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.     

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.     

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.     

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.     

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.     

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.     

基于粒子群算法和卡尔曼滤波器的PID控制

针对PID控制系统中存在参数的整定和控制干扰信号和测量噪声信号问题,提出基于粒子群算法和卡尔曼滤波算法的PID控制方法。利用粒子算法优化PID参数,通过卡尔曼滤波器抑制控制干扰信号和测量噪声信号。仿真结果表明具有响应速度快、抗干扰能力强等特点,且达到了全局最优PID参数整定,有效地剔除系统的控制干扰和测量噪声信号,具有比传统PID控制方法更好的动态和静态控制性能,控制品质有较大的改善和提高。为PID控制系统的研究提供了一种新方法。     

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]     

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.     

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.     

An average queue‐length‐difference–based congestion detection algorithm in TCP/AQM network

Congestion detection in transmission control protocol/active queue management networks remains a challenging problem in which the choosing of congestion signal is one of the most important factors. Exponentially weighted moving average of queue length, the most widely used congestion signal, is facing difficulties in detecting incipient congestion and quantifying the optimal forgetting factor. Aiming at these 2 disadvantages, we propose an average queue‐length‐difference–based congestion detection algorithm where exponentially weighted moving average of queue‐length difference is chosen as the congestion signal with the theoretical optimal forgetting factor deduced. First, by defining the queue‐length difference as the state, the corresponding state equation is derived from the fluid model. Second, we prove that the inflow traffic in state equation is a discrete‐time martingale, which can be transformed to a Wiener process according to the martingale representation theorem. Noticing that the observation of state will be coupled with noise because of the unstable transmission, the state estimation is then derived with the application of recursive least squares filter. The filter gain of state estimation, which is a function of the noise‐signal ratio, corresponds to the optimal forgetting factor in average queue‐length‐difference–based congestion detection algorithm. Simulation results in NS‐3 and MATLAB illustrate the effectiveness of the proposed algorithm.     

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.     

Robust self‐tuning PI decoupling control of uncertain multivariable systems

In this paper, for a class of multivariable systems with strong couplings, a robust self‐tuning PI decoupling controller is developed by combining a self‐tuning PI controller with a feedforward decoupling compensator and a filter. To determine the gains and other parameters of the PI decoupling controller, we first introduced a reduced order model. The parameters of the reduced order model are identified by using a normalized projection algorithm with dead zone. The gains of the PI controller together with other parameters are tuned online according to the certainty equivalent principle. By resorting to time‐varying operation, we presented the bounded‐input bounded‐output stability conditions and convergence conditions of the closed‐loop system. Simulation results on a synthetic system and a twin‐tank level system show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

基于卡尔曼滤波的汽包水位多传感器信息融合方法研究

汽包水位是锅炉安全运行的重要参数,列举了影响汽包水位变化的各种因素并且建立了锅炉汽包系统各输入、输出变量间的影响模型。分析了卡尔曼滤波在多传感器信息融合处理中的特点,在DRZ/T01-2004规定的基础上,提出了一个以卡尔曼滤波为底层传感信号融合方法为基础,结合其他聚类融合方法,引入多种类、多数量传感器信号和控制决策预测信号的汽包水位多传感器数据融合控制系统。基于此,设计了卡尔曼滤波在多传感器数据融合处理中的具体实现方法,并借助Matlab仿真,分别测试了卡尔曼滤波在单通道传感信号滤波以及多传感器信息融合中使用的效果。仿真结果证明了所设计的系统能够准确、快速的融合处理底层传感器信号,并作出有效的控制决策。     

Average information‐weighted consensus filter for target tracking in distributed sensor networks with naivety issues

In the consensus‐based state estimation, multiple neighboring nodes iteratively exchange their local information with each other and the goal is to get more accurate and more convergent state estimation on each node. In order to improve network scalability and fault tolerance, the distributed sensor networks are desirable because the requirements of the fusion node are eliminated. However, the state estimation becomes challenging in the case of limited sensing regions and/or distinct measurement‐noise covariances. A novel distributed average information‐weighted consensus filter (AICF) is proposed, which does not require the knowledge of the total number of sensor nodes. Based on the weighted average consensus, AICF effectively addresses the naivety issues caused by unequal measurement‐noise covariances. Theoretical analysis and experimental verification show that AICF can approach the optimal centralized state estimation.     

A design method of strong stability self‐tuning controller based on on‐demand type feedback control

This paper proposes a design method of strong stability self‐tuning controller based on on‐demand type feedback control. For safety in industrial applications, although it is important to consider on‐demand type feedback control system, the previous papers about on‐demand type feedback control did not consider the influence of noise and fixed the design parameter to constant value. Therefore, this paper extends the design parameter of on‐demand type feedback control as stable rational function through the design method of strong stability system using coprime factorization. Moreover the self‐tuning controller of the proposed method is given and the control result with noise is shown by numerical example.