Magnitude and variability of loading on the osseointegrated implant of transfemoral amputees during walking

This study directly measured the load acting on the abutment of the osseointegrated implant system of transfemoral amputees during level walking, and studied the variability of the load within and among amputees. Twelve active transfemoral amputees (age: 54��12 years, mass:84.3��16.3 kg, height: 17.8��0.10 m) fitted with an osseointegrated implant for over 1 year participated in the study. The load applied on the abutment was measured during unimpeded, level walking in a straight line using a commercial six-channel transducer mounted between the abutment and the prosthetic knee. The pattern and the magnitude of the three-dimensional forces and moments were revealed. Results showed a low step-to-step variability of each subject, but a high subject-to-subject variability in local extrema of body-weight normalized forces and moments and impulse data. The high subject-to-subject variability suggests that the mechanical design of the implant system should be customized for each individual, or that a fit-all design should take into consideration the highest values of load within a broad range of amputees. It also suggests specific loading regime in rehabilitation training are necessary for a given subject. Thus the loading magnitude and variability demonstrated should be useful in designing an osseointegrated implant system better able to resist mechanical failure and in refining the rehabilitation protocol.

Duplicity/complicity : misperforming the social drama of disability

In this paper, I investigate the (mis)performance of ���passing��� in the context of bodies with disabilities. The desire to conceal, control or contain a body���s idiosyncrasies can be a deceitful act, complicit with dominant cultural assumptions about the benefits of fitting in. Passing, and the performative tricks, techniques and prostheses that support the ���lie��� of passing, upholding a social contract in which a closeting-as-cure approach accommodates discomfort with difference. In this paper, I consider moments of non-passing, where people are caught out by mistakes or deliberate misperformances of the daily social drama of ability and disability. I reference the work of disabled artists Bill Shannon, Aaron Williamson and Katherine Araniello, who re-perform their daily personal interactions in the public sphere as a sort of guerilla theatre. Their work brings hidden assumptions about how disabled people should act and interact to the brink of visibility. It challenges passers-by to confront their complicity in these discourses by pressing them to re-perform their own spontaneous reactions to bodies that misperform the ���lie��� of normalcy.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(���) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(���) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(���) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(���) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Apparatus for monitoring load bearing rehabilitation exercises of a transfemoral amputee fitted with an osseointegrated fixation : a proof-of-concept study

The purpose of this proof-of-concept study was to determine the relevance of direct measurements to monitor the load applied on the osseointegrated fixation of transfemoral amputees during static load bearing exercises. The objectives were (A) to introduce an apparatus using a three-dimensional load transducer, (B) to present a range of derived information relevant to clinicians, (C) to report on the outcomes of a pilot study and (D) to compare the measurements from the transducer with those from the current method using a weighing scale. One transfemoral amputee fitted with an osseointegrated implant was asked to apply 10 kg, 20 kg, 40 kg and 80 kg on the fixation, using self-monitoring with the weighing scale. The loading was directly measured with a portable kinetic system including a six-channel transducer, external interface circuitry and a laptop. As the load prescribed increased from 10 kg to 80 kg, the forces and moments applied on and around the antero-posterior axis increased by 4 fold anteriorly and 14 fold medially, respectively. The forces and moments applied on and around the medio-lateral axis increased by 9 fold laterally and 16 fold from anterior to posterior, respectively. The long axis of the fixation was overloaded and underloaded in 17 % and 83 % of the trials, respectively, by up to ��10 %. This proof-of-concept study presents an apparatus that can be used by clinicians facing the challenge of improving basic knowledge on osseointegration, for the design of equipment for load bearing exercises and for rehabilitation programs.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Load on osseointegrated fixation of a transfemoral amputee during a fall : loading, descent, impact and recovery analysis

Falling represents a health risk for lower limb amputees fitted with an osseointegrated fixation mainly because of the potential damage to the fixation. The purpose of this study was to characterise a real forward fall that occurred inadvertently to a transfemoral amputee fitted with an osseointegrated fixation while attending a gait measurement session to assess the load applied on the residuum. The objective was to analyse the load applied on the fixation with an emphasis on the sequence of events, the pattern and the magnitude of the forces and moments. The load was measured directly at 200 Hz using a six-channel transducer. Complementary video footage was also studied. The fall was divided into four phases: loading (240 ms), descent (620 ms), impact (365 ms) and recovery (2495 ms). The main impact forces and moments occurred 870 ms and 915 ms after the heel contact, and corresponded to 133 %BW and 17 %BWm, or 1.2 and 11.2 times the maximum forces and moments applied during the previous steps of the participant, respectively. This study provided key information to engineers and clinicians facing the challenge to design equipment, and rehabilitation and exercise programs to restore safely the locomotion of lower limb amputees.

The experience of emotional expression in the context of social relations for people diagnosed with schizophrenia : a phenomenological explication

The experience of emotional expression in the context of social relations is not well understood for people diagnosed with schizophrenia. Early phenomenological research on the experience of people diagnosed with schizophrenia traditionally focussed on self experience in isolation from others, with later research explicating isolated aspects of self experience in relation to others. The current research aimed to focus on the progressive experience of emotional expression of people diagnosed with schizophrenia in relation to others over 12 months, in order to gain a broad spectrum of experience. This study involved unstructured interviews with 7 participants, an average of 4 times each, over a period of 12 months. Due to the unstructured nature of the interviews, a great breadth of experience was explicated. From the interviews there emerged 6 themes grouped together as a transition into, and 5 themes grouped together as a recovery from, symptoms associated with a diagnosis of schizophrenia. Special significance was given to the theme of relational confusion as an experience that provides an understanding of the relationship between social stressors and personal characteristics with responses that are associated with a diagnosis of schizophrenia. It was suggested that participants experienced themselves, including their distancing and isolating responses, as a part of a social system. The breadth of experiences that emerged afforded a framework of experiences within which prior phenomenological research findings on static moments of experience have been located. A more meaningful understanding of the transitioning into and recovery from the experiences associated with a diagnosis of schizophrenia will afford advances in mental health practice.

Effects of pediatric obesity on joint kinematics and kinetics during 2 walking cadences

Objective: To determine whether differences existed in lower-extremity joint biomechanics during self-selected walking cadence (SW) and fast walking cadence (FW) in overweight- and normal-weight children.---------- Design: Survey.---------- Setting: Institutional gait study center.---------- Participants: Participants (N=20; mean age �� SD, 10.4��1.6y) from referred and volunteer samples were classified based on body mass index percentiles and stratified by age and sex. Exclusion criteria were a history of diabetes, neuromuscular disorder, or recent lower-extremity injury.---------- Main Outcome Measures: Sagittal, frontal, and transverse plane angular displacements (degrees) and peak moments (newton meters) at the hip, knee, and ankle joints.---------- Results: The level of significance was set at P less than .008. Compared with normal-weight children, overweight children had greater absolute peak joint moments at the hip (flexor, extensor, abductor, external rotator), the knee (flexor, extensor, abductor, adductor, internal rotator), and the ankle (plantarflexor, inverter, external/internal rotators). After including body weight as a covariate, overweight children had greater peak ankle dorsiflexor moments than normal-weight children. No kinematic differences existed between groups. Greater peak hip extensor moments and less peak ankle inverter moments occurred during FW than SW. There was greater angular displacement during hip flexion as well as less angular displacement at the hip (extension, abduction), knee (flexion, extension), and ankle (plantarflexion, inversion) during FW than SW.---------- Conclusions: Overweight children experienced increased joint moments, which can have long-term orthopedic implications and suggest a need for more nonweight-bearing activities within exercise prescription. The percent of increase in joint moments from SW to FW was not different for overweight and normal-weight children. These findings can be used in developing an exercise prescription that must involve weight-bearing activity.

Forecasting time-varying value-at-risk

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices ���ASX 200, S&P 500 and FT 30���, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.

Vision-based detection and tracking of aerial targets for UAV collision avoidance

Machine vision represents a particularly attractive solution for sensing and detecting potential collision-course targets due to the relatively low cost, size, weight, and power requirements of the sensors involved (as opposed to radar). This paper describes the development and evaluation of a vision-based collision detection algorithm suitable for fixed-wing aerial robotics. The system was evaluated using highly realistic vision data of the moments leading up to a collision. Based on the collected data, our detection approaches were able to detect targets at distances ranging from 400m to about 900m. These distances (with some assumptions about closing speeds and aircraft trajectories) translate to an advanced warning of between 8-10 seconds ahead of impact, which approaches the 12.5 second response time recommended for human pilots. We make use of the enormous potential of graphic processing units to achieve processing rates of 30Hz (for images of size 1024-by- 768). Currently, integration in the final platform is under way.

Airborne vision-based collision-detection system

Machine vision represents a particularly attractive solution for sensing and detecting potential collision-course targets due to the relatively low cost, size, weight, and power requirements of vision sensors (as opposed to radar and TCAS). This paper describes the development and evaluation of a real-time vision-based collision detection system suitable for fixed-wing aerial robotics. Using two fixed-wing UAVs to recreate various collision-course scenarios, we were able to capture highly realistic vision (from an onboard camera perspective) of the moments leading up to a collision. This type of image data is extremely scarce and was invaluable in evaluating the detection performance of two candidate target detection approaches. Based on the collected data, our detection approaches were able to detect targets at distances ranging from 400m to about 900m. These distances (with some assumptions about closing speeds and aircraft trajectories) translate to an advanced warning of between 8-10 seconds ahead of impact, which approaches the 12.5 second response time recommended for human pilots. We overcame the challenge of achieving real-time computational speeds by exploiting the parallel processing architectures of graphics processing units found on commercially-off-the-shelf graphics devices. Our chosen GPU device suitable for integration onto UAV platforms can be expected to handle real-time processing of 1024 by 768 pixel image frames at a rate of approximately 30Hz. Flight trials using manned Cessna aircraft where all processing is performed onboard will be conducted in the near future, followed by further experiments with fully autonomous UAV platforms.

An application of near-infrared and mid-infrared spectroscopy to the study of natural halotrichites : halotrichite, apjohnite and wupatkiite

Near-infrared (NIR) and Fourier transform infrared (FTIR) spectroscopy have been used to determine the mineralogical character of isomorphic substitutions for Mg2+ by divalent transition metals Fe, Mn, Co and Ni in natural halotrichite series. The minerals are characterised by d-d transitions in NIR region 12000-7500 cm-1. NIR spectrum of halotrichite reveals broad feature from 12000 to 7500 cm-1 with a splitting of two bands resulting from ferrous ion transition 5T2g �� 5Eg. The presence of overtones of OH- fundamentals near 7000 cm-1 confirms molecular water in the mineral structure of the halotrichite series. The appearance of the most intense peak at around 5132 cm-1 is a common feature in the three minerals and is derived from combination of OH- vibrations of water molecules and ���2 water bending modes. The influence of cations like Mg2+, Fe2+, Mn2+, Co2+, Ni2+ shows on the spectra of halotrichites. Especially wupatkiite-OH stretching vibrations in which bands are distorted conspicuously to low wave numbers at 3270, 2904 and 2454 cm-1. The observation of high frequency ���2 mode in the infrared spectrum at 1640 cm-1 indicates coordination of water molecules is strongly hydrogen bonded in natural halotrichites. The splittings of bands in ���3 and ���4 (SO4)2- stretching regions may be attributed to the reduction of symmetry from Td to C2v for sulphate ion. This work has shown the usefulness of NIR spectroscopy for the rapid identification and classification of the halotrichite minerals.

Submarine dynamic modelling

This paper discusses the development of a dynamic model for a torpedo shaped sub- marine. Expressions for hydrostatic, added mass, hydrodynamic, control surface and pro- peller forces and moments are derived from first principles. Experimental data obtained from flume tests of the submarine are inserted into the model in order to provide computer simulations of the open loop behavior of the system.

A hidden Markov model and relative entropy rate approach to vision-based dim target detection for UAV sense-and-avoid

Uninhabited aerial vehicles (UAVs) are a cutting-edge technology that is at the forefront of aviation/aerospace research and development worldwide. Many consider their current military and defence applications as just a token of their enormous potential. Unlocking and fully exploiting this potential will see UAVs in a multitude of civilian applications and routinely operating alongside piloted aircraft. The key to realising the full potential of UAVs lies in addressing a host of regulatory, public relation, and technological challenges never encountered be- fore. Aircraft collision avoidance is considered to be one of the most important issues to be addressed, given its safety critical nature. The collision avoidance problem can be roughly organised into three areas: 1) Sense; 2) Detect; and 3) Avoid. Sensing is concerned with obtaining accurate and reliable information about other aircraft in the air; detection involves identifying potential collision threats based on available information; avoidance deals with the formulation and execution of appropriate manoeuvres to maintain safe separation. This thesis tackles the detection aspect of collision avoidance, via the development of a target detection algorithm that is capable of real-time operation onboard a UAV platform. One of the key challenges of the detection problem is the need to provide early warning. This translates to detecting potential threats whilst they are still far away, when their presence is likely to be obscured and hidden by noise. Another important consideration is the choice of sensors to capture target information, which has implications for the design and practical implementation of the detection algorithm. The main contributions of the thesis are: 1) the proposal of a dim target detection algorithm combining image morphology and hidden Markov model (HMM) filtering approaches; 2) the novel use of relative entropy rate (RER) concepts for HMM filter design; 3) the characterisation of algorithm detection performance based on simulated data as well as real in-flight target image data; and 4) the demonstration of the proposed algorithm's capacity for real-time target detection. We also consider the extension of HMM filtering techniques and the application of RER concepts for target heading angle estimation. In this thesis we propose a computer-vision based detection solution, due to the commercial-off-the-shelf (COTS) availability of camera hardware and the hardware's relatively low cost, power, and size requirements. The proposed target detection algorithm adopts a two-stage processing paradigm that begins with an image enhancement pre-processing stage followed by a track-before-detect (TBD) temporal processing stage that has been shown to be effective in dim target detection. We compare the performance of two candidate morphological filters for the image pre-processing stage, and propose a multiple hidden Markov model (MHMM) filter for the TBD temporal processing stage. The role of the morphological pre-processing stage is to exploit the spatial features of potential collision threats, while the MHMM filter serves to exploit the temporal characteristics or dynamics. The problem of optimising our proposed MHMM filter has been examined in detail. Our investigation has produced a novel design process for the MHMM filter that exploits information theory and entropy related concepts. The filter design process is posed as a mini-max optimisation problem based on a joint RER cost criterion. We provide proof that this joint RER cost criterion provides a bound on the conditional mean estimate (CME) performance of our MHMM filter, and this in turn establishes a strong theoretical basis connecting our filter design process to filter performance. Through this connection we can intelligently compare and optimise candidate filter models at the design stage, rather than having to resort to time consuming Monte Carlo simulations to gauge the relative performance of candidate designs. Moreover, the underlying entropy concepts are not constrained to any particular model type. This suggests that the RER concepts established here may be generalised to provide a useful design criterion for multiple model filtering approaches outside the class of HMM filters. In this thesis we also evaluate the performance of our proposed target detection algorithm under realistic operation conditions, and give consideration to the practical deployment of the detection algorithm onboard a UAV platform. Two fixed-wing UAVs were engaged to recreate various collision-course scenarios to capture highly realistic vision (from an onboard camera perspective) of the moments leading up to a collision. Based on this collected data, our proposed detection approach was able to detect targets out to distances ranging from about 400m to 900m. These distances, (with some assumptions about closing speeds and aircraft trajectories) translate to an advanced warning ahead of impact that approaches the 12.5 second response time recommended for human pilots. Furthermore, readily available graphic processing unit (GPU) based hardware is exploited for its parallel computing capabilities to demonstrate the practical feasibility of the proposed target detection algorithm. A prototype hardware-in- the-loop system has been found to be capable of achieving data processing rates sufficient for real-time operation. There is also scope for further improvement in performance through code optimisations. Overall, our proposed image-based target detection algorithm offers UAVs a cost-effective real-time target detection capability that is a step forward in ad- dressing the collision avoidance issue that is currently one of the most significant obstacles preventing widespread civilian applications of uninhabited aircraft. We also highlight that the algorithm development process has led to the discovery of a powerful multiple HMM filtering approach and a novel RER-based multiple filter design process. The utility of our multiple HMM filtering approach and RER concepts, however, extend beyond the target detection problem. This is demonstrated by our application of HMM filters and RER concepts to a heading angle estimation problem.