Distributed consensus estimation for diffusion systems with missing measurements over sensor networks

In this paper, the problem of distributed consensus estimation with randomly missing measurements is investigated for a diffusion system over the sensor network. A random variable, the probability of which is known a priori, is used to model the randomly missing phenomena for each sensor. The aim of the addressed estimation problem is to design distributed consensus estimators depending on the neighbouring information such that, for all random measurement missing, the estimation error systems are guaranteed to be globally asymptotically stable in the mean square. By using Lyapunov functional method and the stochastic analysis approach, the sufficient conditions are derived for the convergence of the estimation error systems. Finally, a numerical example is given to demonstrate the effectiveness of the proposed distributed consensus estimator design scheme.     

Distributed estimation for adaptive sensor selection in wireless sensor networks

Wireless sensor networks (WSNs) are usually deployed for monitoring systems with the distributed detection and estimation of sensors. Sensor selection in WSNs is considered for target tracking. A distributed estimation scenario is considered based on the extended information filter. A cost function using the geometrical dilution of precision measure is derived for active sensor selection. A consensus-based estimation method is proposed in this paper for heterogeneous WSNs with two types of sensors. The convergence properties of the proposed estimators are analyzed under time-varying inputs. Accordingly, a new adaptive sensor selection (ASS) algorithm is presented in which the number of active sensors is adaptively determined based on the absolute local innovations vector. Simulation results show that the tracking accuracy of the ASS is comparable to that of the other algorithms.     

Distributed resilient estimation over sensor networks for nonlinear time‐delayed systems with stochastic perturbations

This paper is concerned with the distributed resilient estimation problem for a class of nonlinear time‐delayed systems subject to stochastic perturbations. The plant and the measurements are disturbed by two Gaussian white stochastic processes with known statistical information, respectively. In addition, a resilient estimator is designed for each node by means of the parameter uncertainties and Bernoulli‐distributed random variables. Then, a novel exponential‐bounded performance index is put forward to measure the disturbance rejection level of the distributed estimators against the external disturbances and the impact of the initial values. A new vector dissipation definition including multiple vectors of energy storage functions is established to deal with the time‐delay estimation error dynamics. Within the framework of local performance analysis inspired by this new definition of vector dissipation, sufficient conditions in terms of recursive linear matrix inequalities are constructed for each node to guarantee the desirable performance index. Next, a local optimization problem subject to a set of recursive linear matrix inequalities is presented for each node to minimize the upper bound in the performance index, where the calculations can be conducted on every node in a distributed manner and the estimator gains are also calculated. Finally, an illustrative simulation example is provided to verify the applicability of the proposed estimators.     

Distributed state estimation for uncertain sensor networks with mixed time delays subject to sensor saturations

In this paper, the distributed state estimation problem is investigated for a class of uncertain sensor networks. The target plant is described by a set of uncertain difference equations with both discrete-time and infinite distributed delays, where two random variables are introduced to account for the randomly occurring nonlinearities. The sensor measurement outputs are subject to randomly occurring sensor saturations due to the physical limitations of the sensors. Through available output measurements from each individual sensor and its neighboring sensors, this paper aims to design distributed state estimators to approximate the states of the target plant in a distributed way. Sufficient conditions are presented which not only guarantee the estimation error systems to be globally asymptotically stable in the mean square sense but also ensure the existence of the desired estimator gains.     

Distributed extended object tracking information filter over sensor networks

This work aims to design a distributed extended object tracking system over a realistic network, where both the extent and kinematics are required to retain consensus within the entire network. To this end, we resort to the multiplicative error model (MEM) that allows the extent parameters of perpendicular axis-symmetric objects to have individual uncertainty. To incorporate the MEM into the information filter (IF) style, we use the moment-matching technique to derive two pair linear models with only additive noise. The separation is merely in a fashion, and the cross-correlation between states is preserved as parameters in each other's model. As a result, the closed-form expressions are transferred into an alternating iteration of two linear IFs. With the two models, a centralized IF is proposed wherein the measurements are converted into a summation of innovation parts. Later, under a sensor network with the communication nodes and sensor nodes, we present two distributed IFs through the consensus on information and consensus on measurement schemes, respectively. Moreover, we prove the estimation errors of the proposed filter are exponentially bounded in the mean square. The benefits are testified by numerical experiments in comparison to state-of-the-art filters in literature.     

Reliable fusion estimation over sensor networks with outliers and energy constraints

This paper provides a reliable fusion scheme over sensor networks subject to abnormal measurements and energy constraints. Two kinds of channels are employed to implement the information transmission in order to extend the lifetime. Specifically, the one has the merit of high reliability by sacrificing energy cost and the other reduces the energy cost but could result in packet loss. For the addressed problem, a χ² detection in local state estimator is first designed to remove abnormal measurements, which could come from outliers or a malicious modification by attackers. Then, a new strategy is developed to compensate the lost local estimation transmitted by low‐reliable channels. Furthermore, by view of matrix operation and probability theory, a set of recursive formulas are developed to calculate desired error covariance matrices of local state estimation, compensated state estimation as well as fusion estimation. The optimal fusion weights are obtained analytically and the advantage of fusion estimation is disclosed by resorting to these covariance matrices. Finally, a numerical example is used to illustrate the effectiveness of the proposed method.     

Distributed Kalman filtering via node selection in heterogeneous sensor networks

In this paper, we propose a strategy for distributed Kalman filtering over sensor networks, based on node selection, rather than on sensor fusion. The presented approach is particularly suitable when sensors with limited sensing capability are considered. In this case, strategies based on sensor fusion may exhibit poor results, as several unreliable measurements may be included in the fusion process. On the other hand, our approach implements a distributed strategy able to select only the node with the most accurate estimate and to propagate it through the whole network in finite time. The algorithm is based on the definition of a metric of the estimate accuracy, and on the application of an agreement protocol based on max-consensus. We prove the convergence, in finite time, of all the local estimates to the most accurate one at each discrete iteration, as well as the equivalence with a centralised Kalman filter with multiple measurements, evolving according to a state-dependent switching dynamics. An application of the algorithm to the problem of distributed target tracking over a network of heterogeneous range-bearing sensors is shown. Simulation results and a comparison with two distributed Kalman filtering strategies based on sensor fusion confirm the suitability of the approach.     

Distributed control for energy-efficient and fast consensus in wireless sensor networks

The paper proposes a distributed control of nodes transmission radii in energy-harvesting wireless sensor networks for simultaneously coping with energy consumption and consensus responsiveness requirement. The stability of the closed-loop network under the proposed control law is proved. Simulation validations show the effectiveness of the proposed approach in nominal scenario as well as in the presence of uncertain node power requirements and harvesting system supply.     

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.     

Event-triggered robust distributed state estimation for sensor networks with state-dependent noises

This paper is concerned with the event-triggered distributed state estimation problem for a class of uncertain stochastic systems with state-dependent noises and randomly occurring uncertainties over sensor networks. An event-triggered communication scheme is proposed in order to determine whether the measurements on each sensor should be transmitted to the estimators or not. The norm-bounded uncertainty enters into the system in a random way. Through available output measurements from not only the individual sensor but also its neighbouring sensors, a sufficient condition is established for the desired distributed estimator to ensure that the estimation error dynamics are exponentially mean-square stable. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities, and then the explicit expression is given for the distributed estimator gains. Finally, a simulation example is provided to show the effectiveness of the proposed event-triggered distributed state estimation scheme.     

Distributed fault detection over sensor networks with Markovian switching topologies

This paper deals with the distributed fault detection for discrete-time Markov jump linear systems over sensor networks with Markovian switching topologies. The sensors are scatteredly deployed in the sensor field and the fault detectors are physically distributed via a communication network. The system dynamics changes and sensing topology variations are modeled by a discrete-time Markov chain with incomplete mode transition probabilities. Each of these sensor nodes firstly collects measurement outputs from its all underlying neighboring nodes, processes these data in accordance with the Markovian switching topologies, and then transmits the processed data to the remote fault detector node. Network-induced delays and accumulated data packet dropouts are incorporated in the data transmission between the sensor nodes and the distributed fault detector nodes through the communication network. To generate localized residual signals, mode-independent distributed fault detection filters are proposed. By means of the stochastic Lyapunov functional approach, the residual system performance analysis is carried out such that the overall residual system is stochastically stable and the error between each residual signal and the fault signal is made as small as possible. Furthermore, a sufficient condition on the existence of the mode-independent distributed fault detection filters is derived in the simultaneous presence of incomplete mode transition probabilities, Markovian switching topologies, network-induced delays, and accumulated data packed dropouts. Finally, a stirred-tank reactor system is given to show the effectiveness of the developed theoretical results.     

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.     

传感器网络一致性分布式滤波算法

为了改善分布式传感器网络的估计性能,提出了一种基于状态预测一致的滤波算法.在对局部估计值进行一致化处理的基础上,重点研究了利用邻居节点前一时刻的估计值对当前局部状态预测值进行修正来提高估计精度.给出了一种一致性增益的选择方法,利用李雅普诺夫方法得到了算法收敛的充分条件,并讨论了影响算法收敛速度的因素.仿真结果表明了算法的有效性,并发现节点度较大的传感器在网络估计中发挥着重要作用,可通过调整这类节点的一致性系数来改善算法性能.     

分布式传感网络的自适应一致性算法

为了提高分布式传感网络的估计精度,提出了一种新的自适应一致性算法。该算法在每次迭代时只需部分节点工作,即进行目标状态的监测。通过节点之间二进制信息的交换来调整每次迭代时的一致性权值,使得每次迭代时工作节点所占的权值更大,进而将该一致性算法与卡尔曼滤波相结合对目标状态进行估计。对该算法进行数值仿真,并与其他一致性加权算法进行比较,验证了该算法的有效性。     

传感器网络分布式事件触发多目标估计

本文主要研究无线传感器网络中目标数目已知且固定的一类分布式多目标跟踪问题,提出了一种完全分布式的基于事件触发的测量和通信策略使得每个节点在不需要全局信息的情况下实现估计误差和能量消耗之间的平衡.监测区域存在多个移动目标,传感器能否测量到单个目标由事件触发测量机制和节点的测量半径来综合决定.基于节点和邻居的信息采用k-means聚类算法来解决数据关联问题,同时提出了基于最小迹原则的一致性卡尔曼滤波算法.从理论上证明了该事件触发策略不仅在性能指标上优于基于时间触发的算法,而且在网络中如果存在节点对多目标协同可观,系统估计误差在均方意义下是稳定的.最后给出了仿真例子验证了该算法的有效性和可行性.     

基于无线传感器网络的分布递阶信息融合算法

提出了基于无线传感器网络的分布递阶信息融合方法,下层源节点采用卡尔曼滤波及基于减少能耗和网络冲突的数据处理方法,上层汇聚节点采用方差最小的加权信息融合方法,该方法能有效降低传感器网络能耗和网络信息冲突,仿真结果表明了该方法的有效性和可靠性。     

Distributed LMS estimation over networks with quantised communications

This article investigates the problem of distributed least mean-square (D-LMS) estimation over a network with quantised communication. Each node in the network has a quantiser consisting of a first-order dynamical encoder-decoder and can only communicate with its neighbours. Then a new D-LMS estimator is proposed by employing a weighted sum of the internal state differences between each node's quantiser and those of its neighbours. Performance analysis of the proposed quantised D-LMS algorithm is studied in terms of mean-square transient and steady-state measurements. We show that for Gaussian data and sufficiently small step sizes, the proposed cooperative D-LMS with quantisation is mean-square stable in all quantisation levels including the 1-bit case, and its performance approaches the cooperative D-LMS without quantisation when the quantisation step size is fairly small. Furthermore, although in unquantised case (infinite precision), the cooperative D-LMS always outperforms the non-cooperative D-LMS scheme (without communications among the neighbours); however, we show that due to the existence of quantisation error, the cooperative D-LMS with quantisation does not always outperform the non-cooperative D-LMS scheme, especially when the quantisation step size is quite large. Finally, numerical simulations also demonstrate that our theoretical performance matches well with experimental performance.     

Distributed data source verification in wireless sensor networks

In-network data aggregation is favorable for wireless sensor networks (WSNs): It allows in-network data processing while reducing the network traffic and hence saving the sensors energy. However, due to the distributed and unattended nature of WSNs, several attacks aiming at compromising the authenticity of the collected data could be perpetrated. For example, an adversary could capture a node to create clones of the captured one. These clones disseminated through the network could provide malicious data to the aggregating node, thus poisoning/disrupting the aggregation process. In this paper we address the problem of detecting cloned nodes; a requirement to be fulfilled to provide authenticity of the data fusion process.First, we analyze the desirable properties a distributed clone detection protocol should meet. Specifically: It should avoid having a single point of failure; the load should be totally distributed across the nodes in the network; the position of the clones in the network should not influence the detection probability. We then show that current solutions do not meet the exposed requirements. Next, we propose the Information Fusion Based Clone Detection Protocol (ICD). ICD is a probabilistic, completely distributed protocol that efficiently detects clones. ICD combines two cryptographic mechanisms: The pseudo-random key pre-distribution, usually employed to secure node pairwise communications, with a sparing use of asymmetric crypto primitives. We show that ICD matches all the requirements above mentioned and compare its performance with current solutions in the literature; experimental results show that ICD has better performance than existing solutions for all the cost parameters considered: Number of messages sent, per sensor storage requirement, and signature verification. These savings allow to increase the network operating lifetime. Finally, note that ICD protocol could be used as an independent layer by any data aggregation mechanism.