Optimal estimation retrieval is a nonlinear regression scheme to determine the conditions statistically most-likely to produce a given measurement, weighted against any a priori knowledge. The technique is applied to three problems within the field of lidar data analysis. A retrieval of the aerosol backscatter and either the extinction or lidar ratio from two-channel Raman lidar data is developed using the lidar equations as a forward model. It produces profiles consistent with existing techniques at a resolution of 10-1000 m and uncertainty of 5-20%, dependent on the quality of data. It is effective even when applied to noisy, daytime data but performs poorly in the presence of cloud. Two of the most significant sources of uncertainty in that retrieval are the nonlinearity of the detectors and the instrument's calibration (known as the dead time and overlap function). Attempts to retrieve a nonlinear correction from a pair of lidar profiles, one attenuated by a neutral density filter, are not successful as uncertainties in the forward model eliminate any information content in the measurements. The technique of Whiteman et al. [1992] is found to be the most accurate. More successful is a retrieval of the overlap function of a Raman channel using a forward model combining an idealised extinction profile and an adaptation of the equations presented in Halldórsson and Langerholc [1978]. After refinement, the retrieval is shown to be at least as accurate, and often superior to, existing methods of calibration from routine measurements, presenting uncertainties of 5-15%. These techniques are then applied to observations of ash over southern England from the Eyjafjallajökull eruption of April 2010. Lidar ratios of 50-60 sr were observed when the plume first appeared, which reduced to 20-30 sr after several days within the planetary boundary layer, indicating an alteration of the particles over time.

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A new retrieval algorithm has been developed based on the Optimal Estimation (OE) approach, which retrieves lognormal aerosol size distribution parameters from multiwavelength aerosol extinction data, as measured by the Stratospheric Aerosol and Gas Experiment (SAGE) II in the lower stratosphere. Retrieving these aerosol properties becomes increasingly more difficult under aerosol background conditions, when tiny particles (« 0.1 µm) prevail, to which the experiment is nearly or entirely insensitive. A successful retrieval algorithm must then be able (a) to fill the 'blind spot' with suitable information about the practically invisible particles, and (b) to identify 'the best' of many possible solutions. The OE approach differs from other previously used aerosol retrieval techniques by taking a statistical approach to the multiple solution problem, in which the entire range of possible solutions are considered (including the smallest particles) and characterized by probability density functions. The three main parts of this thesis are (1) the development of the new OE retrieval algorithm, (2) the validation of this algorithm on the basis of synthetic extinction data, and (3) application of the new algorithm to SAGE II measurements of stratospheric background aerosol. The validation results indicate that the new method is able to retrieve the particle size of typical background aerosols reasonably well, and that the retrieved uncertainties are a good estimate of the true errors. The derived surface area densities (A), and volume densities (V ) tend to be closer to the correct solutions than the directly retrieved number density (N), median radius (R), and lognormal distribution width (S). Aerosol properties as retrieved from SAGE II measurements (recorded in 1999) are observed to be close to correlative in situ data. In many cases the OE and in situ data agree within the (OE and/or the in situ ) uncertainties. The retrieved error estimates are of the order of 69% (σN), 33% (σR), 14% (σS), 23% (σA), 12% (σV), and 13% (σReff ). The OE number densities are generally larger, and the OE median particle sizes are generally smaller than those N and R retrieved by Bingen et al. (2004a), who suggest that their results underestimate (N) or overestimate (R) correlative in situ data due to the 'small particle problem'. The OE surface area estimates are generally closer to correlative in situ profiles (courtesy of T. Deshler, University of Wyoming), and larger than Principal Component Analysis (PCA) retrieval solutions of A (courtesy of L. W. Thomason, NASA LaRC) that have been observed to underestimate correlative in situ data by 40-50%. These observations suggest that the new OE retrieval algorithm is a successful approach to the aerosol retrieval problem, which is able to add to the current knowledge by improving current estimates of aerosol properties in the lower stratosphere under low aerosol loading conditions.

Recent spectroscopic observations of transiting exoplanets have permitted the derivation of the thermal structure and molecular abundances of H₂O, CO, CO₂, CH₄, metallic oxides and alkali metals in these extreme atmospheres. Here, for the first time, a fully-fledged retrieval algorithm has been applied to exoplanet spectra to determine the thermal structure and composition. The development of a suite of radiative transfer and retrieval tools for exoplanet atmospheres is described, building upon an optimal estimation retrieval algorithm extensively used in solar system studies. Firstly, the collection of molecular line lists and the pre-tabulation of the absorption coefficients (k-distribution tables) for high temperature application are discussed. Secondly, the best-fit spectra for hot Jupiters are demonstrated and discussed case by case. Available sets of primary and secondary transit observations of exoplanets are used to retrieve atmospheric properties from these spectra, quantifying the limits of our knowledge of exoplanetary atmospheres based on the current quality of the data. The contribution functions and the vertical sensitivity to the molecules are fully utilised to interpret these spectra, probing the structure and composition of the atmosphere. Finally, the retrievals provide our best estimates of the thermal and compositional structure to date, using the covariance matrices to properly assess the degeneracy between different parameters and the uncertainties on derived quantities for the first time. This sheds light on the range of diverse interpretations offered by other authors so far, and allows us to scrutinise further atmospheric features by maximising the capability of the current retrieval algorithm and to demonstrate the need for broadband spectroscopy from future missions.

In this thesis we study the general problem of reconstructing a function, defined on a finite lattice from a set of incomplete, noisy and/or ambiguous observations. The goal of this work is to demonstrate the generality and practical value of a probabilistic (in particular, Bayesian) approach to this problem, particularly in the context of Computer Vision. In this approach, the prior knowledge about the solution is expressed in the form of a Gibbsian probability distribution on the space of all possible functions, so that the reconstruction task is formulated as an estimation problem. Our main contributions are the following: (1) We introduce the use of specific error criteria for the design of the optimal Bayesian estimators for several classes of problems, and propose a general (Monte Carlo) procedure for approximating them. This new approach leads to a substantial improvement over the existing schemes, both regarding the quality of the results (particularly for low signal to noise ratios) and the computational efficiency. (2) We apply the Bayesian appraoch to the solution of several problems, some of which are formulated and solved in these terms for the first time. Specifically, these applications are: teh reconstruction of piecewise constant surfaces from sparse and noisy observationsl; the reconstruction of depth from stereoscopic pairs of images and the formation of perceptual clusters. (3) For each one of these applications, we develop fast, deterministic algorithms that approximate the optimal estimators, and illustrate their performance on both synthetic and real data. (4) We propose a new method, based on the analysis of the residual process, for estimating the parameters of the probabilistic models directly from the noisy observations. This scheme leads to an algorithm, which has no free parameters, for the restoration of piecewise uniform images. (5) We analyze the implementation of the algorithms that we develop in non-conventional hardware, such as massively parallel digital machines, and analog and hybrid networks.

A new retrieval algorithm has been developed based on the Optimal Estimation (OE) approach, which retrieves lognormal aerosol size distribution parameters from multiwavelength aerosol extinction data, as measured by the Stratospheric Aerosol and Gas Experiment (SAGE) II in the lower stratosphere. Retrieving these aerosol properties becomes increasingly more difficult under aerosol background conditions, when tiny particles (« 0.1 µm) prevail, to which the experiment is nearly or entirely insensitive. A successful retrieval algorithm must then be able (a) to fill the 'blind spot' with suitable information about the practically invisible particles, and (b) to identify 'the best' of many possible solutions. The OE approach differs from other previously used aerosol retrieval techniques by taking a statistical approach to the multiple solution problem, in which the entire range of possible solutions are considered (including the smallest particles) and characterized by probability density functions. The three main parts of this thesis are (1) the development of the new OE retrieval algorithm, (2) the validation of this algorithm on the basis of synthetic extinction data, and (3) application of the new algorithm to SAGE II measurements of stratospheric background aerosol. The validation results indicate that the new method is able to retrieve the particle size of typical background aerosols reasonably well, and that the retrieved uncertainties are a good estimate of the true errors. The derived surface area densities (A), and volume densities (V ) tend to be closer to the correct solutions than the directly retrieved number density (N), median radius (R), and lognormal distribution width (S). Aerosol properties as retrieved from SAGE II measurements (recorded in 1999) are observed to be close to correlative in situ data. In many cases the OE and in situ data agree within the (OE and/or the in situ ) uncertainties. The retrieved error estimates are of the order of 69% (σN), 33% (σR), 14% (σS), 23% (σA), 12% (σV), and 13% (σReff ). The OE number densities are generally larger, and the OE median particle sizes are generally smaller than those N and R retrieved by Bingen et al. (2004a), who suggest that their results underestimate (N) or overestimate (R) correlative in situ data due to the 'small particle problem'. The OE surface area estimates are generally closer to correlative in situ profiles (courtesy of T. Deshler, University of Wyoming), and larger than Principal Component Analysis (PCA) retrieval solutions of A (courtesy of L. W. Thomason, NASA LaRC) that have been observed to underestimate correlative in situ data by 40-50%. These observations suggest that the new OE retrieval algorithm is a successful approach to the aerosol retrieval problem, which is able to add to the current knowledge by improving current estimates of aerosol properties in the lower stratosphere under low aerosol loading conditions.

Συστήματα μαγνητικών ταινιών χρησιμοποιούνται ευρέως ως μέσα αποθήκευσης και αποκατάστασης δεδομένων. Λόγω του χαμηλού τους κόστους αναλογικά των σκληρών δίσκων συνεχίζουν να προτιμούνται σε μεγάλο πλήθος εφαρμογών όπως δευτερεύουσες συσκευές αποθήκευσης, εγγραφής και επεξεργασίας ηχητικών δεδομένων,βιντεοκάμερες κ.ά. Σε περιπτώσεις όπου θέλουμε να επεξεργαστούμε μια μαγνητοταινία για γρήγορη μεταφορά ή εγγραφή δεδομένων θα πρέπει -η ταινία- να μεταφέρεται σε υψηλή ταχύτητα από το μηχανισμό του συστήματος. Η ταχύτητα αυτή να διατηρείται σταθερή και να βρίσκεται σε συγχρονισμό ε την κεφαλή ανάγνωσης/εγγραφής προς αποφυγή σφαλμάτων μεταφοράς και αναγνώρισης δεδομένων, αναπηδήσεων και χρονικών σφαλμάτων. Σε πιθανά σφάλματα η επαναφορά της ταινίας στο επιθυμητό σημείο αποτελεί τη λύση για την αποκατάσταση του σφάλματος. Η επιτάχυνση και επιβράδυνση που δέχεται η ταινία σε κάθε γρήγορη αναζήτηση δεδομένων προκαλούν τη μεγαλύτερη επιβάρυνση σε αυτή. Ειδικά η συχνή επανατοποθέτηση της ταινίας στο ίδιο ση είο λόγω της βαθμιαίας εξασθένισης του σήματος ανάγνωσης. Σκοπός είναι ο σχεδιασμός ενός μηχανισμού εταφοράς της ταινίας ο οποίος προσφέρει μια ικανοποιητική τάση στην ταινία όπως και ταχύτητα μεταφοράς αυτής. / Optimal control and estimation of a magnetic tape-drive system.

Aircraft flight test data are processed by optimal estimation programs to estimate the aircraft state trajectory (3 DOF) and to identify the unknown parameters, including constant biases and scale factor of the measurement instrumentation system. The methods applied in processing aircraft flight test data are the iterative extended Kalman filter/smoother and fixed-point smoother (IEKFSFPS) method and the two-step estimator (TSE) method. The models of an aircraft flight dynamic system and measurement instrumentation system are established. The principles of IEKFSFPS and TSE methods are derived and summarized, and their algorithms are programmed with MATLAB codes. Several numerical experiments of flight data processing and parameter identification are carried out by using IEKFSFPS and TSE algorithm programs. Comparison and discussion of the simulation results with the two methods are made. The TSE+IEKFSFPS combination method is presented and proven to be effective and practical. Figures and tables of the results are presented.

This thesis tackles the visual tracking problem as a target contour estimation problem in the face of corrupted measurements. The major aim is to design robust recursive curve filters for accurate contour-based tracking. The state-space representation adopted comprises of a group component and a shape component describing the rigid motion and the non-rigid shape deformation respectively; filtering strategies on each component are then decoupled. The thesis considers two implicit curve descriptors, a classification probability field and the traditional signed distance function, and aims to develop an optimal probabilistic contour observer and locally optimal curve filters. For the former, introducing a novel probabilistic shape description simplifies the filtering problem on the infinite-dimensional space of closed curves to a series of point-wise filtering tasks. The definition and justification of a novel update model suited to the shape space, the derivation of the filtering equations and the relation to Kalman filtering are studied. In addition to the temporal consistency provided by the filtering, extensions involving distributed filtering methods are considered in order to maintain spatial consistency. For the latter, locally optimal closed curve filtering strategies involving curve velocities are explored. The introduction of a local, linear description for planar curve variation and curve uncertainty enables the derivation of a mechanism for estimating the optimal gain associated to the curve filtering process, given quantitative uncertainty levels. Experiments on synthetic and real sequences of images validate the filtering designs.

Reactive halogen species (RHS) are responsible for ozone depletion and oxidation of gaseous elemental mercury and dimethyl sulphide in the polar boundary layer, but the sources and mechanisms controlling their catalytic reaction cycles are still not completely understood. To further investigate these processes, ground– based Multi–Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) observations of boundary layer BrO and IO were made from a portable instrument platform in McMurdo Sound during the Antarctic spring of 2006 and 2007. Measurements of surface ozone, temperature, pressure, humidity, and wind speed and direction were also made, along with fourteen tethersonde soundings and the collection of snow samples for mercury analysis. A spherical multiple scattering Monte Carlo radiative transfer model (RTM) was developed for the simulation of box-air-mass-factors (box-AMFs), which are used to determine the weighting functions and forward model differential slant column densities (DSCDs) required for optimal estimation. The RTM employed the backward adjoint simulation technique for the fast calculation of box-AMFs for specific solar zenith angles (SZA) and MAX-DOAS measurement geometries. Rayleigh and Henyey-Greenstein scattering, ground topography and reflection, refraction, and molecular absorption by multiple species were included. Radiance and box-AMF simulations for MAX-DOAS measurements were compared with nine other RTMs and showed good agreement. A maximum a posteriori (MAP) optimal estimation algorithm was developed to retrieve trace gas concentration profiles from the DSCDs derived from the DOAS analysis of the measured absorption spectra. The retrieval algorithm was validated by performing an inversion of artificial DSCDs, simulated from known NO2 profiles. Profiles with a maximum concentration near the ground were generally well reproduced, but the retrieval of elevated layers was less accurate. Retrieved partial vertical column densities (VCDs) were similar to the known values, and investigation of the averaging kernels indicated that these were the most reliable retrieval product. NO₂ profiles were also retrieved from measurements made at an NO₂ measurement and profiling intercomparison campaign in Cabauw, Netherlands in July 2009. Boundary layer BrO was observed on several days throughout both measurement periods in McMurdo Sound, with a maximum retrieved surface mixing ratio of 14.4±0.3 ppt. The median partial VCDs up to 3km were 9.7±0.07 x 10¹² molec cm ⁻ in 2007, with a maximum of 2.3±0.07 x 10¹³ molec cm⁻², and 7.4±0.06 x 10¹² molec cm⁻² in 2006, with a maximum of 1.05 ± 0.07 x 1013 molec cm⁻². The median mixing ratio of 7.5±0.5 ppt for 2007 was significantly higher than the median of 5.2±0.5 ppt observed in 2006, which may be related to the more extensive first year sea ice in 2007. These values are consistent with, though lower than estimated boundary layer BrO concentrations at other polar coastal sites. Four out of five observed partial ozone depletion events (ODEs) occurred during strong winds and blowing snow, while BrO was present in the boundary layer in both stormy and calm conditions, consistent with the activation of RHS in these two weather extremes. Air mass back trajectories, modelled using the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model, indicated that the events were locally produced rather than transported from other sea ice zones. Boundary layer IO mixing ratios of 0.5–2.5±0.2 ppt were observed on several days. These values are low compared to measurements at Halley and Neumayer Stations, as well as mid-latitudes. Significantly higher total mercury concentrations observed in 2007 may be related to the higher boundary layer BrO concentrations, but further measurements are required to verify this.