Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors

The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts and chirps from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps with an arbitrary phase/frequency vs. time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting/spinning sources. We expect quasi-periodic nature of the waveform to be preserved independent of the physics which governs the source motion. Several methods have been introduced to address the detection of unmodeled chirps using the data of a single detector. Those include the best chirplet chain (BCC) algorithm introduced by the authors. In the next years, several detectors will be in operation. The joint coherent analysis of GW by multiple detectors can improve the sight horizon, the estimation of the source location and the wave polarization angles. Here, we extend the BCC search to the multiple detector case. The method amounts to searching for salient paths in the combined time-frequency representation of two synthetic streams. The latter are time-series which combine the data from each detector linearly in such a way that all the GW signatures received are added constructively. We give a proof of principle for the full sky blind search in a simplified situation which shows that the joint estimation of the source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure

Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations

Modeling and estimation of ambiguities in linear arrays

Published versio

Essays on Artefactual and Virtual Field Experiments in Choice Under Uncertainty

In the area of transportation policy, congestion pricing has been used to alleviate traffic congestion in metropolitan areas. The focus of Chapter 1 is to examine drivers’ perceived risk of traffic delay as one determinant of reactions to congestion pricing. The experiment reported in this essay recruits commuters from the Atlanta and Orlando metropolitan areas to participate in a naturalistic experiment where they are asked to make repeated route decisions in a driving simulator. Chapter 1 examines belief formation and adjustments under an endogenous information environment where information about a route can be obtained only conditional on taking the route. If the subjects arrive to the destination late, i.e. beyond an assigned time threshold, they are faced with a discrete (flat) penalty. In contrast, Chapter 2 examines subjective beliefs in a setting where the penalty for a late arrival is continuous, such that a longer delay incurs additional penalty on the driver. The primary research question is: does belief formation differ when the late penalty is induced as a continuous amount compared to when it is induced as a discrete amount? In particular, will we observe a difference in learning across the range of congestion probabilities under different penalty settings? In the continuous penalty setting, we do not observe a difference in learning across the range of congestion probabilities. In contrast, in the discrete penalty setting we observe significant belief adjustments in the lowest congestion risk scenario. In Chapter 3 the “source method” is used to examine how uncertainty aversion differs across events that have the same underlying objective probabilities but are presented under varying degrees of uncertainty. Subjects are presented with three lottery tasks that rank in order of increasing uncertainty. Given the choices observed in each task a source function is estimated jointly with risk attitudes under different probability weighting specifications of the source function. Results from the Prelec probability weighting suggest that, as the degree of uncertainty increases, subjects display increased pessimism; in contrast, the Tversky-Kahneman (1992) and the Power probability weightings detect no such difference. Thus, the conclusion regarding uncertainty aversion are contingent on which probability weighting specification is assumed for the source function

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

Investigative study of planar array ambiguities based on "hyperhelical" parameterization

Published versio

Array communications in wireless sensor networks

Imperial Users onl