<div>Distributed estimation algorithms have received considerable attention lately, owing to the advancements in computing, communication and battery technologies. They offer increased scalability, robustness and efficiency. In applications such as formation flight, where any discrepancies between sensor estimates has severe consequences, it becomes crucial to require consensus of estimates amongst all sensors. The Kalman Consensus Filter (KCF) is a seminal work in the field of distributed consensus-based estimation, which accomplishes this. </div><div><br></div><div>However, the KCF algorithm is mathematically sub-optimal, and does not account for the cross-correlation between the estimates of sensors. Other popular algorithms, such as the Information weighted Consensus Filter (ICF) rely on ad-hoc definitions and approximations, rendering them sub-optimal as well. Another major drawback of KCF is that it utilizes unweighted consensus, i.e., each sensor assigns equal weightage to the estimates of its neighbors. This fact has been shown to cause severely degraded performance of KCF when some sensors cannot observe the target, and can even cause the algorithm to be unstable.</div><div><br></div><div>In this work, we develop a novel algorithm, which we call Optimal Kalman Consensus Filter for Weighted Directed Graphs (OKCF-WDG), which addresses both of these limitations of existing algorithms. OKCF-WDG integrates the KCF formulation with that of matrix-weighted consensus. The algorithm achieves consensus on a weighted digraph, enabling a directed flow of information within the network. This aspect of the algorithm is shown to offer significant performance improvements over KCF, as the information may be directed from well-performing sensors to other sensors which have high estimation error due to environmental factors or sensor limitations. We validate the algorithm through simulations and compare it to existing algorithms. It is shown that the proposed algorithm outperforms existing algorithms by a considerable margin, especially in the case where some sensors are naive (i.e., cannot observe the target).</div>

<div>In this thesis, we focus on the problem of estimating an unknown quantity of interest, when the information required to do so is dispersed over a network of agents. In particular, each agent in the network receives sequential observations generated by the unknown quantity, and the collective goal of the network is to eventually learn this quantity by means of appropriately crafted information diffusion rules. The abstraction described above can be used to model a variety of problems ranging from environmental monitoring of a dynamical process using autonomous robot teams, to statistical inference using a network of processors, to social learning in groups of individuals. The limited information content of each agent, coupled with dynamically changing networks, the possibility of adversarial attacks, and constraints imposed by the communication channels, introduce various unique challenges in addressing such problems. We contribute towards systematically resolving some of these challenges.</div><div><br></div><div>In the first part of this thesis, we focus on tracking the state of a dynamical process, and develop a distributed observer for the most general class of LTI systems, linear measurement models, and time-invariant graphs. To do so, we introduce the notion of a multi-sensor observable decomposition - a generalization of the Kalman observable canonical decomposition for a single sensor. We then consider a scenario where certain agents in the network are compromised based on the classical Byzantine adversary model. For this worst-case adversarial setting, we identify certain fundamental necessary conditions that are a blend of system- and network-theoretic requirements. We then develop an attack-resilient, provably-correct, fully distributed state estimation algorithm. Finally, by drawing connections to the concept of age-of-information for characterizing information freshness, we show how our framework can be extended to handle a broad class of time-varying graphs. Notably, in each of the cases above, our proposed algorithms guarantee exponential convergence at any desired convergence rate.</div><div><br></div><div>In the second part of the thesis, we turn our attention to the problem of distributed hypothesis testing/inference, where each agent receives a stream of stochastic signals generated by an unknown static state that belongs to a finite set of hypotheses. To enable each agent to uniquely identify the true state, we develop a novel distributed learning rule that employs a min-protocol for data-aggregation, as opposed to the large body of existing techniques that rely on "belief-averaging". We establish consistency of our rule under minimal requirements on the observation model and the network structure, and prove that it guarantees exponentially fast convergence to the truth with probability 1. Most importantly, we establish that the learning rate of our algorithm is network-independent, and a strict improvement over all existing approaches. We also develop a simple variant of our learning algorithm that can account for misbehaving agents. As the final contribution of this work, we develop communication-efficient rules for distributed hypothesis testing. Specifically, we draw on ideas from event-triggered control to reduce the number of communication rounds, and employ an adaptive quantization scheme that guarantees exponentially fast learning almost surely, even when just 1 bit is used to encode each hypothesis. </div>

Master of Science / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / In this thesis, we first consider the problem of distributed estimation in an energy and rate-constrained wireless sensor network. To this end, we study three estimators namely - (1) Best Linear Unbiased Estimator (BLUE-1) that accounts for the variance of noise in measurement, uniform quantization and channel, and derive its variance and its lower bound; (2) Best Linear Unbiased Estimator (BLUE-2) that accounts for the variance of noise in measurement and uniform quantization, and derive lower and upper bounds for its variance; (3) Best Linear Unbiased Estima- tor (BLUE-3) that incorporates the effects of probabilistic quantization noise and measurement noise, and derive an upper bound for its variance. Then using BLUE-1, we analyze the tradeoff between estimation error (BLUE variance) at the fusion center and the total amount of resources utilized (power and rate) using three different system design approaches or optimization formulations. For all the formulations, we determine optimum quantization bits and transmission power per bit (or optimum actions) for all sensors jointly. Unlike prior efforts, we in- corporate the operating state (characterized by the amount of residual battery power) of the sensors in the optimization framework. We study the e®ect of channel quality, local measurement noise, and operating states of the sensors on their optimum choice for quantization bits and transmit power per bit. In the sequel, we consider a problem in distributed detection and signal processing in the context of biomedical wireless sensors and more specifically pulse- oximeter devices that record photoplethysmographic data. We propose an automated, two-stage PPG data processing method to minimize the effect of motion artifact. Regarding stage one, we present novel and consistent techniques to detect the presence of motion artifact in photoplethysmograms given higher order statistical information present in the data.For stage two, we propose an effective motion artifact reduction method that involves enhanced PPG data preprocessing followed by frequency domain Independent Component Analysis (FD-ICA). Experimental results are presented to demonstrate the efficacy of the overall motion artifact reduction method. Finally, we analyze a wireless ad hoc/sensor network where nodes are connected via random channels and information is transported in the network in a cooperative multihop fashion using amplify and forward relay strategy.

This dissertation develops optimal algorithms for distributed detection and estimation in static and mobile sensor networks. In distributed detection or estimation scenarios in clustered wireless sensor networks, sensor motes observe their local environment, make decisions or quantize these observations into local estimates of finite length, and send/relay them to a Cluster-Head (CH). For event detection tasks that are subject to both measurement errors and communication errors, we develop an algorithm that combines a Maximum a Posteriori (MAP) approach for local and global decisions with low-complexity channel codes and processing algorithms. For event estimation tasks that are subject to measurement errors, quantization errors and communication errors, we develop an algorithm that uses dithered quantization and channel compensation to ensure that each mote's local estimate received by the CH is unbiased and then lets the CH fuse these estimates into a global one using a Best Linear Unbiased Estimator (BLUE). We then determine both the minimum energy required for the network to produce an estimate with a prescribed error variance and show how this energy must be allocated amongst the motes in the network. In mobile wireless sensor networks, the mobility model governing each node will affect the detection accuracy at the CH and the energy consumption to achieve this level of accuracy. Correlated Random Walks (CRWs) have been proposed as mobility models that accounts for time dependency, geographical restrictions and nonzero drift. Hence, the solution to the continuous-time, 1-D, finite state space CRW is provided and its statistical behavior is studied both analytically and numerically. The impact of the motion of sensor on the network's performance is also studied.

Wireless sensor networks (WSN) are an emerging technology with a wide range of applications including environment monitoring, security and surveillance, health care, smart homes, etc. Subject to severe resource constraints in wireless sensor networks, in this research, we address the distributed estimation of unknown parameters by studying the correlation among resource, distortion, and lifetime, which are three major concerns for WSN applications. The objective of the proposed research is to design efficient distributed estimation algorithms for resource-constrained wireless sensor networks, where the major challenge is the integrated design of local signal processing operations and strategies for inter-sensor communication and networking so as to achieve a desirable tradeoff among resource efficiency (bandwidth and energy), system performance (estimation distortion and network lifetime), and implementation simplicity. More specifically, we address the efficient distributed estimation from the following perspectives: (i) rate-distortion perspective, where the objective is to study the rate-distortion bound for the distributed estimation and to design practical and distributed algorithms suitable for wireless sensor networks to approach the performance bound by optimally allocating the bit rate for each sensor, (ii) energy-distortion perspective, where the objective is to study the energy-distortion bound for the distributed estimation and to design practical and distributed algorithms suitable for wireless sensor networks to approach the performance bound by optimally allocating the bit rate and transmission energy for each sensor, and (iii) lifetime-distortion perspective, where the objective is to maximize the network lifetime while meeting estimation distortion requirements by jointly optimizing the source coding, source throughput and multi-hop routing. Also, energy-efficient cluster-based distributed estimation is studied, where the objective is to minimize the overall energy cost by appropriately dividing the sensor field into multiple clusters with data aggregation at cluster heads.

Les réseaux de capteurs sans fils (RCSFs) suscitent un intérêt croissant depuis une vingtaine d'années. La première partie de cette thèse est consacré à l'étude de l'efficacité de compression de données corrélées provenant d'un RCSF et acheminées vers un point de collecte à l'aide du codage réseau linéaire aléatoire. Les conditions nécessaires et suffisantes sont obtenues pour récupérer parfaitement les données que les capteurs mesurent. Puis on considère les nœuds dans un RCSF collaborant afin d'exécuter une tâche donnée (acquisition, détection...), pour laquelle chaque nœud a potentiellement un niveau d'expertise différent. La seconde partie de cette thèse est dédiée à la conception et à l'analyse d'algorithmes d'auto-évaluation distribués (AED), qui permettent à chaque nœud d'auto-évaluer son niveau d’expert. Trois types de problèmes sont considérés: i) la détection distribuée des nœuds défaillants (DDD), qui permet d'identifier les nœuds équipés de capteurs défectueux dans un RCSF; ii) la DDD dans un réseau tolérant aux déconnections (RTD) dont la topologie est dynamique et le degré de connectivité très faible; iii) la AED avec interactions pair à pair. Les résultats théoriques sont utiles pour configurer les paramètres des algorithmes. / Wireless sensor networks (WSNs) have attracted much interests in the last decade. The first part of this thesis considers sparse random linear network coding is for data gathering and compression in WSNs. An information-theoretic approach is applied to demonstrate the necessary and sufficient conditions to realize the asymptotically perfect reconstruction under MAP estimation. The second part of the thesis concerns the distributed self-rating (DSR) problem, for WSNs with nodes that have different ability of performing some task (sensing, detection...). The main assumption is that each node does not know and needs to estimate its ability. Depending on the number of ability levels and the communication conditions, three sub-problems have been addressed: i) distributed faulty node detection (DFD) to identify the nodes equipped with defective sensors in dense WSNs; ii) DFD in delay tolerant networks (DTNs) with sparse and intermittent connectivity; iii) DSR using pairwise comparison. Distributed algorithms have been proposed and analyzed. Theoretical results assess the effectiveness of the proposed solution and give guidelines in the design of the algorithm.

This dissertation lays out a multi-static radar system with mobile receivers. The transmitter is at a known location emitting a radar signal that bounces off a target. The echo is received by a team of UAVs that are capable of estimating both time-delay and Doppler from the received signal. Several methods for controlling the movement of mobile sensor platforms are presented to improve target tracking performance. Two optimization criteria are derived for the problem, both of which require some type of search procedure to find the desired solution. Simulations are used to show the benefit of using closed-loop sensor control for the special case of an EKF tracking filter. In addition, a simpler closed-form approach based on one of the algorithms is also presented and is shown to have performance similar to that obtained using the optimal algorithms. To decentralize the estimation in the UAV network, an information consensus filter (ICF) is presented. In the ICF each agent maintains a local estimate, which is shown to be unbiased and conservative with respect to the local covariance matrix estimate. The ICF does not take into account unknown track-to-track correlation that occurs when local independent estimates pass through a common process model. However, it does eliminate the redundancy incurred when communicating information through general network topologies, including graphs containing loops. In the ICF a discrete-time consensus filter is used to handle the communication of information between nodes (UAVs) in the network. Communication is local in that each agent can only communicate with local neighbors and not the entire network. A second-order discrete-time consensus protocol is developed. Necessary and sufficient conditions are given that ensure the team of agents achieves consensus using the second-order protocol. Using insights from the analysis of the ICF an extension is made by adding an observation buffer to the ICF. The new filter is called the information consensus filter with an observation buffer (ICFOB). The track-to-track correlation occurring from independent estimates passing through a common process model does not affect the ICFOB as it does other decentralized estimation methods. The ICFOB is shown to be equivalent to a centralized filter that has access to every measurement in a network. There are two caveats to this equivalency. First, at any point in time, the prior ICFOB estimate is equal to the prior centralized filter estimate found by fusing the observations that are taken before those stored in the buffer. The a posteriori estimates using observations in the buffer are not equal to estimates from the centralized filter since the agents have not finished disseminating those observations throughout the sensor network. Second, the ICFOB needs to know the number of active sensors in the network. The number of sensors is global information; therefore, the ICFOB is not fully decentralized. If the number of sensors is not known, the local estimates are conservative.

One of the problems with the modern radio communication is the lack of availableradio frequencies. Recent studies have shown that, while the available licensed radiospectrum becomes more occupied, the assigned spectrum is significantly underutilized.To alleviate the situation, cognitive radio (CR) technology has been proposedto provide an opportunistic access to the licensed spectrum areas. Secondary CRsystems need to cyclically detect the presence of a primary user by continuouslysensing the spectrum area of interest. Radiowave propagation effects like fading andshadowing often complicate sensing of spectrum holes. When spectrum sensing isperformed in a cooperative manner, then the resulting sensing performance can beimproved and stabilized. In this thesis, two fully distributed and adaptive cooperative Primary User (PU)detection solutions for CR networks are studied. In the first part of this thesis we study a distributed energy detection schemewithout using any fusion center. Due to reduced communication such a topologyis more energy efficient. We propose the usage of distributed, diffusion least meansquare (LMS) type of power estimation algorithms with different network topologies.We analyze the resulting energy detection performance by using a commonframework and verify the theoretical findings through simulations. In the second part of this thesis we propose a fully distributed detection scheme,based on the largest eigenvalue of adaptively estimated correlation matrices, assumingthat the primary user signal is temporally correlated. Different forms of diffusionLMS algorithms are used for estimating and averaging the correlation matrices overthe CR network. The resulting detection performance is analyzed using a commonframework. In order to obtain analytic results on the detection performance, theadaptive correlation matrix estimates are approximated by a Wishart distribution.The theoretical findings are verified through simulations. / <p>QC 20170908</p>

L’apprentissage adaptatif distribué sur les réseaux permet à un ensemble d’agents de résoudre des problèmes d’estimation de paramètres en ligne en se basant sur des calculs locaux et sur des échanges locaux avec les voisins immédiats. La littérature sur l’estimation distribuée considère essentiellement les problèmes à simple tâche, où les agents disposant de fonctions objectives séparables doivent converger vers un vecteur de paramètres commun. Cependant, dans de nombreuses applications nécessitant des modèles plus complexes et des algorithmes plus flexibles, les agents ont besoin d’estimer et de suivre plusieurs vecteurs de paramètres simultanément. Nous appelons ce type de réseau, où les agents doivent estimer plusieurs vecteurs de paramètres, réseau multitâche. Bien que les agents puissent avoir différentes tâches à résoudre, ils peuvent capitaliser sur le transfert inductif entre eux afin d’améliorer les performances de leurs estimés. Le but de cette thèse est de proposer et d’étudier de nouveaux algorithmes d’estimation distribuée sur les réseaux multitâches. Dans un premier temps, nous présentons l’algorithme diffusion LMS qui est une stratégie efficace pour résoudre les problèmes d’estimation à simple-tâche et nous étudions théoriquement ses performances lorsqu’il est mis en oeuvre dans un environnement multitâche et que les communications entre les noeuds sont bruitées. Ensuite, nous présentons une stratégie de clustering non-supervisé permettant de regrouper les noeuds réalisant une même tâche en clusters, et de restreindre les échanges d’information aux seuls noeuds d’un même cluster / Distributed adaptive learning allows a collection of interconnected agents to perform parameterestimation tasks from streaming data by relying solely on local computations and interactions with immediate neighbors. Most prior literature on distributed inference is concerned with single-task problems, where agents with separable objective functions need to agree on a common parameter vector. However, many network applications require more complex models and flexible algorithms than single-task implementations since their agents involve the need to estimate and track multiple objectives simultaneously. Networks of this kind, where agents need to infer multiple parameter vectors, are referred to as multitask networks. Although agents may generally have distinct though related tasks to perform, they may still be able to capitalize on inductive transfer between them to improve their estimation accuracy. This thesis is intended to bring forth advances on distributed inference over multitask networks. First, we present the well-known diffusion LMS strategies to solve single-task estimation problems and we assess their performance when they are run in multitask environments in the presence of noisy communication links. An improved strategy allowing the agents to adapt their cooperation to neighbors sharing the same objective is presented in order to attain improved learningand estimation over networks. Next, we consider the multitask diffusion LMS strategy which has been proposed to solve multitask estimation problems where the network is decomposed into clusters of agents seeking different

This research proposes a novel approach for improving autonomous mobile system navigation in dynamic and potentially occluded environments. The research introduces a tracking framework that combines data from stationary sensing units and on-board sensors, addressing challenges of computational efficiency, reliability, and scalability. The work innovates by integrating spatially-distributed LiDAR and RGB-D Camera sensors, with the optional inclusion of on-board IMU-based dead-reckoning, forming a robust and efficient coordination framework for autonomous systems. Two key developments are achieved. Firstly, a point cloud object detection technique, "Generalized L-Shape Fitting”, is advanced, enhancing bounding box fitting over point cloud data. Secondly, a new estimation framework, the Distributed Edge Node Switching Filter (DENS-F), is established. The DENS-F optimizes resource utilization and coordination, while minimizing reliance on on-board computation. Furthermore, it incorporates a short-term predictive feature, thanks to the Adaptive-Constant Acceleration motion model, which utilizes behaviour-based control inputs. The findings indicate that the DENS-F substantially improves accuracy and computational efficiency compared to the Kalman Consensus Filter (KCF), particularly when additional inertial data is provided by the vehicle. The type of sensor deployed and the consistency of the vehicle's path are also found to significantly influence the system's performance. The research opens new viewpoints for enhancing autonomous vehicle tracking, highlighting opportunities for future exploration in prediction models, sensor selection, and precision coordination. / Denna forskning föreslår en ny metod för att förbättra autonom mobil systemsnavigering i dynamiska och potentiellt skymda miljöer. Forskningen introducerar ett spårningsramverk som kombinerar data från stationära sensorenheter och ombordssensorer, vilket hanterar utmaningar med beräkningsefektivitet, tillförlitlighet och skalbarhet. Arbetet innoverar genom att integrera spatialt distribuerade LiDAR- och RGB-D-kamerasensorer, med det valfria tillägget av ombord IMU-baserad dödräkning, vilket skapar ett robust och efektivt samordningsramverk för autonoma system. Två nyckelutvecklingar uppnås. För det första avanceras en punktmolnsobjektdetekteringsteknik, “Generaliserad L-formig anpassning”, vilket förbättrar anpassning av inneslutande rutor över punktmolnsdata. För det andra upprättas ett nytt uppskattningssystem, det distribuerade kantnodväxlingsfltret (DENSF). DENS-F optimerar resursanvändning och samordning, samtidigt som det minimerar beroendet av ombordberäkning. Vidare införlivar det en kortsiktig prediktiv funktion, tack vare den adaptiva konstanta accelerationsrörelsemodellen, som använder beteendebaserade styrentréer. Resultaten visar att DENS-F väsentligt förbättrar noggrannhet och beräknings-efektivitet jämfört med Kalman Consensus Filter (KCF), särskilt när ytterligare tröghetsdata tillhandahålls av fordonet. Den typ av sensor som används och fordonets färdvägs konsekvens påverkar också systemets prestanda avsevärt. Forskningen öppnar nya synvinklar för att förbättra spårning av autonoma fordon, och lyfter fram möjligheter för framtida utforskning inom förutsägelsemodeller, sensorval och precisionskoordinering. / Questa ricerca propone un nuovo approccio per migliorare la navigazione dei sistemi mobili autonomi in ambienti dinamici e potenzialmente ostruiti. La ricerca introduce un sistema di tracciamento che combina dati da unità di rilevazione stazionarie e sensori di bordo, afrontando le sfde dell’effcienza computazionale, dell’affdabilità e della scalabilità. Il lavoro innova integrando sensori LiDAR e telecamere RGB-D distribuiti nello spazio, con l’inclusione opzionale di una navigazione inerziale basata su IMU di bordo, formando un robusto ed effciente quadro di coordinamento per i sistemi autonomi. Vengono raggiunti due sviluppi chiave. In primo luogo, viene perfezionata una tecnica di rilevazione di oggetti a nuvola di punti, “Generalized L-Shape Fitting”, migliorando l’adattamento del riquadro di delimitazione sui dati della nuvola di punti. In secondo luogo, viene istituito un nuovo framework di stima, il Distributed Edge Node Switching Filter (DENS-F). Il DENS-F ottimizza l’utilizzo delle risorse e il coordinamento, riducendo al minimo la dipendenza dal calcolo di bordo. Inoltre, incorpora una caratteristica di previsione a breve termine, grazie al modello di movimento Adaptive-Constant Acceleration, che utilizza input di controllo basati sul comportamento del veicolo. I risultati indicano che il DENS-F migliora notevolmente l’accuratezza e l’effcienza computazionale rispetto al Kalman Consensus Filter (KCF), in particolare quando il veicolo fornisce dati inerziali aggiuntivi. Si scopre anche che il tipo di sensore impiegato e la coerenza del percorso del veicolo infuenzano signifcativamente le prestazioni del sistema. La ricerca apre nuovi punti di vista per migliorare il tracciamento dei veicoli autonomi, evidenziando opportunità per future esplorazioni nei modelli di previsione, nella selezione dei sensori e nel coordinamento di precisione.