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.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Modelling of inflatable rescue boats (IRBs) in surf conditions to reduce injuries

The Inflatable Rescue Boat (IRB) is arguably the most effective rescue tool used by the Australian surf lifesavers. The exceptional features of high mobility and rapid response have enabled it to become an icon on Australia's popular beaches. However, the IRB's extensive use within an environment that is as rugged as it is spectacular, has led it to become a danger to those who risk their lives to save others. Epidemiological research revealed lower limb injuries to be predominant, particularly the right leg. The common types of injuries were fractures and dislocations, as well as muscle or ligament strains and tears. The concern expressed by Surf Life Saving Queensland (SLSQ) and Surf Life Saving Australia (SLSA) led to a biomechanical investigation into this unique and relatively unresearched field. The aim of the research was to identify the causes of injury and propose processes that may reduce the instances and severity of injury to surf lifesavers during IRB operation. Following a review of related research, a design analysis of the craft was undertaken as an introduction to the craft, its design and uses. The mechanical characteristics of the vessel were then evaluated and the accelerations applied to the crew in the IRB were established through field tests. The data were then combined and modelled in the 3-D mathematical modelling and simulation package, MADYMO. A tool was created to compare various scenarios of boat design and methods of operation to determine possible mechanisms to reduce injuries. The results of this study showed that under simulated wave loading the boats flex around a pivot point determined by the position of the hinge in the floorboard. It was also found that the accelerations experienced by the crew exhibited similar characteristics to road vehicle accidents. Staged simulations indicated the attributes of an optimum foam in terms of thickness and density. Likewise, modelling of the boat and crew produced simulations that predicted realistic crew response to tested variables. Unfortunately, the observed lack of adherence to the SLSA footstrap Standard has impeded successful epidemiological and modelling outcomes. If uniformity of boat setup can be assured then epidemiological studies will be able to highlight the influence of implementing changes to the boat design. In conclusion, the research provided a tool to successfully link the epidemiology and injury diagnosis to the mechanical engineering design through the use of biomechanics. This was a novel application of the mathematical modelling software MADYMO. Other craft can also be investigated in this manner to provide solutions to the problem identified and therefore reduce risk of injury for the operators.

Dangerous places: A novel

Dangerous Places is a novel about the gap between mythological (or 'dreamed') constructions of reality and actual life. The story centres on V en, a married woman with two young children. Her love for her children is fiercely protective and encompassing, but she feels alienated from her husband and to a certain extent her society; so when her first love, Yanni, re-enters her life,she is strongly tempted to resume her affair with him. She is however seduced more by the memories she has 'mythologized' about him than by his physical reality; in the course of the novel she is forced to come to terms with her own delusions. The subplot of the novel involves other characters who are caught between illusion and reality as well, and who deal with 'truth' in differing ways. The themes of the book are explored using a number of structures which underlie and support the surface story. The Greek myths of Adonis/ Aphrodite and Hades/Persephone are framing agents for the plot, and the setting in contemporary Brisbane and North Stradbroke Island is symbolic.

Re-visioning a "novel concept" : beyond vision and revision to advanced editing strategies

This thesis is a work of creative practice-led research comprising two components. The first component is a speculative thriller novel, entitled Diamond Eyes. (Contracted for publication in 2009 by Harper Collins: Voyager as the first in a trilogy, under the name AA Bell.) The second component is an exegesis exploring the notion of re-visioning a novel. Re-visioning, not to be confused with revision, refers to advance editing strategies required when the original vision of a novel changes during development.