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.     

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.     

Average information‐weighted consensus filter for target tracking in distributed sensor networks with naivety issues

In the consensus‐based state estimation, multiple neighboring nodes iteratively exchange their local information with each other and the goal is to get more accurate and more convergent state estimation on each node. In order to improve network scalability and fault tolerance, the distributed sensor networks are desirable because the requirements of the fusion node are eliminated. However, the state estimation becomes challenging in the case of limited sensing regions and/or distinct measurement‐noise covariances. A novel distributed average information‐weighted consensus filter (AICF) is proposed, which does not require the knowledge of the total number of sensor nodes. Based on the weighted average consensus, AICF effectively addresses the naivety issues caused by unequal measurement‐noise covariances. Theoretical analysis and experimental verification show that AICF can approach the optimal centralized state estimation.     

Unscented summation information‐weighted consensus filter for distributed sensor networks with incomplete information

In order to improve network scalability and fault tolerance, the distributed sensor networks are desirable. However, the distributed state estimation becomes challenging when some sensors have insufficient information due to restricted observability, and/or have imparity information due to unequal measurement‐noise covariances. Centralized summation information‐fusion (CSI) model is presented which performs weighted least‐squares estimation for all measurement information to achieve the optimal centralized state estimation. The CSI model revises the initialization and covariance propagation in the original information‐weighted consensus filter (ICF). Since centralized information fusion is a summation mode and is approached by the average consensus protocol, all the covariances involved in the CSI model contain the information regarding the total number of nodes. The artificially preset initial values are considered as measurement information and fused in accordance with the CSI model. By combining the CSI model with unscented transform, distributed unscented summation information‐weighted consensus filter (USICF) is proposed. USICF realizes the nonlinear estimation in the context of highly incomplete information. Theoretical analysis and experimental verification showed that USICF achieves better performance than UICF that is based on ICF.     

Adaptive filtering‐based multi‐innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi‐innovation identification theory, an adaptive filtering‐based multi‐innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi‐innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering‐based multi‐innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm.     

A novel variable‐length sliding window blockwise least‐squares algorithm for on‐line estimation of time‐varying parameters

Motivated by the advances in computer technology and the fact that the batch/block least‐squares (LS) produces more accurate parameter estimates than its recursive counterparts, several important issues associated with the block LS have been re‐examined in the framework of on‐line identification of systems with abrupt/gradual change parameters in this paper. It is no surprise that the standard block LS performs unsatisfactorily in such a situation. To overcome this deficiency, a novel variable‐length sliding window‐based LS algorithm, known as variable‐length sliding window blockwise least squares, is developed. The algorithm consists of a change detection scheme and a data window with adjustable length. The window length adjustment is triggered by the change detection scheme. Whenever a change in system parameters is detected, the window is shortened to discount ‘old’ data and place more weight on the latest measurements. Several strategies for window length adjustment have been considered. The performance of the proposed algorithm has been evaluated through numerical studies. In comparison with the recursive least squares (RLS) with forgetting factors, superior results have been obtained consistently for the proposed algorithm. Robustness analysis of the algorithm to measurement noise have also been carried out. The significance of the work reported herein is that this algorithm offers a viable alternative to traditional RLS for on‐line parameter estimation by trading off the computational complexity of block LS for improved performance over RLS, because the computational complexity becomes less and less an issue with the rapid advance in computer technologies. Copyright © 2004 John Wiley & Sons, Ltd.     

FPGA‐based embedded platform for fiber optic gyroscope signal denoising

This paper presents System on Chip (SoC) implementation of a proposed denoising algorithm for fiber optic gyroscope (FOG) signal. The SoC is developed using an Auxillary Processing Unit of the proposed algorithm and implemented in the Xilinx Virtex‐5‐FXT‐1136 field programmable gate array. SoC implementation of this application is first of its kind. The proposed algorithm namely adaptive moving average‐based dual‐mode Kalman filter (AMADMKF) is a hybrid of adaptive moving average and Kalman filter (KF) technique. The performance of the proposed AMADMKF algorithm is compared with the discrete wavelet transform and KF of different gains. Allan variance analysis, standard deviation and signal to noise ratio (SNR) are used to measure the efficiency of the algorithm. The experimental result shows that AMADMKF algorithm reduces the standard deviation or drift of the signal by an order of 100 and improves the SNR approximately by 80 dB. The Allan variance analysis result shows that this algorithm also reduces different types of random errors of the signal significantly. The proposed algorithm is found to be the best suited algorithm for denoising the FOG signal in both the static and dynamic environments. Copyright © 2013 John Wiley & Sons, Ltd.     

Steiglitz–McBride adaptive notch filter based on a variable‐step‐size LMS algorithm and its application to active noise control

This paper proposes a new Steiglitz–McBride (SM) adaptive notch filter (SM‐ANF) based on a robust variable‐step‐size least‐mean‐square algorithm and its application to active noise control (ANC). The proposed SM‐ANF not only has fast convergence but also has small misadjustment. The variable‐step‐size algorithm uses the sum of the squared cross correlation between the error signal and the delayed inputs corresponding to the adaptive weights. The cross correlation provides robustness to the broadband signal, which plays the role of noise. The proposed SM‐ANF is computationally simpler than the existing Newton/recursive least‐squares‐type ANF. The frequency response of the new SM‐ANF has a notch depth of about ?25 dB (for each of the three frequencies considered) and has spectral flatness within 5 dB (peak to peak). This robust notch filter algorithm is used as an observation noise canceller for the secondary path estimation of an ANC system based on the SM method. The ANC with proposed SM‐ANF provides not only faster convergence but also an 11‐dB improvement in noise attenuation over the SM‐based ANC without such a SM‐ANF. Copyright © 2015 John Wiley & Sons, Ltd.     

Least‐squares‐based adaptive target localization by mobile distance measurement sensors

A least‐squares‐based adaptive algorithm with forgetting factor is proposed for localization of a target by a mobile distance measurement sensor. This problem, in its most general form, was tackled in a recent paper using a gradient adaptive algorithm, assuming distance measurements are directly available. We establish that the proposed algorithm bears the same stability and convergence properties as the gradient algorithm previously studied. It is demonstrated via simulations that the proposed algorithm converges significantly faster to the location estimates than the gradient algorithm for high forgetting factor values and significantly reduces the noise effects for small values of the forgetting factor. Furthermore, a more challenging form of the original problem is considered, where distance information is required to be deduced from time of flight measurements, considering a time of flight‐based active distance measurement sensor and an environment with unknown signal permittivity/speed; the proposed algorithm is redesigned to solve this problem. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

基于自适应容积卡尔曼滤波的动态谐波检测

对电网中的谐波进行实时、准确的检测是有效治理谐波的前提。针对某些运行工况下电网中出现的动态谐波,提出了一种基于自适应容积卡尔曼滤波的动态谐波检测算法估计谐波信号的幅值和相角。首先针对传统卡尔曼滤波处理非线性关系上的局限性,利用容积卡尔曼滤波不需要任何线性化关系的特性估计谐波的状态向量和误差偏差矩阵,然后引入噪声估值遗忘因子来实时更新系统的噪声矩阵方程。最后通过对比实验,验证了该算法在动态谐波检测上的优越性能,并将其应用于有源滤波器的谐波检测中。     

Convergence analysis of the RLS identification algorithm with exponential forgetting in stationary ARX‐structures

The recursive least‐squares (RLS) identification algorithm is often extended with exponential forgetting as a tool for parameter estimation in time‐varying stochastic systems. The statistical properties of the parameter estimates obtained from such an extended RLS‐algorithm depend in a non‐linear way on the time‐varying characteristics and on the forgetting factor. In this paper, the RLS‐estimator with exponential forgetting is applied to time‐invariant Gaussian autoregressions with second‐order stationary external inputs, i.e.to Gaussian ARX‐processes. Approximate expressions for the asymptotic bias and covariance of the parameter estimates when the forgetting factor tends to one and time to infinity are given, showing that the bias is non‐zero and that the covariance function decays exponentially with a rate that is given by the forgetting factor. The orders of magnitude of the errors in the asymptotic expressions are also derived. Copyright © 1999 John Wiley & Sons, Ltd.     

An improved adaptive unscented Kalman filter for estimating the states of in‐wheel‐motored electric vehicle

Vehicle state is essential for active safety stability control. However, the accurate measurement of some vehicle states is difficult to achieve without the use of expensive equipment. To improve estimation accuracy in real time, this paper proposes an estimator of vehicle velocity based on the adaptive unscented Kalman filter (AUKF) for an in‐wheel‐motored electric vehicle (IWMEV). Given the merits of an independent drive structure, the tire forces of the IWMEV can be directly calculated through a vehicle dynamic model. Additionally, by means of the normalized innovation square, the validity of vehicle velocity estimation can be detected, and the sliding window length can be adjusted adaptively; thus, the steady‐state error and the dynamic performance of the IWMEV are demonstrated to be simultaneously improved over an alternative approach in comparisons. Then, an adaptive adjustment strategy for the noise covariance matrices is introduced to overcome the impact of parameter uncertainties. The numerically simulated and experimental results prove that the proposed vehicle velocity estimator based on AUKF not only improves estimation accuracy but also possesses strong robustness against parameter uncertainties. The deployment of the estimation algorithm by using a single‐chip microcomputer verifies the strong real‐time performance and easy‐to‐implement characteristics of the proposed algorithm.     

FPGA‐based implementation for improved control scheme of grid‐connected PV system with 3‐phase 3‐level NPC‐VSI

The large scale penetration of renewable energy resources has boosted the need of using improved control technique and modular power electronic converter structures for efficient and reliable operation of grid‐connected systems. This study investigates the performance of a grid‐connected 3‐phase 3‐level neutral‐point clamped voltage source inverter for renewable energy integration by using improved current control technique. For medium or high‐voltage grid interfacing, the multilevel inverter structure is generally used to reduce the voltage stress across the switching device as well as the harmonic distortion. The neutral‐point clamped voltage source inverter is controlled by using decoupling technique along with the proper grid synchronization via moving average filter–based phase‐locked loop. The moving average filter–based phase‐locked loop is used to reduce the delay in grid angle estimation under balanced as well as distorted grid conditions. A Lyapunov‐based approach for analysing the stability of the system has also been discussed. In this study, the hardware‐in‐loop (HIL) simulation of the control algorithm and the grid synchronization technique is realized using Virtex‐6 FPGA ML605 evaluation kit. The performance of the system is analyzed by conducting a time‐domain simulation in the Matlab/Simulink platform and its performance is examined in the HIL environment. The simulation and the hardware cosimulation results are presented to validate the effectiveness of the proposed control scheme.     

基于TVFFRLS-ACKF的锂离子电池SOC估算

实现电池荷电状态(SOC)的估算预测是电池管理系统(BMS)的重要任务之一。电池模型参数的辨识是实现锂离子电池SOC估算的前提,也是决定其估算精度的关键因素。本文以18650型锂离子单体电池为研究对象,采用带时变遗忘因子的递推最小二乘法(TVFFRLS)对电池参数进行在线辨识,实现遗忘因子自适应的自动寻优,提高参数在线辨识的稳定性。在此基础上,采用自适应容积卡尔曼滤波(ACKF)对锂离子电池SOC进行估算,对过程噪声、量测噪声的协方差实时更新,并在不同工况下进行算法验证。结果表明,该算法噪声抑制性能良好,可以提高SOC的估算精度,最大估算误差不超过1.5%,且ACKF算法具有较强的鲁棒性。     

Tracking time‐varying‐coefficient functions

A method for adaptive and recursive estimation in a class of non‐linear autoregressive models with external input is proposed. The model class considered is conditionally parametric ARX‐models (CPARX‐models), which is conventional ARX‐models in which the parameters are replaced by smooth, but otherwise unknown, functions of a low‐dimensional input process. These coefficient functions are estimated adaptively and recursively without specifying a global parametric form, i.e. the method allows for on‐line tracking of the coefficient functions. Essentially, in its most simple form, the method is a combination of recursive least squares with exponential forgetting and local polynomial regression. It is argued, that it is appropriate to let the forgetting factor vary with the value of the external signal which is the argument of the coefficient functions. Some of the key properties of the modified method are studied by simulation. Copyright © 2000 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.     

有源电力滤波器多重因子自适应谐波检测法

针对电网负载电流的低信噪比问题,提出一种用于有源电力滤波器(APF)谐波检测的多重因子变步长自适应谐波检测方法.该方法以自适应噪声对消技术为基础,通过引入动态因子,增加相邻时刻误差信号的自相关值及静态因子对权值迭代的影响,并利用误差信号的时间均值估计来控制步长更新,不但加快了动态响应速度,而且减小了低信噪比情况下的稳态...     

Distributed two‐stage state estimation with event‐triggered strategy for multirate sensor networks

This paper investigates the state estimation issue for a class of wireless sensor networks (WSNs) with the consideration of limited energy resources. First, a multirate estimation model is established, and then, a new event‐triggered two‐stage information fusion algorithm is developed based on the optimal fusion criterion weighted by matrices. Compared with the existing methods, the presented fusion algorithm can significantly reduce the communication cost in WSNs and save energy resources of sensors efficiently. Furthermore, by presetting a desired containment probability over the interval [0,1] with the developed event‐triggered mechanism, one can obtain a suitable compromise between the communication cost and the estimation accuracy. Finally, a numerical simulation for the WSN tracking system is given to demonstrate the effectiveness of the proposed method.