Analysis and Accuracy Improvement of UWB-TDoA-Based Indoor Positioning System

Positioning systems are used in a wide range of applications which require determining the position of an object in space, such as locating and tracking assets, people and goods; assisting navigation systems; and mapping. Indoor Positioning Systems (IPSs) are used where satellite and other outdoor positioning technologies lack precision or fail. Ultra-WideBand (UWB) technology is especially suitable for an IPS, as it operates under high data transfer rates over short distances and at low power densities, although signals tend to be disrupted by various objects. This paper presents a comprehensive study of the precision, failure, and accuracy of 2D IPSs based on UWB technology and a pseudo-range multilateration algorithm using Time Difference of Arrival (TDoA) signals. As a case study, the positioning of a 4×4m2 area, four anchors (transceivers), and one tag (receiver) are considered using bitcraze’s Loco Positioning System. A Cramér–Rao Lower Bound analysis identifies the convex hull of the anchors as the region with highest precision, taking into account the anisotropic radiation pattern of the anchors’ antennas as opposed to ideal signal distributions, while bifurcation envelopes containing the anchors are defined to bound the regions in which the IPS is predicted to fail. This allows the formulation of a so-called flyable area, defined as the intersection between the convex hull and the region outside the bifurcation envelopes. Finally, the static bias is measured after applying a built-in Extended Kalman Filter (EKF) and mapped using a Radial Basis Function Network (RBFN). A debiasing filter is then developed to improve the accuracy. Findings and developments are experimentally validated, with the IPS observed to fail near the anchors, precision around ±3cm, and accuracy improved by about 15cm for static and 5cm for dynamic measurements, on average

THEORETICAL ASPECTS AND REAL ISSUES IN AN INTEGRATED MULTIRADAR SYSTEM

In the last few years Homeland Security (HS) has gained a considerable interest in the research community. From a scientific point of view, it is a difficult task to provide a definition of this research area and to exactly draw up its boundaries. In fact, when we talk about the security and the surveillance, several problems and aspects must be considered. In particular, the following factors play a crucial role and define the complexity level of the considered application field: the number of potential threats can be high and uncertain; the threat detection and identification can be made more complicated by the use of camouflaging techniques; the monitored area is typically wide and it requires a large and heterogeneous sensor network; the surveillance operation is strongly related to the operational scenario, so that it is not possible to define a unique approach to solve the problem [1]. Information Technology (IT) can provide an important support to HS in preventing, detecting and early warning of threats. Even though the link between IT and HS is relatively recent, sensor integration and collaboration is a widely applied technique aimed to aggregate data from multiple sources, to yield timely information on potential threats and to improve the accuracy in monitoring events [2]. A large number of sensors have already been developed to support surveillance operations. Parallel to this technological effort in developing new powerful and dedicated sensors, interest in integrating a set of stand-alone sensors into an integrated multi-sensor system has been increasing. In fact, rather than to develop new sensors to achieve more accurate tracking and surveillance systems, it is more useful to integrate existing stand-alone sensors into a single system in order to obtain performance improvements In this dissertation, a notional integrated multi-sensor system acting in a maritime border control scenario for HS is considered. In general, a border surveillance system is composed of multiple land based and moving platforms carrying different types of sensors [1]. In a typical scenario, described in [1], the integrated system is composed of a land based platform, located on the coast, and an airborne platform moving in front of the coast line. In this dissertation, we handle two different fundamental aspects. In Part I, we focus on a single sensor in the system, i.e. the airborne radar. We analyze the tracking performance of such a kind of sensor in the presence of two different atmospheric problems: the turbulence (in Chapter 1) and the tropospheric refraction (in Chapter 2). In particular, in Chapter 1, the losses in tracking accuracy of a turbulence-ignorant tracking filter (i.e. a filter that does not take into account the effects of the atmospheric turbulences) acting in a turbulent scenario, is quantified. In Chapter 2, we focus our attention on the tropospheric propagation effects on the radar electromagnetic (em) signals and their correction for airborne radar tracking. It is well known that the troposphere is characterized by a refractive index that varies with the altitude and with the local weather. This variability of the refractive index causes an error in the radar measurements. First, a mathematical model to describe and calculate the em radar signal ray path in the troposphere is discussed. Using this mathematical model, the errors due to the tropospheric propagation are evaluated and the corrupted radar measurements are then numerically generated. Second, a tracking algorithm, based on the Kalman Filter, that is able to mitigate the tropospheric errors during the tracking procedure, is proposed. In Part II, we consider the integrated system in its wholeness to investigate a fundamental prerequisite of any data fusion process: the sensor registration process. The problem of sensor registration (also termed, for naval system, the grid-locking problem) arises when a set of data coming from two or more sensors must be combined. This problem involves a coordinate transformation and the reciprocal alignment among the various sensors: streams of data from different sensors must be converted into a common coordinate system (or frame) and aligned before they could be used in a tracking or surveillance system. If not corrected, registration errors can seriously degrade the global system performance by increasing tracking errors and even introducing ghost tracks. A first basic distinction is usually made between relative grid-locking and absolute grid-locking. The relative grid-locking process aligns remote data to local data under the assumption that the local data are bias free and that all biases reside with the remote sensor. The problem is that, actually, also the local sensor is affected by bias. Chapter 3 of this dissertation is dedicated to the solution of the relative grid-locking problem. Two different estimation algorithms are proposed: a linear Least Squares (LS) algorithm and an Expectation-Maximization-based (EM) algorithm. The linear LS algorithm is a simple and fast algorithm, but numerical results have shown that the LS estimator is not efficient for most of the registration bias errors. Such non-efficiency could be caused by the linearization implied by the linear LS algorithm. Then, in order to obtain a more efficient estimation algorithm, an Expectation-Maximization algorithm is derived. In Chapter 4 we generalize our findings to the absolute grid-locking problem. Part III of this dissertation is devoted to a more theoretical aspect of fundamental importance in a lot of practical applications: the estimate of the disturbance covariance matrix. Due to its relevance, in literature it can be found a huge quantity of works on this topic. Recently, a new geometrical concept has been applied to this estimation problem: the Riemann (or intrinsic) geometry. In Chapter 5, we give an overview on the state of the art of the application of the Riemann geometry for the covariance matrix estimation in radar problems. Particular attention is given for the detection problem in additive clutter. Some covariance matrix estimators and a new decision rule based on the Riemann geometry are analyzed and their performance are compared with the classical ones. [1] Sofia Giompapa, “Analysis, modeling, and simulation of an integrated multi-sensor system for maritime border control”, PhD dissertation, University of Pisa, April 2008. [2] H. Chen, F. Y. Wang, and D. Zeng, “Intelligence and security informatics for Homeland Security: information, communication and transportation,” Intelligent Transportation Systems, IEEE Transactions on, vol. 5, no. 4, pp. 329-341, December 2004

Robust GNSS Carrier Phase-based Position and Attitude Estimation Theory and Applications

Mención Internacional en el título de doctorNavigation information is an essential element for the functioning of robotic platforms and intelligent transportation systems. Among the existing technologies, Global Navigation Satellite Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term for referring to a constellation of satellites which transmit radio signals used primarily for ranging information. Therefore, the successful operation and deployment of prospective autonomous systems is subject to our capabilities to support GNSS in the provision of robust and precise navigational estimates. GNSS signals enable two types of ranging observations: –code pseudorange, which is a measure of the time difference between the signal’s emission and reception at the satellite and receiver, respectively, scaled by the speed of light; –carrier phase pseudorange, which measures the beat of the carrier signal and the number of accumulated full carrier cycles. While code pseudoranges provides an unambiguous measure of the distance between satellites and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets, carrier phase measurements present a much higher precision, at the cost of being ambiguous by an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase observations which, in turn, lead to complicated estimation problems. This thesis deals with the estimation theory behind the provision of carrier phase-based precise navigation for vehicles traversing scenarios with harsh signal propagation conditions. Contributions to such a broad topic are made in three directions. First, the ultimate positioning performance is addressed, by proposing lower bounds on the signal processing realized at the receiver level and for the mixed real- and integer-valued problem related to carrier phase-based positioning. Second, multi-antenna configurations are considered for the computation of a vehicle’s orientation, introducing a new model for the joint position and attitude estimation problems and proposing new deterministic and recursive estimators based on Lie Theory. Finally, the framework of robust statistics is explored to propose new solutions to code- and carrier phase-based navigation, able to deal with outlying impulsive noises.La información de navegación es un elemental fundamental para el funcionamiento de sistemas de transporte inteligentes y plataformas robóticas. Entre las tecnologías existentes, los Sistemas Globales de Navegación por Satélite (GNSS) se han consolidado como la piedra angular para la navegación en exteriores, dando acceso a localización y sincronización temporal a una escala global, irrespectivamente de la condición meteorológica. GNSS es el término genérico que define una constelación de satélites que transmiten señales de radio, usadas primordinalmente para proporcionar información de distancia. Por lo tanto, la operatibilidad y funcionamiento de los futuros sistemas autónomos pende de nuestra capacidad para explotar GNSS y estimar soluciones de navegación robustas y precisas. Las señales GNSS permiten dos tipos de observaciones de alcance: –pseudorangos de código, que miden el tiempo transcurrido entre la emisión de las señales en los satélites y su acquisición en la tierra por parte de un receptor; –pseudorangos de fase de portadora, que miden la fase de la onda sinusoide que portan dichas señales y el número acumulado de ciclos completos. Los pseudorangos de código proporcionan una medida inequívoca de la distancia entre los satélites y el receptor, con una precisión de decímetros cuando no se tienen en cuenta los retrasos atmosféricos y los desfases del reloj. En contraposición, las observaciones de la portadora son super precisas, alcanzando el milímetro de exactidud, a expensas de ser ambiguas por un número entero y desconocido de ciclos. Por ende, el alcanzar la máxima precisión con GNSS queda condicionado al uso de las medidas de fase de la portadora, lo cual implica unos problemas de estimación de elevada complejidad. Esta tesis versa sobre la teoría de estimación relacionada con la provisión de navegación precisa basada en la fase de la portadora, especialmente para vehículos que transitan escenarios donde las señales no se propagan fácilmente, como es el caso de las ciudades. Para ello, primero se aborda la máxima efectividad del problema de localización, proponiendo cotas inferiores para el procesamiento de la señal en el receptor y para el problema de estimación mixto (es decir, cuando las incógnitas pertenecen al espacio de números reales y enteros). En segundo lugar, se consideran las configuraciones multiantena para el cálculo de la orientación de un vehículo, presentando un nuevo modelo para la estimación conjunta de posición y rumbo, y proponiendo estimadores deterministas y recursivos basados en la teoría de Lie. Por último, se explora el marco de la estadística robusta para proporcionar nuevas soluciones de navegación precisa, capaces de hacer frente a los ruidos atípicos.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: José Manuel Molina López.- Secretario: Giorgi Gabriele.- Vocal: Fabio Dovi

Statistical modelling of algorithms for signal processing in systems based on environment perception

One cornerstone for realising automated driving systems is an appropriate handling of uncertainties in the environment perception and situation interpretation. Uncertainties arise due to noisy sensor measurements or the unknown future evolution of a traffic situation. This work contributes to the understanding of these uncertainties by modelling and propagating them with parametric probability distributions

On the recursive joint position and attitude determination in multi-antenna GNSS platforms

Global Navigation Satellite Systems’ (GNSS) carrier phase observations are fundamental in the provision of precise navigation for modern applications in intelligent transport systems. Differential precise positioning requires the use of a base station nearby the vehicle location, while attitude determination requires the vehicle to be equipped with a setup of multiple GNSS antennas. In the GNSS context, positioning and attitude determination have been traditionally tackled in a separate manner, thus losing valuable correlated information, and for the latter only in batch form. The main goal of this contribution is to shed some light on the recursive joint estimation of position and attitude in multi-antenna GNSS platforms. We propose a new formulation for the joint positioning and attitude (JPA) determination using quaternion rotations. A Bayesian recursive formulation for JPA is proposed, for which we derive a Kalman filter-like solution. To support the discussion and assess the performance of the new JPA, the proposed methodology is compared to standard approaches with actual data collected from a dynamic scenario under the influence of severe multipath effects

Localizability Optimization for Multi Robot Systems and Applications to Ultra-Wide Band Positioning

RÉSUMÉ: RÉSUMÉ Les Systèmes Multi-Robots (SMR) permettent d’effectuer des missions de manière efficace et robuste du fait de leur redondance. Cependant, les robots étant des véhicules autonomes, ils nécessitent un positionnement précis en temps réel. Les techniques de localisation qui utilisent des Mesures Relatives (MR) entre les robots, pouvant être des distances ou des angles, sont particulièrement adaptées puisqu’elles peuvent bénéficier d’algorithmes coopératifs au sein du SMR afin d’améliorer la précision pour l’ensemble des robots. Dans cette thèse, nous proposons des stratégies pour améliorer la localisabilité des SMR, qui est fonction de deux facteurs. Premièrement, la géométrie du SMR influence fondamentalement la qualité de son positionnement pour des MR bruitées. Deuxièmement, les erreurs de mesures dépendent fortement de la technologie utilisée. Dans nos expériences, nous nous focalisons sur la technologie UWB (Ultra-Wide Band), qui est populaire pour le positionnement des robots en environnement intérieur en raison de son coût modéré et sa haute précision. Par conséquent, une partie de notre travail est consacrée à la correction des erreurs de mesure UWB afin de fournir un système de navigation opérationnel. En particulier, nous proposons une méthode de calibration des biais systématiques et un algorithme d’atténuation des trajets multiples pour les mesures de distance en milieu intérieur. Ensuite, nous proposons des Fonctions de Coût de Localisabilité (FCL) pour caractériser la géométrie du SMR, et sa capacité à se localiser. Pour cela, nous utilisons la Borne Inférieure de Cramér-Rao (BICR) en vue de quantifier les incertitudes de positionnement. Par la suite, nous fournissons des schémas d’optimisation décentralisés pour les FCL sous l’hypothèse de MR gaussiennes ou log-normales. En effet, puisque le SMR peut se déplacer, certains de ses robots peuvent être déployés afin de minimiser la FCL. Cependant, l’optimisation de la localisabilité doit être décentralisée pour être adaptée à des SMRs à grande échelle. Nous proposons également des extensions des FCL à des scénarios où les robots embarquent plusieurs capteurs, où les mesures se dégradent avec la distance, ou encore où des informations préalables sur la localisation des robots sont disponibles, permettant d’utiliser la BICR bayésienne. Ce dernier résultat est appliqué au placement d’ancres statiques connaissant la distribution statistique des MR et au maintien de la localisabilité des robots qui se localisent par filtrage de Kalman. Les contributions théoriques de notre travail ont été validées à la fois par des simulations à grande échelle et des expériences utilisant des SMR terrestres. Ce manuscrit est rédigé par publication, il est constitué de quatre articles évalués par des pairs et d’un chapitre supplémentaire. ABSTRACT: ABSTRACT Multi-Robot Systems (MRS) are increasingly interesting to perform tasks eÿciently and robustly. However, since the robots are autonomous vehicles, they require accurate real-time positioning. Localization techniques that use relative measurements (RMs), i.e., distances or angles, between the robots are particularly suitable because they can take advantage of cooperative schemes within the MRS in order to enhance the precision of its positioning. In this thesis, we propose strategies to improve the localizability of the SMR, which is a function of two factors. First, the geometry of the MRS fundamentally influences the quality of its positioning under noisy RMs. Second, the measurement errors are strongly influenced by the technology chosen to gather the RMs. In our experiments, we focus on the Ultra-Wide Band (UWB) technology, which is popular for indoor robot positioning because of its mod-erate cost and high accuracy. Therefore, one part of our work is dedicated to correcting the UWB measurement errors in order to provide an operable navigation system. In particular, we propose a calibration method for systematic biases and a multi-path mitigation algorithm for indoor distance measurements. Then, we propose Localizability Cost Functions (LCF) to characterize the MRS’s geometry, using the Cramér-Rao Lower Bound (CRLB) as a proxy to quantify the positioning uncertainties. Subsequently, we provide decentralized optimization schemes for the LCF under an assumption of Gaussian or Log-Normal RMs. Indeed, since the MRS can move, some of its robots can be deployed in order to decrease the LCF. However, the optimization of the localizability must be decentralized for large-scale MRS. We also propose extensions of LCFs to scenarios where robots carry multiple sensors, where the RMs deteriorate with distance, and finally, where prior information on the robots’ localization is available, allowing the use of the Bayesian CRLB. The latter result is applied to static anchor placement knowing the statistical distribution of the MRS and localizability maintenance of robots using Kalman filtering. The theoretical contributions of our work have been validated both through large-scale simulations and experiments using ground MRS. This manuscript is written by publication, it contains four peer-reviewed articles and an additional chapter

Best Axes Composition Extended: Multiple Gyroscopes and Accelerometers Data Fusion to Reduce Systematic Error

Multiple rigidly attached Inertial Measurement Unit (IMU) sensors provide a richer flow of data compared to a single IMU. State-of-the-art methods follow a probabilistic model of IMU measurements based on the random nature of errors combined under a Bayesian framework. However, affordable low-grade IMUs, in addition, suffer from systematic errors due to their imperfections not covered by their corresponding probabilistic model. In this paper, we propose a method, the Best Axes Composition (BAC) of combining Multiple IMU (MIMU) sensors data for accurate 3D-pose estimation that takes into account both random and systematic errors by dynamically choosing the best IMU axes from the set of all available axes. We evaluate our approach on our MIMU visual-inertial sensor and compare the performance of the method with a purely probabilistic state-of-the-art approach of MIMU data fusion. We show that BAC outperforms the latter and achieves up to 20% accuracy improvement for both orientation and position estimation in open loop, but needs proper treatment to keep the obtained gain.Comment: Accepted to Robotics and Autonomous Systems journal. arXiv admin note: substantial text overlap with arXiv:2107.0263

Robust GNSS Carrier Phase-based Position and Attitude Estimation

Navigation information is an essential element for the functioning of robotic platforms and intelligent transportation systems. Among the existing technologies, Global Navigation Satellite Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term for referring to a constellation of satellites which transmit radio signals used primarily for ranging information. Therefore, the successful operation and deployment of prospective autonomous systems is subject to our capabilities to support GNSS in the provision of robust and precise navigational estimates. GNSS signals enable two types of ranging observations: --code pseudorange, which is a measure of the time difference between the signal's emission and reception at the satellite and receiver, respectively, scaled by the speed of light; --carrier phase pseudorange, which measures the beat of the carrier signal and the number of accumulated full carrier cycles. While code pseudoranges provides an unambiguous measure of the distance between satellites and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets, carrier phase measurements present a much higher precision, at the cost of being ambiguous by an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase observations which, in turn, lead to complicated estimation problems. This thesis deals with the estimation theory behind the provision of carrier phase-based precise navigation for vehicles traversing scenarios with harsh signal propagation conditions. Contributions to such a broad topic are made in three directions. First, the ultimate positioning performance is addressed, by proposing lower bounds on the signal processing realized at the receiver level and for the mixed real- and integer-valued problem related to carrier phase-based positioning. Second, multi-antenna configurations are considered for the computation of a vehicle's orientation, introducing a new model for the joint position and attitude estimation problems and proposing new deterministic and recursive estimators based on Lie Theory. Finally, the framework of robust statistics is explored to propose new solutions to code- and carrier phase-based navigation, able to deal with outlying impulsive noises

On the Recursive Joint Position and Attitude Determination in Multi-Antenna GNSS Platforms

Global Navigation Satellite Systems’ (GNSS) carrier phase observations are fundamental in the provision of precise navigation for modern applications in intelligent transport systems. Differential precise positioning requires the use of a base station nearby the vehicle location, while attitude determination requires the vehicle to be equipped with a setup of multiple GNSS antennas. In the GNSS context, positioning and attitude determination have been traditionally tackled in a separate manner, thus losing valuable correlated information, and for the latter only in batch form. The main goal of this contribution is to shed some light on the recursive joint estimation of position and attitude in multi-antenna GNSS platforms. We propose a new formulation for the joint positioning and attitude (JPA) determination using quaternion rotations. A Bayesian recursive formulation for JPA is proposed, for which we derive a Kalman filter-like solution. To support the discussion and assess the performance of the new JPA, the proposed methodology is compared to standard approaches with actual data collected from a dynamic scenario under the influence of severe multipath effects

Quantum Communication, Sensing and Measurement in Space

The main theme of the conclusions drawn for classical communication systems operating at optical or higher frequencies is that there is a well‐understood performance gain in photon efficiency (bits/photon) and spectral efficiency (bits/s/Hz) by pursuing coherent‐state transmitters (classical ideal laser light) coupled with novel quantum receiver systems operating near the Holevo limit (e.g., joint detection receivers). However, recent research indicates that these receivers will require nonlinear and nonclassical optical processes and components at the receiver. Consequently, the implementation complexity of Holevo‐capacityapproaching receivers is not yet fully ascertained. Nonetheless, because the potential gain is significant (e.g., the projected photon efficiency and data rate of MIT Lincoln Laboratory's Lunar Lasercom Demonstration (LLCD) could be achieved with a factor‐of‐20 reduction in the modulation bandwidth requirement), focused research activities on ground‐receiver architectures that approach the Holevo limit in space‐communication links would be beneficial. The potential gains resulting from quantum‐enhanced sensing systems in space applications have not been laid out as concretely as some of the other areas addressed in our study. In particular, while the study period has produced several interesting high‐risk and high‐payoff avenues of research, more detailed seedlinglevel investigations are required to fully delineate the potential return relative to the state‐of‐the‐art. Two prominent examples are (1) improvements to pointing, acquisition and tracking systems (e.g., for optical communication systems) by way of quantum measurements, and (2) possible weak‐valued measurement techniques to attain high‐accuracy sensing systems for in situ or remote‐sensing instruments. While these concepts are technically sound and have very promising bench‐top demonstrations in a lab environment, they are not mature enough to realistically evaluate their performance in a space‐based application. Therefore, it is recommended that future work follow small focused efforts towards incorporating practical constraints imposed by a space environment. The space platform has been well recognized as a nearly ideal environment for some of the most precise tests of fundamental physics, and the ensuing potential of scientific advances enabled by quantum technologies is evident in our report. For example, an exciting concept that has emerged for gravity‐wave detection is that the intermediate frequency band spanning 0.01 to 10 Hz—which is inaccessible from the ground—could be accessed at unprecedented sensitivity with a space‐based interferometer that uses shorter arms relative to state‐of‐the‐art to keep the diffraction losses low, and employs frequency‐dependent squeezed light to surpass the standard quantum limit sensitivity. This offers the potential to open up a new window into the universe, revealing the behavior of compact astrophysical objects and pulsars. As another set of examples, research accomplishments in the atomic and optics fields in recent years have ushered in a number of novel clocks and sensors that can achieve unprecedented measurement precisions. These emerging technologies promise new possibilities in fundamental physics, examples of which are tests of relativistic gravity theory, universality of free fall, frame‐dragging precession, the gravitational inverse‐square law at micron scale, and new ways of gravitational wave detection with atomic inertial sensors. While the relevant technologies and their discovery potentials have been well demonstrated on the ground, there exists a large gap to space‐based systems. To bridge this gap and to advance fundamental‐physics exploration in space, focused investments that further mature promising technologies, such as space‐based atomic clocks and quantum sensors based on atom‐wave interferometers, are recommended. Bringing a group of experts from diverse technical backgrounds together in a productive interactive environment spurred some unanticipated innovative concepts. One promising concept is the possibility of utilizing a space‐based interferometer as a frequency reference for terrestrial precision measurements. Space‐based gravitational wave detectors depend on extraordinarily low noise in the separation between spacecraft, resulting in an ultra‐stable frequency reference that is several orders of magnitude better than the state of the art of frequency references using terrestrial technology. The next steps in developing this promising new concept are simulations and measurement of atmospheric effects that may limit performance due to non‐reciprocal phase fluctuations. In summary, this report covers a broad spectrum of possible new opportunities in space science, as well as enhancements in the performance of communication and sensing technologies, based on observing, manipulating and exploiting the quantum‐mechanical nature of our universe. In our study we identified a range of exciting new opportunities to capture the revolutionary capabilities resulting from quantum enhancements. We believe that pursuing these opportunities has the potential to positively impact the NASA mission in both the near term and in the long term. In this report we lay out the research and development paths that we believe are necessary to realize these opportunities and capitalize on the gains quantum technologies can offer