Unscented summation information‐weighted consensus filter for distributed sensor networks with incomplete information

In order to improve network scalability and fault tolerance, the distributed sensor networks are desirable. However, the distributed state estimation becomes challenging when some sensors have insufficient information due to restricted observability, and/or have imparity information due to unequal measurement‐noise covariances. Centralized summation information‐fusion (CSI) model is presented which performs weighted least‐squares estimation for all measurement information to achieve the optimal centralized state estimation. The CSI model revises the initialization and covariance propagation in the original information‐weighted consensus filter (ICF). Since centralized information fusion is a summation mode and is approached by the average consensus protocol, all the covariances involved in the CSI model contain the information regarding the total number of nodes. The artificially preset initial values are considered as measurement information and fused in accordance with the CSI model. By combining the CSI model with unscented transform, distributed unscented summation information‐weighted consensus filter (USICF) is proposed. USICF realizes the nonlinear estimation in the context of highly incomplete information. Theoretical analysis and experimental verification showed that USICF achieves better performance than UICF that is based on ICF.     

Distributed adaptive state estimation and tracking by using active-passive sensor networks

Heterogeneous sensor networks (HSN) find a wide range of applications in the field of military and civilian environments, where sensor nodes are utilized to estimate the position of a target with both dynamics and control input being unknown for the purposes of tracking. In the HSN, nodes are considered active depending upon their ability to sense the target output while the others are taken passive. Accurate estimation requires local information exchange among the spatially located sensor nodes, so that the active nodes as well as the passive nodes converge simultaneously to the same value. The local information exchange among the nodes is dictated by a connected graph. By using the criterion of collective observability, a novel distributed adaptive estimation scheme is introduced via adaptive observer where the nodes are allowed to have different sensor modalities. Using the estimated information, a subset of active and passive nodes, referred to as mobile nodes, can track the moving target. By using a constant state feedback controller at each mobile node, the state and parameter estimation as well as the tracking errors are shown to be uniformly ultimately bounded. Simulation results verify theoretical claims.     

Distributed Kalman filters with adaptive strategy for linear time‐varying interconnected systems

We consider the problem of distributed state estimation over a sensor network in which a set of nodes collaboratively estimates the state of a continuous‐time linear time‐varying system. In particular, our work focuses on the benefits of weight adaptation of the interconnection gains in distributed Kalman filters. To this end, an adaptation strategy is proposed with the adaptive laws derived via a Lyapunov‐redesign approach. The justification for the gain adaptation stems from a desire to adapt the pairwise difference of state estimates as a function of their agreement, thereby enforcing an interconnection‐dependent gain. In the proposed scheme, an adaptive gain for each pairwise difference of the interconnection terms is used in order to address edge‐dependent differences in the state estimates. Accounting for node‐specific differences, a special case of the scheme is also presented, where it uses a single adaptive gain in each node estimate and which uniformly penalizes all pairwise differences of state estimates in the interconnection term. The filter gains can be designed either by standard Kalman filter or Luenberger observer to construct the adaptive distributed Kalman filter or adaptive distributed Luenberger observer. Stability of the schemes has been shown, and it is not restricted by the graph topology and therefore the schemes are applicable to both directed and undirected graphs. The proposed algorithms offer a significant reduction in communication costs associated with information flow by the nodes. Finally, numerical studies are presented to illustrate the performance and effectiveness of the proposed adaptive distributed Kalman filters. Copyright © 2015 John Wiley & Sons, Ltd.     

电力系统多区域分布式状态估计方法

提出了一种电力系统多区域分布式状态估计方法,各区域估计器利用其数据采集与监视控制系统提供的量测数据进行本地状态估计,并通过平均一致性算法获取全局信息进行系统级状态估计。建立了基于拉格朗日乘子法的状态估计模型并设计了基于一致性的全局信息交换协议,给出了多区域分布式状态估计算法的实现流程。通过IEEE 14节点和118节点系统中的仿真算例验证了所提方法的正确性和有效性,并就估计精度和计算效率与现有状态估计方法进行了比较。仿真结果表明分布式状态估计方法可有效提高集中式状态估计系统的计算效率及可靠性,适用于结构更加复杂、量测数据体量更大电网的状态估计。     

考虑虚假数据注入攻击的有源配电网分布式状态估计

状态估计作为保障电网监测数据质量的关键一环,为能量管理系统提供可靠的数据基础。考虑到有源配电网量测误差大、易遭受网络攻击等问题,本文研究计及虚假数据注入攻击的有源配电网分布式状态估计方法。首先,各子区域根据自身量测进行状态估计,并利用平均一致性算法获取全局信息对内部状态量进行修正,实现完全分布式状态估计;其次,在子区域状态估计中引入权函数动态修正目标极值函数的权重矩阵,增强状态估计的抗差性能;然后,在边界节点和易受到虚假数据注入攻击的节点配置同步相量测量单元,提高辨识虚假数据攻击的能力;最后,利用IEEE 118节点配电网系统进行算例仿真验证。试验结果表明,本文所提出的状态估计方法不仅可以有效减小估计误差,还能准确辨识虚假数据注入攻击,提高了状态估计的精度和虚假数据注入攻击的辨识能力。     

基于等值信息交换的分布式抗差估计算法

提出了一种基于等值信息交换的分布式抗差状态估计算法。各子系统通过等值计算将自身量测信息浓缩成等值信息,协调层收集各子系统的等值信息计算出边界状态量进而实现分布式状态估计。此外,在分布式算法基础上实现了分布式抗差估计。采用等价权原理将指数型目标函数抗差估计方法转换成变权重的加权最小二乘估计,并基于不动点迭代的方法进行求解。在求解过程中,等值信息随着权重值的变化而不断更新,子系统得以综合全系统信息进行抗差估计。最后,构造了多子系统算例和含不良数据的算例对算法进行测试。测试结果表明分布式抗差估计算法具有很高的计算精度和很好的抗差性能。     

Optimal and self‐tuning fusion Kalman filters for discrete‐time stochastic singular systems

Based on the optimal fusion estimation algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion Kalman filter weighted by scalars is presented for discrete‐time stochastic singular systems with multiple sensors and correlated noises. A cross‐covariance matrix of filtering errors between any two sensors is derived. When the noise statistical information is unknown, a distributed identification approach is presented based on correlation functions and the weighted average method. Further, a distributed self‐tuning fusion filter is given, which includes two stage fusions where the first‐stage fusion is used to identify the noise covariance and the second‐stage fusion is used to obtain the fusion state filter. A simulation verifies the effectiveness of the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

Self‐tuning fusion Kalman filter weighted by scalars and its convergence analysis for multi‐channel autoregressive moving average signals

For the multi‐sensor multi‐channel autoregressive (AR) moving average signals with white measurement noises and an AR‐colored measurement noise, a multi‐stage information fusion identification method is presented when model parameters and noise variances are partially unknown. The local estimators of model parameters and noise variances are obtained by the multidimensional recursive instrumental variable algorithm and correlation method, and the fused estimators are obtained by taking the average of the local estimators. They have the strong consistency. Substituting them into the optimal information fusion Kalman filter weighted by scalars, a self‐tuning fusion Kalman filter for multi‐channel AR moving average signals is presented. Applying the dynamic error system analysis method, it is proved that the proposed self‐tuning fusion Kalman filter converges to the optimal fusion Kalman filter in a realization, so that it has asymptotic optimality. A simulation example for a target tracking system with three sensors shows its effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.     

Distributed output estimation error observer-based adaptive fault-tolerant consensus tracking control of multi-agent systems

The purpose of this study is to discuss the fully distributed design of output estimation error observer and fault-tolerant consensus tracking control for a class of multi-agent systems with Lipschitz nonlinear dynamics and actuator faults. Firstly, based on the relative output measurements of neighboring agents, the distributed output estimation error observer is developed to adaptively estimate the state and fault information of each agent, and further overcome the difficulties of online updating the adaptive estimations of unknown hyper-parameters. Secondly, to achieve the state consensus tracking goal and compensate for the negative effects of actuator faults, the distributed fault-tolerant consensus tracking control scheme is proposed on the basis of the state estimation and adaptive fault estimation information, and has excellent robustness and consensus tracking control performance. Moreover, sufficient criteria can ensure that consensus tracking error of each agent converges to a small set near the origin. Finally, numerical simulations are provided to show the effectiveness of the proposed fully distributed algorithm.     

A noise‐constrained algorithm for estimation over distributed networks

Much research has been devoted recently to the development of algorithms to utilize the distributed structure of an ad hoc wireless sensor network for the estimation of a certain parameter of interest. A successful solution is the algorithm called the diffusion least mean squares algorithm. The algorithm estimates the parameter of interest by employing cooperation between neighboring sensor nodes within the network. The present work derives a new algorithm by using the noise constraint that is based on and improves the diffusion least mean squares algorithm. In this work, first the derivation of the noise constraint‐based algorithm is given. Second, detailed convergence and steady‐state analyses are carried out, including analyses for the case where there is mismatch in the noise variance estimate. Finally, extensive simulations are carried out to test the robustness of the proposed algorithm under different scenarios, especially the mismatch scenario. Moreover, the simulation results are found to corroborate the theoretical results very well. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.     

基于状态估计残差比较的配电网故障区段定位方法

针对单端量测的阻抗法在多分支辐射状网络中会出现伪故障点的问题,利用网络中分布的智能量测设备提供的监测信息,提出了基于状态估计残差比较的配电网故障区段定位方法。该方法首先遍历所有节点通过添加故障支路建立不同节点故障网络下的状态方程;其次通过求解状态估计方程获得含网络所有节点的总残差检测值序列;然后搜寻最大残差检测值所在节点判断故障节点位置;最后根据节点相邻区间首末端阻抗角相位变化差异判定故障区间。大量仿真表明,该方法在不同故障类型、过渡电阻等工况下均具有良好的故障定位效果。该方法考虑了量测产生的随机变量成分,利用测量数据的互补性和多源性,在一定程度上提高了不同量测数据误差的抗干扰能力,极大地缩小了配电网在有限量测条件下的故障查找范围。     

Robust centralized and weighted measurement fusion white noise deconvolution estimators for multisensor systems with mixed uncertainties

Estimating the input signal of a system is called deconvolution or input estimation. The white noise deconvolution has important applications in oil seismic exploration, communications, and signal processing. This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) white noise deconvolution estimators for a class of uncertain multisensor systems with mixed uncertainties, including uncertain‐variance multiplicative noises in measurement matrix, missing measurements, and uncertain‐variance linearly correlated measurement and process white noises. By introducing the fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time‐varying white noise deconvolution estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the CF algorithm, the WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust fused steady‐state white noise deconvolution estimators are also presented. A simulation example with respect to the multisensor IS‐136 communication systems shows the effectiveness and correctness of the proposed results.     

基于虚拟同步机的微电网分布式一致性经济控制策略

为降低传统微电网集中式控制对于中心控制器的过度依赖,提高系统的可靠性和经济性,本文建立计及储能电池剩余电能状态(state of charge, SOC)的系统发电成本模型,提出基于虚拟同步机的分布式一致性微电网经济控制策略。以虚拟同步机技术作为底层逆变器控制方法,上层建立基于稀疏通信链路的分布式节点信息交互模型。利用分布式一致性算法得到供二次控制使用的状态信息,基于二次控制生成虚拟同步机优化参数,进而实现各节点边际成本相同,降低微电网系统整体发电成本。此外能够平衡各储能剩余容量,并减少系统平均频率和平均电压的偏差。最后通过基于Matlab/Simulink平台的微电网仿真模型,分析并验证了理论研究及控制策略有效性。     

基于Forney式因子图的主动配电网状态估计

实时准确的运行数据是实现主动配电网在线运行分析与智能化控制管理的基础。为了解决配电网实时量测不足带来的估计结果不理想的问题,依据通信领域的置信传播(BP)算法,提出一种基于Forney式因子图的主动配电网状态估计方法。考虑到具体用户量测的稀缺性及分布式电源运行时受气候影响的随机性,该方法首先通过历史负荷曲线获得先验分布,为配电网建立了统计学的计及光照辐射度及风速的Forney式因子图模型,然后利用BP算法全局推理变量节点及因子节点双向传递的本地置信度和状态信息,来获得各状态变量的边缘分布。通过对某地区11节点配电网系统和IEEE 33节点配电网系统进行仿真,表明了所述方法具有良好的实时性且在配电网实时量测不足的情况下也有较理想的估计结果。     

Decentralized unscented Kalman filter based on a consensus algorithm for multi-area dynamic state estimation in power systems

A decentralized unscented Kalman filter (UKF) method based on a consensus algorithm for multi-area power system dynamic state estimation is presented in this paper. The overall system is split into a certain number of non-overlapping areas. Firstly, each area executes its own dynamic state estimation based on local measurements by using the UKF. Next, the consensus algorithm is required to perform only local communications between neighboring areas to diffuse local state information. Finally, according to the global state information obtained by the consensus algorithm, the UKF is run again for each area. Its performance is compared with the distributed UKF without consensus algorithm on the IEEE 14-bus and 118-bus systems. The low communication requirements and high estimation accuracy of the decentralized UKF make it an alternative solution to the multi-area power system dynamic state estimation.     

基于一致性理论的多区域电力系统分布式状态估计

随着电网规模不断扩大,传统集中式状态估计方法的数据通信与存储任务重、计算量大,难以满足现代电力系统状态估计需求。在计及系统状态估计非线性的基础上,将电力系统划分为若干个不重叠的子区域,并利用拉格朗日乘子法对状态估计方程进行解耦,建立电力系统多区域非线性状态估计模型。基于一致性理论建立全分布式状态估计方法对模型进行求解,该方法无需状态估计控制中心,只需各子区域交换一致性变量和边界节点的状态变量信息,各子区域便可平行独立地计算本地状态变量估计值,较集中式状态估计均衡了通信及计算负担。IEEE 14节点系统仿真结果验证了所提分布式状态估计方法的有效性。     

Joint state estimation for nonlinear state-space model with unknown time-variant noise statistics

This paper considers the joint estimation problem of state and unknown measurement noise covariance for nonlinear state-space models. Using the variational Bayesian inference, the joint posterior distribution of state and measurement noise covariance is approximated by two independent proposal distributions, which is considered as a key idea of the proposed approach. Due to the nonlinearities caused by the system itself, the probability density function (PDF) of state involved in estimation is computationally intractable. Therefore, a set of weighted particles is generated to overlap the empirical density of state, while the PDF of measurement noise covariance is still derived analytically by using the conjugate properties of the Inverse-Gamma distribution. Two simulation examples are presented to demonstrate the effectiveness of the proposed method, which can provide more satisfied estimation performance for nonlinear systems than the commonly used particle filter when measurement noise covariance is unavailable.     

采用RSSI模型的无线传感器网络协作定位算法

由于无线传感器网络定位成本较高,精度不能满足要求以及通信和计算开销过大等问题,提出一种针对定位各阶段实施误差抑制措施的接收信号强度指示(RSSI)测距的协作定位算法。测距阶段通过周期性测量获得模型动态参数,采用相对误差系数对RSSI测距进行校正,定位阶段则基于泰勒级数扩展线性最小二乘方法实现位置估计,采取残差加权法优化位置坐标,减小非视距(NLOS)的不利影响。引入协作定位,将符合要求的节点升级为参考节点参与定位计算,进一步提高定位覆盖率和精度。实验结果表明,所提算法精度接近基于真实坐标的泰勒级数扩展LS算法,相同条件下的精度远高于传统估计算法。节点最大定位误差为0.15,最小定位误差为0.08,网络节点平均定位误差为0.109,能够满足大规模无线传感器网络(WSN)的定位需求。     

区域配电网实时状态估计器及其性能分析

设计了一种基于贝叶斯理论的区域配电网状态估计器,以解决随机性分布式电源接入区域配电网和测量装置数量有限给配电网状态估计带来的困难。首先依据前推回代潮流计算方法建立了配电网电压估计模型,应用贝叶斯理论设计了状态估计器,理论分析了改变监测装置位置和利用不同监测装置信息估计节点电压的影响。通过在IEEE 33节点配电系统仿真验证了文中所提出方法的正确性和有效性。进一步仿真分析了节点注入功率波动方差和测量装置位置对估计精度的影响,给出了监测装置的位置优化结果。文中为高渗透率分布式电源接入的区域配电网状态估计提供了理论和实用方法。