Shapes and Shears, Stars and Smears: Optimal Measurements for Weak Lensing

We present the theoretical and analytical bases of optimal techniques to measure weak gravitational shear from images of galaxies. We first characterize the geometric space of shears and ellipticity, then use this geometric interpretation to analyse images. The steps of this analysis include: measurement of object shapes on images, combining measurements of a given galaxy on different images, estimating the underlying shear from an ensemble of galaxy shapes, and compensating for the systematic effects of image distortion, bias from PSF asymmetries, and `"dilution" of the signal by the seeing. These methods minimize the ellipticity measurement noise, provide calculable shear uncertainty estimates, and allow removal of systematic contamination by PSF effects to arbitrary precision. Galaxy images and PSFs are decomposed into a family of orthogonal 2d Gaussian-based functions, making the PSF correction and shape measurement relatively straightforward and computationally efficient. We also discuss sources of noise-induced bias in weak lensing measurements and provide a solution for these and previously identified biases.Comment: Version accepted to AJ. Minor fixes, plus a simpler method of shape weighting. Version with full vector figures available via http://www.astro.lsa.umich.edu/users/garyb/PUBLICATIONS

Calculation of Weighted Geometric Dilution of Precision

To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP), instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS) devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN) and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error

Acoustic Source Localization by Fusing Distributed Microphone Arrays Measurements

Publication in the conference proceedings of EUSIPCO, Lausanne, Switzerland, 200

NOSS/ALDCS analysis and system requirements definition

The results of system analyses and implementation studies of an advanced location and data collection system (ALDCS) , proposed for inclusion on the National Oceanic Satellite System (NOSS) spacecraft are reported. The system applies Doppler processing and radiofrequency interferometer position location technqiues both alone and in combination. Aspects analyzed include: the constraints imposed by random access to the system by platforms, the RF link parameters, geometric concepts of position and velocity estimation by the two techniques considered, and the effects of electrical measurement errors, spacecraft attitude errors, and geometric parameters on estimation accuracy. Hardware techniques and trade-offs for interferometric phase measurement, ambiguity resolution and calibration are considered. A combined Doppler-interferometer ALDCS intended to fulfill the NOSS data validation and oceanic research support mission is also described

Design Issues for Generalized Linear Models: A Review

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimization of anchor nodes placement in wireless localization networks

This work focuses on optimizing node placement for time-of-flight-based wireless localization networks. Main motivation are critical safety applications. The first part of my thesis is an experimental study on in-tunnel vehicle localization. In- tunnel localization of vehicles is crucial for emergency management, especially for large trucks transporting dangerous goods such as inflammable chemicals. Compared to open roads, evacuation in tunnels is much more difficult, so that fire or other accidents can cause much more damage. We provide distance measurement error characterization inside road tunnels focusing on time of flight measurements. We design a complete system for in-tunnel radio frequency time-of- flight-based localization and show that such a system is feasible and accurate, and that few nodes are sufficient to cover the entire tunnel. The second part of my work focuses on anchor nodes placement optimization for time-of-flight-based localization networks where multilateration is used to obtain the target position based on its distances from fixed and known anchors. Our main motivation are safety at work applications, in particular, environments such as factory halls. Our goal is to minimize the number of anchors needed to localize the target while keeping the localization uncertainty lower than a given threshold in an area of arbitrary shape with obstacles. Our propagation model accounts for the presence of line of sight between nodes, while geometric dilution of precision is used to express the localization error introduced by multilateration. We propose several integer linear programming formulations for this problem that can be used to obtain optimal solutions to instances of reasonable sizes and compare them in terms of execution times by simulation experiments. We extend our approach to address fault tolerance, ensuring that the target can still be localized after any one of the nodes fails. Two dimensional localization is sufficient for most indoor applications. However, for those industrial environments where the ceiling is very high and the worker might be climbing or be lifted from the ground, or if very high localization precision is needed, three-dimensional localization may be required. Therefore, we extend our approach to three-dimensional localization. We derive the expression for geometric dilution of precision for 3D multilateration and give its geometric interpretation. To tackle problem instances of large size, we propose two novel heuristics: greedy placement with pruning, and its improved version, greedy placement with iterative pruning. We create a simulator to test and compare all our proposed approaches by generating multiple test instances. For anchor placement for multilateration-based localization, we obtain solutions with below 2% anchors overhead with respect to the optimum on average, with around 5s average execution time for 130 candidate positions. For the fault-tolerant version of the same problem, we obtain solutions of around 1% number of anchors overhead with respect to the optimum on average, with 0.4s execution time for 65 candidate positions, by using greedy heuristic with pruning. For 3D placement, the greedy heuristic with iterative pruning produced results of 0.05% of optimum on average, with average execution time of around 6s for 250 candidate positions, for the problem instances we tested

A novel satellite mission concept for upper air water vapour, aerosol and cloud observations using integrated path differential absorption LiDAR limb sounding

We propose a new satellite mission to deliver high quality measurements of upper air water vapour. The concept centres around a LiDAR in limb sounding by occultation geometry, designed to operate as a very long path system for differential absorption measurements. We present a preliminary performance analysis with a system sized to send 75 mJ pulses at 25 Hz at four wavelengths close to 935 nm, to up to 5 microsatellites in a counter-rotating orbit, carrying retroreflectors characterized by a reflected beam divergence of roughly twice the emitted laser beam divergence of 15 µrad. This provides water vapour profiles with a vertical sampling of 110 m; preliminary calculations suggest that the system could detect concentrations of less than 5 ppm. A secondary payload of a fairly conventional medium resolution multispectral radiometer allows wide-swath cloud and aerosol imaging. The total weight and power of the system are estimated at 3 tons and 2,700 W respectively. This novel concept presents significant challenges, including the performance of the lasers in space, the tracking between the main spacecraft and the retroreflectors, the refractive effects of turbulence, and the design of the telescopes to achieve a high signal-to-noise ratio for the high precision measurements. The mission concept was conceived at the Alpbach Summer School 2010

Optimization of positioning capabilities in wireless sensor networks : from power efficiency to medium access

In Wireless Sensor Networks (WSN), the ability of sensor nodes to know its position is an enabler for a wide variety of applications for monitoring, control, and automation. Often, sensor data is meaningful only if its position can be determined. Many WSN are deployed indoors or in areas where Global Navigation Satellite System (GNSS) signal coverage is not available, and thus GNSS positioning cannot be guaranteed. In these scenarios, WSN may be relied upon to achieve a satisfactory degree of positioning accuracy. Typically, batteries power sensor nodes in WSN. These batteries are costly to replace. Therefore, power consumption is an important aspect, being performance and lifetime of WSN strongly relying on the ability to reduce it. It is crucial to design effective strategies to maximize battery lifetime. Optimization of power consumption can be made at different layers. For example, at the physical layer, power control and resource optimization may play an important role, as well as at higher layers through network topology and MAC protocols. The objective of this Thesis is to study the optimization of resources in WSN that are employed for positioning purposes, with the ultimate goal being the minimization of power consumption. We focus on anchor-based positioning, where a subset of the WSN nodes know their location (anchors) and send ranging signals to nodes with unknown position (targets) to assist them in estimating it through distance-related measurements. Two well known of such measurements are received signal strength (RSS) and time of arrival (TOA), in which this Thesis focuses. In order to minimize power consumption while providing a certain quality of positioning service, in this dissertation we research on the problems of power control and node selection. Aiming at a distributed implementation of the proposed techniques, we resort to the tools of non-cooperative game theory. First, transmit power allocation is addressed for RSS based ranging. Using game theory formulation, we develop a potential game leading to an iterated best response algorithm with sure convergence. As a performance metric, we introduce the geometric dilution of precision (GDOP), which is shown to help achieving a suitable geometry of the selected anchor nodes. The proposed scheme and relative distributed algorithms provide good equilibrium performance in both static and dynamic scenarios. Moreover, we present a distributed, low complexity implementation and analyze it in terms of computational complexity. Results show that performance close to that of exhaustive search is possible. We then address the transmit power allocation problem for TOA based ranging, also resorting to a game theoretic formulation. In this setup, and also considering GDOP as performance metric, a supermodular game formulation is proposed, along with a distributed algorithm with guaranteed convergence to a unique solution, based on iterated best response. We analyze the proposed algorithm in terms of the price of anarchy (PoA), that is, compared to a centralized optimum solution, and shown to have a moderate performance loss. Finally, this dissertation addresses the effect of different MAC protocols and topologies in the positioning performance. In this direction, we study the performance of mesh and cluster-tree topologies defined in WSN standards. Different topologies place different constraints in network connectivity, having a substantial impact on the performance of positioning algorithms. While mesh topology allows high connectivity with large energy consumption, cluster-tree topologies are more energy efficient but suffer from reduced connectivity and poor positioning performance. In order to improve the performance of cluster-tree topologies, we propose a cluster formation algorithm. It significantly improves connectivity with anchor nodes, achieving vastly improved positioning performance.En les xarxes de sensors sense fils (WSN), l'habilitat dels nodes sensors per conèixer la seva posició facilita una gran varietat d'aplicacions per la monitorització, el control i l'automatització. Així, les dades que proporciona un sensor tenen sentit només si la posició pot ésser determinada. Moltes WSN són desplegades en interiors o en àrees on la senyal de sistemes globals de navegació per satèl.lit (GNSS) no té prou cobertura, i per tant, el posicionament basat en GNSS no pot ésser garantitzat. En aquests escenaris, les WSN poden proporcionar una bona precisió en posicionament. Normalment, en WSN els nodes són alimentats amb bateries. Aquestes bateries són difícils de reemplaçar. Per tant, el consum de potència és un aspecte important i és crucial dissenyar estratègies efectives per maximitzar el temps de vida de la bateria. L'optimització del consum de potència pot ser fet a diferents capes del protocol. Per exemple, en la capa física, el control de potència i l'optimització dels recursos juguen un rol important, igualment que la topologia de xarxa i els protocols MAC en les capes més altes. L'objectiu d'aquesta tesi és estudiar l¿optimització de recursos en WSN que s'utilitzen per fer posicionament, amb el propòsit de minimitzar el consum de potència. Ens focalitzem en el posicionament basat en àncora, en el qual un conjunt de nodes coneixen la seva localització (nodes àncora) i envien missatges als nodes que no saben la seva posició per ajudar-los a estimar les seves coordenades amb mesures de distància. Dues classes de mesures són la potència de la senyal rebuda (RSS) i el temps d'arribada (TOA) en les quals aquesta tesi està focalitzada. Per minimitzar el consum de potència mentre que es proporciona suficient qualitat en el posicionament, en aquesta tesi estudiem els problemes de control de potència i selecció de nodes. Tenint en compte una implementació distribuïda de les tècniques proposades, utilitzem eïnes de teoria de jocs no cooperatius. Primer, l'assignació de potència transmesa és abordada pel càlcul de la distància amb RSS. Utilitzant la teoria de jocs, desenvolupem un joc potencial que convergeix amb un algoritme iteratiu basat en millor resposta (best response). Com a mètrica d'error, introduïm la dilució de la precisió geomètrica (GDOP) que mostra quant d'apropiada és la geometria dels nodes àncora seleccionats. L'esquema proposat i els algoritmes distribuïts proporcionen una bona resolució de l'equilibri en l'escenari estàtic i dinàmic. Altrament, presentem una implementació distribuïda i analitzem la seva complexitat computacional. Els resultats obtinguts són similars als obtinguts amb un algoritme de cerca exhaustiva. El problema d'assignació de la potència transmesa en el càlcul de la distància basat en TOA, també és tractat amb teoria de jocs. En aquest cas, considerant el GDOP com a mètrica d'error, proposem un joc supermodular juntament amb un algoritme distribuït basat en millor resposta amb convergència garantida cap a una única solució. Analitzem la solució proposada amb el preu de l'anarquia (PoA), és a dir, es compara la nostra solució amb una solució òptima centralitzada mostrant que les pèrdues són moderades. Finalment, aquesta tesi tracta l'efecte que causen diferents protocols MAC i topologies en el posicionament. En aquesta direcció, estudiem les topologies de malla i arbre formant clusters (cluster-tree) que estan definides als estàndards de les WSN. La diferència entre les topologies crea diferents restriccions en la connectivitat de la xarxa, afectant els resultats de posicionament. La topologia de malla permet una elevada connectivitat entre els nodes amb gran consum d'energia, mentre que les topologies d'arbre són més energèticament eficients però amb baixa connectivitat entre els nodes i baix rendiment pel posicionament. Per millorar la qualitat del posicionament en les topologies d'arbre, proposem un algoritme de formació de clústers.Postprint (published version