Robust state estimation for uncertain linear systems with deterministic input signals

In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.     

Robust state estimation for uncertain discrete-time stochastic systems with missing measurements

In this paper, results of robust estimation of Zhou (2010a) are extended to state estimation with missing measurements. A new procedure is derived which inherits the main properties of that of Zhou (2010a). In this extension, a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult. Though introducing a monotonic function and using the so-called squeeze rule, this new robust estimator is proved to converge to a stable system. Numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of Wang, Yang, Daniel, and Liu (2005).     

Robust state estimation for wireless sensor networks with data‐driven communication

Robust state estimation problem for wireless sensor networks composed of multiple remote sensor nodes and a fusion node is investigated subject to a limitation on the communication rate. An analytical robust fusion estimator based on a data‐driven transmission strategy is derived to save the sensor energy consumption and reduce the network traffic congestion. The conditions guaranteeing the uniform boundedness of estimation errors of the robust fusion estimator are investigated. Numerical simulations are provided to show the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Event‐triggered robust state estimation for wireless sensor networks

Robust state estimation problem subject to a communication constraint is investigated in this paper for a class of wireless sensor networks constituted by multiple remote sensor nodes and a fusion node. An analytical robust fusion estimator using local event‐triggered transmission strategies is derived aiming to reduce energy consumption of the sensor nodes and refrain from network traffic congestion. Some conditions are presented guaranteeing the uniformly bounded estimation errors of the robust state estimator. Several numerical simulations are presented to show the validity of the proposed method.     

Distributed bounded-error state estimation based on practical robust positive invariance

We propose a state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems. Furthermore, each local estimator reconstructs the state of the corresponding subsystem only. Different from methods based on moving horizon estimation, our approach does not require the online solution to optimisation problems. Our state estimation scheme, which is based on the notion of practical robust positive invariance, also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed.     

Robust state estimation for perturbed systems with error variance and circular pole constraints: The discrete-time case

This paper is concerned with the problem of robust state estimation for linear perturbed discrete-time systems with error variance and circular pole constraints. The goal of this problem addressed is the design of a linear state estimator such that, for all admissible uncertainties in both state and output equations, the following two performance requirements are simultaneously satisfied: (1) the poles of the filtering matrix are all constrained to lie inside a prespecified circular region; and (2) the steady-state variance of the estimation error for each state is not more than the individual prespecified value. It is shown that this problem can be converted to an auxiliary matrix assignment problem and solved by using an algebraic matrix equation/inequality approach. Specifically, the conditions for the existence of desired estimators are obtained and the explicit expression of these estimators is also derived. The main results are then extended to the case when an H performance requirement is added. Finally, a numerical example is presented to demonstrate the significance of the proposed technique.     

网络蠕虫感染率的抗差估计法

网络蠕虫对信息安全构成了威胁,检测和防范蠕虫成为网络安全的研究课题。本文提出了一种网络蠕虫感染率的估法模型,然后根据权函数和残差区间给出了抗差等价权矩阵,分析了误差影响及验后精度估计,最后进行了仿真实验。实验结果表明,这种方法具有良好的抗粗差能力,可靠靠且收敛速度快。     

Delay‐dependent fault estimation for uncertain time‐delay nonlinear systems: an LMI approach

This paper deals with the problem of robust fault estimation for uncertain time‐delay Takagi–Sugeno (TS) fuzzy models. The aim of this study is to design a delay‐dependent fault estimator ensuring a prescribed ??_∞ performance level for the fault estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a robust fault estimator are given in terms of linear matrix inequalities (LMIs). Membership functions' (MFs) characteristics are incorporated into the fault estimator design to reduce the conservativeness of neglecting these characteristics. Finally, a numerical example is given to illustrate the effectiveness of the proposed design techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

离散系统状态和参数鲁棒滤波分离算法

提出了一种离散系统的鲁棒分离滤波方法.为了对状态向量进行较准确估计,将鲁棒滤波器分为:1)零误差状态估计器;2)不确定矩阵估计器;3)鲁棒合成器.零偏差状态估计器是假定系统的不确定部分为零时的状态估计器;其新息作为不确定部分的估计变量,并由此估计系统的不确定部分;最后,根据系统不确定部分估计误差的上下界,用鲁棒合成器对状态向量的估计值进行鲁棒修正.为了在合成器中得到鲁棒滤波的逼近计算式,通过变换状态估计误差的协方差阵,得到了系统矩阵不确定部分的误差上界不等式逼近,并且得到了估计误差协方差阵逆阵的下界不等式逼近,从而给出了鲁棒合成滤波的完整算法.     

线性连续时变系统的状态和输入混合估计:一种对策方法

The $H_\infty$ hybrid estimation problem for linear continuous time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. Based on the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in\hfill terms\hfill of\hfill solutions\hfill to\hfill a\hfill Riccati\hfill diffe-\\rential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix that reflects the internal relations between the unknown input and output estimation error. Both state and unknown inputs estimation are realized by the proposed estimator. Thus, the results in this paper are also capable of dealing with fault diagnosis problems of linear time-varying systems. At last, a numerical example is provided to illustrate the proposed approach.     

线性离散时变系统的状态和输入混合估计: 一种对策方法

本文研究了线性离散时变系统的混合估计问题, 估计信号是状态和输入的线性组合. 设计目标要求满足一个最坏性能指标, 即从扰动到估计误差的能量增益小于一个给定值. 混合估计问题的最优解是二人零和微分对策的鞍点解. 基于微分对策方法, 混合估计问题有解的充要条件表达为 Riccati 微分方程的可解性. 在问题有解时, 给出了符合要求的估计器. 估计器的结构表达为一个增益矩阵和一个输出映射矩阵, 后者反映了未知输入与输出估计误差之间的内在联系. 最后, 通过数值例子证明了本文方法的有效性.     

Robust variance estimation for random effects meta-analysis

In random effects meta-analysis, an overall effect is estimated using a weighted mean, with weights based on estimated marginal variances. The variance of the overall effect is often estimated using the inverse of the sum of the estimated weights, and inference about the overall effect is typically conducted using this ‘usual’ variance estimator, which is not robust to errors in the estimated marginal variances. In this paper, robust estimation for the asymptotic variance of a weighted overall effect estimate is explored by considering a robust variance estimator in comparison with the usual variance estimator and another less frequently used estimator, a weighted version of the sample variance. Three illustrative examples are presented to demonstrate and compare the three estimation methods. Furthermore, a simulation study is conducted to assess the robustness of the three variance estimators using estimated weights. The simulation results show that the robust variance estimator and the weighted sample variance estimator both estimate the variance of an overall effect more accurately than the usual variance estimator when the weights are imprecise due to the use of estimated marginal variances, as is typically the case in practice.Therefore, we argue that inference about an overall effect should be based on the robust variance estimator or the weighted sample variance, which provide protection against the practice of using estimated weights in meta-analytical inference.     

一类连续时间Markov跳跃系统鲁棒H_∞故障估计

研究了受L_2范数有界未知输入影响的一类线性连续时间Markov跳跃系统鲁棒H_∞故障估计问题.应用自适应观测器作为故障估计器,将鲁棒H_∞故障估计问题归结为随机H_∞滤波问题.推导并证明了问题可解的充分条件,并通过求解线性矩阵不等式得到了H_∞故障估计器参数矩阵的解.最后,数字算例验证了所提方法的有效性.

Abstract：

The problem of robust H_∞ fault estimation is studied for a class of continuous-time Markovian jump systems with L_2 norm bounded unknown input.By using an adaptive observer as a fault estimator, the design of robust H_∞ fault estimator is formulated as a stochastic H_∞ filtering problem.A sufficient condition for the existence of a robust H_∞ fault estimator is derived by applying matrix inequality technique, and a solution to the parameter matrices of the fault estimator can be obtained by solving a set of linear matrix inequalities.A numerical example shows the effectiveness of the proposed method.     

Comments on “Robust state estimation for uncertain discrete-time stochastic systems with missing measurements” [Automatica 47 (2011) 1520–1524]

We show that some results presented in the aforementioned article are rather limited. One of the major restrictions on applicability of the obtained results is the ergodic requirement on the received plant output measurements, which is generally not satisfied by a time-varying system. Another major restriction is that the comparisons are not appropriate for its numerical simulations, that is, using the state estimation results of an estimator that utilizing current and past observations to compare with those of a one-step state predictor is not appropriate. To evaluate the filter performances objectively, we do a numerical simulation with the robust state estimator and the well-known Kalman filter that does not take either parametric errors or random measurement loss into account; and the simulation results show that there is no significant difference in filtering performance between these two estimators.     

Minimal-order Wiener filter for a system with exact measurements

Necessary and sufficient conditions for the existence of an optimal steady-state state estimator are derived under the assumption that this estimator is a linear functional of the measurements and a finite number of derivatives of the exact measurements. Our conditions are shown to be dual to the generalized Legendre-Clebsch conditions of the dual optimal singular regulator. A separation principle is derived and it is shown that as all process and measurement noise vanishes, the error covariance of our filter converges to a null matrix.     

Robust H-infmity estimation for continuous-time polytopic uncertain systems

1IntroductionAs a fundamental problem in control area,linearestimation has been extensively investigated since Kalmanpresented the optimal filteringtheory[1].It is well knownthat the Kalmanfilteringtheoryis based onthe assumptionsthat the accurate mathematical models of the consideredsystems and the statistics features of the noise inputs areknown.Inthis setting,the Kalmanfilteringis also called H2filtering,which minimizes the H2norm of the operatorfromthe external input to the estimation er…     

Robust H-infinity estimation for continuous-time polytopic uncertain systems

The design of full_order robust H_infinity estimators is investigated for continuous_time polytopic uncertain systems. The main purpose is to obtain a stable and proper linear estimator such that the estimation error system remains robustly stable with a prescribed H_infinity attenuation level. Based on a recently proposed H_infinity performance criterion which exhibits a kind of decoupling between the Lyapunov matrix and the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameter_dependent Lyapunov functions and hence it is less conservative than earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

A method of robust multi-rate state estimation

The inadequacy of the standard notions of detectability and observability to ascertain robust state estimation is shown. The notion of robust state estimation is defined, and for a class of processes the conditions under which the robust state estimation is possible, are given. A method of robust, nonlinear, multi-rate, state estimator design is presented. It can be used to improve robustness in an existing estimator or design a new robust estimator. Estimator tuning guidelines that ensure the asymptotic stability of the estimator error dynamics are given. To ensure that estimation error does not exceed a desired limit, the sampling period of infrequent measurements should be less than an upper bound that depends on factors such as the size of the process dominant time constant, the magnitude of measurement noise, and the level of process–model mismatch. An expression that can be used to calculate the upper bound on the sampling period of infrequent measurements, is presented. The upper bound is the latest time at which the next infrequent measurements should arrive to ensure that estimation error does not exceed a desired limit. The expression also allows one to calculate the highest quality of estimation achievable in a given process. A binary distillation flash tank and a free-radical polymerization reactor are considered to show the application and performance of the estimator.     

Robust fractional order singular Kalman filter

In this article, the state estimation problem of linear fractional order singular (FOS) systems subject to matrix uncertainties is investigated where a recursive robust algorithm is derived. Considering an uncertain discrete-time linear FOS system with added process and measurement noises, we aim to design a robust Kalman-type state estimation algorithm based on an optimal data fitting approach with a given sequence of observations. As a substitute for the stochastic formulation, this general filter is obtained by minimizing a completely deterministic regularized residual norm in its worst-possible form at each step over admissible uncertainties. Analysis of the algorithm shows that not only does the proposed robust filter cover the traditional robust Kalman filters (KFs), but it also represents an extension of the nominal fractional singular KF (FSKF) when the system is not subject to uncertainties. Furthermore, besides giving a sufficient condition for the existence of the robust filter, we derive conditions for the asymptotic properties of the filter, where we demonstrate that the filter and the Riccati equation are stable and converge when an equivalent system is detectable and stabilizable. A numerical example is included to demonstrate the performance of the introduced filter.     

Sequential Maximum Correntropy Kalman Filtering

This paper explores a linear state estimation problem in non‐Gaussian setting and suggests a computationally simple estimator based on the maximum correntropy criterion Kalman filter (MCC‐KF). The first MCC‐KF method was developed in Joseph stabilized form. It requires two n × n and one m × m matrix inversions, where n is a dimension of unknown dynamic state to be estimated, and m is a dimension of available measurement vector. Therefore, the estimator becomes impractical when the system dimensions increase. Our previous work has suggested an improved MCC‐KF estimator (IMCC‐KF) and its factored‐from (square‐root) implementations that enhance the MCC‐KF estimation quality and numerical robustness against roundoff errors. However, the proposed IMCC‐KF and its square‐root implementations still require the m × m matrix inversion in each iteration step of the filter. For numerical stability and computational complexity reasons it is preferable to avoid the matrix inversion operation. In this paper, we suggest a new IMCC‐KF algorithm that is more accurate and computationally cheaper than the original MCC‐KF and previously suggested IMCC‐KF. Furthermore, compared with stable square‐root algorithms, the new method is also accurate, but less computationally expensive. The results of numerical experiments substantiate the mentioned properties of the new estimator on numerical examples.