Distributed State Estimation for Linear Systems

This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator is first described for estimating the state of a continuous-time, jointly observable, input free, multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal with a fixed dwell time or a variable but with fixed average dwell time, or switch arbitrarily under appropriate assumptions. The estimator is guaranteed to solve the problem, provided a network-widely shared gain is sufficiently large. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is thus studied in which each agent adaptively adjusts a local gain though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that its state estimation errors all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network's graph is strongly connected for all time. This is accomplished by appealing to the ``split-spectrum'' approach and exploiting several well-known properties of invariant subspace. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.Comment: 17 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1903.0548

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

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