Optimal filtering for incompletely measured polynomial states over linear observations

In this paper, the optimal filtering problem for polynomial system states over linear observations with an arbitrary, not necessarily invertible, observation matrix is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. A transformation of the observation equation is introduced to reduce the original problem to the previously solved one with an invertible observation matrix. The procedure for obtaining a closed system of the filtering equations for any polynomial state over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a third‐order state equation. In the example, performance of the designed optimal filter is verified against a conventional extended Kalman–Bucy filter. Copyright © 2007 John Wiley & Sons, Ltd.     

Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

This paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias‐constrained optimal finite impulse response filtering algorithm for linear discrete time‐invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite‐horizon and full‐horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade‐off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full‐horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite‐dimensional optimal linear filtering of nD smooth Gaussian random fields

This paper deals with the optimal filtering problem of nD sampled, Gaussian random fields. The filtering algorithm is based on a state‐space signal model analytically derived from the assumption that the continuous Gaussian random field can be well approximated, almost everywhere, by a continuously differentiable nD surface. An appealing feature of the proposed optimal filter is that it is not based on nD strip processing schemes. The filtering algorithm has a structure which is recursive both with respect to the point‐to‐point scanning procedure of the sampled field and to the dimensionality of the estimate computed at each point. This greatly reduces the numerical complexity of the filtering scheme. The filtering algorithm requires the knowledge of some statistical parameters of the random field. For a greater generality, a procedure for the adaptive estimation of these parameters is also provided. Numerical results are reported to illustrate the applicability and performance of the proposed filter. Copyright © 2006 John Wiley & Sons, Ltd.     

Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties

This paper investigates the problem of robust reliable dissipative filtering for a class of Markovian jump nonlinear systems with uncertainties and time‐varying transition probability matrix described by a polytope. Our main attention is focused on the design of a reliable dissipative filter performance for the filtering error system such that the resulting error system is stochastically stable and strictly dissipative. By introducing a novel augmented Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained for the existence of reliable dissipative filter design in terms of linear matrix inequalities (LMIs). More precisely, a sufficient LMI condition is derived for reliable dissipative filtering that unifies the conditions for filtering with passivity and H_∞ performances. Moreover, the filter gains are characterized in terms of solution to a set of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and potential of the proposed design technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐dependent robust L2–L∞ filtering of T‐S fuzzy systems with time‐varying delays

This paper considers the problem of robust delay‐dependent L₂–L_∞ filtering for a class of Takagi–Sugeno fuzzy systems with time‐varying delays. The purpose is to design a fuzzy filter such that both the robust stability and a prescribed L₂–L_∞ performance level of the filtering error system are guaranteed. A delay‐dependent sufficient condition for the solvability of the problem is obtained and a linear matrix inequality (LMI) approach is developed. A desired filter can be constructed by solving a set of LMIs. Copyright © 2009 John Wiley & Sons, Ltd.     

基于卡尔曼滤波的高精度弹道滤波算法研究

在弹道轨迹估计中,卡尔曼滤波算法是一种普遍使用的算法,常规卡尔曼滤波算法适用于线性离散系统.对于非线性离散系统模型,为了提高滤波的精度,减小系统模型误差以及未知的量测噪声和过程噪声统计特性对滤波精度的影响,提出了一种带有噪声统计估计器的拟线性最优平滑滤波算法.将该算法应用到弹道系统模型中,对弹道轨迹进行滤波估计.通过计算机建模仿真改进的算法和传统的拟线性最优平滑滤波算法,得到的实验结果表明,改进后的算法可以减小由于系统模型不精确带来的误差,很大程度上提高了弹道轨迹滤波估计的精度.     

Optimal state filter from sequential unknown input reconstruction: Application to distributed state filtering

This paper generalizes Kalman filtering with an intermittent unknown input problem to be left invertible discrete‐time stochastic linear systems with zero, one, or more structural delays. Contrary to the state filtering–based system inversion where the unknown input vector is reconstructed with a time delay that is equal to the structural delay of the plant, we propose an optimal state filtering by reconstructing some linear combinations of the unknown input vector with a time delay less than the structural delay. Designed under a sequential unknown input decoupling constraint, which has never been previously studied in the literature, all presented filters are very computationally efficient. The proposed state filtering is used to solve the autonomous distributed state filtering problem in large‐scale networked control systems when the unknown input vector represents interactions between subsystems and when each subsystem receives intermittent information about the interaction from unreliable networks. The stochastic stability conditions of the extended intermittent unknown input Kalman filter are established when the arrival binary sequence of packet dropouts follows a random Bernoulli process.     

Central suboptimal H∞ filter design for nonlinear polynomial systems

This paper presents the central finite‐dimensional H_∞ filter for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H_∞ filtering problem to the corresponding optimal H₂ filtering problem, using the technique proposed in (IEEE Trans. Automat. Control 1989; 34 :831–847). The paper presents the central suboptimal H_∞ filter for the general case of nonlinear polynomial systems based on the optimal H₂ filter given in (Int. J. Robust Nonlinear Control 2006; 16 :287–298). The central suboptimal H_∞ filter is also derived in a closed finite‐dimensional form for third (and less) degree polynomial system states. Numerical simulations are conducted to verify performance of the designed central suboptimal filter for nonlinear polynomial systems against the central suboptimal H_∞ filter available for the corresponding linearized system. Copyright © 2008 John Wiley & Sons, Ltd.     

Implementation of a square‐root filtering approach in marginalized particle filters for mixed linear/nonlinear state‐space models

Marginalized particle filter (MPF) takes advantage of both Kalman filter and particle filter frameworks to estimate nonlinear state‐space models with reduced number of calculations in comparison to particle filter. However, due to existence of Kalman filter framework inside MPF, some limitations are introduced in implementation of MPF especially in embedded systems with finite numerical accuracies. In this paper, for the first time, we propose a novel square‐root filtering strategy for MPFs to alleviate these restrictions using modified factorization. Typical square‐root Kalman filters cannot be employed inside MPF due to the presence of minus operations in some equations of MPF. However, our method can be easily implemented inside the MPF structure. The proposed method can be used in any application that employs MPFs to estimate the mixed linear/nonlinear state‐space models. In order to demonstrate its usefulness, we employed the proposed square‐root filtering method inside a marginalized particle extended Kalman filter (MP‐EKF) structure, which was specifically designed for ECG denoising. The experimental results showed that, in the field of ECG denoising, the square‐root MP‐EKF performs more consistently than MP‐EKF in white Gaussian noises.     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 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 H∞ filtering for uncertain Markovian jump systems with mode‐dependent distributed delays

This paper deals with the problem of robust H_∞ filter design for Markovian jump systems with norm‐bounded time‐varying parameter uncertainties and mode‐dependent distributed delays. Both the state and the measurement equations are assumed to be with distributed delays. Sufficient conditions for the existence of robust H_∞ filters are obtained. Via solving a set of linear matrix inequalities, a desired filter can be constructed. The developed theory is illustrated by a simulation example. Copyright © 2009 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.     

民用导航型C／A码GPS接收机动态定位的强跟踪卡尔曼滤波研究

本文提出了一种改进的强跟踪卡尔曼滤波算法,应用于ＧＰＳ动态定位获得明显效果,首先建立了一种新的ＧＰＳ动态定位滤波模型,该模型与以往采用的非线性卡尔曼滤波模型相比,滤波精度得到提高,且模型简单,系统运算量降低,实时性较好,然后,为了进一步提高滤波器的动态性能,改进了文献中的强跟踪滤波器,大大提高了滤波器的跟踪能力。     

基于复合结构元素的新型自适应形态滤波器设计

针对电力系统信号采集中常见的噪声干扰问题,提出一种使用复合结构元素的自适应形态学滤波器。这种滤波器融合两种及以上结构元素作为复合结构元素,统计分析输入信号与拟输出滤波信号之间的滤波误差,寻找复合结构元素的整体最优尺度,从而优化滤波效果。根据滤波误差极大值原理,调整组成复合结构元素的两种元素的参数占比,进一步优化,可得最优滤波使用的复合结构元素。仿真实验对包含随机白噪声的电力信号进行自适应滤波,结果表明,在面向随机噪声时,所提出的自适应滤波器能够准确寻求到最优结构元素,滤波性能优于使用单一结构元素的传统形态滤波器,具有良好的应用前景。     

Optimal linear filtering for networked systems with communication constraints,fading measurements,and multiplicative noises

This paper is concerned with the filtering problem for discrete‐time networked systems with communication constraints, fading measurements, and multiplicative noises. The communication constraint is that, at each sampling instant, at most one of the various transmission nodes in the networked systems is permitted to access a shared communication channel, and then the received data are transmitted to a remote filter to perform the filtering task. The phenomenon of measurement fading appears in a random way when measurements are transmitted via the communication channel that undergoes slow fading. Using the innovation analysis approach and some results developed in this study, an optimal linear filter is proposed. The proposed optimal filter has a recursive structure and does not increase computation and storage load with time. Computer simulations are conducted to examine the performance of the proposed optimal filter. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust H ∞ filtering for a class of uncertain stochastic hybrid neutral systems with time‐varying delay

This paper is devoted to the problem of robust H _∞ filtering for a class of uncertain switched neutral systems subject to stochastic disturbance and time‐varying delay. Attention is focused on the design of a full‐order switched filter such that the filtering error system is robust mean‐square exponentially stable with a prescribed weighted H _∞ performance. On the basis of the average dwell time approach and the piecewise Lyapunov function technique, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities. Then, by solving the corresponding linear matrix inequalities, the desired full‐order switched filter is derived for all admissible uncertainties, time‐varying delay, and stochastic disturbances. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimization‐based method for shunt hybrid filter compensation in non‐stiff systems

In this contribution, a steady‐state approach for determining the optimal size and control of a shunt hybrid filter (SHF), to control harmonic current mitigation and to provide reactive power compensation, is proposed. The SHF topology is formed by a shunt active power filter (APF) and a shunt capacitor. The APF current injections are determined from the solution of a nonlinear programming problem formulated to meet permissible operation limits, with an optimal APF size. The formulation and control theory for the SHF is developed in the abc reference frame. An important practical aspect such as the application of SHF compensation in non‐stiff systems is included in the analysis and solution of the nonlinear programming problem, as well as in the current control technique, maintaining stringent performance requirements on the tracking of the filtering currents, by allowing the use of the shunt capacitor also as a filter for draining the ripple current inherent to the APF injection currents. Results obtained with matlab /Simulink (MathWorks, Inc., Natick, MA, USA) show that the proposed theory and the control of the optimal SHF compensation constitute an effective system to compensate reactive power and to control harmonic distortion under selected/permissible limits with an optimal APF injection current reducing the APF size. Copyright © 2011 John Wiley & Sons, Ltd.     

两级线性迭代策略下的混合状态估计的研究

基于卡尔曼滤波及线性迭代基本原理,针对当前电力系统混合状态估计精度低、滤波效果差及收敛能力低等问题,提出了一种基于两级线性迭代的电力系统混合状态估计的研究策略:第1级利用相量测量单元(PMU)的量测数据进行线性估计;第2级将其与传统量测值相结合用于状态估计,并利用PMU的高频特性对两级的量测数据进行多次迭代采样。将其在IEEE 14和IEEE 57节点测试系统进行测试,并将结果与其他混合模型比较,结果表明,该策略的估计精度、数据收敛度及量测参数误差均优于其他混合模型。