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.     

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.     

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.     

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.     

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.     

测量噪声方差未知的多传感器组合导航集中融合算法

目前,多传感器组合导航系统的信息融合方法是建立在测量噪声方差已知的基础上,然而测量噪声方差会随着内部及外部的干扰而发生变化。为此,本文首先将基于变分贝叶斯逼近的自适应卡尔曼滤波(variational Bayesian approximation based adaptive Kalman filter, VB-AKF)从单一组合导航系统扩展到多传感器组合导航系统;然后,提出了多传感器组合导航系统的两种集中融合算法,即基于VB-AKF的增广式集中融合算法及基于VB-AKF的序贯式集中融合算法,以解决测量噪声方差未知情况下的多传感器组合导航的信息融合问题;最后,通过SINS/GNSS/CNS/ADS多传感器组合导航系统对上述算法进行了仿真验证。实验结果表明,本文所提两种算法滤波精度相同、且接近于测量噪声方差已知情况下的理想集中融合算法(ICKF)。在整个仿真时段内,相对于传统集中式卡尔曼滤波器(TCKF)及具有容错功能的联邦卡尔曼滤波算法(FT-FKF),本文算法可提高位置精度分别为32%和90%、提高速度精度分别为38%和71%。     

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.     

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.     

多MEMS陀螺数据融合方法性能比较

MEMS陀螺的体积小、成本低,便于集成,但其低精度极大的限制了MEMS陀螺在实际中的应用。利用多传感器融合技术进行误差补偿可提高MEMS陀螺的测量精度,人们提出了多种数据融合方法用于改进MEMS陀螺的测量精度。对多尺度融合方法、卡尔曼滤波融合和小波阈值融合方法进行比较分析。理论分析与实验结果表明,多尺度融合算法相比卡尔曼滤波融合和小波阈值融合方法在标准差、信噪比、功率谱及Allan方差等方面性能获得了较好的效果,其适用范围更宽。     

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。     

基于自适应卡尔曼滤波算法的紧组合导航系统的研究

为了提高子滤波器滤波精度和优化信息融合算法,提出一种基于在线调节因子的自适应卡尔曼滤波算法。首先讨论采用卡尔曼滤波技术的理论依据,设计SINS/GPS紧组合导航系统。提出改进的自适应卡尔曼滤波算法,该方法通过构造自适应参数因子,并利用量测噪声协方差阵与自适应参数的比值实现在线修正量测噪声协方差阵。通过MATLAB仿真,与传统基于标准卡尔曼滤波算法的紧组合导航系统相比,其各向位置误差和速度误差均得到明显降低,从而达到提高组合导航定位精度和优化信息融合算法的目的。     

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.     

State estimation for asynchronous multirate multisensor nonlinear dynamic systems with missing measurements

This paper is concerned with the state estimation for a kind of nonlinear multirate multisensor asynchronous sampling dynamic system. There are N sensors observing a single target independently at multiple sampling rates, and the dynamic system is formulated at the highest sampling rate. Observations are obtained asynchronously, and each sensor may lose data randomly at a certain probability. The fused state estimate is generated using multiscale system theory and the modified sigma point Kalman filter. It is shown that our main results improve and extend the existing sigma point Kalman filter for which the samples are obtained multirate nonuniformly. Measurements randomly missing with Bernoulli distribution could also be allowed in this paper. Finally, the feasibility and efficiency of the presented algorithm is illustrated by a numerical simulation example.Copyright © 2012 John Wiley & Sons, Ltd.     

Estimating the synchronizing and damping torque coefficients using Kalman filtering

This paper presents an optimal approach for optimal estimation of the synchronizing and damping torque coefficients of a synchronous machine using two-state linear Kalman filter. These coefficients can be used as indices which provide insight into the dynamic stability of power systems. The two coefficients are calculated using the time responses of the changes in the rotor angle, rotor speed, and electromagnetic torque. The effect of system noise on the performance of the Kalman filter is also investigated. The performance of Kalman filter is compared with the least-square error technique. The paper shows that the steady-state response of Kalman filter agrees with the least-square solution. The paper shows that Kalman filter can be used as efficient tool for either on-line or off-line estimation of the synchronizing and damping torque coefficients.     

Adaptive estimation of power system frequency deviation and itsrate of change for calculating sudden power system overloads

A novel Kalman filtering-based technique is presented for estimating power system frequency deviation and its average rate of change during emergency operating conditions that may require load shedding. This method obtains the optimal estimate of the power system frequency deviation from noisy voltage samples and the best estimate of the mean system frequency deviation and its rate of change while accounting for low-frequency synchronizing oscillations which occur during large disturbances. The proposed technique is a two-stage algorithm which uses an adaptive extended Kalman filter in series with an adaptive linear Kalman filter. The extended Kalman filter calculates the frequency deviation, magnitude, and phase angle of the voltage phasor, which may change during the time period covered by the estimation window. Both the measurement noise variance and the system noise covariance associated with the voltage samples are calculated online. The instantaneous frequency deviation is used as the input to a linear Kalman filter, which models the frequency deviation as a random walk plus a random ramp process. The estimated average rate of frequency decay is represented by the slope of the random ramp. Results for both single and multiple measurements are reported     

基于 SRCKFw-检测的多传感器融合的姿态解算算法

针对惯性导航系统受模型误差和测量异常值误差的影响,姿态解算结果易出现精度差甚至发散的问题,提出了一种基于平方根容积卡尔曼滤波(square-root cubature Kalman filter, SRCKF)w-检测的多传感器姿态融合算法。利用协方差匹配法对SRCKF的新息序列进行自适应调整,经过调整后的新息在迭代过程中会补偿量测噪声方差阵,减小模型误差影响;再利用调整后的新息进行误差探测,提高w-检测的探测精度,并构造观测值替换准则进行误差观测值替换,解决测量异常值误差带来的影响;最后利用SRCKF进行姿态融合,陀螺仪的姿态作为状态方程,经检测替换后的加速度计和磁力计姿态作为量测方程。实验表明,所提算法可以准确估计系统姿态,与传统算法相比解算精度平均可提升62.43%,在不同条件下,算法整体性能均可得到大幅提升,并能快速进行姿态解算,保证解算精度。     

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.     

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.     

基于改进WOA的鲁棒增广扩展Kalman滤波器设计

本文针对一类非线性系统,提出基于广义系统的鲁棒增广扩展Kalman滤波器,结合改进鲸群优化算法寻优系统噪声,以精确估计系统状态量以及并发执行器和传感器故障。首先,视故障为系统的状态变量,建立广义系统,将非线性系统的故障估计转化为非线性广义系统的状态估计。其次,提出鲁棒上界以降低线性化误差对估计精度的影响。然后,利用改进鲸群算法寻优系统噪声,以优化鲁棒增广扩展Kalman滤波器。最后,给出F-16飞机的纵向运动数值模型,使用本文方法与自适应无迹Kalman滤波器以及基于鲸群算法的鲁棒增广扩展Kalman滤波器进行对比仿真,仿真结果表明,相较于其他两种算法,本文方法的故障估计均方根误差降低了50%左右,验证了其优越性。