Time resolved imaging is concerned with the measurement of photon arrival time. It has a wealth of emerging applications including biomedical uses such as fluorescence lifetime microscopy and positron emission tomography, as well as laser ranging and imaging in three dimensions. The impact of time resolved imaging on human life is significant: it can be used to identify cancerous cells in-vivo, how well new drugs may perform, or to guide a robot around a factory or hospital. Two essential building blocks of a time resolved imaging system are a photon detector capable of sensing single photons, and fast time resolvers that can measure the time of flight of light to picosecond resolution. In order to address these emerging applications, miniaturised, single-chip, integrated arrays of photon detectors and time resolvers must be developed with state of the art performance and low cost. The goal of this research is therefore the design, layout and verification of arrays of low noise Single Photon Avalanche Diodes (SPADs) together with high resolution Time-Digital Converters (TDCs) using an advanced silicon fabrication process. The research reported in this Thesis was carried out as part of the E.U. funded Megaframe FP6 Project. A 32x32 pixel, one million frames per second, time correlated imaging device has been designed, simulated and fabricated using a 130nm CMOS Imaging process from ST Microelectronics. The imager array has been implemented together with required support cells in order to transmit data off chip at high speed as well as providing a means of device control, test and calibration. The fabricated imaging device successfully demonstrates the research objectives. The Thesis presents details of design, simulation and characterisation results of the elements of the Megaframe device which were the author’s own work. Highlights of the results include the smallest and lowest noise SPAD devices yet published for this class of fabrication process and an imaging array capable of recording single photon arrivals every microsecond, with a minimum time resolution of fifty picoseconds and single bit linearity.

This master’s thesis covers the design and implementation of a monopulse directionof arrival (DOA) estimation algorithm on an FPGA. The goal is to implement a complete system that is capable of estimating the bearing of an incident signal. In order to determine the estimate quality both a theoretical and practical noise analysis of the signal chain is performed. Special focus is placed on the statistical properties of the transformation from I/Q-demodulated signals with correlated noise to a polar representation. The pros and cons for three different methods of calculating received signal phasors are also covered.The system is limited to two receiving channels which constrains this report to a 2D analysis. In addition the used hardware is limited to C-band signals. We show that an FPGA implementation of monopulse techniques is definitely viable and that an SNR higher than ten dB allows for a gaussian approximation of the polar representationof an I/Q signal.

A MAP/PH/1 queue is a queue having a Markov arrival process (MAP), and a single server with phase-type (PH -type) distributed service time. This thesis considers the departure process from these type of queues. We use matrix analytic methods, the Jordan canonical form of matrices, non-linear filtering and approximation techniques. The departure process of a queue is important in the analysis of networks of queues, as it may be the arrival process to another queue in the network. If a simple description were to exist for a departure process, the analysis of at least feed-forward networks of these queues would then be analytically tractable. Chapter 1 is an introduction to some of the literature and ideas surrounding the departure process from MAP/PH/1 queues. Chapter 2 sets up the basic notation and establishes some results which are used throughout the thesis. It contains a preliminary consideration of PH -type distributions, PH -renewal processes, MAP s, MAP/PH/1 queues, non-linear filtering and the Jordan canonical form. Chapter 3 is an expansion of "The Output process of an MMPP/M/1 queue", where the question of whether a MAP description can exist for the departure process of a non-trivial MAP/M/1 queue is considered. In a 1994 paper, Olivier and Walrand conjectured that the departure process of a MAP/PH/1 queue is not a MAP unless the queue is a stationary M/M/1 queue. This conjecture was prompted by their claim that the departure process of an MMPP/M/1 queue is not MAP unless the queue is a stationary M/M/1 queue. We show that their proof has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/PH/1 queue is a MAP or not. In Chapter 4, the more fundamental problem of identifying stationary M/M/1 queues in the class of MAP/PH/1 queues is considered. It is essential to be able to determine from its generator when a stationary MAP is a Poisson process. This does not appear to have been discussed in the literature prior to the author's paper, where this deficiency was remedied using ideas from non-linear filtering theory, to give a characterisation as to when a stationary MAP is a Poisson process. Chapter 4 expands upon "When is a MAP Poisson". This investigation of higher order representations of the Poisson process is motivated by first considering when a higher order PH -type distribution is just negative exponential. In Chapter 5, we consider the related question of minimal order representations for PH -type distributions, an issue which has attracted much interest in the literature. A discussion of other authors' ideas is given and these ideas are then inter-related to the work presented in Chapter 4 on the PH -type distributions. The MAP/M/1 queue is then considered in Chapter 6 from the perspective of whether having an exact level and phase independent stationary distribution of the geometric form [Formula - Not available: see pdf version of the abstract] implies that the MAP is Poisson. The answer is in the affirmative for this question, but the converse is not strictly true. Apart from showing the ubiquitous asymptotic form of level and phase independence exhibited by all stable MAP/M/1 queues, we prove that a very large class of stable queues, exhibits what we have termed shift-one level and phase independence. Stable MAP/M/1 queues exhibiting shift-one level and phase independence, are characterised by a stationary distribution of the following form: [Formula - Not Available: see pdf version of the abstract] In Chapter 7, a family of approximations is proposed for the output process of a stationary MAP/PH/1 queue. To check the viability of these approximations, they are used as input to another single server queue. Performance measures for the second server are obtained analytically in both the tandem and approximation cases, thus eliminating the need for simulation to compare results. Comparison of these approximations is also made against other approximation methods in the literature. In Chapter 8, we show that our approximations from Chapter 7 have the property of exactly matching the inter-departure time distribution. Our kth approximation also accurately captures the first k-1 lag-correlation coefficients of the stationary departure process. The proofs of this direct association between lag-correlation coefficients and the level of complexity k are given. / Thesis (Ph.D.)--School of Applied Mathematics, 1999.

In certain applications involving direction of arrival (DOA) estimation the operator may have a-priori information on some of the DOAs. This information could refer to a target known to be present at a certain position or to a reflection. In this study, the authors investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. Algorithms are presented that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. The authors find a major improvement in estimator accuracy in feasible scenarios, and they compare the estimator performance to the corresponding theoretical stochastic Cramer-Rao bounds as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, real data from an ultra-sound array is applied to the investigated estimators. / <p>QC 20130107</p>

Uncertainty is inherent in complex socio-technical systems such as in aviation, military, and surface transportation domains. An improved understanding of how operators comprehend this uncertainty is critical to the development of operations and technology. Towards the development of a model of time of arrival (TOA) uncertainty, Experiment 1 was conducted to determine how air traffic controllers estimate TOA uncertainty and to identify sources of TOA uncertainty. The resulting model proposed that operators first develop a library of speed and TOA profiles through experience. As they encounter subsequent aircraft, they compare each vehicle’s speed profile to their personal library and apply the associated estimate of TOA uncertainty. To test this model, a normative model was adopted to compare inferences made by human observers to the corresponding inferences that would be made by an optimal observer who had knowledge of the underlying distribution. An experimental platform was developed and implemented in which subjects observed vehicles with variable speeds and then estimated the mean and interval that captured 95% of the speeds and TOAs. Experiments 2 and 3 were then conducted and revealed that subjects overestimated TOA intervals for fast stimuli and underestimated TOA intervals for slow stimuli, particularly when speed variability was high. Subjects underestimated the amount of positive skew of the TOA distribution, particularly in slow/high variability conditions. Experiment 3 also demonstrated that subjects overestimated TOA uncertainty for short distances and underestimated TOA uncertainty for long distances. It was shown that subjects applied a representative heuristic by selecting the trained speed profile that was most similar to the observed vehicle’s profile, and applying the TOA uncertainty estimate of that trained profile. Multiple regression analyses revealed that the task of TOA uncertainty estimation contributed the most to TOA uncertainty estimation error as compared to the tasks of building accurate speed models and identifying the appropriate speed model to apply to a stimulus. Two systematic biases that account for the observed TOA uncertainty estimation errors were revealed: Assumption of symmetry and aversion to extremes. Operational implications in terms of safety and efficiency for the aviation domain are discussed.

Uncertainty is inherent in complex socio-technical systems such as in aviation, military, and surface transportation domains. An improved understanding of how operators comprehend this uncertainty is critical to the development of operations and technology. Towards the development of a model of time of arrival (TOA) uncertainty, Experiment 1 was conducted to determine how air traffic controllers estimate TOA uncertainty and to identify sources of TOA uncertainty. The resulting model proposed that operators first develop a library of speed and TOA profiles through experience. As they encounter subsequent aircraft, they compare each vehicle’s speed profile to their personal library and apply the associated estimate of TOA uncertainty. To test this model, a normative model was adopted to compare inferences made by human observers to the corresponding inferences that would be made by an optimal observer who had knowledge of the underlying distribution. An experimental platform was developed and implemented in which subjects observed vehicles with variable speeds and then estimated the mean and interval that captured 95% of the speeds and TOAs. Experiments 2 and 3 were then conducted and revealed that subjects overestimated TOA intervals for fast stimuli and underestimated TOA intervals for slow stimuli, particularly when speed variability was high. Subjects underestimated the amount of positive skew of the TOA distribution, particularly in slow/high variability conditions. Experiment 3 also demonstrated that subjects overestimated TOA uncertainty for short distances and underestimated TOA uncertainty for long distances. It was shown that subjects applied a representative heuristic by selecting the trained speed profile that was most similar to the observed vehicle’s profile, and applying the TOA uncertainty estimate of that trained profile. Multiple regression analyses revealed that the task of TOA uncertainty estimation contributed the most to TOA uncertainty estimation error as compared to the tasks of building accurate speed models and identifying the appropriate speed model to apply to a stimulus. Two systematic biases that account for the observed TOA uncertainty estimation errors were revealed: Assumption of symmetry and aversion to extremes. Operational implications in terms of safety and efficiency for the aviation domain are discussed.

As wireless devices become more common, the ability to position a wireless device has become a topic of importance. Accurate positioning through technologies such as the Global Positioning System is possible for outdoor environments. Indoor environments pose a different challenge, and research continues to position users indoors. Due to the prevalence of wireless local area networks (WLANs) in many indoor spaces, it is prudent to determine their capabilities for the purposes of positioning. Signal strength and time based positioning systems have been studied for WLANs. Direction or angle of arrival (AOA) based positioning will be possible with multiple antenna arrays, such as those included with upcoming devices based on the IEEE 802.11n standard. The potential performance of such a system is evaluated. The positioning performance of such a system depends on the accuracy of the AOA estimation as well as the positioning algorithm. Two different maximum-likelihood (ML) derived algorithms are used to determine the AOA of the mobile user: a specialized simple ML algorithm, and the space- alternating generalized expectation-maximization (SAGE) channel parameter estimation algorithm. The algorithms are used to determine the error in estimating AOAs through the use of real wireless signals captured in an indoor office environment. The statistics of the AOA error are used in a positioning simulation to predict the positioning performance. A least squares (LS) technique as well as the popular extended Kalman filter (EKF) are used to combine the AOAs to determine position. The position simulation shows that AOA- based positioning using WLANs indoors has the potential to position a wireless user with an accuracy of about 2 m. This is comparable to other positioning systems previously developed for WLANs.

Ultra-wideband (UWB) technology and its use in imaging and sensing have drawnsignicant interest in the last two decades. Extensive studies have contributed toutilize UWB transient scattering for automated target recognition and imagingpurposes. In this thesis a near-eld UWB synthetic aperture radar (SAR) imagingalgorithm is presented.It is shown with measurements and simulation, that it is possible to reconstruct an imageof an object in the near eld region using UWB technology and SAR imaging algorithm.However the nal SAR image is highly aected by unwanted scattered elds at each pixelusually observed as an image artifact in the nal image. In this study these artifactsare seen as a smile around the main object. Two methods are suggested in this thesiswork to suppress this artifact. The rst method combines the scattered eld informationreceived from both rear and front of the object to reconstruct two separate images, onefrom rear view and one from front view of the object respectively. Since the scatteredelds from behind the object are mirrored, the pixel by pixel multiplication of thesetwo images for objects with simple geometry will cancel the artifact. This method isvery simple and fast applicable to objects with simple geometry. However this methodcannot be used for objects with rather complex geometry and boundaries. Thereforethe Range Point Migration (RPM) method is used along with the global characteristicsof the observed range map to introduce a new artifact rejection method based on thedirectional of arrival (DOA) of scattered elds at each pixel. DOA information can beused to calculate an optimum theta for each antenna. This optimum angle along withthe real physical direction of arrival at each position can produce a weighting factor thatlater can be used to suppress the eect of undesired scattered elds producing the smileshaped artifact. Final results of this study clearly show that the UWB SAR accompaniedwith DOA can produce an image of an object free of undesired artifact from scatteredeld of adjacent antennas.

The main crux of this thesis was to produce a model that was capable of simulating the theoretical performance of different configurations for a spatial measurement system using radio frequency technology. It has been important to study new modalities of spatial measurement since spatial measurement systems are an enabling technology that have allowed for the creation of better medical procedures and techniques, provided valuable data for motion capture in animation and biomechanics, and have improved the quality of manufacturing processes in many industries. However, there has been room for improvement in the functional design and accuracy of spatial measurement systems that will enhance current applications and further develop new applications in medicine, research and industry. <br /><br /> In this thesis, a modelling framework for the investigation of spatial measurement based on radio frequency signals was developed. The simulation framework was designed for the purpose of investigating different position determination algorithms and sensor geomatries. A finite element model using the FEMLAB partial differential equation modelling tool was created for a time-domain model of electromagnetic wave propagation in order to simulate the radio frequency signals travelling from a transmitting source antenna to a set of receiving antenna sensors. Electronic line signals were obtained using a simple receiving infinitesimal dipole model and input into a time difference of arrival localization algorithm. The finite element model results were validated against a set of analytical solutions for the free space case. The accuracy of the localization algorithm was measured against a set of possible applications for a potential radio frequency spatial measurement system design. <br /><br /> It was concluded that the simulation framework was successful should one significant deficiency be corrected in future research endeavours. A phase error was observed in the signals extracted at the receiving antenna locations. This phase error, which can be up to 40°, was attributed to the zeroth order finite elements implemented in the finite element model. This phase error can be corrected in the future if higher order vector elements are introduced into future versions of FEMLAB or via the development of custom finite element analysis software but were not implemented in this thesis due to time constraints. Other improvements were also suggested for future work.

The seminal paper by Gerber and Shiu (1998) gave a huge boost to the study of risk theory by not only unifying but also generalizing the treatment and the analysis of various risk-related quantities in one single mathematical function - the Gerber-Shiu expected discounted penalty function, or Gerber-Shiu function in short. The Gerber-Shiu function is known to possess many nice properties, at least in the case of the classical compound Poisson risk model. For example, upon the introduction of a dividend barrier strategy, it was shown by Lin et al. (2003) and Gerber et al. (2006) that the Gerber-Shiu function with a barrier can be expressed in terms of the Gerber-Shiu function without a barrier and the expected value of discounted dividend payments. This result is the so-called dividends-penalty identity, and it holds true when the surplus process belongs to a class of Markov processes which are skip-free upwards. However, one stringent assumption of the model considered by the above authors is that all the interclaim times and the claim sizes are independent, which is in general not true in reality. In this thesis, we propose to analyze the Gerber-Shiu functions under various dependent structures. The main focus of the thesis is the risk model where claims follow a Markovian arrival process (MAP) (see, e.g., Latouche and Ramaswami (1999) and Neuts (1979, 1989)) in which the interclaim times and the claim sizes form a chain of dependent variables. The first part of the thesis puts emphasis on certain dividend strategies. In Chapter 2, it is shown that a matrix form of the dividends-penalty identity holds true in a MAP risk model perturbed by diffusion with the use of integro-differential equations and their solutions. Chapter 3 considers the dual MAP risk model which is a reflection of the ordinary MAP model. A threshold dividend strategy is applied to the model and various risk-related quantities are studied. Our methodology is based on an existing connection between the MAP risk model and a fluid queue (see, e.g., Asmussen et al. (2002), Badescu et al. (2005), Ramaswami (2006) and references therein). The use of fluid flow techniques to analyze risk processes opens the door for further research as to what types of risk model with dependency structure can be studied via probabilistic arguments. In Chapter 4, we propose to analyze the Gerber-Shiu function and some discounted joint densities in a risk model where each pair of the interclaim time and the resulting claim size is assumed to follow a bivariate phase-type distribution, with the pairs assumed to be independent and identically distributed (i.i.d.). To this end, a novel fluid flow process is constructed to ease the analysis. In the classical Gerber-Shiu function introduced by Gerber and Shiu (1998), the random variables incorporated into the analysis include the time of ruin, the surplus prior to ruin and the deficit at ruin. The later part of this thesis focuses on generalizing the classical Gerber-Shiu function by incorporating more random variables into the so-called penalty function. These include the surplus level immediately after the second last claim before ruin, the minimum surplus level before ruin and the maximum surplus level before ruin. In Chapter 5, the focus will be on the study of the generalized Gerber-Shiu function involving the first two new random variables in the context of a semi-Markovian risk model (see, e.g., Albrecher and Boxma (2005) and Janssen and Reinhard (1985)). It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation, and some discounted joint densities involving the new variables are derived. Chapter 6 revisits the MAP risk model in which the generalized Gerber-Shiu function involving the maximum surplus before ruin is examined. In this case, the Gerber-Shiu function no longer satisfies a defective renewal equation. Instead, the generalized Gerber-Shiu function can be expressed in terms of the classical Gerber-Shiu function and the Laplace transform of a first passage time that are both readily obtainable. In a MAP risk model, the interclaim time distribution must be phase-type distributed. This leads us to propose a generalization of the MAP risk model by allowing for the interclaim time to have an arbitrary distribution. This is the subject matter of Chapter 7. Chapter 8 is concerned with the generalized Sparre Andersen risk model with surplus-dependent premium rate, and some ordering properties of certain ruin-related quantities are studied. Chapter 9 ends the thesis by some concluding remarks and directions for future research.