Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error (MSE) of subspace-based estimators is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations.Comment: 18 pages, 5 figures, submitted for publication in IEEE Transactions on Signal Processin

Measurement of acoustic properties of South Pole ice for neutrino astronomy

South Pole ice is predicted to be the best medium for acoustic neutrino detection. Moreover, ice is the only medium in which all three dense-medium detection methods (optical, radio, and acoustic) can be used to monitor the same interaction volume. Events detected in coincidence between two methods allow significant background rejection confidence, which is necessary to study rare GZK neutrinos. In 2007 and 2008 the South Pole Acoustic Test Setup (SPATS) was installed as a research and development project associated with the IceCube experiment. The purpose of SPATS is to measure the acoustic ice properties at the South Pole in order to determine the feasibility of a future large hybrid array. The deployment and performance of SPATS are described, as are first results and work in progress on the sound speed, background noise, and attenuation.Comment: 8 pages, 6 figures, 1 table, uses elsart5p.cls, to appear in the proceedings of the Acoustic and Radio EeV Neutrino detection Activities (ARENA) 2008 conferenc

Managing uncertainty in sound based control for an autonomous helicopter

In this paper we present our ongoing research using a multi-purpose, small and low cost autonomous helicopter platform (Flyper ). We are building on previously achieved stable control using evolutionary tuning. We propose a sound based supervised method to localise the indoor helicopter and extract meaningful information to enable the helicopter to further stabilise its flight and correct its flightpath. Due to the high amount of uncertainty in the data, we propose the use of fuzzy logic in the signal processing of the sound signature. We discuss the benefits and difficulties using type-1 and type-2 fuzzy logic in this real-time systems and give an overview of our proposed system

R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6 figure

Estimation of the Number of Sources in Unbalanced Arrays via Information Theoretic Criteria

Estimating the number of sources impinging on an array of sensors is a well known and well investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and non-robust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator, and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multi-dimensional searches. In this paper, motivated by real life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multi-dimensional searches is presented as well, making this estimator a favorable choice for practical applications.Comment: To appear in the IEEE Transactions on Signal Processin

A feasibility study for measuring stratospheric turbulence using metrac positioning system

The feasibility of obtaining measurements of Lagrangian turbulence at stratospheric altitudes is demonstrated by using the METRAC System to track constant-level balloons. The basis for current estimates of diffusion coefficients are reviewed and it is pointed out that insufficient data is available upon which to base reliable estimates of vertical diffusion coefficients. It is concluded that diffusion coefficients could be directly obtained from Lagrangian turbulence measurements. The METRAC balloon tracking system is shown to possess the necessary precision in order to resolve the response of constant-level balloons to turbulence at stratospheric altitudes. A small sample of data recorded from a tropospheric tetroon flight tracked by the METRAC System is analyzed to obtain estimates of small-scale three-dimensional diffusion coefficients. It is recommended that this technique be employed to establish a climatology of diffusion coefficients and to ascertain the variation of these coefficients with altitude, season, and latitude