A novel Kalman filter for frequency estimation of distorted signalsin power systems

A simple and novel approach in the design of an extended Kalman filter (EKF) for the measurement of power system frequency has been presented in this paper. The design principles and the validity of the model have been outlined. The performance of this filter has been compared with some of the existing methods for estimating the frequency of a signal under noisy conditions. The feasibility of the proposed filter has been tested in the laboratory under worst-case measurement and network conditions, which might occur in a typical power system. Also, the proof of the stability for the proposed filter has been discussed for a single sinusoid. It has been found that the proposed algorithm is suitable for real-time applications especially when the frequency changes are abrupt and the signal is corrupted with noise and other disturbances due to harmonics     

Kalman filter based synchronisation methods

Single- and three-phase synchronisation methods based on optimum filtering theory are proposed. These methods are based mainly on the Kalman filter and are therefore termed Kalman filter-phase locked loop. they explicitly include in the problem formulation the presence of harmonics, voltage unbalance, measurement noise, transients and frequency deviation. such perturbations degrade the performance of many synchronisation structures presented in literature. the formulation presented here makes the synchronisation signals less sensitive to these perturbations. it is also shown that the proposed methods can be helpful by also providing the amplitude, instantaneous phase and frequency of grid voltages that can be useful for the analysis of power quality. furthermore, the Kalman filter provides a way of obtaining the best compromise between transient response and measurement noise rejection for the synchronisation signals. The paper sets out the development of the proposed methods together with the choice of tuning parameters and their physical meaning. simulations and experimental results using a DSP TMS320F2812 are presented to show the effectiveness of the proposed schemes.     

基于Sigma点全局迭代参数卡尔曼滤波的折线型本构模型参数识别

折线型本构模型控制参数少,物理意义明确,但其数学表达式复杂因而识别困难。针对折线型本构模型的参数识别,提出基于Sigma点变换的全局迭代参数卡尔曼滤波算法。所提方法以待识别参数作为状态向量,降低状态向量维度,减少计算量;基于Sigma点卡尔曼滤波避免求解雅克比(Jacobian)矩阵,实现非连续型函数本构模型的参数识别;通过设定目标函数进行全局迭代,以获得最优解。由于非线性系统下一时刻响应与历史路径有关,量测更新时由初始时刻计算到当前时刻。最后,在地震荷载下,将隔震支座系统简化为单自由度双线性模型,将桥墩简化为单自由度Takeda模型,根据该文所提出的方法理念,分别基于无迹卡尔曼滤波(unscented Kalman filter,UKF)、容积卡尔曼滤波(cubature Kalman filter,CKF)和球面单纯形径向容积正交卡尔曼滤波(spherical simplex-radial cubature quadrature Kalman filter,SSRCQKF)采样规则识别折线型本构模型参数。结果表明所提方法能够准确识别非线性参数,同时具有较强的鲁棒性,不同滤波器收敛过程及结果也有所差异。     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

A Simple Method for Design of Adaptive Filters for Sinusoidal Signals

Filtering of input signals in algorithms for measurement of power system electrical parameters is very important. Filters are used to minimize the noise effect and eliminate the presence of higher order harmonics. In addition to that, a number of measurement algorithms apply orthogonal signal components obtained by two orthogonal finite-impulse response filters. The frequency response of the filters must have nulls at the higher order harmonic frequencies that are expected to be present in the signal and must have a unity gain at the main harmonic frequency. In the case of a time-varying frequency, the filter parameters have to be adapted during frequency estimation. In this paper, a simple method for online design of digital filters for sinusoidal signals is proposed. It is based on closed-form solutions for calculating filter coefficients. A simple linear algorithm for frequency estimation was used, and a derived algorithm for online adaptation of the filter coefficients is computationally very efficient. The number of subsections in the cascade and data window lengths can also be changed, depending on the frequency variations during measurement.      

Fast Tracking of Power Quality Disturbance Signals Using an Optimized Unscented Filter

This paper presents a hybrid approach for tracking the amplitude, phase, frequency, and harmonic content of power quality disturbance signals occurring in power networks using an unscented Kalman filter (UKF) and swarm intelligence. The UKF is a novel extension of the well-known extended Kalman filter (EKF) using an unscented transformation to overcome the difficulties of linearization and derivative calculations of signals with a low signal-to-noise ratio (SNR). Further, the model and measurement error covariance matrices $Q$ and $R$, along with the UKF parameters, are selected using a modified particle swarm optimization (PSO) algorithm for accurate tracking of signal parameters. To circumvent the problem of premature convergence and local minima in conventional PSO, a dynamically varying inertia weight based on the variance of the population fitness is used. This results in a better local and global searching ability of the particles, which improves the convergence of the velocity, and in a better accuracy of the UKF parameters. Various simulation results for nonstationary sinusoidal signals occurring in power networks with varying amplitudes, phases, and harmonic contents corrupted with noise having a low SNR reveal significant improvements in noise rejection and speed of convergence and accuracy.      

Adaptive autopilot design via model expansion method

Abstract

The concept of an equivalent time constant and model expansion method are introduced for the design of a synthetic stabilization acceleration autopilot. In the autopilot control loop, an extended Kalman filter is employed to estimate the time‐varying airframe parameters. The performance of the autopilot and the extended Kalman filter is investigated through computer simulations. Two main results are found: the model expansion method can efficiently specify the gains of the autopilot control loop, and good command following characteristics of the autopilot have been obtained in the computer simulations. The results also show an acceptable estimation error for the extended Kalman filter.     

光电跟踪的非线性卡尔曼滤波算法

为得到最小方差意义下的光电跟踪目标的最优状态估计,提出将部分状态卡尔曼滤波和非线性系统的一阶线性化思想相结合,构成一种适用于非线性光电跟踪目标的卡尔曼滤波算法,并总结出详细算法结构.同时将此方法应用到非线性测量光电跟踪系统中,并与扩展卡尔曼滤波和U卡尔曼滤波进行性能对比.仿真实验结果证明,将部分状态卡尔曼滤波和非线性系统的一阶线性化思想相结合是有效可行的,而且其性能明显优于扩展卡尔曼滤波和U卡尔曼滤波.     

基于小波滤波器组的涡街流量计信号处理方法

涡街流量计应用比较广泛,但是,由于易受管道振动和流场不稳定等因素干扰,如何从强噪声背景下检测出涡街信号频率,一直是个难题.研究了多相结构ⅡR小波滤波器组的设计方法,给出了Butterworth型小波滤波器组的实现方案,将基于小波滤波器组的信号处理方法应用于涡街流量计,并给出最佳频带的判别准则.仿真结果表明,Butterworth型小波滤波器组具有较好的幅频特性和较高的频率精度.     

小波变换与卡尔曼滤波结合的RLG降噪方法

针对激光陀螺随机游走噪声其非平稳和非正态分布的特性,提出了基于小波变换的卡尔曼滤波的RLG降噪方法,该方法既具有小波变换对自相似过程的去相关作用和多分辨分析的功能,同时又保持了卡尔曼滤波器对未知信号的线性无偏最小方差估计的特点,实现了激光陀螺随机游走噪声的实时多尺度分解和最优估计。实测激光陀螺零偏信号去噪的结果表明,基于小波变换的卡尔曼滤波器使随机游走噪声的标准差降低了10.3%,降噪效果优于传统的卡尔曼滤波器。     

基于自适应滤波的锂电池隔膜卷绕系统张力估计

锂电池隔膜卷绕系统的电机转速、放卷辊的卷材卷径和放卷张力等实时信号都带有高斯白噪声,易形成较大的滞后,从而导致控制系统的稳定性和精度降低。现以协方差匹配技术为滤波发散判据,再结合对于指数加权系数的表达式限定记忆滤波的次数,提高噪声初始值的分配权重,来保持滤波的自适应程度,提出一种基于改进型SageHusa自适应滤波估计张力的方法,实现对系统噪声协方差阵与测量噪声协方差阵的自适应变化。实验结果表明,所提出的方法不仅能更准确、稳定地估计出锂电池隔膜卷绕系统放卷张力,还能在一定范围内使其不受给定的噪声协方差阵初值影响,而且有较高的精度和较强的实时性,优于一般的扩展卡尔曼滤波算法。     

A Robust Asynchrophasor in PMU Using Second-Order Kalman Filter

Phasor Measurement Units (PMUs) provide Global Positioning System (GPS) time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system. Those synchronized data measurements are extracted in the form of amplitude and phase from various locations of the power grid to monitor and control the power system condition. A PMU device is a crucial part of the power equipment in terms of the cost and operative point of view. However, such ongoing development and improvement to PMUs’ principal work are essential to the network operators to enhance the grid quality and the operating expenses. This paper introduces a proposed method that led to low-cost and less complex techniques to optimize the performance of PMU using Second-Order Kalman Filter. It is based on the Asyncrhophasor technique resulting in a phase error minimization when receiving the signal from an access point or from the main access point. The MATLAB model has been created to implement the proposed method in the presence of Gaussian and non-Gaussian. The results have shown the proposed method which is Second-Order Kalman Filter outperforms the existing model. The results were tested using Mean Square Error (MSE). The proposed Second-Order Kalman Filter method has been replaced with a synchronization unit into the PMU structure to clarify the significance of the proposed new PMU.     

误差白化与Kalman滤波的微硅加速度传感器动态补偿

通过模型参考的系统辨识方法建立微硅加速度传感器的动态补偿器。由于测量噪声和补偿器对传感器的频带扩展,使得补偿器的输入/输出信号存在严重的噪声干扰。在噪声干扰下,采用均方误差为代价函数的系统辨识方法,无法得到补偿器参数的无偏估计。补偿器参数的偏差和传感器频带的扩展将会使补偿器的输出信号出现严重失真和高频噪声干扰。为解决噪声对硅加速度传感器的动态补偿的影响,研究了一种新的动态补偿方法,该方法采用误差白化为代价函数的系统辨识方法得到补偿器的参数,可消除补偿器的参数在估计中的测量噪声影响,并通过卡尔曼实时滤波减小因传感器频带扩展所产生的高频噪声干扰。     

基于鲁棒H~∞滤波的光电跟踪机动目标状态预测估计

针对光电跟踪系统中目标机动的特点和电视图像跟踪器信号处理、传输造成的测量时滞以及目标信号测量中存在的不确定干扰和噪声,选取机动目标"当前"统计模型对加速度进行建模,在所建立的光电跟踪目标加速度非零均值相关模型的基础上,采用鲁棒H∞滤波算法对光电成像识别目标运动状态进行预测估计.其预测精度比Kalman滤波提高近1倍.实验结果表明,该方法能有效地克服目标模型变化及随机噪声和干扰不确定性的影响,具有较高的预测精度和良好的鲁棒性.     

Analyzing OTDR Measurement Data Using the Kalman Filter

In this paper, we present a method for calculating the attenuation factor and detecting the reflective and nonreflective events using the Kalman filter. For the part of the data whose signal-to-noise ratio is sufficiently high, we propose a second-order linear model by approximating the measurement data after the logarithm is applied; we design the optimal and suboptimal linear Kalman filters based on this model. Through a representative experiment, the proposed method is verified to precisely calculate the attenuation factor and detect the events with minimal computational resources.     

Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation

The well-known extended Kalman filter (EKF) has been widely applied to the Global Positioning System (GPS) navigation processing. The adaptive algorithm has been one of the approaches to prevent the divergence problem of the EKF when precise knowledge on the system models are not available. One of the adaptive methods is called the strong tracking Kalman filter (STKF), which is essentially a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. Traditional approach for selecting the softening factors heavily relies on personal experience or computer simulation. In order to resolve this shortcoming, a novel scheme called the adaptive fuzzy strong tracking Kalman filter (AFSTKF) is carried out. In the AFSTKF, the fuzzy logic reasoning system based on the Takagi-Sugeno (T-S) model is incorporated into the STKF. By monitoring the degree of divergence (DOD) parameters based on the innovation information, the fuzzy logic adaptive system (FLAS) is designed for dynamically adjusting the softening factor according to the change in vehicle dynamics. GPS navigation processing using the AFSTKF will be simulated to validate the effectiveness of the proposed strategy. The performance of the proposed scheme will be assessed and compared with those of conventional EKF and STKF     

基于扩展卡尔曼滤波的气力输送动态称重系统

为了提高粉料在气力输送过程中动态称重的精度,提出了一种基于扩展卡尔曼滤波算法的动态称重方法。通过设置多个称重传感器,对采集的数据进行融合并滤波处理,以消除干扰噪声对系统测量的影响。同时采用减重计量法,将数据处理结果通过智能控制器实时调节卸料控制阀的开关度,以提高动态称重的精度。实验结果表明:称重30kg二氧化硅粉末,平均误差在0.3%以下。     

结构物理参数识别的多尺度参数卡尔曼滤波方法

经过正交小波变换后,低尺度上测量信号的信噪比提高。应用小波变换将结构的激励信号和响应信号分解到不同尺度上,得到不同尺度上结构的状态方程和测量方程,结合动力学系统辨识的参数卡尔曼滤波方法,提出了结构物理参数的多尺度参数卡尔曼滤波辨识方法。理论分析和数值算例表明:在多尺度上对结构参数进行辨识比在单一尺度上辨识能获得更高的精度。     

卷积伏安法实验数据的自适应卡尔曼滤波 Ⅱ.重叠峰的分辨

本文着重探讨自适应卡尔曼滤波对卷积伏安法重叠响应信号的分辨能力。通过拟合实验数据表明,1:N 自适应卡尔曼滤波器与快速傅里叶变换和标准加入法相结合,用于补偿系统的模型误差和进行重叠峰的分辨,效果良好。应用于 Cd(Ⅱ)～In(Ⅲ)体系重叠峰实测数据的分辨,获得满意的结果。     

Star spot location estimation using Kalman filter for star tracker

Star pattern recognition and attitude determination accuracy is highly dependent on star spot location accuracy for the star tracker. A star spot location estimation approach with the Kalman filter for a star tracker has been proposed, which consists of three steps. In the proposed approach, the approximate locations of the star spots in successive frames are predicted first; then the measurement star spot locations are achieved by defining a series of small windows around each predictive star spot location. Finally, the star spot locations are updated by the designed Kalman filter. To confirm the proposed star spot location estimation approach, the simulations based on the orbit data of the CHAMP satellite and the real guide star catalog are performed. The simulation results indicate that the proposed approach can filter out noises from the measurements remarkably if the sampling frequency is sufficient.