This thesis explores suitable methodological frameworks for modelling geographical hierarchical data sets by bringing together spatial and multilevel modelling approaches. The primary reason is that for a geographically hierarchical data, two types of dependence effect are expected: the spatial dependence arising from the geographical proximity and the membership based group dependence effect. Three different frameworks are proposed in this study. First, in terms of extending the Geographically Weighted Regression (GWR) model to accommodate a hierarchical data structure, a contextualised GWR is developed. The contextual information is incorporated into a GWR model by adjusting the geographical weights matrix to measure proximity not only in terms of distance but also with respect to an attribute space defined by measures of each observation's neighbourhood. Next, by integrating spatial econometric and multilevel modelling approaches, this study develops a hierarchical spatial autoregressive model (HSAR) that allows for simultaneously modelling the group dependence effect and the spatial interaction effect at each level of the data hierarchy. A series of Monte Carlo simulation studies show that the HSAR model performs well in terms of retrieving the true model parameters accurately. In contrast, both the classic spatial econometric and multilevel models perform poorly in the presence of both spatial interactions and group dependence. Finally, turning to a usual two-level hierarchical survey data where individuals nest into areas, this research develops a spatial random slope multilevel model that can simultaneously model spatial interactions across the higher level areas and correlations between random effects within each area. The essence of the spatial random slope multilevel model is to regard random effect at the area level as a spatial process characterised by a multivariate conditional autoregressive (CAR) process. In combination, the thesis makes important contributions to a coming together of spatial and multilevel modelling for better investigating geographically hierarchical data.

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The aim of this thesis is to present robust solutions to technical problems of airborne three-dimensional (3D) Visual Simultaneous Localisation And Mapping (VSLAM). These solutions are developed based on a stereovision system available onboard Unmanned Aerial Vehicles (UAVs). The proposed airborne VSLAM enables unmanned aerial vehicles to construct a reliable map of an unknown environment and localise themselves within this map without any user intervention. Current research challenges related to Airborne VSLAM include the visual processing through invariant feature detectors/descriptors, efficient mapping of large environments and cooperative navigation and mapping of complex environments. Most of these challenges require scalable representations, robust data association algorithms, consistent estimation techniques, and fusion of different sensor modalities. To deal with these challenges, seven Chapters are presented in this thesis as follows: Chapter 1 introduces UAVs, definitions, current challenges and different applications. Next, in Chapter 2 we present the main sensors used by UAVs during navigation. Chapter 3 presents an important task for autonomous navigation which is UAV localisation. In this chapter, some robust and optimal approaches for data fusion are proposed with performance analysis. After that, UAV map building is presented in Chapter 4. This latter is divided into three parts. In the first part, a new imaging alternative technique is proposed to extract and match a suitable number of invariant features. The second part presents an image mosaicing algorithm followed by a super-resolution approach. In the third part, we propose a new feature detector and descriptor that is fast, robust and detect suitable number of features to solve the VSLAM problem. A complete Airborne Visual Simultaneous Localisation and Mapping (VSLAM) solution based on a stereovision system is presented in Chapter (5). Robust data association filters with consistency and observability analysis are presented in this chapter as well. The proposed algorithm is validated with loop closing detection and map management using experimental data. The airborne VSLAM is extended then to the multiple UAVs case in Chapter (6). This chapter presents two architectures of cooperation: a Centralised and a Decentralised. The former provides optimal precision in terms of UAV positions and constructed map while the latter is more suitable for real time and embedded system applications. Finally, conclusions and future works are presented in Chapter (7).

The Red Sea is considered to be one of the most dangerous seas for navigation. The Saudi territorial waters along the Red Sea are characterised by coral reefs, which cause difficulties for local navigation, especially for coast guard vessels. The responsibilities of the Saudi Border guard necessitate safe navigation through out the entire area including the area of coral reefs; in this thesis a new approach and methods of study have been developed to generate navigational charts from photographic images. Two study areas investigated: Rabigh 150km north of Jeddah and Kishran 200 km south of Jeddah. IKONOS multispectral satellite images acquired specifically for this study with a spatial resolution of 4 meters. The images were processed and geo referenced against control points taken during field measurements. The field work was carried out during the period of acquisition with dGPS being the positioning system (with an accuracy of +-5cm), and depths being measured using HTIOO portable digital echo sounder, purchased specifically for this purpose. After calibration of the satellite images and converting the images from digital numbers to radiance and then finally to reflectance, and after collecting the field depths for both study areas linear regression technique have been employed to build suitable models for extracting the estimated depths, this methodology and process led to successful results with an accuracy reached 97%. The same process employed under the most unfavourable conditions, where the humidity and temperature and water vapour reach the maximum, produced results with an accuracy of 65% are not recommended. Application of the study results were carried out for navigational purposes, by converting the images from raster format to a map containing all the necessary information which is normally available in navigational charts such as depths, contour lines (labeled with depth figures), compasses, scales ... etc. This process was carried out using Geographical Information System (GIS) techniques. As a conclusion the results achieved in this study prove that satellite imagery could play an important part in updating navigational charts by deriving the bathymetry of shallow water areas, especially in areas where the traditional survey could not be undertaken due to the spread of coral reefs, islands and underwater obstacles. - Blue band was found to be the best for penetration and extracting depth data - Timing of acquisition was found to be very important factor for achiving the best accuracy (97.3%)

Using single-epoch GPS positioning has many advantages, especially when monitoring dynamic targets (e.g. structural movements). In this technique, errors occurring in previous epochs cannot affect the current epoch’s accuracy. However, careful processing is required. This research uses the GPS Ambiguity Search Program (GASP) single-epoch software. Resolving the phase ambiguities is essential in this technique. Some statistical ambiguity resolution functions have been introduced to estimate the best values of these ambiguities. The function inputs are the base station position, the approximate roving receiver position, and the shared GPS phase measurements at both receivers. This work investigates different GPS pseudorange solutions to find the optimal ambiguity function inputs. The noise level in an undifferenced pseudorange coordinate solution is less than in the double-differenced case; thus, using it in the ambiguity function improves the results. Regional correlation between the pseudorange-computed positioning errors exists; therefore, applying a regional filter reduces their effects. Multipath errors approximately repeat themselves every sidereal day in the case of static or quasi-static receivers and applying a sidereal filter mitigates their effects. The IGS ionospheric model reduces the effect of the ionosphere on the GPS phase measurements. Also, a local code-based ionospheric correction model can be generated. Applying these models improves the quality of the phase measurements, which leads to improvement of the ambiguity function outputs. A Kalman filter applied to the code-based ionospheric model further improves the corrected phase measurements. There is a correlation between the ambiguity function outputs’ quality and the phase measurement residuals’ . Applying a threshold filter reduces the probability of obtaining inaccurate results. Data for various baseline lengths, with synthetic displacements added, indicate that the improved GASP results are reliable for monitoring movements exceeding 10 cm for baselines up to 60 km.

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This thesis primarily concentrates on stochastic and spectral properties of the transfer operator generated by piecewise expanding maps (PWEs) and piecewise isometries (PWIs). We also consider the applications of the transfer operator in thermodynamic formalism. The original motivation stems from studies of one-dimensional PWEs. In particular, any one dimensional mixing PWE admits a unique absolutely continuous invariant probability measure (ACIP) and this ACIP has a bounded variation density. The methodology used to prove the existence of this ACIP is based on a so-called functional analytic approach and a key step in this approach is to show that the corresponding transfer operator has a spectral gap. Moreover, when a PWE has Markov property this ACIP can also be viewed as a Gibbs measure in thermodynamic formalism. In this thesis, we extend the studies on one-dimensional PWEs in several aspects. First, we use the functional analytic approach to study piecewise area preserving maps (PAPs) in particular to search for the ACIPs with multidimensional bounded variation densities. We also explore the relationship between the uniqueness of ACIPs with bounded variation densities and topological transitivity/ minimality for PWIs. Second, we consider the mixing and corresponding mixing rate properties of a collection of piecewise linear Markov maps generated by composing x to mx mod 1 with permutations in SN. We show that typical permutations preserve the mixing property under the composition. Moreover, by applying the Fredholm determinant approach, we calculate the mixing rate via spectral gaps and obtain the max/min spectral gaps when m,N are fixed. The spectral gaps can be made arbitrarily small when the permutations are fully refined. Finally, we consider the computations of fractal dimensions for generalized Moran constructions, where different iteration function systems are applied on different levels. By using the techniques in thermodynamic formalism, we approximate the fractal dimensions via the zeros of the Bowen's equation on the pressure functions truncated at each level.

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In the thirteenth century, following the expansion of seafaring city-states and kingdoms in the Mediterranean, a new form of cartography emerged, known as portolan charts. These maps, more secular and scientific than earlier cartographic genres, were produced between the thirteenth and seventeenth centuries, primarily in the western Mediterranean. While portolan charts and atlases have been studied since the nineteenth century, they remain enigmatic. One of the most important questions about them has been: ‘what was their function’? Most scholars have argued that they were fundamentally utilitarian maps, used for navigation. This thesis challenges that theory, and proposes that portolan maps were not navigational. To critically assess the function of portolan maps, the first chapter evaluates their methods of construction, as determined through an analysis of primary sources, and an original archaeological reconstruction of a portolan chart. The second chapter presents seven case studies of charts, atlases, and their makers, to explore the cartographers’ output, the specific functions of their maps, and how they relate to the genre as a whole. The third chapter analyses the contemporary documentary and literary evidence to gain a better understanding of the economic market for portolan maps. The fourth chapter evaluates their functions, in two parts: the first discusses how the maps could have been used on ships, how they changed over time, and investigates the practical utility of their toponymy and hydrography. The second part explores their alternative functions, which were as administrative and encyclopaedic maps, spiritual and scholarly maps, and aesthetic objets d’art. Although some evidence suggests portolan maps were used at sea, it is largely circumstantial and unspecific. The evaluation of their construction, specific functions, the output of cartographers, and their practical utility, instead indicates that portolan maps were not navigationally useful, but embodied number of other purposes.