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.     

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.     

永磁同步电动机系统参数和状态的推广卡尔曼滤波估计

永磁同步电动机系统具有力矩系数大、力矩波动小以及控制灵活等优点，在许多精密伺服控制系统中得到广泛应用。本文在得到系统模型的基础上，利用推广的卡尔曼滤波器对非线性的永磁同步电动机系统参数和状态进行了估计，仿真结果验证了估计方法在数学上的可行性。     

基于带参数的卡尔曼滤波的河道糙率动态反演研究

河道糙率是洪水水力计算的重要参数,引入控制论理论,应用带参数的卡尔曼滤波法进行河道糙率反演分析。数值计算结果表明状态变化率对带参数的卡尔曼滤波法的滤波性能有较大影响,同时分析了观测断面数量对滤波结果的影响。针对计算量较大的特点,通过敏度矩阵相关性分析,提出了提高计算效率的有效方法。     

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.     

Characterization of power quality disturbances using hybrid technique of linear Kalman filter and fuzzy-expert system

This paper presents a hybrid technique for characterizing power quality (PQ) disturbances. The hybrid technique is based on Kalman filter for extracting three parameters (amplitude, slope of amplitude, harmonic indication) from the captured distorted waveform. Discrete wavelet transform (DWT) is used to help Kalman filter to give a good performance; the captured distorted waveform is passed through the DWT to determine the noise inside it and the covariance of this noise is fed together with the captured voltage waveform to the Kalman filter. The three parameters are the inputs to fuzzy-expert system that uses some rules on these inputs to characterize the PQ events in the captured waveform. This hybrid technique can classify two simultaneous PQ events such as sag and harmonic or swell and harmonic. Several simulation and experimental data are used to validate the proposed technique. The results depict that the proposed technique has the ability to accurately identify and characterize PQ disturbances.     

双UKF算法及其在感应电机矢量控制中的应用

在无轨迹卡尔曼滤波器(UKF)算法的基础上,建立应用于感应电机矢量控制系统的双UKF算法,实现电机状态和参数的同时观测.电机模型选择以定、转子磁链为状态变量的降阶方程,从而有效避免了数值计算的不稳定性.利用Simulink建立感应电机矢量控制系统,通过仿真比较了双UKF与扩展卡尔曼滤波器(EKF)两种算法的性能.实验结果表明,双UKF算法能有效提高状态估计和参数辨识的精度和收敛速度.     

一种基于卡尔曼滤波的板球系统RBF-PID控制研究

板球系统在经典控制对象球杆系统的基础上进行了扩展,是一个多变量、强耦合、非线性控制对象。针对板球系统采用PID控制时小球震荡比较严重及PID控制存在参数镇定依靠经验调整且在控制过程中系统的抗干扰能力差等缺点,利用径向基函数神经网络(radial basis funtion)具有自学习、自适应能力及非线性映射能力,对PID参数进行智能优化,使系统对阶跃信号的响应速度加快了2.8 s。利用卡尔曼滤波实现对控制干扰和测量噪声信号进行抑制,通过MATALB绘制出定点控制实验中小球的轨迹,实验结果表明了此算法相对于传统的PID控制可以有效的提高板球的系统的抗干扰能力以及动态性能,能够使小球的稳定时间由26 s减少到7 s,超调量减少了11.4 mm,X轴方向的控制精度提高了0.7 mm,Y轴方向的控制精度提高了1.7 mm。     

Optimality for the linear quadratic non‐Gaussian problem via the asymmetric Kalman filter

In the linear non‐Gaussian case, the classical solution of the linear quadratic Gaussian (LQG) control problem is known to provide the best solution in the class of linear transformations of the plant output if optimality refers to classical least‐squares minimization criteria. In this paper, the adaptive linear quadratic control problem is solved with optimality based on asymmetric least‐squares approach, which includes least‐squares criteria as a special case. Our main result gives explicit solutions for this optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. The main difficulty is to find the optimal state estimate. For this purpose, an asymmetric version of the Kalman filter based on asymmetric least‐squares estimation is used. We illustrate the applicability of our approach with numerical results. Copyright © 2004 John Wiley & Sons, Ltd.     

Combined state and parameter estimation for Hammerstein systems with time delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time delay. Both the process and the measurement noises are considered in the system. On the basis of the observable canonical state space form and the key term separation, a pseudolinear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman filter–based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms, which are missed for the time delay, the Kalman filter–based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time delay, parameters, and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms.     

The modified extended Kalman filter based recursive estimation for Wiener nonlinear systems with process noise and measurement noise

This article develops the modified extended Kalman filter based recursive estimation algorithms for Wiener nonlinear systems with process noise and measurement noise. The prior estimate of the linear block output is computed based on the auxiliary model, and the posterior estimate is updated by designing a modified extended Kalman filter. A multi-innovation gradient algorithm and a recursive least squares algorithm are derived to estimate the parameters of the linear subsystem, respectively. The simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.     

A novel robust progressive cubature Kalman filter with variable step size for inertial navigationsystem/global navigation satellite system tightly coupled navigation

This article investigates the state estimation problem of the nonlinear system with the large process prior uncertainty but high-accuracy measurement information, the situation is prone to occur in the inertial navigation system (INS)/global navigation satellite system (GNSS) tightly coupled navigation system. Furthermore, the unknown heavy-tailed measurement noises induced by the inaccurate prior navigation information and random measurement outliers are also considered. Given existing methods such as progressive cubature Kalman filter (PCKF) cannot effectively solve the above issues, a novel robust PCKF with variable step size (RVSS-PCKF) is proposed. First, a new Gaussian-uniform-mixing inverse Gamma (GUMIG) distribution is presented to model the variable step size and measurement noise. Next, the GUMIG distribution is expressed as a hierarchical Gaussian presentation and then RVSS-PCKF is derived with the help of the variational Bayesian (VB) inference. In the filter, the state, variable step size and noise statistic are jointly estimated by the fixed-point iterations. Finally, the simulations and real data of the tightly coupled navigation illustrate the superiority of the filter in terms of accuracy and steady-state performance.     

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.     

and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates

This paper addresses the problems of and full‐order filter design for continuous‐time Markov jump linear systems subject to uncertainties. Different from the available methods in the literature, the main novelty of the proposed approach is the possibility of computing bounds to the and norms of the augmented system composed by the uncertain Markov jump linear system plus the robust filter through Lyapunov matrices depending polynomially on the uncertainties affecting independently the matrices of each operation mode and the transition rate matrix. By means of a suitable representation of the uncertainties, the proposed filter design conditions are expressed in terms of linear matrix inequality relaxations associated with searches on scalar parameters. As an additional flexibility, the conditions can be used to synthesize filters with partial, complete, or null Markov mode availability. Numerical experiments illustrate that the proposed approach is more general and can be less conservative than the available methods. Copyright © 2014 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.