Trajectory reconstruction of shooting incidents can help investigators determine critical case information regarding the number of shooters involved, their location(s), and intent. The examination of trace amounts of intermediate target materials collected on the surface of spent bullets provides crucial information needed for trajectory reconstruction. Determining the origin of an unknown material adhered to a spent bullet allows for the identification of intermediate targets the bullet either contacted or penetrated during flight. Although significant information can be obtained from examination of these trace materials adhered to spent bullets, this aspect of trajectory reconstruction is often ignored. The ability of different bullet types to collect trace materials from intermediate targets and the ability to associate these trace materials to their origin was examined using microscopy and Direct Analysis in Real Time (DART). Full metal jacket (FMJ), jacketed hollow point (JHP), and lead round nose (LRN) bullets were fired into sheets of five different commonly used building materials (oriented strand board, sanded plywood, white melamine board, synthetic PVC board, and medium density fiberboard) to produce a total of 45 spent bullets to be examined. All spent bullets were examined and photographed using a DSLR camera paired with a stereomicroscope. The spent bullets were then examined using DART/MS to determine if any ion profiles generated from the trace materials could be associated with those of the intermediate target building materials which the bullets were fired through. The collection of trace material from all five types used was highly dependent on the type of bullet. Very minimal amounts of trace materials were observed on the majority of LRN bullets, which failed to produce an identifiable ion signature. The FMJ bullets that were fired through PVC material collected trace material that produced an ion profile, while all other building materials failed to transfer to the FMJ bullets. All JHP bullets collected significant amounts of the five building materials tested inside the hollow point cavity and along the nose of the bullet. In every spent JHP bullet sample, the trace material collected produced a unique ion profile. Additionally, MS data from four of the five building materials tested matched the MS data generated from trace material collected on JHP bullets from the respective target materials.

The reconstruction of entry, descent and landing (EDL) trajectories is significantly affected by the knowledge of the atmospheric conditions during flight. Away from Earth, this knowledge is generally characterized by a high degree of uncertainty, which drives the accuracy of many important atmosphere-relative states. One method of obtaining the in-flight atmospheric properties during EDL is to utilize the known vehicle aerodynamics in deriving the trajectory parameters. This is the approach taken by this research in developing a methodology for accurate estimation of ambient atmospheric conditions and atmosphere-relative states. The method, referred to as the aerodynamic database (ADB) reconstruction, performs reconstruction by leveraging data from flight measurements and pre-flight models. In addition to the estimation algorithm, an uncertainty assessment for the ADB reconstruction method is developed. This uncertainty assessment is a unique application of a fundamental analysis technique that applies linear covariance mapping to transform input variances into output uncertainties. The ADB reconstruction is applied to a previous mission in order to demonstrate its capability and accuracy. Flight data from the Mars Science Laboratory (MSL) EDL, having successfully completed on August 5th 2012, is used for this purpose. Comparisons of the estimated states are made against alternate reconstruction approaches to understand the advantages and limitations of the ADB reconstruction. This thesis presents a method of reconstruction for EDL systems that can be used as a valuable tool for planetary entry analysis.

Vehicle trajectory data has played a critical role in the recent history of traffic flow and CAV operations-related studies. However, available trajectories have limited coverage, either spatial or temporal. The implementation of CAV technology is expected to produce a large-scale trajectory dataset. However, at the initial implementation level, the trajectory data produced is expected to have gaps in terms of completeness. This research develops a data model for large-scale trajectory data that can be built on CAV-collected trajectories and easily manipulated to produce traffic parameters for CAV control and operation research. A benchmarking process has been applied to test a trajectory reconstruction approach to develop a population database from partial trajectories to fill the expected data gap in CAV feedback. The large-scale trajectory data is then used in CAV operations-related studies focusing on CAV's integration with human drivers and developing performance matrices for CAV-controlled optimized trajectories. This research used large-scale vehicle trajectory data from Wide Area Motion Imagery (WAMI) developed by PVLabs for modeling and analyzing traffic characteristics as a surrogate of CAV-collected trajectories. This timestamped location data capture provides trajectory information at an interval of one second. Trajectories from an approximate area of four-square kilometers in downtown Hamilton, Canada, are used to develop a data model to extract and store traffic characteristics. The video data was collected for two three-hour continuous periods, one in the morning and one in the evening of the same day. Like other moving object detection-based algorithms, this data suffers from false-positive detection, false-negative detection, and other positional inaccuracies caused by faulty image registration. A context-based trajectory filtering algorithm has been developed and validated against ten minutes of vehicle counts from actual WAMI images. The filtered data provides a sample of trajectories over the area, including complete and partial vehicle trajectories, excluding undetected ones. The missing trajectory reconstruction process using a dynamic state estimation process is developed to reconstruct partial and missing trajectories. A data analytics approach predicts the number of missing trajectories between two successive detections in the traffic stream on a roadway lane. A benchmarking test of the performance of the missing trajectory prediction algorithm is conducted using the NGSIM I80 database. A frame-by-frame learning method is developed to join the identified missing trajectories. This data analytics approach preserves the naturalistic property of the trajectory, which was a concern of previous traffic-flow model-based approaches. Joining partial/split trajectories provides a more comprehensive picture of the trajectory population. Due to data structure similarities, including the nature of the split and missing trajectories, the methods developed in this study to recover trajectories can be adopted for future CAV feedback data in a mixed traffic scenario. The applicability of using the large-scale trajectory data model is explored in two performance areas of CAV operations. The first is a scenario-based testing process, which evaluates the "intelligence" of a CAV in handling interactions with Human driven Vehicles (HV) by artificially replacing an HV in the traffic stream with a CAV. Scenario-based testing is conducted for a particular Operational Design Domain (ODD). The ODD is defined as operating conditions under which particular driver assistance or automated control systems are designed to function. Existing literature on scenario-based testing primarily focuses on CAV-HV interaction on highways as large-scale naturalistic trajectory data are available to facilitate such studies. This research explores car-following and lane-changing aspects of arterial CAV testing. The large-scale trajectory data model generates testing scenarios and calibrates the surrogate model for CAV operation. The modification to the trajectory data model to accommodate the scenario-based testing is illustrated. The second consists of using the large-scale trajectory data model to estimate a new trajectory smoothness parameter that can indicate the impact of intersection stop-and-go movement on the smoothness of the entire trajectory. This smoothness parameter can be applied as an optimization variable in future trajectory control-based intersection management. Long-duration trajectories from the large-scale trajectory data are used to estimate the spectral arc length parameter for trajectory smoothness. This research only estimates smoothness parameters for human-driven vehicles to illustrate its applicability for vehicle trajectories. This research developed a framework for applying expected partial trajectories from CAV technology in estimating near-complete trajectories. The large-scale data application process in two CAV operations-related studies is also provided. / Doctor of Philosophy / The decision-making process undertaken by transportation agencies for planning, evaluating, and operating transportation facilities relies on analyzing traffic and driver behavior for prevailing and future traffic conditions. The analytical tools for policy, design, decision-making, and safety analysis use aggregated and disaggregated traffic parameters. Traffic parameters are information about the dynamic state of the traffic. In the case of a vehicle, the dynamic state information can be location, speed, acceleration, heading, and spacing with other vehicles in the traffic stream. The sequence of these dynamic parameters is called vehicle trajectories in a broader term. The trajectory information is collected using several direct and indirect collection systems. The implementation of CAV technologies is expected to provide a new source of vehicle trajectory information. Trajectory data are integral to CAV safety, operational evaluation, and optimization control algorithms. Trajectory data are also used to develop, calibrate, and validate the models representing a particular aspect of human driver behavior, and the recent development of CAV has elevated the necessity and application of trajectory data. As a result, a significant demand exists in academia and industry for the procedure to create trajectories of the vehicle population in the traffic stream. The trajectory population represents the dynamic properties of all the vehicles moving over the data collection area. The primary goal of this research is to develop and apply a large-scale trajectory population database. Trajectories are typically stored in a Moving Object Database (MOD). This research leverages a MOD database collected by a new generation of Wide-Area Motion Imagery (WAMI). The WAMI system collects images from a high-altitude moving aerial platform with high-definition cameras at a fixed time interval, which captures the trajectories of vehicles in the collection area. However, validating the created trajectories for completeness and data noise revealed continuity and consistency gaps in trajectories. A multistep data mining process is undertaken to filter, process, and extract sample trajectories with reduced data noise. A trajectory reconstruction task is undertaken to reduce the data gap. A benchmarking performance test for trajectory reconstruction is conducted using NGSIM I80 data because it has been validated in multiple studies and contains trajectories of all vehicles during the collection period (i.e., trajectory population). The trajectory reconstruction methodology developed in this research can be adapted for future CAV-collected partial trajectory data. The development of the trajectory reconstruction methodology and training data created from NGSIM I80 is one of the main contributions of this research in the field of trajectory reconstruction. Several traffic flow measures are then estimated from the sample trajectories that outline the analytical requirements to integrate trajectory data with roadway infrastructure. A data model is developed to store and manipulate dynamic trajectory parameters efficiently. The resulting data processing and integration process can be applied to CAV-collected trajectories to create an analytical trajectory database. The large-scale trajectory database is used to illustrate its capability in evaluating CAV operating models, specifically the car-following and lane-changing models on an arterial network. The car-following model mimics the longitudinal movement of real-world drivers following another vehicle. The lane-changing model predicts lane-changing behavior due to path-planning requirements and navigating surrounding traffic conditions. The overall operational model evaluation process is called accelerated evaluation, in which the naturalistic vehicle movement data is used to measure CAV's operational and safety performance. For a second application of the large-scale trajectory data, long-duration trajectories are used to develop a trajectory smoothness performance measure that can be used to test different trajectory control approaches for intersection movement management. This research is one of the early attempts to leverage large-scale vehicle trajectory datasets in transportation engineering applications. Its primary contribution is the development of a comprehensive trajectory validation methodology that can be applied to future CAV feedback to produce a trajectory population database with enhanced analytical capability. The secondary output of this research is benchmarking results for different analytical methodologies to develop the trajectories that can be used in future research and development as a reference.

Violent crimes involving bloodshed may result in the formation of a number of blood drops that move through air and impact onto a surface producing a bloodstain pattern. Bloodstain Pattern Analysis (BPA), the analysis of the position, distribution, size and morphology of the stains within the pattern present at a crime scene, may provide information about the events that gave rise to the bloodshed. The location of blood origin, i.e. victim’s position at the moment of wounding and (or) wound location, determination is of major interest to BPA. This study investigated the dynamics of formation and flight of blood drops commonly found at a crime scene (so-called passive, cast-off, impact and gunshot drops) with the aim to facilitate blood origin determination. Features of blood drop formation at passive dripping with correlation to dripping surface characteristics were studied experimentally. A numerical scheme for accurate blood drop flight characteristics modelling, including oscillations, deformation and disintegration, was developed and validated against a number of analytical and experimental cases with special attention to the passive blood drop oscillations and ultimate deformation at terminal velocity, cast-off and impact blood drop deformation and breakup features. This provided an efficient and accurate method for typical blood drop flight reconstruction from the blood origin to impact as well as from the bloodstain location to the possible blood origin. Factors affecting blood drop trajectory and blood origin estimation were studied using the developed scheme.

O cada vez maior número de tecnologias que fornecem serviços de geolocalização tem possibilitado gerar uma grande quantidade de dados de geolocalização. Estes dados, são armazenados principalmente como pontos de localização com informação temporal. Uma trajetória é definida como uma sequência discreta e finita destes pontos de localização. Nos últimos anos, a recente área de mineração de trajetórias visa aproveitar esta abundância de dados. Nesta área, existem várias técnicas de mineração desenvolvidas, mas todas elas dependem diretamente da qualidade das trajetórias. Assim, o preprocessamento tem um papel primordial na mineração de trajetórias. Entre as tarefas de preprocessamento, um problema relevante é a reconstrução ou inferência de trajetórias. Devido ao alto consumo de energia de dispositivos de localização como o GPS e ao crescente uso de geo-marcações nas redes sociais, que possibilita a construção de trajetórias ordenando temporalmente estas marcações, muitas das trajetórias existentes apresentam taxas de amostragem muito baixas. A maioria das pesquisas nesse problema utilizam, no caso de áreas urbanizadas, informações do grafo formado por ruas e cruzamentos. Porém, elas levam em conta apenas trajetórias de veículos principalmente pelo fato que muitos dos percursos dos pedestres ficam fora das ruas. Atualmente, graças às plataformas livres de mapas colaborativos, é possível incluir estes trajetos como parte das informações de ruas. Assim, este projeto tem o objetivo de investigar o uso das informações das ruas na reconstrução de trajetórias, principalmente de pedestres. O escopo da proposta compreende o desenvolvimento de uma rede social geo-localizada com o intuito de capturar dados de localização. Posteriormente, estes dados serão anonimizados, utilizados na reconstrução de trajetórias de pedestres e disponibilizados para uso em pesquisas futuras. / The ever-greater number of technologies providing location-based services has allowed the generation of big amounts of geolocation data. This data is mainly stored as location points in conjunction with temporal information. A trajectory is defined as a discrete and finite sequence of this kind of points. In recent years, the relatively new field of trajectory data mining aims to leverage this abundance of data. On this field, there are several data mining techniques developed, but all of these depend on trajectory quality. Hence, preprocessing becomes relevant to this field. Among trajectory data mining tasks, one important problem is trajectory reconstruction. Due to the high energy consumption of geolocation devices like GPS and the growing usage of geo-tags in social networks, which can represent trajectories by being sorted chronologically, most of these trajectories are collected at low sampling rates. A majority of research on this problem is focused on using road network information in urbanized areas to reconstruct trajectories. However, these approaches take into account vehicle trajectories only due to fact that most pedestrian paths do not always follow the same road network routes than vehicles. Currently, thanks to open collaborative maps, it is possible to add pedestrian paths to the road network structure. Thereby, this project aims to research the usage of road network information in pedestrian trajectories reconstruction. This projects scope comprises the development of a location-based social network to collect geolocation data. Subsequently, this data will be anonymized, used for pedestrian trajectory reconstruction and, finally, made available for research purposes.

O cada vez maior número de tecnologias que fornecem serviços de geolocalização tem possibilitado gerar uma grande quantidade de dados de geolocalização. Estes dados, são armazenados principalmente como pontos de localização com informação temporal. Uma trajetória é definida como uma sequência discreta e finita destes pontos de localização. Nos últimos anos, a recente área de mineração de trajetórias visa aproveitar esta abundância de dados. Nesta área, existem várias técnicas de mineração desenvolvidas, mas todas elas dependem diretamente da qualidade das trajetórias. Assim, o preprocessamento tem um papel primordial na mineração de trajetórias. Entre as tarefas de preprocessamento, um problema relevante é a reconstrução ou inferência de trajetórias. Devido ao alto consumo de energia de dispositivos de localização como o GPS e ao crescente uso de geo-marcações nas redes sociais, que possibilita a construção de trajetórias ordenando temporalmente estas marcações, muitas das trajetórias existentes apresentam taxas de amostragem muito baixas. A maioria das pesquisas nesse problema utilizam, no caso de áreas urbanizadas, informações do grafo formado por ruas e cruzamentos. Porém, elas levam em conta apenas trajetórias de veículos principalmente pelo fato que muitos dos percursos dos pedestres ficam fora das ruas. Atualmente, graças às plataformas livres de mapas colaborativos, é possível incluir estes trajetos como parte das informações de ruas. Assim, este projeto tem o objetivo de investigar o uso das informações das ruas na reconstrução de trajetórias, principalmente de pedestres. O escopo da proposta compreende o desenvolvimento de uma rede social geo-localizada com o intuito de capturar dados de localização. Posteriormente, estes dados serão anonimizados, utilizados na reconstrução de trajetórias de pedestres e disponibilizados para uso em pesquisas futuras. / The ever-greater number of technologies providing location-based services has allowed the generation of big amounts of geolocation data. This data is mainly stored as location points in conjunction with temporal information. A trajectory is defined as a discrete and finite sequence of this kind of points. In recent years, the relatively new field of trajectory data mining aims to leverage this abundance of data. On this field, there are several data mining techniques developed, but all of these depend on trajectory quality. Hence, preprocessing becomes relevant to this field. Among trajectory data mining tasks, one important problem is trajectory reconstruction. Due to the high energy consumption of geolocation devices like GPS and the growing usage of geo-tags in social networks, which can represent trajectories by being sorted chronologically, most of these trajectories are collected at low sampling rates. A majority of research on this problem is focused on using road network information in urbanized areas to reconstruct trajectories. However, these approaches take into account vehicle trajectories only due to fact that most pedestrian paths do not always follow the same road network routes than vehicles. Currently, thanks to open collaborative maps, it is possible to add pedestrian paths to the road network structure. Thereby, this project aims to research the usage of road network information in pedestrian trajectories reconstruction. This projects scope comprises the development of a location-based social network to collect geolocation data. Subsequently, this data will be anonymized, used for pedestrian trajectory reconstruction and, finally, made available for research purposes.

This dissertation is focused on target trajectory identification using CW radar sensor network measuring. An omni-directional radar based on single mixing is considered for measurement in ballistic tunnel, where information about direction of target approaching is a priory known. Applied experimental radar network setup with system controller and acquisition units is demonstrated. Mathematical models and optimized structures have been developed for fitting of system parameters and presented in the theoretical part. The second part is aimed to the multi-trajectory identification. New methodical techniques of this work consist in identification of the points of the closest approach with V model function and utilizing gradient methods for path identification.

L’imagerie RSO circulaire aéroportée permet d’obtenir de nombreuses informations sur les zones imagées et sur les cibles mobiles. Les objets peuvent être observés sous plusieurs angles, et l’illumination continue d’une même scène permet de générer plusieurs images successives de la même zone. L’objectif de cette thèse est de développer une méthode de reconstruction de trajectoire de cibles mobiles en imagerie RSO circulaire monovoie, et d’étudier les performances de la méthode proposée. Nous avons tout d’abord mesuré les coordonnées apparentes des cibles mobiles sur les images RSO et leur paramètre de défocalisation. Ceci permet d’obtenir des informations de mouvement des cibles, notamment de vitesse et d’accélération. Nous avons ensuite utilisé ces mesures pour définir un système d’équations non-linéaires permettant de faire le lien entre les trajectoires réelles des cibles mobiles et leurs trajectoires apparentes. Par une analyse mathématique et numérique de la stabilité de ce système, nous avons montré que seul un modèle de cible mobile avec une vitesse constante permet de reconstruire précisément les trajectoires des cibles mobiles, sous réserve d’une excursion angulaire suffisante. Par la suite, nous avons étudié l’influence de la résolution des images sur les performances de reconstruction des trajectoires, en calculant théoriquement les précisions de mesure et les précisions de reconstruction qui en découlent. Nous avons mis en évidence l’existence théorique d’une résolution azimutale optimale, dépendant de la radiométrie des cibles et de la validité des modèles étudiés. Finalement nous avons validé la méthode développée sur deux jeux de données réelles. / Circular SAR imagery brings a lot of information concerning the illuminated scenes and the moving targets. Objects may be seen from any angle, and the continuity of the illumination allows generating a lot of successive images from the same scene. In the scope of this thesis, we develop a moving target trajectory reconstruction methodology using circular SAR imagery, and we study the performances of this methodology. We have first measured the apparent coordinates of the moving targets on SAR images, and also the defocusing parameter of the targets. This enables us to obtain information concerning target movement, especially the velocity and the acceleration. We then used these measurements to develop a non-linear system that makes the link between the apparent trajectories of the moving targets and the real ones. We have shown, by a mathematical and numerical analysis of the robustness, that only a model of moving target with constant velocity enables us to obtain accurate trajectory reconstructions from a sufficient angular span. Then, we have studied the azimuth resolution influence on the reconstruction accuracy. In order to achieve this, we have theoretically estimated the measurement accuracy and the corresponding reconstruction accuracy. We have highlighted the existence of an optimal azimuth resolution, depending on the target radiometry and on the validity of the two target models. Finally, we have validated the method on two real data sets on X-Band acquired by SETHI and RAMSES NG, the ONERA radar systems, and confirmed the theoretical analyses of its performances.

There is significant uncertainty in our knowledge of the Martian atmosphere and the aerodynamics of the Mars entry, descent, and landing (EDL) systems. These uncertainties result in conservatism in the design of the EDL vehicles leading to higher system masses and a broad range of performance predictions. Data from flight instrumentation onboard Mars EDL systems can be used to quantify these uncertainties, but the existing dataset is sparse and many parameters of interest have not been previously observable. Many past EDL reconstructions neither utilize statistical information about the uncertainty of the measured data nor quantify the uncertainty of the estimated parameters. Statistical estimation methods can blend together disparate data types to improve the reconstruction of parameters of interest for the vehicle. For example, integrating data obtained from aeroshell-mounted pressure transducers, inertial measurement unit, and radar altimeter can improve the estimates of the trajectory, atmospheric profile, and aerodynamic coefficients, while also quantifying the uncertainty in these estimates. These same statistical methods can be leveraged to improve current engineering models in order to reduce conservatism in future EDL vehicle design. The work in this thesis presents a comprehensive methodology for parameter reconstruction and uncertainty quantification while blending dissimilar Mars EDL datasets. Statistical estimation methods applied include the Extended Kalman Filter, Unscented Kalman Filter, and Adaptive Filter. The estimators are applied in a manner in which the observability of the parameters of interest is maximized while using the sparse, disparate EDL dataset. The methodology is validated with simulated data and then applied to estimate the EDL performance of the 2012 Mars Science Laboratory. The reconstruction methodology is also utilized as a tool for improving vehicle design and reducing design conservatism. A novel method of optimizing the design of future EDL atmospheric data systems is presented by leveraging the reconstruction methodology. The methodology identifies important design trends and the point of diminishing returns of atmospheric data sensors that are critical in improving the reconstruction performance for future EDL vehicles. The impact of the estimation methodology on aerodynamic and atmospheric engineering models is also studied and suggestions are made for future EDL instrumentation.

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