A Partial-Nodes-Based Information fusion approach to state estimation for discrete-Time delayed stochastic complex networks

This paper is concerned with the information-fusion-based state estimation problem for a class of discrete-time complex networks with time-varying delays and stochastic perturbations. The measurement outputs available for state estimation are from a fraction of network nodes, and the addressed problem is therefore referred to as the so-called Partial-Nodes-Based (PNB) state estimation problem. By employing the Lyapunov stability theory, a novel framework is established to cope with the PNB state estimation problem by the measurement outputs collected from partial network nodes. By constructing specific Lyapunov-Krasovskii functionals, sufficient criteria are derived for the existence of the desired exponentially ultimately bounded state estimator in mean square for the complex networks. Moreover, a special case is considered where the complex network under investigation is free of stochastic perturbations and the corresponding analysis issue is discussed to ensure the existence of an exponential state estimator. In addition, the explicit expressions of the gains of the desired estimators are characterized. Finally, a numerical illustrative example is presented to demonstrate the effectiveness of the obtained theoretical results.     

Minimum-energy state estimation for systems with perspective outputs

This paper addresses the state estimation of systems with perspective outputs. We derive a minimum-energy estimator which produces an estimate of the state that is "most compatible" with the dynamics, in the sense that it requires the least amount of noise energy to explain the measured outputs. Under suitable observability assumptions, the estimate converges globally asymptotically to the true value of the state in the absence of noise and disturbance. In the presence of noise, the estimate converges to a neighborhood of the true value of the state. These results are also extended to solve the estimation problem when the measured outputs are transmitted through a network. In that case, we assume that the measurements arrive at discrete-time instants, are time-delayed, noisy, and may not be complete. We show that the redesigned minimum-energy estimator preserves the same convergence properties. We apply these results to the estimation of position and orientation for a mobile robot that uses a monocular charged-coupled device (CCD) camera mounted on-board to observe the apparent motion of stationary points. In the context of our application, the estimator can deal directly with the usual problems associated with vision systems such as noise, latency and intermittency of observations. Experimental results are presented and discussed.     

Reduced order state estimators for discrete-time stochastic systems

A reduced order, least squares, state estimator is developed for linear discrete-time systems having both input disturbance noise and output measurement noise with no output being free of measurement noise. The order reduction is achieved by using a Luenberger observer in connection with some of the system outputs and a Kalman filter to estimate the state of the Luenberger observer. The order of the resulting state estimator is reduced from the order of the usual Kalman filter system state estimator by the number of system outputs selected for use as inputs to the Luenberger Observer. The manner in which the noise associated with the selected system outputs affects the state estimation error covariance provides considerable insight into the compromise being attempted.     

Event‐triggered robust state estimation for wireless sensor networks

Robust state estimation problem subject to a communication constraint is investigated in this paper for a class of wireless sensor networks constituted by multiple remote sensor nodes and a fusion node. An analytical robust fusion estimator using local event‐triggered transmission strategies is derived aiming to reduce energy consumption of the sensor nodes and refrain from network traffic congestion. Some conditions are presented guaranteeing the uniformly bounded estimation errors of the robust state estimator. Several numerical simulations are presented to show the validity of the proposed method.     

能量和带宽受限下的分布式一致性融合估计器

针对网络化多传感器分布式估计中传感器能量和通信网络带宽约束问题,提出一种基于降低发送频率和数据压缩降维的分布式一致性融合估计算法.为了满足通信网络带宽要求,各传感器节点直接选取局部估计信号的部分分量进行传输;与此同时,各节点随机间歇式发送数据包到其他节点来节省能量.在给定一致性权重下,建立以一致性估计器增益为决策变量,以所有传感器节点有限时域下状态融合估计误差协方差矩阵的迹的和为代价函数的优化问题,基于Lyapunov稳定性理论给出使得融合估计误差在无噪声时渐近稳定的一致性估计器增益存在的充分条件,并通过最小化代价函数的上界得到一组次优的一致性估计器增益值.最后,通过算例仿真验证算法的有效性.     

两种网络约束下NNSs分布式有限时域FIR融合估计器

针对带宽受限和网络拓扑随机切换约束下组网导航系统(NNSs)的分布式位姿状态估计问题,建立网络约束综合作用下的离散组网滤波增广系统模型,提出一种分布式有限时域FIR融合估计算法.目标节点从邻节点集合中接收经量化效应和饱和效应处理后的普通数据包和跟踪数据包,在给出无偏约束条件的前提下,以使得状态估计值的估计误差满足最小方差为准则,充分考虑有色噪声的影响,设计有限时域FIR估计器及其差分形式,通过普通数据包得到目标节点状态的区域估计值,建立系统本地状态估计的统一机制.同时,考虑网络约束,将跟踪数据包引入系统的融合过程,在以均方准则确定时变加权矩阵的前提下,给出最优权值所满足的线性代数方程以及融合误差协方差的差分形式,将目标节点状态的区域估计值与各邻节点随机发送的协作估计值加权融合,得到目标节点状态的全局融合估计值.最后通过算例仿真验证算法的有效性.     

Kullback–Leibler average,consensus on probability densities,and distributed state estimation with guaranteed stability

This paper addresses distributed state estimation over a sensor network wherein each node–equipped with processing, communication and sensing capabilities–repeatedly fuses local information with information from the neighbors. Estimation is cast in a Bayesian framework and an information-theoretic approach to data fusion is adopted by formulating a consensus problem on the Kullback–Leibler average of the local probability density functions (PDFs) to be fused. Exploiting such a consensus on local posterior PDFs, a novel distributed state estimator is derived. It is shown that, for a linear system, the proposed estimator guarantees stability, i.e. mean-square boundedness of the state estimation error in all network nodes, under the minimal requirements of network connectivity and system observability, and for any number of consensus steps. Finally, simulation experiments demonstrate the validity of the proposed approach.     

Robust state estimation for wireless sensor networks with data‐driven communication

Robust state estimation problem for wireless sensor networks composed of multiple remote sensor nodes and a fusion node is investigated subject to a limitation on the communication rate. An analytical robust fusion estimator based on a data‐driven transmission strategy is derived to save the sensor energy consumption and reduce the network traffic congestion. The conditions guaranteeing the uniform boundedness of estimation errors of the robust fusion estimator are investigated. Numerical simulations are provided to show the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed state estimation for uncertain Markov‐type sensor networks with mode‐dependent distributed delays

In this paper, the distributed state estimation problem is investigated for a class of sensor networks described by uncertain discrete‐time dynamical systems with Markovian jumping parameters and distributed time‐delays. The sensor network consists of sensor nodes characterized by a directed graph with a nonnegative adjacency matrix that specifies the interconnection topology (or the distribution in the space) of the network. Both the parameters of the target plant and the sensor measurements are subject to the switches from one mode to another at different times according to a Markov chain. The parameter uncertainties are norm‐bounded that enter into both the plant system as well as the network outputs. Furthermore, the distributed time‐delays are considered, which are also dependent on the Markovian jumping mode. Through the measurements from a small fraction of the sensors, this paper aims to design state estimators that allow the nodes of the sensor network to track the states of the plant in a distributed way. It is verified that such state estimators do exist if a set of matrix inequalities is solvable. A numerical example is provided to demonstrate the effectiveness of the designed distributed state estimators. Copyright © 2011 John Wiley & Sons, Ltd.     

复杂网络的事件驱动故障估计

针对一类非线性耦合的复杂网络系统，提出了一种基于复杂网络估计器的近似最优故障估计方法.首先将复杂网络的状态与故障进行增广，然后对增广后的状态和故障进行了联合状态估计.为了处理多信号传输可能发生的数据冲突，采用了事件驱动的方法使复杂网络的输出传输至远程估计器.通过递推矩阵方程方法给出了估计误差协方差矩阵的上界，并通过设计估计器参数使得该上界在迹的意义下最小.最后，通过仿真例子验证了所提联合估计方案的可行性和有效性.     

Distributed fusion filters from uncertain measured outputs in sensor networks with random packet losses

This paper addresses the distributed fusion filtering problem for discrete-time random signals from measured outputs perturbed by random parameter matrices and correlated additive noises. These measurements are obtained by a sensor network with a given topology, where random packet dropouts occur during the data transmission through the different network communication channels. The distributed fusion estimation is accomplished in two phases. Firstly, by an innovation approach and using the last observation that successfully arrived if a packet is lost, a preliminary distributed least-squares estimator is designed at each sensor node using its own measurements and those from its neighbors. Secondly, every sensor collects the preliminary filters that are successfully received from its neighbors and fuses this information with its own one to generate the least-squares linear matrix-weighted distributed fusion estimator. The accuracy of the proposed estimators, which is measured by the estimation error covariances, is examined by a numerical simulation example.     

Optimal linear estimation for networked systems with communication constraints

This paper is concerned with the optimal linear estimation problem for discrete time-varying networked systems with communication constraints. The communication constraint considered is that only one network node is allowed to gain access to a shared communication channel, then the various network nodes of the networked systems are scheduled to transmit data according to a specified media access control protocol, and a remote estimator performs the estimation task with only partially available measurements. The channel accessing processes of those network nodes are modeled by Bernoulli processes, and optimal linear filters are designed by using the orthogonal projection principle and the innovation analysis approach. It is shown that the optimal estimation performances critically depend on the channel accessing probabilities of the network nodes and the packet loss probability, and the optimal filters can be obtained by solving recursive Lyapunov and Riccati equations. An illustrative example is finally given to show the effectiveness of the proposed filters.     

Unknown disturbance inputs estimation based on a state functional observer design

We consider the problem of function of state plus unknown input estimation of a linear time-invariant system using only the measured outputs. Two reduced-order input estimators built upon a state functional observer are proposed. The first is an extension of a state/input estimator, while the second is based on adaptive observer design technique. The proposed estimator can be designed under less restrictive conditions than those of the previous work, and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems.     

Robust H2/H∞-state estimation forsystems with error variance constraints: the continuous-time case

The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H_∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H_∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approach     

Constrained state estimation for stochastic jump systems: moving horizon approach

We discuss the state estimation advantages for a class of linear discrete-time stochastic jump systems, in which a Markov process governs the operation mode, and the state variables and disturbances are subject to inequality constraints. The horizon estimation approach addressed the constrained state estimation problem, and the Bayesian network technique solved the stochastic jump problem. The moving horizon state estimator designed in this paper can produce the constrained state estimates with a lower error covariance than under the unconstrained counterpart. This new estimation method is used in the design of the restricted state estimator for two practical applications.     

State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case

This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.     

Co-design of H∞ jump observers for event-based measurements over networks

This work presents a strategy to minimise the network usage and the energy consumption of wireless battery-powered sensors in the observer problem over networks. The sensor nodes implement a periodic send-on-delta approach, sending new measurements when a measure deviates considerably from the previous sent one. The estimator node implements a jump observer whose gains are computed offline and depend on the combination of available new measurements. We bound the estimator performance as a function of the sending policies and then state the design procedure of the observer under fixed sending thresholds as a semidefinite programming problem. We address this problem first in a deterministic way and, to reduce conservativeness, in a stochastic one after obtaining bounds on the probabilities of having new measurements and applying robust optimisation problem over the possible probabilities using sum of squares decomposition. We relate the network usage with the sending thresholds and propose an iterative procedure for the design of those thresholds, minimising the network usage while guaranteeing a prescribed estimation performance. Simulation results and experimental analysis show the validity of the proposal and the reduction of network resources that can be achieved with the stochastic approach.     

State estimation for coupled output discrete-time complex network with stochastic measurements and different inner coupling matrices

A state estimation problem is studied for a class of coupled outputs discrete-time networks with stochastic measurements, i.e., the measurements are missing and disturbed with stochastic noise. The considered networks are coupled with outputs rather than states, are coupled with different inner coupling matrices rather than identical inner ones. By using Lyapunov stability theory combined with stochastic analysis, a novel state estimation scheme is proposed to estimate the states of discrete-time complex networks through the available output measurements, where the measurements are stochastic missing and are disturbed with Brownian motions which are caused by data transmission among nodes due to communication unreliability. State estimation conditions are derived in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the validity of the proposed scheme.     

State estimation for complex systems with randomly occurring nonlinearities and randomly missing measurements

This paper is concerned with the state estimation problem for the complex networked systems with randomly occurring nonlinearities and randomly missing measurements. The nonlinearities are included to describe the phenomena of nonlinear disturbances which exist in the network and may occur in a probabilistic way. Considering the fact that probabilistic data missing may occur in the process of information transmission, we introduce the randomly data missing into the sensor measurements. The aim of this paper is to design a state estimator to estimate the true states of the considered complex network through the available output measurements. By using a Lyapunov functional and some stochastic analysis techniques, sufficient criteria are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the state estimator gain is also obtained. Finally, a numerical example is employed to illustrate the effectiveness of the proposed state estimation conditions.     

Decentralized robust set-valued state estimation in networked multiple sensor systems

This paper addresses a decentralized robust set-valued state estimation problem for a class of uncertain systems via a data-rate constrained sensor network. The uncertainties of the systems satisfy an energy-type constraint known as an integral quadratic constraint. The sensor network consists of spatially distributed sensors and a fusion center where set-valued state estimation is carried out. The communications from the sensors to the fusion center are through data-rate constrained communication channels. We propose a state estimation scheme which involves coders that are implemented in the sensors, and a decoder–estimator that is located at the fusion center. Their construction is based on the robust Kalman filtering techniques. The robust set-valued state estimation results of this paper involve the solution of a jump Riccati differential equation and the solution of a set of jump state equations.