Multi-sensor distributed fusion filtering for networked systems with different delay and loss rates

This paper mainly focuses on the multi-sensor distributed fusion estimation problem for networked systems with time delays and packet losses. Measurements of individual sensors are transmitted to local processors over different communication channels with different random delay and packet loss rates. Several groups of Bernoulli distributed random variables are employed to depict the phenomena of different time delays and packet losses. Based on received measurements of individual sensors, local processors produce local estimates that have been developed in a new recent literature. Then local estimates are transmitted to the fusion center over a perfect connection, where a distributed fusion filter is obtained by using the well-known matrix-weighted fusion estimation algorithm in the linear minimum variance sense. The filtering error cross-covariance matrices between any two local filters are derived. The steady-state property of the proposed distributed fusion filter is analyzed. A simulation example verifies the effectiveness of the algorithm.     

带相关噪声异步采样系统的分布式最优线性递推融合估计

对带相关噪声的异步均匀采样线性离散系统, 研究了分布式最优线性递推融合预报和滤波问题. 通过引入 满足伯努利分布的随机变量将系统同步化, 给出了局部Kalman预报器和滤波器. 分别推导了局部估值间的互协方 差阵、分布式最优线性融合估值与局部估值间的互协方差阵. 提出了分布式最优线性递推融合预报器和滤波器. 与 局部估值按矩阵加权的分布式融合估计算法相比, 所提出的算法具有更高的估计精度, 但与集中式融合相比有精度 损失. 为了进一步提高估计精度, 又提出了带反馈的分布式最优线性递推融合预报器和滤波器, 证明了带反馈的融 合估计与集中式融合估计具有相同的精度. 仿真例子验证了所提算法的有效性.     

Centralized filtering and smoothing algorithms from outputs with random parameter matrices transmitted through uncertain communication channels

The least-squares linear centralized estimation problem is addressed for discrete-time signals from measured outputs whose disturbances are modeled by random parameter matrices and correlated noises. These measurements, coming from different sensors, are sent to a processing center to obtain the estimators and, due to random transmission failures, some of the data packet processed for the estimation may either contain only noise (uncertain observations), be delayed (sensor delays) or even be definitely lost (packet dropouts). Different sequences of Bernoulli random variables with known probabilities are employed to describe the multiple random transmission uncertainties of the different sensors. Using the last observation that successfully arrived when a packet is lost, the optimal linear centralized fusion estimators, including filter, multi-step predictors and fixed-point smoothers, are obtained via an innovation approach; this approach is a general and useful tool to find easily implementable recursive algorithms for the optimal linear estimators under the least-squares optimality criterion. The proposed algorithms are obtained without requiring the evolution model of the signal process, but using only the first and second-order moments of the processes involved in the measurement model.     

State estimation for stochastic time‐varying multisensor systems with multiplicative noises: Centralized and decentralized data fusion

In this paper, the state estimation problems, including filtering and one‐step prediction, are solved for uncertain stochastic time‐varying multisensor systems by using centralized and decentralized data fusion methods. Uncertainties are considered in all parts of the state space model as multiplicative noises. For the first time, both centralized and decentralized estimators are designed based on the regularized least‐squares method. To design the proposed centralized fusion estimator, observation equations are first rewritten as a stacked observation. Then, an optimal estimator is obtained from a regularized least‐squares problem. In addition, for decentralized data fusion, first, optimal local estimators are designed, and then fusion rule is achieved by solving a least‐squares problem. Two recursive equations are also obtained to compute the unknown covariance matrices of the filtering and prediction errors. Finally, a three‐sensor target‐tracking system is employed to demonstrate the effectiveness and performance of the proposed estimation approaches.     

New distributed fusion filtering algorithm based on covariances over sensor networks with random packet dropouts

This paper studies the distributed fusion estimation problem from multisensor measured outputs perturbed by correlated noises and uncertainties modelled by random parameter matrices. Each sensor transmits its outputs to a local processor over a packet-erasure channel and, consequently, random losses may occur during transmission. Different white sequences of Bernoulli variables are introduced to model the transmission losses. For the estimation, each lost output is replaced by its estimator based on the information received previously, and only the covariances of the processes involved are used, without requiring the signal evolution model. First, a recursive algorithm for the local least-squares filters is derived by using an innovation approach. Then, the cross-correlation matrices between any two local filters is obtained. Finally, the distributed fusion filter weighted by matrices is obtained from the local filters by applying the least-squares criterion. The performance of the estimators and the influence of both sensor uncertainties and transmission losses on the estimation accuracy are analysed in a numerical example.     

受有线无线异构网络诱导延时和数据丢包约束的分布式网络化H2/H∞滤波研究

针对分布式有线无线异构网络化滤波系统中部署在不同地理空间的多传感器通过无线网络与每个局部融合中心通信, 然后测量数据被传到网关并进行协议转换后通过有线网络传输到对应的分布式滤波器, 会导致数据传输出现分布式有线无线网络诱导延时和数据丢包, 使得H₂/H_∞滤波更加困难的问题, 本文首先采用有向图描述分布式传感器节点的通信拓扑, 然后运用Markov链和伯努利分布分别刻画分布式有线无线网络诱导延时和数据丢包特性, 进而建立了融合分布式滤波器参数、有线无线异构网络通信约束的普适滤波误差动态系统综合模型.理论上证明了在分布式有线无线异构网络通信约束下所设计的滤波器使得滤波误差动态系统随机稳定且满足给定的H₂/H_∞性能指标, 并建立了系统随机稳定性、分布式滤波器参数及最长有线无线网络诱导延时和数据丢包之间的关系.最后, 仿真实例验证了本文所提方法是可行且有效.     

Optimal Kalman filtering fusion with cross-correlated sensor noises

When there is no feedback from the fusion center to local sensors, we present a distributed Kalman filtering fusion formula for linear dynamic systems with sensor noises cross-correlated, and prove that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements, therefore, it achieves the best performance. Then, for the same dynamic system, when there is feedback, a modified Kalman filtering fusion with feedback for distributed recursive state estimators is proposed, and prove that the fusion formula with feedback is, as the fusion without feedback, still exactly equivalent to the corresponding centralized Kalman filtering fusion formula; the various P matrices in the feedback Kalman filtering at both local filters and the fusion center are still the covariance matrices of tracking errors; the feedback does reduce the covariance of each local tracking error.     

带未知模型参数和衰减观测率系统自校正分布式融合估计

研究了带未知模型参数和衰减观测率多传感器线性离散随机系统的信息融合估计问题.在模型参数和衰减观测率未知的情形下, 应用递推增广最小二乘(Recursive extend least squares, RELS)算法和加权融合估计算法提出了分布式融合未知模型参数辨识器; 应用相关函数对描述衰减观测现象的随机变量的数学期望和方差进行在线辨识.将辨识后的模型参数、数学期望和方差代入到最优分布式融合状态滤波器中, 获得了相应的自校正融合状态滤波算法.应用动态误差系统分析(Dynamic error system analysis, DESA)方法证明了算法的收敛性.仿真例子验证了算法的有效性.     

带多丢包和滞后随机不确定系统的最优线性估计

研究了带多丢包和滞后网络化随机不确定系统的最优线性估计问题. 通过白色乘性噪声来描述系统参数的随机不确定性. 通过一组满足Bernoulli分布的随机变量来描述数据传输过程中发生的丢包和滞后现象. 应用新息分析方法, 设计了线性最小方差意义下的最优线性估值器, 包括滤波器, 预报器和平滑器. 给出了稳态估值器存在的一个充分条件. 仿真例子验证了其有效性.     

Observer-based H∞ fuzzy control for discrete-time Takagi–Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises

This paper investigates the observer-based H_∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then a linear matrix inequality approach for designing such an observer-based H_∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

具有一步随机滞后和多丢包的网络系统的最优线性估计

研究了具有随机时滞和丢包的网络系统的最优线性估计问题.本文通过两个满足 Bernoulli分布的随机变量来描述网络数据传输中可能存在的一步随机滞后和多丢包现象. 并基于新息分析方法,提出了线性最小方差下的最优线性状态滤波器、预报器和平滑器. 它们通过解一个Riccati方程和一个Lyapunov方程得到.最后,给出了稳态估值器存在的一个充分条件. 并通过仿真例子验证其有效性.     

一种不完全信息下递推辨识方法及收敛性分析

针对信号在网络环境下传输带来不完全信息使得在线参数辨识算法和收敛性困难的问题, 不同于传统递推最小二乘方法, 本文提出了一种不完全信息下递推辨识方法并分析其收敛性. 首先运用伯努利分布刻画引起不完全信息的数据丢包特性, 然后基于辅助模型方法补偿不完全信息并构造了新的数据信息矩阵, 并运用矩阵正交变换性质对数据信息矩阵进行QR分解, 推导了融合网络参数的递推辨识新算法, 理论证明了在不完全信息下递推参数辨识算法的收敛性. 最后仿真结果验证了所提方法的可行性和有效性.     

丢包和量化约束下的不确定系统分布式滚动时域估计

研究了数据丢包和量化约束下的随机不确定系统分布式状态估计问题.将丢包现象描述为随机Bernoulli序列,采用预测补偿机制对数据丢包进行补偿,将量化引入的误差转化为观测方程中的不确定参数,将系统的模型不确定性描述为系数矩阵受到随机扰动;利用固定时域内的所有观测值构造代价函数,将状态估计问题建模为带不确定参数的鲁棒最小二...     

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.     

Markov-chain-based output feedback control for stabilization of networked control systems with random time delays and packet losses

This paper proposes an output feedback method to stabilize and control networked control systems (NCSs). Random time delays and packet losses are treated separately when an NCS is modeled. The random time delays in the controller-to-actuator and sensor-to-controller links are modeled with two time-homogeneous Markov chains, while the packet losses are treated by the Dirac delta functions. An asymptotic mean-square stability criterion is established to compensate for the network-induced random time delays and packet losses in both the controller-to-actuator and sensor-to-controller links simultaneously. An algorithm to implement the asymptotic mean-square stability criterion is also proposed. Further, a DC-motor speed-control test bed with Ethernet using User Datagram Protocol (UDP) is constructed and employed for experimental verification. Two sets of experiments, with and without 10% packet losses in the links, are conducted on this NCS. Experimental results illustrate the effectiveness of the proposed output feedback method compared to conventional controllers. This method could compensate for the effects of the random time delays and packet losses and guarantee the system performance and stability. The integral time and absolute error (ITAE) of the experiments without packet losses is reduced by 13% with the proposed method, and the ITAE of experiments with 10% packet losses, by 30%. The NCS can track the reference command faithfully with the proposed method when random time delays and packet losses exist in the links, whereas the NCS fails to track the reference command with the conventional control algorithms.     

具有一步随机时滞和多丢包的网络系统H∞滤波器设计

在网络系统中由于连接传感器和滤波器的网络带宽有限,系统测量数据在传输中会出现随机时延甚至丢失. 本文讨论了具有一步随机时延和丢包的网络系统的H∞滤波器设计问题.基于新近提出的同时描述随机时延和丢包的模型,利用线性矩阵不等式方法设计线性滤波器,使得滤波误差系统均方指数稳定,并具有给定的H∞性能. 滤波器参数通过求解一个线性矩阵不等式得到.仿真研究说明了所提出算法的有效性.     

Modeling and estimation for networked systems with multiple random transmission delays and packet losses

In networked systems, data packets are transmitted through networks from a sensor to a data processing center. Due to the unreliability of communication channels, a packet may be delayed even lost during the transmission. At each moment, the data processing center may receive one or multiple data packets or nothing at all. A novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of Bernoulli distributed random variables. It is transformed to a measurement model with multiple random delayed states and noises. Based on the model, an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate. It does not have a steady-state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment. So it needs to be computed online. To reduce the online computational cost, a suboptimal linear filter dependent on the probabilities of random variables is also proposed. However, it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities. It can be computed offline since it has the steady-state performance. A sufficient condition of existence for the steady-state performance is given. A simulation example shows the effectiveness.     

广义系统信息融合稳态与自校正满阶Kalman滤波器

基于线性最小方差标量加权融合算法和射影理论,对带多个传感器和带相关噪声的广义系统,提出了分布式标量加权融合稳态满阶Kalman滤波器.推得了任两个传感器子系统之间的稳态满阶滤波误差互协方差阵,其解可任选初值离线迭代计算.所提出的稳态融合滤波器避免了每时刻计算协方差阵和融合权重,减小了在线计算负担.当系统含有未知模型参数时,基于递推增广最小二乘算法和标量加权融合算法,提出了一种两段融合自校正状态滤波器.其中第1段融合获得未知参数的融合估计;第2段融合获得分布式自校正融合状态滤波器.与局部估计和加权平均融合估计相比,所提出的标量加权融合参数估计和自校正状态估计都具有更高的精度.仿真研究验证了其有效性.     

Optimal linear estimators for systems with multiple random measurement delays and packet dropouts

This article is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with possible multiple random measurement delays and packet dropouts, where the largest random delay is limited within a known bound and packet dropouts can be infinite. A new model is constructed to describe the phenomena of multiple random delays and packet dropouts by employing some random variables of Bernoulli distribution. By state augmentation, the system with random delays and packet dropouts is transferred to a system with random parameters. Based on the new model, the least mean square optimal linear estimators including filter, predictor and smoother are easily obtained via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state estimators is given. An example shows the effectiveness of the proposed algorithms.     

带有丢包的线性参数变化系统的H∞控制

主要研究了一类带有Lipschitz非线性和随机通信丢包的线性参数变化系统（LPV）基于观测器的[H∞]控制问题。针对信号传递中的随机丢包,使用了已知条件概率分布的Bernoulli分布序列来描述。在随机丢包存在的情况下,利用李雅普诺夫稳定性定理得到了基于观测器的反馈控制器存在的充分条件,使得闭环网络LPV系统不仅是均方指数稳定的,而且满足预定的[H∞]扰动抑制性能指标;然后利用近似基函数和网格技术将无限维的线性矩阵不等式组的求解问题近似为有限维线性矩阵不等式组的求解问题,提出了一种线性矩阵不等式的方法,设计出了相应的[H∞]控制器。最后,通过数值仿真验证了所提方法的有效性。