82 research outputs found

    Cramer-Rao Lower Bounds for the Synchronization of UWB Signals

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    We present Cramér-Rao lower bounds (CRLBs) for the synchronization of UWB signals which should be tight lower bounds for the theoretical performance limits of UWB synchronizers. The CRLBs are investigated for both single-pulse systems and time-hopping systems in AWGN and multipath channels. Insights are given into the relationship between CRLBs for different Gaussian monocycles. An approximation method of the CRLBs is discussed when nuisance parameters exist. CRLBs in multipath channels are studied and formulated for three scenarios depending on the way multipath interference is treated. We find that a larger number of multipaths implies higher CRLBs and inferior performance of the synchronizers, and multipath interference on CRLBs cannot be eliminated completely except in very special cases. As every estimate of time delay could not be perfect, the least influence of the synchronization error on the performance of receivers is quantified

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

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    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

    Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

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    Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin

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

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    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

    Analysis of synchronous localization systems for UAVs urban applications

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    [EN] Unmanned-Aerial-Vehicles (UAVs) represent an active research topic over multiple fields for performing inspection, delivery and surveillance applications among other operations. However, achieving the utmost efficiency requires drones to perform these tasks without the need of human intervention, which demands a robust and accurate localization system for achieving a safe and efficient autonomous navigation. Nevertheless, currently used satellite-based localization systems like GPS are insufficient for high-precision applications, especially in harsh scenarios like indoor and deep urban environments. In these contexts, Local Positioning Systems (LPS) have been widely proposed for satisfying the localization requirements of these vehicles. However, the performance of LPS is highly dependent on the actual localization architecture and the spatial disposition of the deployed sensor distribution. Therefore, before the deployment of an extensive localization network, an analysis regarding localization architecture and sensor distribution should be taken into consideration for the task at hand. Nonetheless, no actual study is proposed either for comparing localization architectures or for attaining a solution for the Node Location Problem (NLP), a problem of NP-Hard complexity. Therefore, in this paper, we propose a comparison among synchronous LPS for determining the most suited system for localizing UAVs over urban scenarios. We employ the Cràmer–Rao-Bound (CRB) for evaluating the performance of each localization system, based on the provided error characterization of each synchronous architecture. Furthermore, in order to attain the optimal sensor distribution for each architecture, a Black-Widow-Optimization (BWO) algorithm is devised for the NLP and the application at hand. The results obtained denote the effectiveness of the devised technique and recommend the implementation of Time Difference Of Arrival (TDOA) over Time of Arrival (TOA) systems, attaining up to 47% less localization uncertainty due to the unnecessary synchronization of the target clock with the architecture sensors in the TDOA architecture.S

    Accuracy Bounds and Measurements of a Contactless Permittivity Sensor for Gases Using Synchronized Low-Cost mm-Wave Frequency Modulated Continuous Wave Radar Transceivers

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    A primary concern in a multitude of industrial processes is the precise monitoring of gaseous substances to ensure proper operating conditions. However, many traditional technologies are not suitable for operation under harsh environmental conditions. Radar-based time-of-flight permittivity measurements have been proposed as alternative but suffer from high cost and limited accuracy in highly cluttered industrial plants. This paper examines the performance limits of low-cost frequency-modulated continuous-wave (FMCW) radar sensors for permittivity measurements. First, the accuracy limits are investigated theoretically and the Cramér-Rao lower bounds for time-of-flight based permittivity and concentration measurements are derived. In addition, Monte-Carlo simulations are carried out to validate the analytical solutions. The capabilities of the measurement concept are then demonstrated with different binary gas mixtures of Helium and Carbon Dioxide in air. A low-cost time-of-flight sensor based on two synchronized fully-integrated millimeter-wave (MMW) radar transceivers is developed and evaluated. A method to compensate systematic deviations caused by the measurement setup is proposed and implemented. The theoretical discussion underlines the necessity of exploiting the information contained in the signal phase to achieve the desired accuracy. Results of various permittivity and gas concentration measurements are in good accordance to reference sensors and measurements with a commercial vector network analyzer (VNA). In conclusion, the proposed radar-based low-cost sensor solution shows promising performance for the intended use in demanding industrial applications

    Pilot Signal Design and Direct Ranging Methods for Radio Localization Using OFDM Systems

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    On the trade-off between uncertainty and delay in UWB and 5G localization

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    Location-aware technologies in combination with emerging wireless communication systems\ua0have revolutionized many aspects of our daily lives by means of applications within\ua0the commercial, public and military sectors. Ultra-wideband (UWB) and 5G stand\ua0out as emerging radio frequency (RF) based technologies that tackle the limitations of\ua0Global Positioning System solutions. The thrive in search for better accuracy involves\ua0improved ranging algorithms, higher transmission powers, network densification, larger\ua0bandwidths, and the use of cooperation among nodes in the network. However, practical\ua0implementations introduce communication related constraints. In this thesis, we study\ua0the trade-off between localization accuracy and communication constraints in terms of\ua0delay. This trade-off is investigated and quantified for two of the most rapidly growing\ua0RF technologies for high precision positioning: UWB and 5G.In UWB, we investigate the trade-off between medium access control (MAC) delay and\ua0accuracy based on a two-way-ranging and a spatial time division multiple access scheme.\ua0We quantify this relationship by deriving lower bounds on localization accuracy and MAC\ua0delay during the measurements phase, which is often neglected in the analyses. We find\ua0that the traditional means to improve accuracy such as increased number of anchors,\ua0increased communication range, and cooperation among nodes, come at a significant cost\ua0in terms of delay, which can be mitigated by means of techniques such as selective ranging\ua0and eavesdropping. We summarize and generalize our findings by characterizing the\ua0position error and delay lower bounds by deriving asymptotic scaling laws. These scaling\ua0laws are presented for dense noncooperative and cooperative networks in combination\ua0with delay mitigation techniques. Moreover, we introduce a delay/accuracy trade-off\ua0parameter, which can uniquely quantify the trade-off as a function of the agent and\ua0anchor density. Finally, we consider the problem of fast link scheduling and propose an\ua0optimization strategy to perform robust ranging scheduling with localization constraints.\ua0We propose two MAC-aware link selection heuristic approximation approaches which\ua0show similar performance as the optimal solution, but alleviate the problem complexity.In 5G, we analyze the interplay between communication and positioning within the initial\ua0access procedure between a transmitter and a receiver in a millimeter-wave multipleinput\ua0multiple-output system. We exploit the ability of the receiver to determine its\ua0location during the beam selection process and thus, improve the subsequent selection\ua0of beams within initial access. First, assuming that only the transmitter has beamforming\ua0capabilities, we propose an in-band position-aided transmitter beam selection\ua0protocol for scenarios with direct line-of-sight and scattering. Then, we extend the work\ua0and propose an in-band position-aided beam selection protocol where we also allow for\ua0the receiver to perform beamforming in scenarios with line-of-sight, reflected paths, and\ua0possible beam alignment errors. Both protocols show similar performance compared to\ua0their conventional counterparts in terms of final achieved signal-to-noise ratio, but they\ua0are significantly faster and can additionally provide the position and orientation of the\ua0devices in an accurate manner
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