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.     

Optimal analog‐to‐digital transformation of fractional‐order Butterworth filter using binomial series expansion with Al‐Alaoui operator

This paper deals with the optimal analog‐to‐digital transformation of fractional‐order Butterworth filter (FOBF) in terms of infinite impulse response templates. The fractional‐order transfer function of the analog FOBF is transformed into its digital counterpart by employing the Binomial series expansion of different truncation orders, based on the Al‐Alaoui operator. This nonoptimal solution is then treated as an initial point for a local search optimizer such as the Nelder–Mead simplex (NMS) algorithm and also injected as a super‐fit individual in the initial population of a global search constrained evolutionary optimization algorithm (CEOA). Design stability and minimum‐phase response constraints are formulated for the super‐fit scheme. Both the techniques demonstrate good modeling performance; however, the super‐fit CEOA can markedly outperform the NMS method as the problem dimensionality increases.     

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.     

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.     

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.     

卡尔曼滤波对油中溶解气体含量的预测

准确测量变压器油中溶解气体的浓度是对变压器进行色谱分析的关键,为此,以卡尔曼滤波理论为基础研究了新型油浸式电力变压器油中溶解气体含量的预测模式及其应用特性,并分析了卡尔曼滤波的稳定性、实用性及其适应数值变化的能力,展示了卡尔曼滤波在数据预测方面的优越性。在卡尔曼滤波算法的迭代计算中以观测量的最小均方误差阵为准则,推导出了用预测误差向量进行方差估计,求出最小方差意义下预测量的最优估计。理论推导和仿真结果表明,该方法计算简单、可靠,可以大大地降低预测误差,提高预测模型的预报能力,能满足工程实践的需要。     

Design of IIR linear‐phase nonuniform‐division filter banks with signed powers‐of‐two coefficients

This paper deals with the minimax design of two‐channel linear‐phase (LP) nonuniform‐division filter (NDF) banks using infinite impulse response (IIR) digital all‐pass filters (DAFs) with signed powers‐of‐two (SPT) coefficients. Based on the theory of two‐channel NDF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired phase responses of the IIR DAFs. Through a frequency sampling and iterative approximation method, the optimization problem for finding the SPT coefficients for the IIR DAFs can be solved by utilizing a weighted least‐squares approach in conjunction with a coordinate rotational digital computer (CORDIC) algorithm. The resulting two‐channel SPT coefficient NDF banks can possess approximately LP response without magnitude distortion. Several simulation examples are presented for illustration and comparison. Copyright © 2008 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.     

Fault‐tolerant control of linear multivariable controllers using iterative feedback tuning

This paper introduces the iterative feedback tuning (IFT) into a Youla parameterization scheme for fault‐tolerant control. By off‐line IFT‐experiments of tuning Youla parameters, the proposed algorithm deals with a number of conditional failures that are described by the dual Youla parameter. The main contribution of this paper is to show how Youla scheme‐based IFT can be constructed for multivariable linear time‐invariant systems. Particular attention is given to the issue of the structure of the Youla parameter (filter), in which both finite impulse response and infinite impulse response filters are presented and compared. As an illustration, the method is applied to a simulation model of a continuous stirred tank heater system. Copyright © 2014 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。     

基于自适应CKF的锂离子电池SOC估算

扩展卡尔曼滤波(EKF)和无迹卡尔曼滤波(UKF)算法估算电池荷电状态(SOC)依赖等效模型参数的准确性,估算精度低。容积卡尔曼滤波(CKF)算法的滤波性能良好。利用自适应CKF(ACKF)算法估算电池SOC,自适应调节过程噪声协方差和量测噪声协方差,提高估算SOC的精度。对锂离子电池建立二阶RC等效电路模型,在不同工况下进行充放电,用卡尔曼滤波算法在线辨识等效模型的参数,ACKF算法实时估算SOC。ACKF算法估算SOC的鲁棒性较强,精度在1.5%以内。     

A fast convergence normalized least‐mean‐square type algorithm for adaptive filtering

A new adaptive algorithm with fast convergence and low complexity is presented. By using the calculation structure of the dual Kalman variables of the fast transversal filter algorithm and a simple decorrelating technique for the input signal, we obtain an algorithm that exhibits faster convergence speed and enhanced tracking ability compared with the normalized least‐mean‐square algorithm with similar computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

基于MATLAB的FIR数字滤波器设计与仿真

数字滤波器的设计和应用是数字信号处理中的核心内容之一。利用MATLAB信号处理工具箱中的FDATool工具设计出具有去噪滤波功能的有限脉冲响应滤波器,根据滤波器的不同应用需求,利用FDATool工具设计出具不同滤波功能的有限脉冲响应滤波器,并且根据设计要求和滤波器特性随时调整参数,直观简便,极大地减轻了工作量,极大方便了滤波器的设计,达到理想的应用目的。最后,对所设计的滤波器进行滤波仿真验证,对含有噪声的信号进行去噪处理,通过比较分析滤波器去噪前后信号时域及频域波形图,得出所设计的滤波器能够达到理想的去噪效果。     

Adaptive two‐stage Kalman filter in the presence of unknown random bias

The well‐known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. In a number of practical situations, the system model has unknown bias and the Kalman filter with unknown bias may be degraded or even diverged. The two‐stage Kalman filter (TKF) to consider this problem has been receiving considerable attention for a long time. Until now, the optimal TKF for system with a constant bias or a random bias has been proposed by several researchers. In case of a random bias, the optimal TKF assumes that the information of a random bias is known. But the information of a random bias is unknown or incorrect in general. To solve this problem, this paper proposes two adaptive filters, such as an adaptive fading Kalman filter (AFKF) and an adaptive two‐stage Kalman filter (ATKF). Firstly, the AFKF is designed by using the forgetting factor obtained from the innovation information and the stability of the AFKF is analysed. Secondly, the ATKF to estimate unknown random bias is designed by using the AFKF and the performance of the ATKF is verified by simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Short‐Term Wind Power Prediction for Wind Turbine via Kalman Filter Based on JIT Modeling

This paper addresses wind power prediction, which is known to be a key technology in energy management systems. In this paper, a 24‐h‐ahead power prediction method using a filter theory is proposed for wind power generation. The prediction method is a simple algorithm. The procedure of prediction consists of two steps: the data processing and the calculation of the predicted values. In data processing, in order to obtain the correlative data from the database, we employ just‐in‐time modeling. In the calculation of the predicted values, we propose a regression model for wind speed and wind power, and the unknown parameters are estimated using a constrained Kalman filter. Moreover, in the procedure used to estimate the unknown parameters, reduction and convergence of the variables are also guaranteed. Finally, the advantages of the proposed method over the conventional method are shown through actual prediction evaluations.     

分数阶Kalman滤波算法回溯长度选择方法研究

提出了一种分数阶Kalman滤波算法的回溯长度选择方法。与整数阶Kalman滤波算法相比,分数阶Kalman滤波算法的精度较高,但算法的实时性较差。研究发现,在分数阶Kalman滤波算法中,影响其精度和实时性的一个重要因素是算法的回溯长度。针对这一问题,基于分数阶Kalman滤波的基本原理,研究了回溯长度对算法的估计精度及算法实时性的影响,提出了可变回溯长度的分数阶Kalman滤波算法,在保证较高精度的前提下,有效地提高了算法的实时性。仿真实验结果证明,当精度要求较高时,在相同估计精度的情况下,采用可变的回溯长度能显著提高算法的实时性。     

Alternative optimal filter for linear state delay systems

In this paper, the optimal filtering problem for linear systems with state delay over linear observations is treated using the optimal estimate of the state transition matrix. As a result, the alternative optimal filter is derived in the form similar to the traditional Kalman–Bucy one, i.e. consists of only two equations, for the optimal estimate and the estimation error variance. This presents a significant advantage in comparison to the previously obtained optimal filter (IEEE Trans. Autom. Control 2005; 50 :684–690), which includes a variable number of covariance equations, unboundedly growing as the filtering horizon tends to infinity. Performances of the two optimal filters are compared in example; the obtained results are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Modified multiplicative quaternion cubature Kalman filter for attitude estimation

In this paper, a modified multiplicative quaternion cubature Kalman filter (CKF) for attitude estimation is proposed. For high‐dimensional state estimation, the CKF that uses third‐degree spherical‐radial cubature rule can provide a more accurate estimation than the unscented Kalman filter. However, for the attitude estimation in the case of larger initial conditional errors, the results may be reversed. To take full advantage of the CKF, the Lagrange cost function method is introduced to solve the quaternion weighted mean, then, the mean is used as the reference quaternion for the measurement update in the CKF framework. The choice of the reference quaternions and the quaternion update method is different from the existing literature to avoid the algorithm from failing. In addition, the unconstrained three‐component vectors represent the attitude error quaternion in the filtering algorithm, whereas the quaternion is used to perform attitude propagation. Simulation results demonstrate the better performance of the proposed modifying filter algorithm in comparison with the multiplicative extended Kalman filter, the unscented Kalman filter, and the CKF under larger initial condition errors.