Bootstrap signal processing: doing the impossible?

Classical signal processing techniques are developed under prior statistical knowledge of the kind of data we are processing. Unfortunately, one does not know too much about reality in practice, therefore inferring information about the statistical behaviour of our data is needed in addition of processing. To properly infer information about the statistics, one may need more than one realization of the experiment, although this is not possible in some real-life environments, as one may have just a single realization of the random process or low amount of available samples. If one would like to tackle both issues at once using classical signal processing approaches, it may lead to an almost impossible problem. This is where Bootstrap statistical inference shines, which suits perfectly this kind of problems. Moreover, we want to fuse all available data, which comes from different sources, to improve our knowledge of the working environment and eventual accuracy in further operations, such as estimating some parameter. However, there is a risk of fusing too much corrupted data without taking into account how contaminated a data set is, so the integrity of the final estimation gets compromised. We will still consider small amount of data available to tackle this issue. In reponse to the mentioned problems, the purpose of this project is to explore and analyze the potentials of the Bootstrap techniques. In particular, we will focus on the issues of data integrity and getting benefits from data redundancy in Precise Point Positioning receivers, whose context suits perfectly this kind of framework. Las técnicas clásicas de procesamiento de señales se desarrollan a partir de conocimiento a priori de los datos que procesamos. Desgraciadamente, en la práctica uno puede desconocer este conocimiento a priori, entonces, tenemos la necesidad de inferir información del comportamiento estadístico de los datos, además del propio procesamiento. Para inferir de manera precisa, es necesaria más de una realización del experimento, pero es posible que el entorno de estudio no nos lo permita o haya datos insuficientes. Si se intentase resolver este problema usando técnicas clásicas, uno es podría encontrar un problema casi imposible. Aquí es donde las técnicas Bootstrap brillan, puesto que se adaptan muy bien a este tipo de problemas. Además del problema mencionado, también queremos fusionar todas los posibles fuentes de información, para mejorar el conocimiento que disponemos d