A neural system to robust Nonlinear optimization subject to disjoint and constrained sets

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel method using artificial neural networks to solve robust parameter estimation problems for nonlinear models with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Semiparametric Estimation of Models for Natural Direct and Indirect Effects

In recent years, researchers in the health and social sciences have become increasingly interested in mediation analysis. Specifically, upon establishing a non-null total effect of an exposure, investigators routinely wish to make inferences about the direct (indirect) pathway of the effect of the exposure not through (through) a mediator variable that occurs subsequently to the exposure and prior to the outcome. Natural direct and indirect effects are of particular interest as they generally combine to produce the total effect of the exposure and therefore provide insight on the mechanism by which it operates to produce the outcome. A semiparametric theory has recently been proposed to make inferences about marginal mean natural direct and indirect effects in observational studies (Tchetgen Tchetgen and Shpitser, 2011), which delivers multiply robust locally efficient estimators of the marginal direct and indirect effects, and thus generalizes previous results for total effects to the mediation setting. In this paper we extend the new theory to handle a setting in which a parametric model for the natural direct (indirect) effect within levels of pre-exposure variables is specified and the model for the observed data likelihood is otherwise unrestricted. We show that estimation is generally not feasible in this model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations, given high-dimensional covariates. We thus consider multiply robust estimation and propose a more general model which assumes a subset but not all of several working models holds.

Road environment modeling using robust perspective analysis and recursive Bayesian segmentation

Recently, vision-based advanced driver-assistance systems (ADAS) have received a new increased interest to enhance driving safety. In particular, due to its high performance–cost ratio, mono-camera systems are arising as the main focus of this field of work. In this paper we present a novel on-board road modeling and vehicle detection system, which is a part of the result of the European I-WAY project. The system relies on a robust estimation of the perspective of the scene, which adapts to the dynamics of the vehicle and generates a stabilized rectified image of the road plane. This rectified plane is used by a recursive Bayesian classi- fier, which classifies pixels as belonging to different classes corresponding to the elements of interest of the scenario. This stage works as an intermediate layer that isolates subsequent modules since it absorbs the inherent variability of the scene. The system has been tested on-road, in different scenarios, including varied illumination and adverse weather conditions, and the results have been proved to be remarkable even for such complex scenarios.

Robust Adaptive Control with Applications to Multi-Agent Systems and Mobile Robotics

This thesis deals with robust adaptive control and its applications, and it is divided into three main parts. The first part is about the design of robust estimation algorithms based on recursive least squares. First, we present an estimator for the frequencies of biased multi-harmonic signals, and then an algorithm for distributed estimation of an unknown parameter over a network of adaptive agents. In the second part of this thesis, we consider a cooperative control problem over uncertain networks of linear systems and Kuramoto systems, in which the agents have to track the reference generated by a leader exosystem. Since the reference signal is not available to each network node, novel distributed observers are designed so as to reconstruct the reference signal locally for each agent, and therefore decentralizing the problem. In the third and final part of this thesis, we consider robust estimation tasks for mobile robotics applications. In particular, we first consider the problem of slip estimation for agricultural tracked vehicles. Then, we consider a search and rescue application in which we need to drive an unmanned aerial vehicle as close as possible to the unknown (and to be estimated) position of a victim, who is buried under the snow after an avalanche event. In this thesis, robustness is intended as an input-to-state stability property of the proposed identifiers (sometimes referred to as adaptive laws), with respect to additive disturbances, and relative to a steady-state trajectory that is associated with a correct estimation of the unknown parameter to be found.

Sistema de visão para percepção e navegação de um UAV Quadrotor

Mestrado em Engenharia Electrotécnica e de Computadores

Interpretation of partial fingermarks using an automated fingerprint identification system

Abstract : In the subject of fingerprints, the rise of computers tools made it possible to create powerful automated search algorithms. These algorithms allow, inter alia, to compare a fingermark to a fingerprint database and therefore to establish a link between the mark and a known source. With the growth of the capacities of these systems and of data storage, as well as increasing collaboration between police services on the international level, the size of these databases increases. The current challenge for the field of fingerprint identification consists of the growth of these databases, which makes it possible to find impressions that are very similar but coming from distinct fingers. However and simultaneously, this data and these systems allow a description of the variability between different impressions from a same finger and between impressions from different fingers. This statistical description of the withinand between-finger variabilities computed on the basis of minutiae and their relative positions can then be utilized in a statistical approach to interpretation. The computation of a likelihood ratio, employing simultaneously the comparison between the mark and the print of the case, the within-variability of the suspects' finger and the between-variability of the mark with respect to a database, can then be based on representative data. Thus, these data allow an evaluation which may be more detailed than that obtained by the application of rules established long before the advent of these large databases or by the specialists experience. The goal of the present thesis is to evaluate likelihood ratios, computed based on the scores of an automated fingerprint identification system when the source of the tested and compared marks is known. These ratios must support the hypothesis which it is known to be true. Moreover, they should support this hypothesis more and more strongly with the addition of information in the form of additional minutiae. For the modeling of within- and between-variability, the necessary data were defined, and acquired for one finger of a first donor, and two fingers of a second donor. The database used for between-variability includes approximately 600000 inked prints. The minimal number of observations necessary for a robust estimation was determined for the two distributions used. Factors which influence these distributions were also analyzed: the number of minutiae included in the configuration and the configuration as such for both distributions, as well as the finger number and the general pattern for between-variability, and the orientation of the minutiae for within-variability. In the present study, the only factor for which no influence has been shown is the orientation of minutiae The results show that the likelihood ratios resulting from the use of the scores of an AFIS can be used for evaluation. Relatively low rates of likelihood ratios supporting the hypothesis known to be false have been obtained. The maximum rate of likelihood ratios supporting the hypothesis that the two impressions were left by the same finger when the impressions came from different fingers obtained is of 5.2 %, for a configuration of 6 minutiae. When a 7th then an 8th minutia are added, this rate lowers to 3.2 %, then to 0.8 %. In parallel, for these same configurations, the likelihood ratios obtained are on average of the order of 100,1000, and 10000 for 6,7 and 8 minutiae when the two impressions come from the same finger. These likelihood ratios can therefore be an important aid for decision making. Both positive evolutions linked to the addition of minutiae (a drop in the rates of likelihood ratios which can lead to an erroneous decision and an increase in the value of the likelihood ratio) were observed in a systematic way within the framework of the study. Approximations based on 3 scores for within-variability and on 10 scores for between-variability were found, and showed satisfactory results. Résumé : Dans le domaine des empreintes digitales, l'essor des outils informatisés a permis de créer de puissants algorithmes de recherche automatique. Ces algorithmes permettent, entre autres, de comparer une trace à une banque de données d'empreintes digitales de source connue. Ainsi, le lien entre la trace et l'une de ces sources peut être établi. Avec la croissance des capacités de ces systèmes, des potentiels de stockage de données, ainsi qu'avec une collaboration accrue au niveau international entre les services de police, la taille des banques de données augmente. Le défi actuel pour le domaine de l'identification par empreintes digitales consiste en la croissance de ces banques de données, qui peut permettre de trouver des impressions très similaires mais provenant de doigts distincts. Toutefois et simultanément, ces données et ces systèmes permettent une description des variabilités entre différentes appositions d'un même doigt, et entre les appositions de différents doigts, basées sur des larges quantités de données. Cette description statistique de l'intra- et de l'intervariabilité calculée à partir des minuties et de leurs positions relatives va s'insérer dans une approche d'interprétation probabiliste. Le calcul d'un rapport de vraisemblance, qui fait intervenir simultanément la comparaison entre la trace et l'empreinte du cas, ainsi que l'intravariabilité du doigt du suspect et l'intervariabilité de la trace par rapport à une banque de données, peut alors se baser sur des jeux de données représentatifs. Ainsi, ces données permettent d'aboutir à une évaluation beaucoup plus fine que celle obtenue par l'application de règles établies bien avant l'avènement de ces grandes banques ou par la seule expérience du spécialiste. L'objectif de la présente thèse est d'évaluer des rapports de vraisemblance calcul és à partir des scores d'un système automatique lorsqu'on connaît la source des traces testées et comparées. Ces rapports doivent soutenir l'hypothèse dont il est connu qu'elle est vraie. De plus, ils devraient soutenir de plus en plus fortement cette hypothèse avec l'ajout d'information sous la forme de minuties additionnelles. Pour la modélisation de l'intra- et l'intervariabilité, les données nécessaires ont été définies, et acquises pour un doigt d'un premier donneur, et deux doigts d'un second donneur. La banque de données utilisée pour l'intervariabilité inclut environ 600000 empreintes encrées. Le nombre minimal d'observations nécessaire pour une estimation robuste a été déterminé pour les deux distributions utilisées. Des facteurs qui influencent ces distributions ont, par la suite, été analysés: le nombre de minuties inclus dans la configuration et la configuration en tant que telle pour les deux distributions, ainsi que le numéro du doigt et le dessin général pour l'intervariabilité, et la orientation des minuties pour l'intravariabilité. Parmi tous ces facteurs, l'orientation des minuties est le seul dont une influence n'a pas été démontrée dans la présente étude. Les résultats montrent que les rapports de vraisemblance issus de l'utilisation des scores de l'AFIS peuvent être utilisés à des fins évaluatifs. Des taux de rapports de vraisemblance relativement bas soutiennent l'hypothèse que l'on sait fausse. Le taux maximal de rapports de vraisemblance soutenant l'hypothèse que les deux impressions aient été laissées par le même doigt alors qu'en réalité les impressions viennent de doigts différents obtenu est de 5.2%, pour une configuration de 6 minuties. Lorsqu'une 7ème puis une 8ème minutie sont ajoutées, ce taux baisse d'abord à 3.2%, puis à 0.8%. Parallèlement, pour ces mêmes configurations, les rapports de vraisemblance sont en moyenne de l'ordre de 100, 1000, et 10000 pour 6, 7 et 8 minuties lorsque les deux impressions proviennent du même doigt. Ces rapports de vraisemblance peuvent donc apporter un soutien important à la prise de décision. Les deux évolutions positives liées à l'ajout de minuties (baisse des taux qui peuvent amener à une décision erronée et augmentation de la valeur du rapport de vraisemblance) ont été observées de façon systématique dans le cadre de l'étude. Des approximations basées sur 3 scores pour l'intravariabilité et sur 10 scores pour l'intervariabilité ont été trouvées, et ont montré des résultats satisfaisants.

Leprosy reactions: the effect of gender and household contacts

Various host-related factors have been reported as relevant risk factors for leprosy reactions. To support a new hypothesis that an antigenic load in local tissues that is sufficient to trigger the immune response may come from an external supply of Mycobacterium leprae organisms, the prevalence of reactional leprosy was assessed against the number of household contacts. The number of contacts was ascertained at diagnosis in leprosy patients coming from an endemic area of Brazil. The prevalence of reactions (patients with reactions/total patients) was fitted by binomial regression and the risk difference (RD) was estimated with a semi-robust estimation of variance as a measure of effect. Five regression models were fitted. Model 1 included only the main exposure variable "number of household contacts"; model 2 included all four explanatory variables ("contacts", "fertile age", "number of skin lesions" and "bacillary index") that were found to be associated with the outcome upon univariate analysis; models 3-5 contained various combinations of three predictors. Male and female patients were analyzed separately. In females, household contacts were a significant predictor for leprosy reactions in model 1 [crude RD = 0.06; 95% confidence interval (CI) = 0.01; 0.12] and model 5 (RD = 0.05; CI = 0.02; 0.09), which included contacts, bacillary index and skin lesions as predictors. Other models were unsatisfactory because the joint presence of fertile age and bacillary index was a likely source of multicollinearity. No significant results were obtained for males. The likely interpretation of our findings might suggest that in female patients, leprosy reactions may be triggered by an external spreading of M. leprae by healthy carrier family members. The small number of observations is an obvious limitation of our study which requires larger confirmatory studies.

Evidence-based Economic Policy - Three Essays in Applied Microeconometrics

Over thirty years ago, Leamer (1983) - among many others - expressed doubts about the quality and usefulness of empirical analyses for the economic profession by stating that "hardly anyone takes data analyses seriously. Or perhaps more accurately, hardly anyone takes anyone else's data analyses seriously" (p.37). Improvements in data quality, more robust estimation methods and the evolution of better research designs seem to make that assertion no longer justifiable (see Angrist and Pischke (2010) for a recent response to Leamer's essay). The economic profes- sion and policy makers alike often rely on empirical evidence as a means to investigate policy relevant questions. The approach of using scientifically rigorous and systematic evidence to identify policies and programs that are capable of improving policy-relevant outcomes is known under the increasingly popular notion of evidence-based policy. Evidence-based economic policy often relies on randomized or quasi-natural experiments in order to identify causal effects of policies. These can require relatively strong assumptions or raise concerns of external validity. In the context of this thesis, potential concerns are for example endogeneity of policy reforms with respect to the business cycle in the first chapter, the trade-off between precision and bias in the regression-discontinuity setting in chapter 2 or non-representativeness of the sample due to self-selection in chapter 3. While the identification strategies are very useful to gain insights into the causal effects of specific policy questions, transforming the evidence into concrete policy conclusions can be challenging. Policy develop- ment should therefore rely on the systematic evidence of a whole body of research on a specific policy question rather than on a single analysis. In this sense, this thesis cannot and should not be viewed as a comprehensive analysis of specific policy issues but rather as a first step towards a better understanding of certain aspects of a policy question. The thesis applies new and innovative identification strategies to policy-relevant and topical questions in the fields of labor economics and behavioral environmental economics. Each chapter relies on a different identification strategy. In the first chapter, we employ a difference- in-differences approach to exploit the quasi-experimental change in the entitlement of the max- imum unemployment benefit duration to identify the medium-run effects of reduced benefit durations on post-unemployment outcomes. Shortening benefit duration carries a double- dividend: It generates fiscal benefits without deteriorating the quality of job-matches. On the contrary, shortened benefit durations improve medium-run earnings and employment possibly through containing the negative effects of skill depreciation or stigmatization. While the first chapter provides only indirect evidence on the underlying behavioral channels, in the second chapter I develop a novel approach that allows to learn about the relative impor- tance of the two key margins of job search - reservation wage choice and search effort. In the framework of a standard non-stationary job search model, I show how the exit rate from un- employment can be decomposed in a way that is informative on reservation wage movements over the unemployment spell. The empirical analysis relies on a sharp discontinuity in unem- ployment benefit entitlement, which can be exploited in a regression-discontinuity approach to identify the effects of extended benefit durations on unemployment and survivor functions. I find evidence that calls for an important role of reservation wage choices for job search be- havior. This can have direct implications for the optimal design of unemployment insurance policies. The third chapter - while thematically detached from the other chapters - addresses one of the major policy challenges of the 21st century: climate change and resource consumption. Many governments have recently put energy efficiency on top of their agendas. While pricing instru- ments aimed at regulating the energy demand have often been found to be short-lived and difficult to enforce politically, the focus of energy conservation programs has shifted towards behavioral approaches - such as provision of information or social norm feedback. The third chapter describes a randomized controlled field experiment in which we discuss the effective- ness of different types of feedback on residential electricity consumption. We find that detailed and real-time feedback caused persistent electricity reductions on the order of 3 to 5 % of daily electricity consumption. Also social norm information can generate substantial electricity sav- ings when designed appropriately. The findings suggest that behavioral approaches constitute effective and relatively cheap way of improving residential energy-efficiency.

Automatic low baseline stereo in urban areas

In this work we propose a new automatic methodology for computing accurate digital elevation models (DEMs) in urban environments from low baseline stereo pairs that shall be available in the future from a new kind of earth observation satellite. This setting makes both views of the scene similarly, thus avoiding occlusions and illumination changes, which are the main disadvantages of the commonly accepted large-baseline configuration. There still remain two crucial technological challenges: (i) precisely estimating DEMs with strong discontinuities and (ii) providing a statistically proven result, automatically. The first one is solved here by a piecewise affine representation that is well adapted to man-made landscapes, whereas the application of computational Gestalt theory introduces reliability and automation. In fact this theory allows us to reduce the number of parameters to be adjusted, and tocontrol the number of false detections. This leads to the selection of a suitable segmentation into affine regions (whenever possible) by a novel and completely automatic perceptual grouping method. It also allows us to discriminate e.g. vegetation-dominated regions, where such an affine model does not apply anda more classical correlation technique should be preferred. In addition we propose here an extension of the classical ”quantized” Gestalt theory to continuous measurements, thus combining its reliability with the precision of variational robust estimation and fine interpolation methods that are necessary in the low baseline case. Such an extension is very general and will be useful for many other applications as well.

Source separation techniques applied to linear prediction

The prediction filters are well known models for signal estimation, in communications, control and many others areas. The classical method for deriving linear prediction coding (LPC) filters is often based on the minimization of a mean square error (MSE). Consequently, second order statistics are only required, but the estimation is only optimal if the residue is independent and identically distributed (iid) Gaussian. In this paper, we derive the ML estimate of the prediction filter. Relationships with robust estimation of auto-regressive (AR) processes, with blind deconvolution and with source separation based on mutual information minimization are then detailed. The algorithm, based on the minimization of a high-order statistics criterion, uses on-line estimation of the residue statistics. Experimental results emphasize on the interest of this approach.

A domain-general perspective on medial frontal brain activity during performance monitoring

Activity of the medial frontal cortex (MFC) has been implicated in attention regulation and performance monitoring. The MFC is thought to generate several event-related potential (ERPs) components, known as medial frontal negativities (MFNs), that are elicited when a behavioural response becomes difficult to control (e.g., following an error or shifting from a frequently executed response). The functional significance of MFNs has traditionally been interpreted in the context of the paradigm used to elicit a specific response, such as errors. In a series of studies, we consider the functional similarity of multiple MFC brain responses by designing novel performance monitoring tasks and exploiting advanced methods for electroencephalography (EEG) signal processing and robust estimation statistics for hypothesis testing. In study 1, we designed a response cueing task and used Independent Component Analysis (ICA) to show that the latent factors describing a MFN to stimuli that cued the potential need to inhibit a response on upcoming trials also accounted for medial frontal brain responses that occurred when individuals made a mistake or inhibited an incorrect response. It was also found that increases in theta occurred to each of these task events, and that the effects were evident at the group level and in single cases. In study 2, we replicated our method of classifying MFC activity to cues in our response task and showed again, using additional tasks, that error commission, response inhibition, and, to a lesser extent, the processing of performance feedback all elicited similar changes across MFNs and theta power. In the final study, we converted our response cueing paradigm into a saccade cueing task in order to examine the oscillatory dynamics of response preparation. We found that, compared to easy pro-saccades, successfully preparing a difficult anti-saccadic response was characterized by an increase in MFC theta and the suppression of posterior alpha power prior to executing the eye movement. These findings align with a large body of literature on performance monitoring and ERPs, and indicate that MFNs, along with their signature in theta power, reflects the general process of controlling attention and adapting behaviour without the need to induce error commission, the inhibition of responses, or the presentation of negative feedback.

Méthodes de rééchantillonnage en méthodologie d'enquête

Le sujet principal de cette thèse porte sur l'étude de l'estimation de la variance d'une statistique basée sur des données d'enquête imputées via le bootstrap (ou la méthode de Cyrano). L'application d'une méthode bootstrap conçue pour des données d'enquête complètes (en absence de non-réponse) en présence de valeurs imputées et faire comme si celles-ci étaient de vraies observations peut conduire à une sous-estimation de la variance. Dans ce contexte, Shao et Sitter (1996) ont introduit une procédure bootstrap dans laquelle la variable étudiée et l'indicateur de réponse sont rééchantillonnés ensemble et les non-répondants bootstrap sont imputés de la même manière qu'est traité l'échantillon original. L'estimation bootstrap de la variance obtenue est valide lorsque la fraction de sondage est faible. Dans le chapitre 1, nous commençons par faire une revue des méthodes bootstrap existantes pour les données d'enquête (complètes et imputées) et les présentons dans un cadre unifié pour la première fois dans la littérature. Dans le chapitre 2, nous introduisons une nouvelle procédure bootstrap pour estimer la variance sous l'approche du modèle de non-réponse lorsque le mécanisme de non-réponse uniforme est présumé. En utilisant seulement les informations sur le taux de réponse, contrairement à Shao et Sitter (1996) qui nécessite l'indicateur de réponse individuelle, l'indicateur de réponse bootstrap est généré pour chaque échantillon bootstrap menant à un estimateur bootstrap de la variance valide même pour les fractions de sondage non-négligeables. Dans le chapitre 3, nous étudions les approches bootstrap par pseudo-population et nous considérons une classe plus générale de mécanismes de non-réponse. Nous développons deux procédures bootstrap par pseudo-population pour estimer la variance d'un estimateur imputé par rapport à l'approche du modèle de non-réponse et à celle du modèle d'imputation. Ces procédures sont également valides même pour des fractions de sondage non-négligeables.

Asymmetries in Business Cycles

Esta disertación busca estudiar los mecanismos de transmisión que vinculan el comportamiento de agentes y firmas con las asimetrías presentes en los ciclos económicos. Para lograr esto, se construyeron tres modelos DSGE. El en primer capítulo, el supuesto de función cuadrática simétrica de ajuste de la inversión fue removido, y el modelo canónico RBC fue reformulado suponiendo que des-invertir es más costoso que invertir una unidad de capital físico. En el segundo capítulo, la contribución más importante de esta disertación es presentada: la construcción de una función de utilidad general que anida aversión a la pérdida, aversión al riesgo y formación de hábitos, por medio de una función de transición suave. La razón para hacerlo así es el hecho de que los individuos son aversos a la pérdidad en recesiones, y son aversos al riesgo en auges. En el tercer capítulo, las asimetrías en los ciclos económicos son analizadas junto con ajuste asimétrico en precios y salarios en un contexto neokeynesiano, con el fin de encontrar una explicación teórica de la bien documentada asimetría presente en la Curva de Phillips.

Demand of children in Colombia : guessing or planning

El artículo analiza los determinantes de la presencia de hijos no deseados en Colombia. Se utiliza la información de la Encuesta Nacional de Demografía y Salud (ENDS, 2005), específicamente para las mujeres de 40 años o más. Dadas las características especiales de la variable que se analiza, se utilizan modelos de conteo para verificar si determinadas características socioeconómicas como la educación o el estrato económico explican la presencia de hijos no deseados. Se encuentra que la educación de la mujer y el área de residencia son determinantes significativos de los nacimientos no planeados. Además, la relación negativa entre el número de hijos no deseados y la educación de la mujer arroja implicaciones clave en materia de política social.

A proposal to estimate the motion of an underwater vehicle through visual mosaicking

This thesis proposes a solution to the problem of estimating the motion of an Unmanned Underwater Vehicle (UUV). Our approach is based on the integration of the incremental measurements which are provided by a vision system. When the vehicle is close to the underwater terrain, it constructs a visual map (so called "mosaic") of the area where the mission takes place while, at the same time, it localizes itself on this map, following the Concurrent Mapping and Localization strategy. The proposed methodology to achieve this goal is based on a feature-based mosaicking algorithm. A down-looking camera is attached to the underwater vehicle. As the vehicle moves, a sequence of images of the sea-floor is acquired by the camera. For every image of the sequence, a set of characteristic features is detected by means of a corner detector. Then, their correspondences are found in the next image of the sequence. Solving the correspondence problem in an accurate and reliable way is a difficult task in computer vision. We consider different alternatives to solve this problem by introducing a detailed analysis of the textural characteristics of the image. This is done in two phases: first comparing different texture operators individually, and next selecting those that best characterize the point/matching pair and using them together to obtain a more robust characterization. Various alternatives are also studied to merge the information provided by the individual texture operators. Finally, the best approach in terms of robustness and efficiency is proposed. After the correspondences have been solved, for every pair of consecutive images we obtain a list of image features in the first image and their matchings in the next frame. Our aim is now to recover the apparent motion of the camera from these features. Although an accurate texture analysis is devoted to the matching pro-cedure, some false matches (known as outliers) could still appear among the right correspon-dences. For this reason, a robust estimation technique is used to estimate the planar transformation (homography) which explains the dominant motion of the image. Next, this homography is used to warp the processed image to the common mosaic frame, constructing a composite image formed by every frame of the sequence. With the aim of estimating the position of the vehicle as the mosaic is being constructed, the 3D motion of the vehicle can be computed from the measurements obtained by a sonar altimeter and the incremental motion computed from the homography. Unfortunately, as the mosaic increases in size, image local alignment errors increase the inaccuracies associated to the position of the vehicle. Occasionally, the trajectory described by the vehicle may cross over itself. In this situation new information is available, and the system can readjust the position estimates. Our proposal consists not only in localizing the vehicle, but also in readjusting the trajectory described by the vehicle when crossover information is obtained. This is achieved by implementing an Augmented State Kalman Filter (ASKF). Kalman filtering appears as an adequate framework to deal with position estimates and their associated covariances. Finally, some experimental results are shown. A laboratory setup has been used to analyze and evaluate the accuracy of the mosaicking system. This setup enables a quantitative measurement of the accumulated errors of the mosaics created in the lab. Then, the results obtained from real sea trials using the URIS underwater vehicle are shown.