Optimising low-cost GNSS positioning for road constrained vehicles using a Bayesian filter Andrej Peisker ORCID 0000-0002-3379-6645 Doctor of Philosophy (PhD) March 2018 Department of Infrastructure Engineering, The University of Melbourne Submitted for the total fulfilment of the PhD Abstract Co-operative Intelligent Transportation Systems (C-ITS) are a growing industry that have significant implications for the safety and efficiency of on-road vehicle use. Accurate and reliable vehicle positioning is a critical component in C-ITS in order for the component vehicles and infrastructure to interact effectively and information-share for col- lectively enhanced services. Such services include vehicle navigation, collision-avoidance systems, driver assistance and emergency notifications (for example, mobilised if an ambulance needs to pass through the street occupied by the positioned vehicle). A range of existing and emerging technologies have been developed and tailored to improve the accuracy and continuity of positioning for C-ITS, which include Global Navigation Satellite Systems (GNSS), digital road maps, inertial sensor technologies, dedicated short-range communication (DSRC) and other technologies. However many of these technologies are expensive and in many cases prohibitive for large scale roll- out and general public use. Therefore it is important to develop and optimise low-cost vehicle positioning methods to complement more expensive technologies in order to assist with the large scale feasibility of C-ITS, as well as meet individual-scale immediate user needs at viable cost. The subject of this PhD research is optimising low-cost vehicle positioning; that is maximising the accuracy and continuity of position estimates generated from exclusively low-cost data sources. The focus of this research is improving mathematical methods for data fusion (the statistical combination of diverse data inputs for estimation), and a new Bayesian approach is presented for real-time vehicle positioning from the data fusion of low-cost GNSS data and freely available digital road map data. The design of this new method, the Gaussian Cluster Approximate Filter (GCAF), is driven in part by a detailed study of common shortcomings and the causes of failure-modes of existing methods in a range of common urban vehicular situations, in order to be robust to these positioning challenges. Through robust testing it is demonstrated that effective combination of these two low-cost data sources using statistically robust mathematical methods provides substantial improvement to existing approaches, and lessens the need for more expensive sensors in many common vehicular environments. The method is designed to be easily modified to allow fusion with other data sources as future applications may require. 1 Declarations I declare that: 1. This thesis comprises original work of Andrej Peisker towards the PhD except where indicated and cited in the text 2. Due acknowledgment has been made in the text to all other material used 3. the thesis has fewer words than the maximum word limit, exclusive of tables, maps, bibliographies and appendices Signed Andrej Peisker (PhD candidate) 2 Preface This is to indicate that: 1. This thesis was not carried out in collaboration with others; all original work is the work of Andrej Peisker 2. No work towards the thesis has been submitted for other qualifications 3. No work towards the thesis was done prior to enrolment in this PhD degree 4. Other than immediate supervisors' feedback, third party editorial assistance was also provided in preparation of the thesis. Professor Stefan Winter read and provided feedback, and is a professor in the Geomatics field at the University of Melbourne and has significant experience in the discipline. Dr Adrian Flitney read and provided feedback on grammar, spelling and overall interpretability but not on subject matter content; he has a background in Physics but not Geomatics. 5. No publications or articles have been produced for or from this thesis 6. The PhD research was funded by a Strategic Australian Postgraduate Award (StrAPA), funded in part by the Defence Sciences Institute. 3 Acknowledgments Sincere thanks go to my family, friends, supervisors and university colleagues who have provided an eternal source of encouragement, inspiration and valuable external perspective during my work on this thesis. This includes my mum, dad, their respective partners and my grandparents for their continued support through this process. Partic- ular thanks go to my supervisors Professor Allison Kealy and Associate Professor Mark Morelande for their wisdom, time, effort and patience shown over a number of years to a student learning the ropes of inter-disciplinary research in a relatively unfamiliar field at a higher level. I also thank Dr Adrian Flitney and Professor Stefan Winter for their time and effort given generously to reading providing feedback on my thesis, and Azmir Hasnur Rabiain for his generous guidance and help at the start of my candidature and throughout. I would like to acknowledge the Wurundjeri people of the Kulin Nation and their elders past and present, on whose lands the University of Melbourne resides, and on which I was offered, studied for and completed my PhD. 4 Contents 1 Research problem, aims, hypotheses and methodology 10 1.1 Positioning in Intelligent Transportation Systems: Background and Definitions . 10 1.2 Research Aims and Hypotheses . 12 1.3 Research Challenges . 12 1.3.1 Positioning-Hostile Environments . 13 1.3.2 Integrating Road Constraints into Positioning . 15 1.3.3 Positioning Performance Requirements of C-ITS . 15 1.4 Methodology and Contributions . 16 1.4.1 Chapters 2 and 3: Understanding the Accuracy and Continuity Impacts of Positioning Envi- ronments and Road Constraint Integration . 16 1.4.2 Developing a New Solution for Road Constrained Vehicle Positioning . 17 2 Literature Review 21 2.1 Classifying positioning-hostile environments in urban GNSS-aided positioning . 21 2.1.1 Positioning-hostile environments . 21 2.2 A review of existing positioning methods and their performance characteristics in urban areas . 25 2.2.1 Some standard methods and statistical models used in positioning . 25 2.2.2 Standard methods for integrating road maps into the position estimation process . 31 2.3 A quantitative evaluation of the performance of existing positioning solutions . 35 2.3.1 Quantitative positioning performance survey across a range of positioning environments . 36 2.3.2 Some remarks on the reliability of self-evaluation experiments . 39 2.3.3 Conclusions . 39 3 Quantifying Low-Cost Positioning Performance Impacts of Vehicular Environments 41 3.1 Introduction . 41 3.2 Methodology for measuring impacts of the vehicle's environment on low-cost positioning performance 41 3.2.1 The Bayesian Root-Mean-Square Error (BRMSE) measure of positioning performance in sim- ulated environments . 42 3.2.2 Parameters and design of environmental impact data collection experiments . 44 3.2.3 Road Network Representation . 44 3.2.4 Models for generating vehicle trajectories and GNSS measurements . 46 3.2.5 Estimation Model Co-ordinates and input Parameters . 48 3.3 Evaluation of the BRMSE closed-form solution . 50 3.4 Numerical evaluation of closed form BRMSE solution to generate positioning error impact dataset . 53 3.5 Discussion of numerical results and comparison with surveyed performance validations . 65 3.5.1 Performance impacts of single-factor environments on low-cost positioning . 66 3.5.2 Analysis of findings . 67 3.6 Conclusions . 68 5 4 The Gaussian Cluster Approximate Filter: A new low-cost solution for statistically robust urban vehicle positioning 69 4.1 GCAF: Algorithm methodology and quantitative models . 70 4.1.1 Introduction . 70 4.1.2 GCAF: Estimation framework, co-ordinate systems and modeling road constraints . 70 4.1.3 State space and initialisation of the filter . 71 4.1.4 Stochastic models for vehicle state dynamics and GNSS measurements . 73 4.2 Bringing the elements together: Mathematical solution to the Bayes equation for the GCAF position estimator . 80 4.2.1 Gaussian cluster evolution . 80 4.2.2 Handling segment boundary crossing during propagation . 81 4.2.3 Component sampling regions . 83 4.2.4 GNSS measurement integration into positioning . 83 4.2.5 Reducing computational complexity of P¯pxi|Ziq for subsequent iterations . 86 4.2.6 Modeling and estimating the evolution of vehicle motion state . 90 4.2.7 Gaussian cluster merging with multiple model dynamics . 90 4.2.8 Gaussian cluster component elimination and re-normalisation . 91 4.2.9 Computing position estimates from P^pxi|Ziq ........................... 92 4.3 Conclusions . 94 5 Positioning Performance Evaluation of the Gaussian Cluster Approximate Filter 95 5.1 Introduction . 95 5.2 Experimental design and results of the GCAF positioning performance tests . 96 5.2.1 Performance evaluation methodology and challenges . 96 5.2.2 GCAF Performance test design based on batch Monte-Carlo simulations (Part 1) . 96 5.2.3 GCAF Performance test design based on real GNSS-SPP measurement data (Part 2) . 103 5.2.4 Results summary . 122 5.3 Key findings and analysis of the GCAF performance evaluation results . 123 5.3.1 Key findings of the performance evaluation tests . 123 5.3.2 Analysis of key findings from the GCAF performance evaluation tests . 125 5.4 Conclusions . 127 6 Conclusions 128 6.1 Conclusions from the research . 128 6.1.1 Overview . 128 6.1.2 Validation of hypotheses based on key findings . 128 6.1.3 Achievement of research aims . 130 6.2 Further Work . 131 6.2.1 Multi-sensor integration . 131 6.2.2 Accounting for geographical errors in the road map . 133 Bibliography 135 Appendices 139 Appendix A Proof of Lemma 1 140 A.1 Nonlinear road constraint integration with GNSS: analytical challenges . 140 A.2 Background to this analysis . 140 6 A.3 Road segment boundary effects . 140 A.4 Loss of Truncated Gaussian Structure following linear propagation .