A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.Comment: 9 pages, 3 figure

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed

Computation-Communication Trade-offs and Sensor Selection in Real-time Estimation for Processing Networks

Recent advances in electronics are enabling substantial processing to be performed at each node (robots, sensors) of a networked system. Local processing enables data compression and may mitigate measurement noise, but it is still slower compared to a central computer (it entails a larger computational delay). However, while nodes can process the data in parallel, the centralized computational is sequential in nature. On the other hand, if a node sends raw data to a central computer for processing, it incurs communication delay. This leads to a fundamental communication-computation trade-off, where each node has to decide on the optimal amount of preprocessing in order to maximize the network performance. We consider a network in charge of estimating the state of a dynamical system and provide three contributions. First, we provide a rigorous problem formulation for optimal real-time estimation in processing networks in the presence of delays. Second, we show that, in the case of a homogeneous network (where all sensors have the same computation) that monitors a continuous-time scalar linear system, the optimal amount of local preprocessing maximizing the network estimation performance can be computed analytically. Third, we consider the realistic case of a heterogeneous network monitoring a discrete-time multi-variate linear system and provide algorithms to decide on suitable preprocessing at each node, and to select a sensor subset when computational constraints make using all sensors suboptimal. Numerical simulations show that selecting the sensors is crucial. Moreover, we show that if the nodes apply the preprocessing policy suggested by our algorithms, they can largely improve the network estimation performance.Comment: 15 pages, 16 figures. Accepted journal versio

Outdated Measurements Are Still Useful For Multi-Sensor Linear Control Systems With Random Communication Delays

Linear systems are a widely used model for the control tasks of modern cyber physical systems around their stationary state(s), e.g., smart grids, remote health applications, and autonomous driving systems. Specifically, each sensor first compresses its own measurement and then sends it to the controller. Due to the inevitable random communication delay, the controller needs to decide how to fuse the received information to compute the desired control action. Suppose a fusion center has received several measurements over time. One common belief is that the control decision should be made solely based on the latest measurement of each sensor while ignoring the older/stale measurements from the same sensor. This work shows that while such a strategy is optimal in a single-sensor environment, it can be strictly suboptimal for a multi-sensor system. Namely, if one properly fuses both the latest and outdated measurements from each of the sensors, one can strictly improve the underlying control system performance. The numerical evaluation shows that even at a very low communication rate of 8 bits per measurement per sensor, the proposed scheme achieves a state variance of only 5% away from the best possible achievable L2 norm. It is 15% better than the MMSE fusion scheme using exclusively the freshest measurements (while discarding outdated ones)

State Estimation for Distributed and Hybrid Systems

This thesis deals with two aspects of recursive state estimation: distributed estimation and estimation for hybrid systems. In the first part, an approximate distributed Kalman filter is developed. Nodes update their state estimates by linearly combining local measurements and estimates from their neighbors. This scheme allows nodes to save energy, thus prolonging their lifetime, compared to centralized information processing. The algorithm is evaluated experimentally as part of an ultrasound based positioning system. The first part also contains an example of a sensor-actuator network, where a mobile robot navigates using both local sensors and information from a sensor network. This system was implemented using a component-based framework. The second part develops, a recursive joint maximum a posteriori state estimation scheme for Markov jump linear systems. The estimation problem is reformulated as dynamic programming and then approximated using so called relaxed dynamic programming. This allows the otherwise exponential complexity to be kept at manageable levels. Approximate dynamic programming is also used to develop a sensor scheduling algorithm for linear systems. The algorithm produces an offline schedule that when used together with a Kalman filter minimizes the estimation error covariance

State Estimation Fusion for Linear Microgrids over an Unreliable Network

Microgrids should be continuously monitored in order to maintain suitable voltages over time. Microgrids are mainly monitored remotely, and their measurement data transmitted through lossy communication networks are vulnerable to cyberattacks and packet loss. The current study leverages the idea of data fusion to address this problem. Hence, this paper investigates the effects of estimation fusion using various machine-learning (ML) regression methods as data fusion methods by aggregating the distributed Kalman filter (KF)-based state estimates of a linear smart microgrid in order to achieve more accurate and reliable state estimates. This unreliability in measurements is because they are received through a lossy communication network that incorporates packet loss and cyberattacks. In addition to ML regression methods, multi-layer perceptron (MLP) and dependent ordered weighted averaging (DOWA) operators are also employed for further comparisons. The results of simulation on the IEEE 4-bus model validate the effectiveness of the employed ML regression methods through the RMSE, MAE and R-squared indices under the condition of missing and manipulated measurements. In general, the results obtained by the Random Forest regression method were more accurate than those of other methods.This research was partially funded by public research projects of Spanish Ministry of Science and Innovation, references PID2020-118249RB-C22 and PDC2021-121567-C22 - AEI/10.13039/ 501100011033, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, reference EPUC3M17

State Estimation for Distributed Systems with Stochastic and Set-membership Uncertainties

State estimation techniques for centralized, distributed, and decentralized systems are studied. An easy-to-implement state estimation concept is introduced that generalizes and combines basic principles of Kalman filter theory and ellipsoidal calculus. By means of this method, stochastic and set-membership uncertainties can be taken into consideration simultaneously. Different solutions for implementing these estimation algorithms in distributed networked systems are presented