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 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 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.     

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.     

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.     

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 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.     

Variance analysis of robust state estimation in power system using influence function

An analytical equation is derived using influence function approximation to calculate the variance of the state estimate for traditional robust state estimators such as the Quadratic-Constant, Quadratic-Linear, Square-Root, Schweppe-Huber Generalized-M and Multiple-Segment estimator. The equation gives insights into the precision of the estimation. Using the equation, the variance of a state estimate can be expressed as a function of measurement noise variances enabling the selection of sensors for a specified estimator precision. It can also be used to search for the optimum estimator parameters to give the minimum sum of variances. The well-known Weighted-Least-Squares variance formula is a special case of the equation and simulations on the IEEE 14-bus system are given to show the usefulness of the equation.     

Uncertainty analysis of a commercial microwave noise temperature measurement system using Monte Carlo simulations

A Monte Carlo simulation, a non‐linear fitting routine, and an uncertainty extraction routine are used to analyze the uncertainty of a commercial microwave noise temperature measurement system. Measured data for an S/C band synthetic FET‐based cold load, two microwave solid‐state noise diode hot loads, and an ambient load is obtained, and the measurement system uncertainties are subsequently assessed using different DUTs. An estimation of the measurement system uncertainties is determined for a range of DUT temperatures, and the results are consistent with the noise temperature uncertainties calculated from the measured data at the same frequency. Copyright © 2010 John Wiley & Sons, Ltd.     

Bias‐eliminating least‐squares identification of errors‐in‐variables models with mutually correlated noises

This paper proposes a bias‐eliminating least‐squares (BELS) approach for identifying linear dynamic errors‐in‐variables (EIV) models whose input and output are corrupted by additive white noise. The method is based on an iterative procedure involving, at each step, the estimation of both the system parameters and the noise variances. The proposed identification algorithm differs from previous BELS algorithms in two aspects. First, the input and output noises are allowed to be mutually correlated, and second, the estimation of the noise covariances is obtained by exploiting the statistical properties of the equation error of the EIV model. 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]     

Noise covariance estimation for Kalman filter tuning using Bayesian approach and Monte Carlo

Linear time‐invariant systems play significant role in the control field. A number of methods have been published for identification of the deterministic part of a process. However, identification of the stochastic part has had much less attention. This paper deals with estimation of covariance matrices of the noise entering a linear system. The process and measurement noise covariance matrices are tuning parameters of the Kalman filter, and they affect the quality of the state estimation. The noise covariance matrices are generally not known, and their estimation from the measured data is a challenging task. This paper introduces a method for estimation of the noise covariance matrices using Bayesian approach along with Monte Carlo numerical methods. Performance of the approach is tested on various systems and noise properties. The second part of the paper compares Monte Carlo approach with the recently published methods. The speed of convergence is compared with the Cramér–Rao bounds. Copyright © 2012 John Wiley & Sons, Ltd.     

Time series modeling and filtering method of electric power load stochastic noise

Stochastic noises have a great adverse effect on the prediction accuracy of electric power load. Modeling online and filtering real-time can effectively improve measurement accuracy. Firstly, pretreating and inspecting statistically the electric power load data is essential to characterize the stochastic noise of electric power load. Then, set order for the time series model by Akaike information criterion (AIC) rule and acquire model coefficients to establish ARMA (2,1) model. Next, test the applicability of the established model. Finally, Kalman filter is adopted to process the electric power load data. Simulation results of total variance demonstrate that stochastic noise is obviously decreased after Kalman filtering based on ARMA (2,1) model. Besides, variance is reduced by two orders, and every coefficient of stochastic noise is reduced by one order. The filter method based on time series model does reduce stochastic noise of electric power load, and increase measurement accuracy     

Optimal configuration analysis for acampus microgrid—a case study

The foremost issues of 21st century are challenging demand of electrical energy and to control the emission of Green House Gases (GHG) emissions. Renewable energy resources based sustainable microgrid emerges as one of the best feasible solution for future energy demand while considering zero carbon emission, fossil fuel independency, and enhanced reliability. In this paper, optimization and implementation of institutional based sustainable microgrid are discussed based on cost analysis, carbon emission, and availability of energy resources. Various microgrid topologies are considered for addressing the most ideal solution. The metrological data such as irradiance is acquired from solar satellite data of NASA (National Aero Space Agency) while the data for wind speed is taken from synergy enviro engineer’s site. HOMER® simulation tool is used for modelling and optimization purpose.     

An adaptive regulation method for a class of uncertain time‐delay systems

In this paper, a new adaptive robust stabilization scheme is proposed for uncertain neutral time‐delay systems. No upper bounds on the uncertainties are assumed to be available. An update law is first used to find estimates of these upper bounds. A state‐feedback controller is then designed, which is shown to stabilize the underlying system under some mild conditions. The asymptotic stability of the state trajectories is proved using the Lyapunov–Krasovskii approach. An example is provided, which demonstrates the efficacy of the proposed adaptive control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

基于噪声相关特性的数学形态学消噪原理研究

结合电力信号采集中噪声的相关性理论和数学形态学基本原理,通过数值仿真详细研究了自相关噪声和随机白噪声干扰下,数学形态学滤波中关于结构元素如何选取的问题。分析指出,针对自相关噪声,结构元素的选择与噪声的周期性,最大峰值及采样率等因素密切相关。类似高频正弦噪声,通过选择合适尺度的正余弦形或三角形结构元素进行形态滤波均能取得良好的滤波效果。而对于随机白噪声而言,由于不具有自相关特性,因此并不存在类似相关噪声下的结构元素选取规律,多数情况需要通过预先的仿真或根据经验来合理选择结构元素。     

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.     

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。