Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks

Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally, conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002 and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140

Gossip Algorithms for Distributed Signal Processing

Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

Smart grid state estimation and its applications to grid stabilization

University of Technology Sydney. Faculty of Engineering and Information Technology.The smart grid is expected to modernize the current electricity grid by commencing a new set of technologies and services that can make the electricity networks more secure, automated, cooperative and sustainable. The smart grid can integrate multiple distributed energy resources (DERs) into the main grid. The need for DERs is expected to become more important in the future smart grid due to the global warming and energy problems. Basically, the smart grid can spread the intelligence of the energy distribution and control system from the central unit to long-distance remote areas, thus enabling accurate state estimation and wide-area real-time monitoring of these intermittent energy sources. Reliable state estimation is a key technique to fulfil the control requirement and hence is an enabler for the automation of power grids. Driven by these motivations, this research explores the problem of state estimation and stabilization taking disturbances, cyber attacks and packet losses into consideration for the smart grid. The first contribution of this dissertation is to develop a least square based Kalman filter (KF) algorithm for state estimation, and an optimal feedback control framework for stabilizing the microgrid states. To begin with, the environment-friendly renewable microgrid incorporating multiple DERs is modelled to obtain discrete-time state-space linear equations where sensors are deployed to obtain system state information. The proposed smart grid communication system provides an opportunity to address the state regulation challenge by offering two-way communication links for microgrid information collection, estimation and stabilization. Interestingly, the developed least square based centralised KF algorithm is able to estimate the system states properly even at the beginning of the dynamic process, and the proposed H2 based optimal feedback controller is able to stabilize the microgrid states in a fairly short time. Unfortunately, the smart grid is susceptible to malicious cyber attacks, which can create serious technical, economic, social and control problems in power network operations. In contrast to the traditional cyber attack minimization techniques, this study proposes a recursive systematic convolutional (RSC) code and KF based method in the context of smart grids. The proposed RSC code is used to add redundancy in the microgrid states, and the log maximum a-posterior is used to recover the state information which is affected by random noises and cyber attacks. Once the estimated states are obtained, a semidefinite programming (SDP) based optimal feedback controller is proposed to regulate the system states. Test results show that the proposed approach can accurately mitigate the cyber attacks and properly estimate as well as regulate the system states. The other significant contribution of this dissertation is to develop an adaptive-then-combine distributed dynamic approach for monitoring the grid under lossy communication links between wind turbines and the energy management system. Based on the mean squared error principle, an adaptive approach is proposed to estimate the local state information. The global estimation is designed by combining local estimation results with weighting factors, which are calculated by minimizing the estimation error covariances based on SDP. Afterwards, the convergence analysis indicates that the estimation error is gradually decreased, so the estimated state converges to the actual state. The efficacy of the developed approach is verified using the wind turbine and IEEE 6-bus distribution system. Furthermore, the distribution power sub-systems are usually interconnected to each other, so this research investigates the interconnected optimal filtering problem for distributed dynamic state estimation considering packet losses. The optimal local and neighbouring gains are computed to reach a consensus estimation after exchanging their information with the neighbouring estimators. Then the convergence of the developed algorithm is theoretically proved. Afterwards, a distributed controller is designed based on the SDP approach. Simulation results demonstrate the accuracy of the developed approaches. The penultimate contribution of this dissertation is to develop a distributed state estimation algorithm for interconnected power systems that only needs a consensus step. After modelling the interconnected synchronous generators, the optimal gain is determined to obtain a distributed state estimation. The consensus of the developed approach is proved based on the Lyapunov theory. From the circuit and system point of view, the proposed framework is useful for designing a practical energy management system as it has less computational complexity and provides accurate estimation results. The distributed state estimation algorithm is further modified by considering different observation matrices with both local and consensus steps. The optimal local gain is computed after minimizing the mean squared error between the true and estimated states. The consensus gain is determined by a convex optimization process with a given local gain. Moreover, the convergence of the proposed scheme is analysed after stacking all the estimation error dynamics. The efficacy of the developed approach is demonstrated using the environment-friendly renewable microgrid and IEEE 30-bus power system. Overall, the findings, theoretical development and analysis of this research represent a comprehensive source of information for smart grid state estimation and stabilization schemes, and will shed light on green smart energy management systems and monitoring centre design in future smart grid implementations. It is worth pointing out that the aforementioned contributions are very important in the smart grid community as communication impairments have a significant impact on grid stability and the distributed strategies can reduce communication burden and offer a sparse communication network

Gossip and Distributed Kalman Filtering: Weak Consensus under Weak Detectability

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.Comment: Submitted to the IEEE Transactions, 30 pages

Distributing the Kalman Filter for Large-Scale Systems

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German