer the posterior mean of but entails
computing the principal eigenvectors of the posterior mean of .
Derivation of the MMSD estimator is carried out in a few illustrative examples
including a linear Gaussian model for the data and a Bingham or von Mises
Fisher prior distribution for . In all scenarios, posterior distributions
are derived and the MMSD estimator is obtained either analytically or
implemented via a Markov chain Monte Carlo simulation method. The method is
shown to provide accurate estimates even when the number of samples is lower
than the dimension of . An application to hyperspectral imagery is finally
investigated
The impact of noise on detecting the arrival angle using the root-WSF algorithm
This article discusses three standards of Wi-Fi: traditional, current and next-generation Wi-Fi. These standards have been tested for their ability to detect the arrival angle of a noisy system. In this study, we chose to work with an intelligent system whose noise becomes more and more important to detect the desired angle of arrival. However, the use of the weighted subspace fitting (WSF) algorithm was able to detect all angles even for the 5th generation Wi-Fi without any problem, and therefore proved its robustness against noise
Direction of arrival estimation in a mixture of K-distributed and Gaussian noise
We address the problem of estimating the directions-of-arrival (DoAs) of multiple signals received in the presence of a combination of a strong compound-Gaussian external noise and weak internal white Gaussian noise. Since the exact distribution of the mixture is not known, we get an insight into optimum procedure via a related model where we consider the texture of the compound-Gaussian component as an unknown and deterministic quantity to be estimated together with DoAs or a basis of the signal subspace. Alternate maximization of the likelihood function is conducted and it is shown that it operates a separation between the snapshots with small/large texture values with respect to the additive noise power. The modified Cramér-Rao bound is derived and a prediction of the actual mean-square error is presented, based on separation between external/internal-noise dominated samples. Numerical simulations indicate that the suggested iterative DoA estimation technique comes close to the introduced bound and outperform a number of existing routines
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