Stability of Kalman Filtering with a Random Measurement Equation: Application to Sensor Scheduling with Intermittent Observations
Guandong University of Technology（广东工业大学）；French-Argentinean International Center for Information and Systems Sciences, National Scientific and Technical Research Council（法阿信息与系统科学国际中心，国家科学技术研究委员会）；Dalian University of Technology（大连理工大学）；ABB Corporate Research Center（ABB企业研究中心）；University of Newcastle（纽卡斯尔大学）
Damián Marelli, Tianju Sui, Eduardo Rohr, Minyue Fu
Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement equation, i.e., the measurement matrix and the measurement error covariance, are random. Our result also generalizes existing ones in the sense that it does not require the system matrix to be diagonalizable. For this general setting, we state a necessary and a sufficient condition for stability, and address its numerical computation. An important application of our generalization is a networking setting with multiple sensors which transmit their measurement to the estimator using a sensor scheduling protocol over a lossy network. We demonstrate how our result is used for assessing the stability of a Kalman filter in this multi-sensor setting.
Time-scale theory, due to its ability to unify the continuous and discrete cases, allows handling intractable non-uniform measurements, such as intermittent received signals. In this work, we address the state estimation problem of a vibration-induced intermittent optical wireless communication (OWC) system by designing a Kalman filter on time scales. First, the algorithm of the time-scale Kalman filter is introduced and a numerical example is given for illustration. Then the studied intermittent OWC system is presented, and experimental data are collected to determine the time scale's form, w…
KTH Royal Institute of Technology（KTH皇家理工学院）；University of Cyprus（塞浦路斯大学）；Aalto University（阿尔托大学）；Cyprus University of Technology（塞浦路斯理工大学）
We present a multisensor fusion framework for the onboard real-time navigation of a quadrotor in an indoor environment. The framework integrates sensor readings from an Inertial Measurement Unit (IMU), a camera-based object detection algorithm, and an Ultra-WideBand (UWB) localisation system. Often the sensor readings are not always readily available, leading to inaccurate pose estimation and hence poor navigation performance. To effectively handle and fuse sensor readings, and accurately estimate the pose of the quadrotor for tracking a predefined trajectory, we design a Maximum Correntropy C…
Motivated by various distributed control applications, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We characterize the stationary optimal sensor scheduling policy for the finite horizon, discounted, and long-term average cost problems and show that the value iteration algorithm converges to a solution of the average cost problem. We further show that the suboptimal policies provided by the rolling horizon truncation of the value iteration also guarantee stability and provide near-optimal average cost. La…
Power Scheduling of Kalman Filtering in Wireless Sensor Networks with Data Packet Drops
School of Automation, Beijing Institute of Technology（北京理工大学自动化学院）；Key Laboratory of Intelligent Control and Decision of Complex Systems（复杂系统智能控制与决策重点实验室）
KTH Royal Institute of Technology（瑞典皇家理工学院）；Cyprus University of Technology（塞浦路斯理工大学）；University of Cyprus（塞浦路斯大学）；Aalto University（阿尔托大学）
We propose a multisensor fusion framework for onboard real-time navigation of a quadrotor in an indoor environment, by integrating sensor readings from an Inertial Measurement Unit (IMU), a camera-based object detection algorithm, and an Ultra-WideBand (UWB) localization system. The sensor readings from the camera-based object detection algorithm and the UWB localization system arrive intermittently, since the measurements are not readily available. We design a Kalman filter that manages intermittent observations in order to handle and fuse the readings and estimate the pose of the quadrotor f…
System Identification for Continuous-time Linear Dynamical Systems
Princeton University（普林斯顿大学）；Princeton Neuroscience Institute（普林斯顿神经科学研究所）；Columbia University（哥伦比亚大学）；Data Science Institute, Columbia University（哥伦比亚大学数据科学研究所）；New York Genome Center（纽约基因组中心）
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental tension in the control of underactuated vector systems -- the need to balance the growth of the system in different dimensions. We characterize the stabilizability of $d$-dimensional systems with symmetric gain matrices by providing tight necessary and sufficient conditions that depend on the eigenvalues of the system. The proof technique is slightly different…
Underwater Dead Reckoning with Deployable Situation-Triggered Covariance Scheduling
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；U.S. Army Engineer Research and Development Center, Construction Engineering Research Laboratory（美国陆军工程师研究与发展中心建筑工程研究实验室）
Western University（西安大略大学）；University of Quebec in Outaouais（魁北克大学乌塔韦校区）；Lakehead University（湖首大学）
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and…
This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information, such as sensor deployment and city traffic scheduling. This work is built upon our previous work [1] which presented a (centralized) density filter to estimate the dynamic density of large-scale systems through a novel integration of mean-field models, kernel density estimation (KDE), and infinite-dimensional Kalman filters. In this work, we further study ho…
Large-scale agent systems have foreseeable applications in the near future. Estimating their macroscopic density is critical for many density-based optimization and control tasks, such as sensor deployment and city traffic scheduling. In this paper, we study the problem of estimating their dynamically varying probability density, given the agents' individual dynamics (which can be nonlinear and time-varying) and their states observed in real-time. The density evolution is shown to satisfy a linear partial differential equation uniquely determined by the agents' dynamics. We present a density f…
