Contributions aux bornes inférieures de l’erreur quadratique moyenne en traitement du signal

A l’aide des bornes inférieures de l’erreur quadratique moyenne, la caractérisation du décrochement des estimateurs, l’analyse de la position optimale des capteurs dans un réseau ainsi que les limites de résolution statistiques sont étudiées dans le contexte du traitement d’antenne et du radar

A review of closed-form Cramér-Rao Bounds for DOA estimation in the presence of Gaussian noise under a unified framework

The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case

Array signal processing for maximum likelihood direction-of-arrival estimation

Emitter Direction-of-Arrival (DOA) estimation is a fundamental problem in a variety of applications including radar, sonar, and wireless communications. The research has received considerable attention in literature and numerous methods have been proposed. Maximum Likelihood (ML) is a nearly optimal technique producing superior estimates compared to other methods especially in unfavourable conditions, and thus is of significant practical interest. This paper discusses in details the techniques for ML DOA estimation in either white Gaussian noise or unknown noise environment. Their performances are analysed and compared, and evaluated against the theoretical lower bounds

A Fisher Information Analysis of Joint Localization and Synchronization in Near Field

In 5G communication, arrays are used for both positioning and communication. As the arrays become larger, the far-field assumption is increasingly being violated and curvature of the wavefront should be taken into account. We explicitly contrast near-field and far-field uplink localization performance in the presence of a clock bias from a Fisher information perspective and show how a simple algorithm can provide a coarse estimate of a user's location and clock bias.Comment: Submitted to IEEE ICC 2020 Workshop

Ein Beitrag zur effizienten Richtungsschätzung mittels Antennenarrays

Sicherlich gibt es nicht den einen Algorithmus zur Schätzung der Einfallsrichtung elektromagnetischer Wellen. Statt dessen existieren Algorithmen, die darauf optimiert sind Hunderte Pfade zu finden, mit uniformen linearen oder kreisförmigen Antennen-Arrays genutzt zu werden oder möglichst schnell zu sein. Die vorliegende Dissertation befasst sich mit letzterer Art. Wir beschränken uns jedoch nicht auf den reinen Algorithmus zur Richtungsschätzung (RS), sondern gehen das Problem in verschiedener Hinsicht an. Die erste Herangehensweise befasst sich mit der Beschreibung der Array-Mannigfaltigkeit (AM). Bisherige Interpolationsverfahren der AM berücksichtigen nicht inhärent Polarisation. Daher wird separat für jede Polarisation einzeln interpoliert. Wir übernehmen den Ansatz, eine diskrete zweidimensionale Fouriertransformation (FT) zur Interpolation zu nutzen. Jedoch verschieben wir das Problem in den Raum der Quaternionen. Dort wenden wir eine zweidimensionale diskrete quaternionische FT an. Somit können beide Polarisationszustände als eine einzige Größe betrachtet werden. Das sich ergebende Signalmodell ist im Wesentlichen kompatibel mit dem herkömmlichen komplexwertigen Modell. Unsere zweite Herangehensweise zielt auf die fundamentale Eignung eines Antennen-Arrays für die RS ab. Zu diesem Zweck nutzen wir die deterministische Cramér-Rao-Schranke (Cramér-Rao Lower Bound, CRLB). Wir leiten drei verschiedene CRLBs ab, die Polarisationszustände entweder gar nicht oder als gewünschte oder störende Parameter betrachten. Darüber hinaus zeigen wir auf, wie Antennen-Arrays schon während der Design-Phase auf RS optimiert werden können. Der eigentliche Algorithmus zur RS stellt die letzte Herangehensweise dar. Mittels einer MUSIC-basierte Kostenfunktion leiten wir effiziente Schätzer ab. Hierfür kommt eine modifizierte Levenberg- bzw. Levenberg-Marquardt-Suche zum Einsatz. Da die eigentliche Kostenfunktion hier nicht angewendet werden kann, ersetzen wir diese durch vier verschiedene Funktionen, die sich lokal ähnlich verhalten. Diese Funktionen beruhen auf einer Linearisierung eines Kroneckerproduktes zweier polarimetrischer Array-Steering-Vektoren. Dabei stellt sich heraus, dass zumindest eine der Funktionen in der Regel zu sehr schneller Konvergenz führt, sodass ein echtzeitfähiger Algorithmus entsteht.It is save to say that there is no such thing as the direction finding (DF) algorithm. Rather, there are algorithms that are tuned to resolve hundreds of paths, algorithms that are designed for uniform linear arrays or uniform circular arrays, and algorithms that strive for efficiency. The doctoral thesis at hand deals with the latter type of algorithms. However, the approach taken does not only incorporate the actual DF algorithm but approaches the problem from different perspectives. The first perspective concerns the description of the array manifold. Current interpolation schemes have no notion of polarization. Hence, the array manifold interpolation is performed separately for each state of polarization. In this thesis, we adopted the idea of interpolation via a 2-D discrete Fourier transform. However, we transform the problem into the quaternionic domain. Here, a 2-D discrete quaternionic Fourier transform is applied. Hence, both states of polarization can be viewed as a single quantity. The resulting interpolation is applied to a signal model which is essentially compatible to conventional complex model. The second perspective in this thesis is to look at the fundamental DF capability of an antenna array. For that, we use the deterministic Cramér-Rao Lower Bound (CRLB). We point out the differences between not considering polarimetric parameters and taking them as desired parameters or nuisance parameters. Such differences lead to three different CRLBs. Moreover, insight is given how a CRLB can be used to optimize an antenna array already during the design process to improve its DF performance. The actual DF algorithm constitutes the third perspective that is considered in this thesis. A MUSIC-based cost function is used to derive efficient estimators. To this end, a modified Levenberg search and Levenberg-Marquardt search are employed. Since the original cost function is not eligible to be used in this framework, we replace it by four different functions that locally show the same behavior. These functions are based on a linearization of Kronecker products of two polarimetric array steering vectors. It turns out that at least one of these functions usually exhibits very fast convergence leading to real-time capable algorithms

Topics in the accuracy and resolution of superresolution systems

Since their introduction in the 1970s and 1980s superresolution systems for point source parameter estimation have received theoretical attention regarding their potential performance. Two aspects of performance in particular are of interest, the accuracy of the parameter estimation and the resolution achievable. Limitations on performance may be considered to be due to noise affecting the data, or to errors in the system. Superresolution methods divide roughly into two groups – ‘spectral’ methods and maximum likelihood (ML) methods. MUSIC is perhaps the most effective example of a spectral method and has been studied in considerable detail, in both performance measures, but mainly only for the case of a single parameter. In this study the accuracy of MUSIC in the application of two-dimensional direction finding (DF) has been analysed, with and without system errors, using a general array. Theoretical results are confirmed by simulations. An aim has been to produce simpler results for use in estimating the potential performance of practical systems. Little work has been reported on the resolution of ML methods and this is the second main topic of this work, particularly for the two-dimensional DF case using a general array, with a ML method (IMP) similar to the better known Alternating Projection. Some results are obtained for resolution with and without errors for the case of noncoherent signals. For coherent signals (including the standard radar case) the performance is found to depend on the relative phase of the signals, varying from the quadrature case, where the performance is as for the non-coherent case, to the in-phase (or antiphase) case where only one signal peak is seen

Reliable Inference from Unreliable Agents

Distributed inference using multiple sensors has been an active area of research since the emergence of wireless sensor networks (WSNs). Several researchers have addressed the design issues to ensure optimal inference performance in such networks. The central goal of this thesis is to analyze distributed inference systems with potentially unreliable components and design strategies to ensure reliable inference in such systems. The inference process can be that of detection or estimation or classification, and the components/agents in the system can be sensors and/or humans. The system components can be unreliable due to a variety of reasons: faulty sensors, security attacks causing sensors to send falsified information, or unskilled human workers sending imperfect information. This thesis first quantifies the effect of such unreliable agents on the inference performance of the network and then designs schemes that ensure a reliable overall inference. In the first part of this thesis, we study the case when only sensors are present in the system, referred to as sensor networks. For sensor networks, the presence of malicious sensors, referred to as Byzantines, are considered. Byzantines are sensors that inject false information into the system. In such systems, the effect of Byzantines on the overall inference performance is characterized in terms of the optimal attack strategies. Game-theoretic formulations are explored to analyze two-player interactions. Next, Byzantine mitigation schemes are designed that address the problem from the system\u27s perspective. These mitigation schemes are of two kinds: Byzantine identification schemes and Byzantine tolerant schemes. Using learning based techniques, Byzantine identification schemes are designed that learn the identity of Byzantines in the network and use this information to improve system performance. When such schemes are not possible, Byzantine tolerant schemes using error-correcting codes are developed that tolerate the effect of Byzantines and maintain good performance in the network. Error-correcting codes help in correcting the erroneous information from these Byzantines and thereby counter their attack. The second line of research in this thesis considers humans-only networks, referred to as human networks. A similar research strategy is adopted for human networks where, the effect of unskilled humans sharing beliefs with a central observer called \emph{CEO} is analyzed, and the loss in performance due to the presence of such unskilled humans is characterized. This problem falls under the family of problems in information theory literature referred to as the \emph{CEO Problem}, but for belief sharing. The asymptotic behavior of the minimum achievable mean squared error distortion at the CEO is studied in the limit when the number of agents $L$ and the sum rate $R$ tend to infinity. An intermediate regime of performance between the exponential behavior in discrete CEO problems and the $1/R$ behavior in Gaussian CEO problems is established. This result can be summarized as the fact that sharing beliefs (uniform) is fundamentally easier in terms of convergence rate than sharing measurements (Gaussian), but sharing decisions is even easier (discrete). Besides theoretical analysis, experimental results are reported for experiments designed in collaboration with cognitive psychologists to understand the behavior of humans in the network. The act of fusing decisions from multiple agents is observed for humans and the behavior is statistically modeled using hierarchical Bayesian models. The implications of such modeling on the design of large human-machine systems is discussed. Furthermore, an error-correcting codes based scheme is proposed to improve system performance in the presence of unreliable humans in the inference process. For a crowdsourcing system consisting of unskilled human workers providing unreliable responses, the scheme helps in designing easy-to-perform tasks and also mitigates the effect of erroneous data. The benefits of using the proposed approach in comparison to the majority voting based approach are highlighted using simulated and real datasets. In the final part of the thesis, a human-machine inference framework is developed where humans and machines interact to perform complex tasks in a faster and more efficient manner. A mathematical framework is built to understand the benefits of human-machine collaboration. Such a study is extremely important for current scenarios where humans and machines are constantly interacting with each other to perform even the simplest of tasks. While machines perform best in some tasks, humans still give better results in tasks such as identifying new patterns. By using humans and machines together, one can extract complete information about a phenomenon of interest. Such an architecture, referred to as Human-Machine Inference Networks (HuMaINs), provides promising results for the two cases of human-machine collaboration: \emph{machine as a coach} and \emph{machine as a colleague}. For simple systems, we demonstrate tangible performance gains by such a collaboration which provides design modules for larger, and more complex human-machine systems. However, the details of such larger systems needs to be further explored

Photonic Quantum Metrology

Quantum Metrology is one of the most promising application of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here we review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to phase estimation. We describe the current state of the art in the field in terms of platforms and quantum resources. Furthermore, we present the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time. We conclude by discussing the current experimental and theoretical challenges, and the open questions towards implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise.Comment: 51 pages, 9 figures, 967 references. Comments and feedbacks are very welcom

Direction of arrival estimation based on a mixed signal transmission model employing a linear tripole array

Direction of arrival (DOA) estimation is an important topic in array signal processing. Currently, most research activities are focused on the single signal transmission (SST) type of signals, i.e. only one physical signal is used to carry the information from a transmitter to a receiver with a given polarisation setting. However, to make full use of the degrees of freedom in spatial domain, signals based on the dual signal transmission (DST) model are more and more widely used, i.e., two signals with different polarisations carrying different information are employed for communication between the transmitter and the receiver. But there is rarely any work on DOA estimation of DST signals. Motivated by such a problem, the paper proposes two methods for DOA estimation of signals based on a mixed signal transmission (MST) model, i.e., a mixture of SST and DST signals. The first method provides a two-step solution and estimate the DOA of the SST signals first and then the DST signals second. The second method estimates the DOA of all signals in one step. Moreover, CRB (Cramér-Rao Bound) for the estimation model is derived to evaluate the performance the proposed methods