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.     

Robust integrated covariance intersection fusion Kalman estimators for networked systems with random measurement delays,multiplicative noises,and uncertain noise variances

In this article, the robust distributed fusion Kalman filtering problems are addressed for the networked mixed uncertain multisensor systems with random one-step measurement delays, multiplicative noises, and uncertain noise variances. A new augmented state approach with fictitious measurement noises modeled by the first-order moving average models is presented, by which the original system is transformed into a standard uncertain system only with uncertain-variance fictitious white noises. Based on the minimax robust estimation principle and Kalman filtering theory, a universal integrated covariance intersection (ICI) fusion approach is presented in the sense that first of all the robust local estimators and their conservative error variances and crosscovariances are presented, and then integrating the local estimation information yields ICI fusers. An extended Lyapunov equation approach with two kinds of Lyapunov equations is presented in order to prove the robustness and to compute fictitious noise statistics. Applying these approaches, the minimax robust local, ICI, and fast ICI fused Kalman estimators (predictor, filter, and smoother) are presented, such that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, accuracy relations, and convergence are also proved. The proposed ICI fusers improve the robust accuracies and overcome the drawbacks of the original covariance intersection fusers, such that the robust local estimators and their conservative variances are assumed to be known, and their conservative crosscovariances are ignored. Two simulation examples applied to the offshore platform system verify their correctness, effectiveness, and applicability.     

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.     

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.     

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 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.     

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.     

Analysis of a low‐complexity change detection scheme

In many applications, for example in fault detection, it is important to discriminate between changes in system dynamics and abrupt changes in the disturbance level. A new low‐complexity change detection method based on the average behaviour of the estimated impulse response parameters of the normalized least mean‐square (NLMS) algorithm is presented. The solution includes second‐order Kalman filters based on exponential transient models for parameter convergence. Explicit formulas for time‐varying state covariances and Kalman gains are given. The receiver operating characteristics (ROC) is also computed and used for performance evaluation. The effects of the approximations in the averaging analysis that occur for high adaptation gains are handled with an experimental ROC analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Self‐tuning weighted fusion Kalman filter for ARMA signal with colored measurement noise and its convergence analysis

For the multisensor single‐channel autoregressive moving average (ARMA) signal with colored measurement noise, when the partial model parameters and the noise variance are unknown, a self‐tuning fusion Kalman filter weighted by scalar is presented based on the ARMA innovation model by the modern time series analysis method. With the application of the recursive instrumental variable algorithm and the Gevers–Wouters iterative algorithm with dead band, the information fusion estimators for the unknown model parameters and noise variance are obtained, and their consistence is proved by the existence and continuity theorem of implicit function. Then, substituting them into the optimal weighted fusion Kalman filter, one can obtain the corresponding self‐tuning weighted fusion Kalman filter. Further, with the application of the dynamic variance error system analysis method, the convergence of the self‐tuning Lyapunov equations for filtering error cross‐covariances is proved. With the application of the dynamic error system analysis method, it is rigorously proved that the self‐tuning weighted fusion Kalman filter converges to the optimal weighted fusion Kalman filter in a realization; that is, it has asymptotic optimality. A simulation example shows its effectiveness.Copyright © 2012 John Wiley & Sons, Ltd.     

Self-tuning decoupled fusion Kalman filter based on the Riccati equation

An online noise variance estimator for multisensor systems with unknown noise variances is proposed by using the correlationmethod. Based on the Riccati equation and optimal fusion rule weighted by scalars for state components, a self-tuning component decoupled information fusion Kalman filter is presented. It is proved that the filter converges to the optimal fusion Kalman filter in a realization by dynamic error system analysis method, so that it has asymptotic optimality. Its effectiveness is demonstrated by simulation for a tracking system with 3 sensors. __________ Translated from Control and Decision, 2008, 23(2): 195–199 [译自: 控制与决策]     

Accurate tracking of harmonic signals in VSC-HVDC systems using PSO based unscented transformation

This paper presents the estimation of harmonics in a voltage source converter based HVDC (VSC-HVDC) system for designing AC side filters. The extended Kalman filter (EKF) is well known for estimating amplitude, phase, frequency, and harmonic content of a signal corrupted with noise. However, the EKF algorithm suffers from instability due to linearization and costly calculation of Jacobian matrices, and its performance deteriorates when the signal model is highly nonlinear. This paper, therefore, proposes an unscented Kalman filter (UKF) to overcome these difficulties of linearization and derivative calculations for robust tracking of harmonics in VSC-HVDC system. The model and measurement error covariance matrices Q and R along with the UKF parameters are selected using a modified particle swarm optimization (PSO) algorithm. To circumvent the problem of premature convergence and local minima, a dynamically varying inertia weight based on the variance of the population fitness is used. This results in a better local and global searching ability of the particles, which improves the convergence of the velocity and better accuracy of the UKF parameters. Various simulation results for harmonic signals corrupted with noise obtained from VSC-HVDC system reveal significant improvement in noise rejection and speed of convergence and accuracy.     

基于改进WOA的鲁棒增广扩展Kalman滤波器设计

本文针对一类非线性系统,提出基于广义系统的鲁棒增广扩展Kalman滤波器,结合改进鲸群优化算法寻优系统噪声,以精确估计系统状态量以及并发执行器和传感器故障。首先,视故障为系统的状态变量,建立广义系统,将非线性系统的故障估计转化为非线性广义系统的状态估计。其次,提出鲁棒上界以降低线性化误差对估计精度的影响。然后,利用改进鲸群算法寻优系统噪声,以优化鲁棒增广扩展Kalman滤波器。最后,给出F-16飞机的纵向运动数值模型,使用本文方法与自适应无迹Kalman滤波器以及基于鲸群算法的鲁棒增广扩展Kalman滤波器进行对比仿真,仿真结果表明,相较于其他两种算法,本文方法的故障估计均方根误差降低了50%左右,验证了其优越性。     

基于强跟踪UKF的视频目标跟踪算法

针对无迹卡尔曼滤波（unscented Kalman filter ,UKF）在非线性系统状态估计中存在的跟踪缓慢和稳态偏差问题,提出一种基于强跟踪UKF的视频目标跟踪算法。该算法以无迹变换（unscented transform ,UT）为基础,结合强跟踪滤波器和UKF滤波器的优点,在状态预测协方差矩阵中引入时变渐消因子调节卡尔曼增益,强迫输出残差序列保持正交,并提取残差序列的有效信息,提高滤波器对状态变化的跟踪能力。仿真结果表明,利用强跟踪UKF算法对视频中的运动目标进行跟踪,具有更高的跟踪精度,状态滤波均方误差更小。     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

The Kalman filter in the context of adaptive filter theory

Model‐based adaptive algorithms are usually derived with the help of the Wiener‐Hopf equation based on empirical statistics. They are often interpreted as an extension to their model‐independent counterparts, i.e. the stochastic‐gradient based adaptive filters. As a consequence, it is generally not considered worthwhile to show the analogy between Kalman filters and adaptive filters. This article pursues just these two goals. First, it tries to remove the notion that the Kalman filter is a complicated and unnecessary detour from the subject of adaptive filtering. Second, the advantage of a deeper insight into adaptive algorithms from Kalman's viewpoint emerges from our treatment. Based on a time‐varying FIR filter model, the Kalman filter is completely derived and serves as a general framework for the special case of model‐based adaptive filters. Copyright © 2004 John Wiley & Sons, Ltd.     

A decentralized model following controllers for a class of large‐scale interconnected dynamical systems with uncertainties

The problem of decentralized robust tracking and model following is considered for a class of large‐scale interconnected systems with uncertainties. A class of linear decentralized state feedback controllers are proposed for robust tracking of dynamical signals in such a class of uncertain large‐scale systems. The proposed decentralized tracking controllers can guarantee that the tracking errors between each subsystem and local reference model are uniformly ultimately bounded. Moreover, we modify the linear controllers by introducing some nonlinear parts so that the tracking errors decrease asymptotically to zero in the presence of uncertain parameters and interconnection terms. Finally, an illustrative example is given to demonstrate the validity of our results. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 48–58, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10101     

Guaranteed cost control for large‐scale systems under control gain perturbations

The guaranteed cost control problem of the decentralized robust control for large‐scale systems with the norm‐bounded time‐varying parameter uncertainties and a given quadratic cost function is considered. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality (LMI). It is shown that decentralized local state feedback controllers can be obtained by solving the LMI. The problem of guaranteed cost control for large‐scale systems under the gain perturbations is also considered. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 146(4): 43–57, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10265     

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.     

基于无迹卡尔曼滤波的电力系统抗差动态估计

为解决电力系统动态状态估计准确性易受量测不良数据影响的问题,提出基于无迹卡尔曼滤波(Unscented Kalman Filter,UKF)的电力系统抗差动态估计方法。在预测过程中引入时变噪声估计器处理未知系统噪声;利用新息向量判断量测是否存在异常,并使用基于测点正常率最大的静态估计方法辨识不良数据;然后构建更新因子矩阵降低不良数据在动态估计更新过程中的影响。将算法运用于IEEE 14节点标准系统中,仿真结果表明该方法估计结果准确且抗差效果良好。