Optimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels

In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the method of Markovian jump linear systems, an optimal stationary estimator that minimizes the error variance in the steady state is obtained, based on the mean-square (MS) stabilizing solution to the coupled algebraic Riccati equations. An explicit necessary and sufficient condition is derived for the existence of the MS stabilizing solution, which coincides with that of the standard Kalman filter. More importantly, we provide a sufficient condition under which the MS detectability with multiple Markovian packet drop channels can be decoupled, and propose a locally optimal stationary estimator but computationally more tractable. Analytic sufficient and necessary MS detectability conditions are presented for the decoupled subsystems subsequently. Finally, numerical simulations are conducted to illustrate the results on the MS stabilizing solution, the MS detectability, and the performance of the optimal and locally optimal stationary estimators

Distributed Kalman Filters over Wireless Sensor Networks: Data Fusion, Consensus, and Time-Varying Topologies

Kalman filtering is a widely used recursive algorithm for optimal state estimation of linear stochastic dynamic systems. The recent advances of wireless sensor networks (WSNs) provide the technology to monitor and control physical processes with a high degree of temporal and spatial granularity. Several important problems concerning Kalman filtering over WSNs are addressed in this dissertation. First we study data fusion Kalman filtering for discrete-time linear time-invariant (LTI) systems over WSNs, assuming the existence of a data fusion center that receives observations from distributed sensor nodes and estimates the state of the target system in the presence of data packet drops. We focus on the single sensor node case and show that the critical data arrival rate of the Bernoulli channel can be computed by solving a simple linear matrix inequality problem. Then a more general scenario is considered where multiple sensor nodes are employed. We derive the stationary Kalman filter that minimizes the average error variance under a TCP-like protocol. The stability margin is adopted to tackle the stability issue. Second we study distributed Kalman filtering for LTI systems over WSNs, where each sensor node is required to locally estimate the state in a collaborative manner with its neighbors in the presence of data packet drops. The stationary distributed Kalman filter (DKF) that minimizes the local average error variance is derived. Building on the stationary DKF, we propose Kalman consensus filter for the consensus of different local estimates. The upper bound for the consensus coefficient is computed to ensure the mean square stability of the error dynamics. Finally we focus on time-varying topology. The solution to state consensus control for discrete-time homogeneous multi-agent systems over deterministic time-varying feedback topology is provided, generalizing the existing results. Then we study distributed state estimation over WSNs with time-varying communication topology. Under the uniform observability, each sensor node can closely track the dynamic state by using only its own observation, plus information exchanged with its neighbors, and carrying out local computation

Sum-Rate Maximization for Linearly Precoded Downlink Multiuser MISO Systems with Partial CSIT: A Rate-Splitting Approach

This paper considers the Sum-Rate (SR) maximization problem in downlink MU-MISO systems under imperfect Channel State Information at the Transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This Rate-Splitting (RS) approach was shown to boost the achievable Degrees of Freedom (DoF) when CSIT errors decay with increased SNR. In this work, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized Ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of Sample Average Approximation (SAA) coupled with the Weighted Minimum Mean Square Error (WMMSE) approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared to conventional transmission with NoRS.Comment: accepted to IEEE Transactions on Communication

Compressive Privacy for a Linear Dynamical System

We consider a linear dynamical system in which the state vector consists of both public and private states. One or more sensors make measurements of the state vector and sends information to a fusion center, which performs the final state estimation. To achieve an optimal tradeoff between the utility of estimating the public states and protection of the private states, the measurements at each time step are linearly compressed into a lower dimensional space. Under the centralized setting where all measurements are collected by a single sensor, we propose an optimization problem and an algorithm to find the best compression matrix. Under the decentralized setting where measurements are made separately at multiple sensors, each sensor optimizes its own local compression matrix. We propose methods to separate the overall optimization problem into multiple sub-problems that can be solved locally at each sensor. We consider the cases where there is no message exchange between the sensors; and where each sensor takes turns to transmit messages to the other sensors. Simulations and empirical experiments demonstrate the efficiency of our proposed approach in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately

Fault detection and isolation in a networked multi-vehicle unmanned system

Recent years have witnessed a strong interest and intensive research activities in the area of networks of autonomous unmanned vehicles such as spacecraft formation flight, unmanned aerial vehicles, autonomous underwater vehicles, automated highway systems and multiple mobile robots. The envisaged networked architecture can provide surpassing performance capabilities and enhanced reliability; however, it requires extending the traditional theories of control, estimation and Fault Detection and Isolation (FDI). One of the many challenges for these systems is development of autonomous cooperative control which can maintain the group behavior and mission performance in the presence of undesirable events such as failures in the vehicles. In order to achieve this goal, the team should have the capability to detect and isolate vehicles faults and reconfigure the cooperative control algorithms to compensate for them. This dissertation deals with the design and development of fault detection and isolation algorithms for a network of unmanned vehicles. Addressing this problem is the main step towards the design of autonomous fault tolerant cooperative control of network of unmanned systems. We first formulate the FDI problem by considering ideal communication channels among the vehicles and solve this problem corresponding to three different architectures, namely centralized, decentralized, and semi-decentralized. The necessary and sufficient solvability conditions for each architecture are also derived based on geometric FDI approach. The effects of large environmental disturbances are subsequently taken into account in the design of FDI algorithms and robust hybrid FDI schemes for both linear and nonlinear systems are developed. Our proposed robust FDI algorithms are applied to a network of unmanned vehicles as well as Almost-Lighter-Than-Air-Vehicle (ALTAV). The effects of communication channels on fault detection and isolation performance are then investigated. A packet erasure channel model is considered for incorporating stochastic packet dropout of communication channels. Combining vehicle dynamics and communication links yields a discrete-time Markovian Jump System (MJS) mathematical model representation. This motivates development of a geometric FDI framework for both discrete-time and continuous-time Markovian jump systems. Our proposed FDI algorithm is then applied to a formation flight of satellites and a Vertical Take-Off and Landing (VTOL) helicopter problem. Finally, we investigate the problem of fault detection and isolation for time-delay systems as well as linear impulsive systems. The main motivation behind considering these two problems is that our developed geometric framework for Markovian jump systems can readily be applied to other class of systems. Broad classes of time-delay systems, namely, retarded, neutral, distributed and stochastic time-delay systems are investigated in this dissertation and a robust FDI algorithm is developed for each class of these systems. Moreover, it is shown that our proposed FDI algorithms for retarded and stochastic time-delay systems can potentially be applied in an integrated design of FDI/controller for a network of unmanned vehicles. Necessary and sufficient conditions for solvability of the fundamental problem of residual generation for linear impulsive systems are derived to conclude this dissertation

Distributed estimation over a low-cost sensor network: a review of state-of-the-art

Proliferation of low-cost, lightweight, and power efficient sensors and advances in networked systems enable the employment of multiple sensors. Distributed estimation provides a scalable and fault-robust fusion framework with a peer-to-peer communication architecture. For this reason, there seems to be a real need for a critical review of existing and, more importantly, recent advances in the domain of distributed estimation over a low-cost sensor network. This paper presents a comprehensive review of the state-of-the-art solutions in this research area, exploring their characteristics, advantages, and challenging issues. Additionally, several open problems and future avenues of research are highlighted

Wireless Positioning and Tracking for Internet of Things in GPS-denied Environments

Wireless positioning and tracking have long been a critical technology for various applications such as indoor/outdoor navigation, surveillance, tracking of assets and employees, and guided tours, among others. Proliferation of Internet of Things (IoT) devices, the evolution of smart cities, and vulnerabilities of traditional localization technologies to cyber-attacks such as jamming and spoofing of GPS necessitate development of novel radio frequency (RF) localization and tracking technologies that are accurate, energy-efficient, robust, scalable, non-invasive and secure. The main challenges that are considered in this research work are obtaining fundamental limits of localization accuracy using received signal strength (RSS) information with directional antennas, and use of burst and intermittent measurements for localization. In this dissertation, we consider various RSS-based techniques that rely on existing wireless infrastructures to obtain location information of corresponding IoT devices. In the first approach, we present a detailed study on localization accuracy of UHF RF IDentification (RFID) systems considering realistic radiation pattern of directional antennas. Radiation patterns of antennas and antenna arrays may significantly affect RSS in wireless networks. The sensitivity of tag antennas and receiver antennas play a crucial role. In this research, we obtain the fundamental limits of localization accuracy considering radiation patterns and sensitivity of the antennas by deriving Cramer-Rao Lower Bounds (CRLBs) using estimation theory techniques. In the second approach, we consider a millimeter Wave (mmWave) system with linear antenna array using beamforming radiation patterns to localize user equipment in an indoor environment. In the third approach, we introduce a tracking and occupancy monitoring system that uses ambient, bursty, and intermittent WiFi probe requests radiated from mobile devices. Burst and intermittent signals are prominent characteristics of IoT devices; using these features, we propose a tracking technique that uses interacting multiple models (IMM) with Kalman filtering. Finally, we tackle the problem of indoor UAV navigation to a wireless source using its Rayleigh fading RSS measurements. We propose a UAV navigation technique based on Q-learning that is a model-free reinforcement learning technique to tackle the variation in the RSS caused by Rayleigh fading