Petr Tichavský

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A mean-square error lower bound for the discretetime nonlinear filtering problem is derived based on the Van Trees (posterior) version of the Cramér–Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular(More)
FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by(More)
We propose a new low-complexity approximate joint diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted least-squares (WLS) AJD criterion. Often in blind source separation (BSS), when the sources are nearly separated, the optimal weight matrix for WLS-based AJD takes a (nearly) block-diagonal form.(More)
The problem of estimating the angles of arrival of M plane waves incident simultaneously on a line array with L > M sensors utilizing the special eigenstructure of the covariance matrix R of the signal plus noise at the output of the array is considered. The asymptotical analysis of the two most popular— MUSIC and Minimum-Norm— methods following the paper(More)
The FastICA or fixed point algorithm is one of the most successful algorithms for linear independent component analysis (ICA) in terms of accuracy and computational complexity. Two versions of the algorithm are available in literature and software: a one-unit (deflation) algorithm and a symmetric algorithm. The main result of this paper are analytic closed(More)
Blind inversion of a linear and instantaneous mixture of source signals is a problem often encountered in many signal processing applications. Efficient fastICA (EFICA) offers an asymptotically optimal solution to this problem when all of the sources obey a generalized Gaussian distribution, at most one of them is Gaussian, and each is independent and(More)
This paper introduces a new underwater acoustic eigenstructure ESPRIT-based algorithm that yields closed-form direction-of-arrival (DOA) estimates using a single vector hydrophone. A vector hydrophone is composed of two or three spatially co-located but orthogonally oriented velocity hydrophones plus another optional co-located pressure hydrophone. This(More)
CANDECOMP/PARAFAC (CP) has found numerous applications in wide variety of areas such as in chemometrics, telecommunication, data mining, neuroscience, separated representations. For an order- N tensor, most CP algorithms can be computationally demanding due to computation of gradients which are related to products between tensor unfoldings and Khatri-Rao(More)
The problem of adaptive parameter estimation for a single nonstationary noisy cisoid, where the sinusoidal frequency evolves according to Gaussian random walks, is studied. The lower hound on the minimum mean-square estimation error, which was derived by van Trees, is evaluated for the problem. It is shown that two estimation methods attain this lower bound.