A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Transmission delays in residual computation

The design of control, estimation or diagnosis algorithms most often assumes that all available process variables represent the system state at the same instant of time. However, this is never true in current network systems, because of the unknown deterministic or stochastic transmission delays introduced by the communication network. During the diagnosing stage, this will often generate false alarms. Under nominal operation, the different transmission delays associated with the variables that appear in the computation form produce discrepancies of the residuals from zero. A technique aiming at the minimisation of the resulting false alarms rate, that is based on the explicit modelling of communication delays and on their best-case estimation is proposed

Estimació mètrica. Factors determinats de la capacitat intuïtiva. Una proposta didàctica pel seu aprenentatge

Objectius de l'estudi: - Determinar els factors i característiques que configuren la capacitat estimativa i la intuïció mètrica. - Conèixer el procés genètic de la capacitació estimativa. - Potenciar la intuïció matemàtica com a nivell d’alta competència matemàtica i la necessitat del seu aprenentatge. - Dissenyar propostes didàctiques que ajudi a potenciar la capacitat estimativa

Efficient topology estimation for large scale optical mapping

Large scale image mosaicing methods are in great demand among scientists who study different aspects of the seabed, and have been fostered by impressive advances in the capabilities of underwater robots in gathering optical data from the seafloor. Cost and weight constraints mean that lowcost Remotely operated vehicles (ROVs) usually have a very limited number of sensors. When a low-cost robot carries out a seafloor survey using a down-looking camera, it usually follows a predetermined trajectory that provides several non time-consecutive overlapping image pairs. Finding these pairs (a process known as topology estimation) is indispensable to obtaining globally consistent mosaics and accurate trajectory estimates, which are necessary for a global view of the surveyed area, especially when optical sensors are the only data source. This thesis presents a set of consistent methods aimed at creating large area image mosaics from optical data obtained during surveys with low-cost underwater vehicles. First, a global alignment method developed within a Feature-based image mosaicing (FIM) framework, where nonlinear minimisation is substituted by two linear steps, is discussed. Then, a simple four-point mosaic rectifying method is proposed to reduce distortions that might occur due to lens distortions, error accumulation and the difficulties of optical imaging in an underwater medium. The topology estimation problem is addressed by means of an augmented state and extended Kalman filter combined framework, aimed at minimising the total number of matching attempts and simultaneously obtaining the best possible trajectory. Potential image pairs are predicted by taking into account the uncertainty in the trajectory. The contribution of matching an image pair is investigated using information theory principles. Lastly, a different solution to the topology estimation problem is proposed in a bundle adjustment framework. Innovative aspects include the use of fast image similarity criterion combined with a Minimum spanning tree (MST) solution, to obtain a tentative topology. This topology is improved by attempting image matching with the pairs for which there is the most overlap evidence. Unlike previous approaches for large-area mosaicing, our framework is able to deal naturally with cases where time-consecutive images cannot be matched successfully, such as completely unordered sets. Finally, the efficiency of the proposed methods is discussed and a comparison made with other state-of-the-art approaches, using a series of challenging datasets in underwater scenarios