Weighted fusion robust steady-state estimators for multisensor networked systems with one-step random delay and inconsecutive packet dropouts

In this paper, the weighted fusion robust steady-state Kalman filtering problem is studied for a class of multisensor networked systems with mixed uncertainties. The uncertainties include same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one-step random delay and inconsecutive packet dropouts, which modeled by sequences of Bernoulli variables with different probabilities. By defining a new observation vector and applying the augmented method, the system under study is converted into one with only uncertain noise variances. The sufficient conditions for the existence of steady-state estimators are given. According to the minimax robust estimation principle, based on the worst-case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady-state Kalman estimators (predictor, filter, and smoother) are proposed. Applying the optimal fusion algorithm weighted by matrices and the covariance intersection fusion algorithm, the two kinds of robust fusion steady-state Kalman estimators are derived in a unified framework. The robustness of the proposed fusion estimators is proved by applying the permutation matrices and the global Lyapunov equations method, such that, for all admissible uncertainties, the actual steady-state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fusion steady-state Kalman estimators are proved. An example with application to autoregressive moving average signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.     

Robust time‐varying Kalman estimators for systems with packet dropouts and uncertain‐variance multiplicative and linearly correlated additive white noises

This paper is concerned with robust estimation problem for a class of time‐varying networked systems with uncertain‐variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with conservative upper bounds of uncertain noise variance, the robust time‐varying Kalman estimators (filter, predictor, and smoother) are presented. A unified approach of designing the robust Kalman estimators is presented based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust steady‐state Kalman estimators are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman estimators is proved. Finally, a simulation example applied to uninterruptible power system shows the correctness and effectiveness of the proposed results.     

Hierarchical fusion robust Kalman filter for clustering sensor network time‐varying systems with uncertain noise variances

For the clustering time‐varying sensor network systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst‐case conservative system with conservative upper bounds of noise variances, applying the optimal Kalman filtering, the two‐level hierarchical fusion time‐varying robust Kalman filter is presented, where the first‐level fusers consist of the local decentralized robust fusers for the clusters, and the second‐level fuser is a global decentralized robust fuser for the cluster heads. It can reduce the communication load and save energy resources of sensors. Its robustness is proved by the proposed Lyapunov equation method. The concept of robust accuracy is presented, and the robust accuracy relations of the local, decentralized, and centralized fused robust Kalman filters are proved. Specially, the corresponding steady‐state robust local and fused Kalman filters are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman filters is proved by the dynamic error system analysis method. A simulation example shows correctness and effectiveness. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Robust CAWOF Kalman predictors for uncertain multi-sensor generalized system

Robust centralized and weighted observation fusion (CAWOF) prediction algorithm is addressed in this article for an uncertain multi-sensor generalized system with linear correlation between observation noises and an input white noise. This uncertainty in the generalized system primarily means that the variances of the aforementioned types of noise, as well as the multiplicative noise variances, are uncertain. Through singular value decomposition and virtual noise compensation, the original generalized system is changed to non-generalized reduced-order subsystems in which only noise variances are uncertain. Utilizing the minimax robustness estimation criterion, robust CAWOF Kalman predictors are put forward on account of the first subsystem with conservative upper bounds of noise variances. Eventually, robust observation fusion Kalman predictors of the original generalized system are proposed. The Lyapunov equation method is applied to verify two fusion predictors' robustness. With regard to all permissible uncertain practical noise variances, CAWOF predictors are robust, namely, the practical prediction error variances of two robust predictors will have minimum upper bounds. This equivalence between CAWOF Kalman predictors is proved by an information filter. In this article, the precision relationship of fusion predictors is given. Meanwhile, robust Kalman predictors for steady-state case are proposed, and the astringency of robust time-variant Kalman predictors is analyzed through the analysis of dynamic error system. The validity and correctness of proposed algorithm are proved by the simulation example of random dynamic input and output system in an economic system.     

Distributed fusion white noise deconvolution estimators

The white noise deconvolution or input white noise estimation problem has important applications in oil seismic exploration, communication and signal processing. By combining the Kalman filtering method with the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, new distributed fusion white noise deconvolution estimators are presented by weighting local input white noise estimators for general multisensor systems with different local dynamic models and correlated noises. The new estimators can handle input white noise fused filtering, prediction and smoothing problems, and are applicable to systems with colored measurement noise. Their accuracy is higher than that of local white noise deconvolution estimators. To compute the optimal weights, the new formula for local estimation error cross-covariances is given. A Monte Carlo simulation for the system with Bernoulli-Gaussian input white noise shows their effectiveness and performance.     

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.     

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.     

观测模型误差不确定的锂电池SOC估计方法

建立的锂电池非线性系统中存在不确定的观测模型误差时,会影响滤波器估计的精度和稳定性,严重时还会导致估计结果发散。针对这一问题,基于变分贝叶斯自适应滤波方法,提出了一种鲁棒UKF算法。该算法构建虚拟观测噪声用来补偿观测模型误差,并采用逆Wishart分布对虚拟观测噪声协方差建模。在变分迭代过程中,实现对系统状态和虚拟观测噪声协方差的联合后验概率估计,使估计结果自适应地逼近到真实分布。利用无迹卡尔曼滤波对系统状态进行更新。结合锰酸钾锂电池非线性模型进行仿真实验表明,该算法估计锂电池荷电状态具有很好的精度、跟踪速度以及鲁棒性。     

Convergence analysis of self-tuning Riccati equation for systems with correlation noises

For linear discrete time-invariant stochastic system with correlated noises, and with unknown state transition matrix and unknown noise statistics, substituting the online consistent estimators of the state transition matrix and noise statistics into steady-state optimal Riccati equation, a new self-tuning Riccati equation is presented. A dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of self-tuning Riccati equation into the stability problem of a time-varying Lyapunov equation. Two decision criterions of the stability for the Lyapunov equation are presented. Using the DVESA method and Kalman filtering stability theory, it proves that with probability 1, the solution of self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation or time-varying optimal Riccati equation. The proposed method can be applied to design a new selftuning information fusion Kalman filter and will provide the theoretical basis for solving the convergence problem of self-tuning filters. A numerical simulation example shows the effectiveness of the proposed method.     

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.     

基于WAMS／SCADA混合量测的电力系统强跟踪滤波动态状态估计

针对当前电力系统动态状态估计主要采用的扩展卡尔曼滤波(EKF)法存在鲁棒性差、建模具有不确定性等缺点,提出一种强跟踪滤波动态状态估计算法.该算法在扩展卡尔曼滤波器中引入时变次优渐消因子,在线调整状态预报误差协方差矩阵和相应的增益矩阵,使状态估计残差方差最小.同时,引入广域测量系统(WAMS)/-数据采集与监视控制(SCADA)系统的混合量测数据,增加了系统的冗余量测,进一步提高了动态状态估计的性能.仿真结果表明,所提方法在正常情况以及负荷突变、存在坏数据、网络拓扑错误各种情况下具有较好的预测和滤波效果.     

一类带有等式约束的不确定系统的滤波方法

研究了一类离散不确定系统中存在等式约束时的最优滤波问题,在均方误差最小的意义下利用卡尔曼滤波给出了最优解。与传统的不确定滤波结果相比,从理论证明了利用更多信息的约束滤波的估计误差协方差的迹更小。计算机仿真验证了理论结果。     

基于WLS-KF的UWB室内定位滤波算法研究

针对室内超宽带(UWB)定位过程中受到非视距误差(NLOS)干扰而导致定位精度下降的问题,提出了基于抗差估计原理的自适应卡尔曼滤波方法,结合加权最小二乘法对测距信息解算得到定位坐标。在通视环境下进行测距,利用测得的数据计算新息向量和协方差,并基于此构建阈值信息,对NLOS环境产生的量测异常值进行判别,在此基础上利用Sage-Husa滤波对系统噪声协方差进行估计。采用加权最小二乘法对测距信息进行处理,得到标签解算坐标的最优估计。通过MATLAB仿真验证算法的可行性和有效性并在室内环境下进行测距、定位试验验证。仿真和实验结果表明,基于抗差估计原理的自适应卡尔曼滤波方法,结合加权最小二乘法能有效识别NLOS误差,且对定位过程中发生的状态突变能有效进行跟踪,解算得到的标签坐标x方向误差1 cm左右,y方向误差2 cm左右,提高了UWB室内定位的精度。     

Computer vision algorithms for intersection monitoring

The goal of this project is to monitor activities at traffic intersections for detecting/predicting situations that may lead to accidents. Some of the key elements for robust intersection monitoring are camera calibration, motion tracking, incident detection, etc. In this paper, we consider the motion-tracking problem. A multilevel tracking approach using Kalman filter is presented for tracking vehicles and pedestrians at intersections. The approach combines low-level image-based blob tracking with high-level Kalman filtering for position and shape estimation. An intermediate occlusion-reasoning module serves the purpose of detecting occlusions and filtering relevant measurements. Motion segmentation is performed by using a mixture of Gaussian models which helps us achieve fairly reliable tracking in a variety of complex outdoor scenes. A visualization module is also presented. This module is very useful for visualizing the results of the tracker and serves as a platform for the incident detection module.     

考虑参数不确定性影响的发电机动态状态估计方法

噪声统计特性和模型参数的不确定性,会严重影响动态状态估计的精度。针对该问题,文中提出了一种基于H∞容积卡尔曼滤波(HCKF)的动态状态估计新方法。首先,建立发电机动态状态估计模型;其次,依据H∞滤波理论构造模型不确定性约束准则,并在容积卡尔曼滤波(CKF)中依据该准则计算更新估计误差协方差阵,抑制参数不确定性对状态估计精度的影响;最后,通过对IEEE 10机39节点系统和某实际大区域电网系统的算例测试,将所提方法与CKF方法和改进插值扩展卡尔曼滤波(IEKF)方法的估计性能进行对比。算例仿真结果表明,HCKF方法在估计精度和对模型不确定性的鲁棒性方面较CKF和IEKF方法均有所提高,能够有效抑制模型不确定性对发电机动态状态估计的影响。     

Combined estimation of the parameters and states for a multivariable state-space system in presence of colored noise

This article addresses the combined estimation issues of parameters and states for multivariable systems in the state-space form disturbed by colored noises. By utilizing the Kalman filtering principle and the coupling identification concept, we derive a Kalman filtering based partially coupled recursive generalized extended least squares (KF-PC-RGELS) algorithm to jointly estimate the parameters and the states. Using the past and the current data in parameter estimation, we propose a Kalman filtering based multi-innovation partially coupled recursive generalized extended least-squares algorithm to enhance the parameter estimation accuracy of the KF-PC-RGELS algorithm. Finally, a simulation example is provided to test and compare the performance of the proposed algorithms.     

Distributed Kalman filter for linear system with complex multi-channel stochastic uncertain parameter and decoupled local filters

This article considers a distributed Kalman filtering problem for linear system contaminated by complex multi-channel random uncertain parameter in which a number of nodes cooperative without central coordination to estimate a common state based on local measurements and data received from neighbors. We propose an approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. Then, we extend this method to smoothing and deconvolution algorithm. Finally, simulation experiments demonstrate the validity of the proposed approach.     

基于自适应容积卡尔曼滤波算法的电力系统动态谐波状态估计

由于传统的谐波状态估计的参数辨识算法要求噪声的协方差矩阵固定不变,而实际工程中噪声的协方差矩阵是随时间变化的,工程中存在错误的量测数据,导致传统参数辨识算法估计的谐波电流参数的准确度较低。因此,提出自适应容积卡尔曼滤波算法来提高辨识谐波电流参数的准确度。首先,针对时变噪声干扰,采用基于渐消记忆指数加权法的噪声估值器算法生成时变噪声的协方差矩阵;其次,针对错误的量测数据,采用开窗估计算法修正错误的量测数据;然后,将修正的噪声协方差矩阵和量测数据代入容积卡尔曼滤波算法中,对谐波电流参数进行估计;最后,搭建IEEE 13节点系统仿真模型,验证了自适应容积卡尔曼滤波算法在时变噪声干扰及量测数据错误情况下仍可准确地估计谐波电流参数,确保了动态谐波状态估计的准确性。     

Distributed Student's t filtering algorithm for heavy‐tailed noises

In this paper, a distributed Student's t filtering algorithm to deal with heavy‐tailed noises is developed. In the traditional Kalman filter, the distribution of the signal is assumed. However, in reality, outliers in the signal are often encountered for which the assumption of Gaussian distribution is no longer valid. The Student's t distribution can describe noises in the presence of outliers. As a result, the weight on each data point within the filter adapts to the data quality so that the filter becomes insensitive to the outliers. We first derive the distributed filtering algorithm from the centralized Student's t filter, which is able to handle heavy‐tailed noises such as outliers and then analyze properties of the proposed method. It is shown that the proposed algorithm provides the same accuracy as the centralized Student's t filtering with no performance loss. Furthermore, the distributed Student's t filtering with feedback is developed, which is in accordance with centralized filtering, and the local error covariance is reduced as expected. Two numerical examples support the theoretical results and illustrate the validity of the proposed method.